The Art of Puzzles

What If ...? #4 - Sudoku Retesting

Thu, 26 Nov 2009 09:57:06 GMT

About four weeks ago, a former sudoku champion rang a bell that cannot be unrung by claiming a fellow finalist was a cheater. While a lot of circumstantial evidence supported this case, no smoking gun was likely to be found from looking at video and photography from the event itself. Sudoku-related curiosities such as "unreasonable sticking points" or "missing pencilmarks" were unlikely to satisfy all parties necessary to disqualify the competitor. However, the tournament organizers came up with a process that could clarify matters: the contestant would be offered a second chance to solve more sudoku puzzles under closer watch to demonstrate his proficiency and to deflect the allegations of cheating. This leads to this week's topic:

What if you had to conduct a retest for sudoku? What kind of standardized puzzles or times would suffice to conclusively prove either the ability or inability to finish three puzzles in 14 minutes? How many puzzles would be needed and what would these be? Can sudoku be made "retestable" to indeed prove Eugene is detestable?

These questions necessarily lead to a discussion of mean and variance and nuances of the solving process; a fitting answer requires a careful analysis of how an actual human solver performs from puzzle to puzzle in a controlled setting. Fortunately, I know an eccentric scientist with an advanced degree in "Number Placement" who has a relevant manuscript to share with you:

Effects of Transformations of Sudoku Puzzles on Solution Times of an Advanced Solver
A Case Study by Dr. Sudoku

Abstract:

We generated five isomorphic copies of five sudoku puzzles using digit reassignment, row/column swapping, and rotation/reflection. A sixth puzzle with an unusual solving property was also transformed and added to the set for twenty-six test puzzles. Our subject, an advanced division contestant at the recent Sudoku National Championship, was able to identify the grid with the unusual solving property from the set of 26 puzzles, and also identified several commonalities within the remaining isomorphic puzzles. Considering his solution times, a 15-20% standard deviation in time was observed across the isomorphic versions of each puzzle. The fastest/slowest grid outliers were then resolved without further transformation. The subject's results suggest that the likely mean and standard deviation in solving time on an exact duplicate is very close to that of a transformed grid.

We also examined how transformations would affect computer ratings, specifically those of Scanraid Sudoku. Both number ordering and top-to-bottom, left-to-right biases were observed in the grading of isomorphic puzzles. In one extreme case, a 90 degree rotation of a puzzle led to a 50% increase in the rating for the puzzle. While the varied ratings may apply to the most esoteric human solvers, who persist with perfect top to bottom or 1 to 9 scanning, these ratings in general seem inconsistent with the expected human solving experience of sudoku.

Introduction:

Sudoku is a logic-based constraint-satisfaction puzzle, most typically presented on a 9x9 grid of squares that must be filled with numbers from 1-9 such that no number repeats in any row, column, or 3x3 bold region; other sizes and the use of symbols other than numbers in the cells are possible. The regions add a third constraint onto each cell which separates sudoku from Latin Square-based puzzles with solely row and column constraints. Despite some reports to the contrary [Crook, 2009], sudoku puzzles must have a single solution to be considered valid; valid sudoku with as few as 17 given numbers are known, although this has not yet been proven to be the lower bound.

Following years of research and individual experiences with making deductions in sudoku, a number of strategies have been formalized for their solution [see, for example, Scanraid Sudoku solver; Stuart (2005-9)]. Many of the basic strategies fit into the categories of either positive inference or negative inference depending on whether the presence, or absence, of particular numbers is used in the placement of further digits. Different solvers may vary in their preferences for or abilities with positive versus negative inference which presents a challenge for the "retesting" of a competitor, as in the recent Varshavsky case [Philadelphia Inquirer, 2009], as a high variance in solving times might be encountered by a particular solver if presented a random sudoku to solve in under 5 minutes. Additionally, the breadth of a solution path can also influence the solving time, with a smaller variance of times expected for a puzzle with many places to identify digits by logical means compared to those with fewer such places. Given the puzzle by puzzle variation seen in sudoku, single puzzle finals (and playoffs in general) are not viewed by many members of the advanced solving community as an appropriate way to select the best overall sudoku solver [see motris.livejournal.com].

An individual sudoku puzzle can be transformed into a large number of isomorphic grids using number reordering, row/column/chute swapping, and rotations/reflections. For this reason, while 6,670,903,752,021,072,936,960 possible solutions have been reported for sudoku, only 5,472,730,538 are considered "essentially different". [Russel, Jarvis, 2005] It is speculated, but has not yet been demonstrated, that isomorphic puzzles can lead to highly variable solution times due to various esoteric tendencies of the solver. A solver who approaches sudoku in a cyclic 1-9 search order may be affected by reassigning the values of the givens. Similarly, a solver who starts from the top to bottom or from the left to the right could be affected by row/column/chute swapping as well as rotations or diagonal mirroring. However, despite these nuances of the solution process, the essential steps along the solution path will be unchanged in these isomorphic grids. If one had to retest a competitor, isomorphic forms of the puzzle might be valid for such a test. If the competitor had, for example, memorized the solution of a particular puzzle (even in an extreme case where he has memorized an order of digits to enter, perhaps from receiving a copy of the puzzle before the test and needing to reproduce a "solution path" while under increased scrutiny), an isomorphic version of the same puzzle will be protected from such an attack as it will be impossible to memorize the approximately one trillion isomorphic grids that are possible for any individual puzzle. Further, if a solver claims he is better at, say, negative inference - excelling at naked singles but not hidden singles for example - and tries to use this to explain a much slower time for a particular puzzle, the use of an isomorphic grid containing an identical number of potential starting points for a particular kind of logic rule will negate any "variation of solving method" rebuttal for a poor retest. (Of course, according to Thomas Snyder [personal communication], the most fascinating element of the Varshavsky case was that after 4 weeks of being under suspicion, the competitor actually showed up for a retest without any practice to make it remotely possible he could deceive the invigilators, even on identical puzzles to the ones under suspicion! We are therefore considering the case of catching smarter cheaters, with an altered ratio of intelligence to hubris, in this study).

Here, we have tested a set of puzzles randomly ordered following transformations to determine how consistent or inconsistent the solving process is. We also added a single puzzle with a particularly unusual solving property into the mix - and alerted the subject to its presence - to see if the step would be encountered on his solving path and identifiable amidst many other puzzles.

Materials and Methods:

A perl script was written to output a specified number of isomorphic forms of an input classic 9x9 sudoku puzzle by performing number replacement, then row and horizontal chute permutations, then column and vertical chute permutations, and then possibly performing a rotation/reflection to reach the final altered state. 5 puzzles (3 of approximately 4 star difficulty, 2 of approximately 5 star difficulty, all appropriate to reward logical methods instead of bifurcation using the identification of pairs and triples as the hardest steps by Scanraid analysis) were selected for analysis and five versions of each were generated. A sixth puzzle with an unusual solving property, specifically an Order 5 Franciscan Rectangle that fits into a class of "uniqueness" techniques, was chosen and randomized as well. This advanced technique is not required to solve the puzzle, but is a potential shortcut an advanced solver might find and exploit. All puzzles had between 24 and 28 givens and the number of givens was not unique for any of the six puzzles.

The 26 puzzles (now labeled A-Z) were printed on 4.5" by 4.5" square grids, identical to the size used at the Sudoku National Championship, and then solved in batches of 5 (in one case 6) puzzles at a time with short 5 minute breaks. A recorded, pre-watched, episode of "Sportscenter" was playing in the background throughout the testing as a kind of white noise. The subject, selected for being a high-finishing participant in many sudoku championships, chose to solve the puzzles while seated in a comfy chair, writing against a notebook surface with .9 mm Pentel Twist-Erase III pencils. The subject timed himself on the solution of these puzzles, and the finished grids were checked for completeness of filling, but not checked for accuracy. From anecdotal evidence provided by the subject, about 95% of puzzles will be correctly solved in this manner so, in this study, approximately 1 puzzle may have an error such as a transposition.

In addition to the human testing, the puzzles were also scored in Scanraid Sudoku to determine how "computer rating" itself varies as a result of grid transformations.

The 26 puzzles are provided in Appendix B.

Results:

The subject's initial solve data (and paper notes) follow:

A - 3'22", B - 2'39", C - 3'56", D - 3'57" (franciscan-like), E - 3'41", F - 2'40", G - 3'3", H - 1'48", I - 2'12", J - 2'2", K - 2'27", L - 3'31" (Order 5 Franciscan), M - 3'18", N - 3'1", O - 1'52", P - 4'21" (franciscan-like), Q - 1'39", R - 1'53", S - 3'16", T - 3'17" (franciscan-like), U - 3'41" (franciscan-like), V - 3'7", W - 2'53", X - 2'6", Y - 3'35", Z - 2'1"

The subject completed the 26 puzzles in a range of times from as short as 99 seconds to as long as 261 seconds. The average solving time was approximately 2 minutes, 54 seconds, with a standard deviation of 46 seconds. The median solve time was approximately 3 minutes, 2 seconds. During solving, the subject never had to make an erasure or correction to his puzzles, which would lead to a higher than expected time for his solving process on that individual grid. If such an event had occurred, we would have suggested a future retesting of the same puzzle as "clean" solving times are of the most interest to us for comparison.

The subject also made notes on some of his puzzles. Given the expectation of a Franciscan puzzle of order 5, the subject related that "when I saw 4 similar pairs that could make such a situation, but didn't resolve properly, I noted 'franciscan-like' at the end of the solution process." For 4 solutions (D, P, T, U) this text was indeed written in the margins of that test paper. For a fifth puzzle, L, Order 5 Franciscan was written. Puzzle L is indeed the sudoku with an Order 5 Franciscan Rectangle. D, P, T, U (and M) are all isomorphic forms of another puzzle. It is unclear why the subject did not mark M as Franciscan-like but it is within a second of the fastest time over the trials for this puzzle meaning the critical steps may have been identified before the relevant pair property was noted in a period of being "stuck". It also occurred in the trial immediately after the Order 5 Franciscan grid (L) and could have been missed due to increased laxity after identifying the hidden sixth puzzle.

After the testing, the subject also noted to experimenters that "deja vu" feelings about the starting steps of puzzles would happen such as "I've chased this kind of digit by pointing pairs around the grid before." While we did not ask the subject to try to isolate each individual puzzle, the solver indicated that if he noted the kinds of starting steps, as well as sticking points, he could possibly have accomplished this assignment with some accuracy. Because of this alleged "memory" of a puzzle, we did consider whether the solver got "better" at a particular puzzle, even with isomorphism, as the trials went on.

Rearranging the 26 puzzles into the 6 unique types, and ordering by apparent difficulty, these are the subject's times in chronological order:

1 - HJKQZ - 1'48", 2'2", 2'27", 1'39", 2'1" - average time 1'59", deviation 18", range 1'39"-2'27"
2 - BGOVX - 2'39", 3'3", 1'52", 3'7", 2'6" - average time 2'33", deviation 33", range 1'52"-3'3"
3 - EFIRY - 3'41", 2'40", 2'12", 1'53", 3'35" - average time 2'48", deviation 48", range 1'53"-3'41"
4 - ACNSW - 3'22", 3'56", 3'1", 3'16", 2'53" - average time 3'18", deviation 24", range 2'53"-3'56"
5 - DMPTU - 3'57", 3'18", 4'21", 3'17", 3'41" - average time 3'43", deviation 27", range 3'17"-4'21"
6 - L - 3'41"

The tightest solution times exist for the puzzle with the fastest solution, but the next two tightest distributions are for the two puzzles that respectively take the longest. When sorted by average solve time, both the fastest time on a puzzle, and the slowest time on a puzzle (the "range") are also in the indicated 1-5 order. Considering the relative position of the fastest versus the slowest solve, for these three puzzles the fastest solutions were #4, 3, 4, 5, and 4 (average of 4.0) and the slowest were #3, 4, 1, 2, 3 (average of 2.6) which suggests a slight possibility of some learning throughout the process although in a few cases, as on the puzzle with the highest variance (3), a very fast fourth solution was followed by a much slower fifth solution (by 102 seconds) that was only slight ahead of the overall slowest solution so a matter of a few seconds would change a 1 to a 5 and affect this averaging. Another hypothesis that accounts for the results is that, after solving several puzzles, the subject had "warmed up" and was more likely to achieve faster times.

Following a day off, the outliers - the 10 puzzles with the fastest and slowest respective times - were resolved in random order to determine if these differences were based on variations in the grids themselves, or by the stochastic nature of the subject's solution process. This test would also help determine if the "exact" puzzles have more consistent times than permuted grids.

Q - 1'39" first time, 1'47" second time, +8 seconds difference
K - 2'37" first time, 2'55" second time, +18 seconds difference

O - 1'52" first time, 2'40" second time, +48 seconds difference
V - 3'7" first time, 2'14" second time, -53 seconds difference

R - 1'53" first time, 2'9" second time, +16 seconds difference
E - 3'41" first time, 2'40" second time, -61 seconds difference

W - 2'43" first time, 2'43" second time, 0 seconds difference
C - 3'56" first time, 2'23" second time, -93 seconds difference

T - 3'17" first time, 3'38" second time, +21 seconds difference
P - 4'21" first time, 2'45" second time, -96 seconds difference

In 8 of the cases, the second time on a puzzle moved towards the mean by being slower for the fastest puzzle or faster for the slowest puzzle. In one case the exact time reoccurred; in the last case, a slightly slower time was observed for the slowest time. In 3 of the 5 pairs of puzzles, the slower puzzle in the first trial was solved faster than its partner in the second iteration. In 2 cases, for C and P, the worst solution time actually led to a new fastest solving time. Collectively, these results suggest that the outliers were not perceived as easier/harder by the solver consistently but were rather the result of random variation in the subject's search process from puzzle to puzzle. Given the magnitude of the time differences in the retest, we also conclude that the variation between "exact" duplicates of a puzzle is close to identical to the variation from transforming the grid.

The 26 puzzles were then evaluated by Scanraid Sudoku to determine their "grades".

1 - HJKQZ - 74, 75, 73, 74, 75 - average 74.2, deviation .8
2 - BGOVX - 92, 102, 113, 108, 94 - average 101.8, deviation 9.0
3 - EFIRY - 154, 104, 104, 109, 150 - average 124.2, deviation 25.5
4 - ACNSW - 165, 132, 147, 156, 137 - average 147.4, deviation 13.5
5 - DMPTU - 139, 139, 147, 130, 143 - average 139.6, deviation 6.3
6 - L - 96

Scanraid's score agrees on the "easiest" puzzles by rating, although it differs on the order of 4 and 5. 6 (the order 5 Franciscan rectangle) takes about as long in its single solve as the average time of the hardest puzzle, but scores much less by Scanraid. Intriguingly, the rating of some of the isomorphic grids, particularly E and Y, compared to F, I, and R, was grossly different. The subject's solving of the puzzles E and Y was also much slower than those for FIR for this highest variance case, well beyond expectation, which drew our interest.

To account for the variation observed between the isomorphic puzzles E and F, we first checked our software to confirm the puzzles were isomorphic and indeed they were. We then considered the relative Scanraid solving path for E versus F as comparison.

E displays two instances of Singles in Row/Col, then two instances of Singles in Box, then one instance of Naked Pairs/Triples, then sixteen consecutive uses of show possibles (one choice cells) solves the rest.

F displays two instances of Singles in Row/Col, then one instance of Singles in Box, then one instance of Naked Pairs/Triples, then thirteen consecutive uses of show possibles solves the rest.

The first major difference in E and F occurs in the Singles in Box step, with an extra instance of this occurring for E but with the same total number of digits (2) being placed after this step concludes. In the specific case of E, a single (7) then allows another single (6) in the same box and this is done in two steps. For F, the isomorphic position in just one step uses a single (8) to then allow another single (9). Digit order therefore seems to be hard-coded into Scanraid's approach of step counting. Swapping 6 and 7 in E does not change the overall rating from 154, but does reduce the number of iterations of Singles in Box from two to one to be more F-like.

The next major difference in the two solution paths is in the Naked Pairs/Triples step. Unfortunately, hidden pairs and triples are more common than naked pairs and triples for most solvers (and are identified one at a time, not en masse), but Scanraid identifies a slew of naked pairs/triples in a single step. In E, 1 pair (eliminating 9 candidates) and 6 triples (eliminating 16 candidates) are identified. In F, 1 pair (eliminating 9 candidates) and 7 triples (eliminating 17 candidates) are identified. The extra triple (and extra missing candidate) change the solving profile slightly at the end with 3 fewer "one option only" steps needed. This faster solution path must account for the relative difference in score.

To further examine how different transforms affect the Scanraid rating, distinct transformation types were generated and rescored for the grids E and F. Varying just the number identity of either E or F led to only small changes in the score (across five grids E varied from 151 to 163 and F varied from 104 to 113). Varying the row/horizontal chute ordering had a much larger effect on the score (E varied from 105 to 154 over five grids; F varied from 104 to 151). This shows that geometry (perhaps in top/bottom or left/right order) is also a meaningful difference in the scoring of puzzles by scanraid. Taking a mirror (across the main upper-left to lower-right diagonal) of E turns a 154 rating into a 108 rating. This transformation is minor so the large change in rating seems astounding and speaks further to top/bottom or left/right bias. Similarly, just rotating E 90 degrees counter-clockwise turns a 154 rating into a 108 rating. Since the numbers are just symbols and an 8 can be seen as an infinity symbol if looked at sideways, this is not a meaningful transformation at all but it accounts for the entire magnitude of the difference in rating between E and F. The 90 degree rotation also changes the 1 pair and 6 triples for 25 eliminated candidates step of E into the 1 pair and 7 triples for 26 eliminated candidates step seen for F.

Discussion:

While Scanraid does offer some value in rating the fastest versus the slowest puzzles for this solver, we do not believe, within isomorphisms of a given puzzle, that the variation in Scanraid scores is meaningfully correlated with the experience of the tested solver. We posit that isomorphic grids should receive the same/similar scores from an ideal computer rater, but minor effects including digit order and top/bottom or left/right bias in this particular algorithm lead to large differences in rating (matching the untested hypothesis that a solver that goes in 1-9 order may find numbers at a different rate). An ideal rating system may require both a reordering of steps, as well as a consideration of solving path breadth. It should be noted that Scanraid's rating is not considered, even by its creator, more than a very rough estimate of difficulty and some of the identified esoteric behavior may or may not speak to differences encountered by solvers that do use top to bottom or 1 to 9 searching in various ways. Accurately rating the increased difficulty of spotting naked singles (and pairs and triples) for a human compared to a computer that always sees and considers all candidates remains a challenge for any rating system.

In contrast to Scanraid's approach, the given subject's style (see appendix A for a description of his heuristic) seems more tuned to individual occurrences of digits and geometry, and is therefore blind to most of these changes. The "deja vu" feel of certain puzzles at the start or end, as well as the identification of 4 puzzles out of 5 that felt close to the Franciscan Order 5 at some stage, suggests that many commonalities in solving path are found despite the highly transformed grids. Still, in any single trial, slight differences in searching pattern, particularly on the puzzles with the narrowest solving path, can lead to variations in times. On average, about 15-20% variation in solve times seems likely on any single puzzle at these difficulties, although in the extreme a 2x time might be observed. At these difficulties, similar to those used by the Sudoku National Championship, all puzzles are being solved in less than 4 and a half minutes. Retesting with transformed grids should not lead to extremely high variations in round time.

For this finisher of three puzzles in 9-12 minutes, being retested and taking more than 16 minutes is not expected from this study. Consider if puzzles 3-5 constituted a round of the competition. The "best possible day" for the subject, taking his fastest times across all iterations, would allow for the round to be finished in 8 minutes, 3 seconds. The average times for the subject would lead to completing the round in 9 minutes, 49 seconds. The "worst possible day" for the subject would leave a round time of 11 minutes, 58 seconds. The gap of "best" to "worst" day is less than a 50% increase of the fastest times. Of course, making an error while solving a sudoku puzzle which requires full erasure of a grid would lead to much worse times than any of the instances observed here. Such errors occur all the time, but for identifying what a solver can do these "scrub" times should not be used.

In the Varshavsky case, having observed a single data point of finishing 3 specific puzzles in 14 minutes, we can now begin to consider what upper limit of solving time would be consistent with a legitimate competitor. Consider retesting the suspect on some number of identical (meaning isomorphic) puzzles from one to one trillion for the three round puzzles (~3 of each seems reasonable). These trials would establish both a "mean" and "best" time for a solver. Certainly, if the combined "mean" over three puzzles came within a minute of or even bested the observed time, this would remove suspicion from this solver. A "best" time that does not approach even a reasonable "mean" time, such as one 50% higher than the competition time or 20 minutes, would instead suggest cheating had occurred. Without actual proof of a method of cheating, organizers could allow the suspect to continue solving the 1 trillion possible puzzles until his "best" time could beat the 14 minute time, but by then his "mean" time and variance will be very well established allowing a less biased estimate of the probability that a legitimate solving approach was used during the competition.

In performing retesting with different solvers, it is likely that certain solving styles, particularly those with a high level of bifurcation/guessing, will have a particularly high variance in solving time. This study does not contain enough participants to report on such cases. Still, consider an extreme case in which a very difficult puzzle has an obvious bifurcation spot which will lead to a solution or not. The times for this puzzle will be bimodal, say 4 or 6 minutes per puzzle, tied to a coin-flip. A lucky run of three heads would lead to a 12 minute round while an unlucky performance would lead to an 18 minute round. Neither the "mean" time in this situation, nor the "best" time, would eventually come under scrutiny, particularly as it will be obvious by direct observation that the solver employs bifurcation, has high variance in his times, and may therefore just need a 1 in 8 chance of being lucky in each of three puzzles to qualify for the stage. Indeed, direct observation of the solver during retesting, to classify his solving heuristics in addition to assessing his speed, will clarify the results of invigilation.

All considered, whatever method Varshavsky used in Philadelphia to accomplish a 14 minute time in round 3 was not resistant to discovery after retesting, although without his failure to perform even adequately in the finals he would have escaped undetected at this championship under current protocol. Following retesting, where finishing even a single puzzle in 30 minutes was unlikely, it was not a hard decision to disqualify. Consider instead the more difficult case of a competitor who, on significant retesting, can only achieve a best time of 20 minutes, with ~6.5 minutes being the fastest he can solve any puzzle with an average of 8.5 minutes per and 1 minute standard deviation. One possible cheating strategy, relatively low-tech but still well-known in many testing situations, is to situate oneself near a more talented solver. Given the two-page booklet used in these championships, and the fact most solvers start on puzzle one and then just slide the booklet over to solve the second puzzle, imagine a cheater who solves puzzle two, then copies puzzle one from his neighbor to the right (taking about one minute which is a reasonable time for copying ~60 digits into a grid), and then solves puzzle three. This solver with a 6.5 minute "best" time per puzzle could then accomplish a 14 minute round by cheating, but under retesting could never come "close" in a probabilistic sense. A sufficiently stringent retesting procedure should prove the cheating even in this difficult case where a majority of the solving of a round was legitimate, but slower than other competitors. Ideally organizers would situate proctors and physical obstructions between competitors to reduce the opportunity for such an approach (or even a lesser variant of the approach where, after solving puzzle 3, a quick glance around after a "look at the clock" would allow for the copying of a handful of digits into both puzzles 1 and 2 to get a head-start on each).

In a world with many potential "Eugenes", with valuable prizes, and with increasingly miniaturized technologies that can assist cheating, it is reassuring to know that a relevant retesting approach may exist to identify cheaters if subjected to such testing. Particularly proactive organizers may make a mandatory "retest" a requirement for a podium finisher, similar to a drug test for a winning athlete. It is further reassuring to consider that basic steps such as handing out randomly permuted forms of the same puzzles to neighboring competitors could be used to remove/minimize the potential of the most common forms of cheating including prior knowledge of the test (there is no longer one test to memorize) and copying off a neighbor for sudoku. It is unlikely such steps are possible with almost any other kind of puzzle, including other logic puzzles or crossword puzzles.

While this study may seem like a rather extensive analysis for such a basic and fundamental result on puzzle-to-puzzle variation in solving times, it is the first study of its kind and should also serve as a good foundation for further studies that use isomorphic puzzles to explore the solving process. For example, differences in time for using "notes" versus "pencilmark-less" solving, differences arising from grid size both on paper and on whiteboards, and differences arising from the use of "reckless bifurcation" versus logical methods on puzzles of varying difficulties, should all be fruitful areas of further research. We will pursue these areas, and others, as our time and research budget allow.

Appendix A:

The subject defined his general heuristic in this way:

Modes:
A. Randomly search, using chute-scanning, digit repetition, or geometry-based visual cues likely identified from memory due to pattern recognition, for the placement of either a number or an either/or notation for a single digit in a single region. Once a spot to write something is found, this is pushed onto a mental "stack" of information while the physical writing is occurring.
B. When there is a stack, consider the top-most position of the stack, searching for consequences in the row/column/box where the progress was made. Consequences include positive inferences about the digit on the stack, as well as negative inferences about other digits in the row/column/box. If a new spot to write a digit or note is found, this is pushed onto the stack while the writing is occurring.

Additional Considerations:
1. If, while in B mode, no consequences are found for the top element in the stack, that element is popped off the stack and solving continues in B or A mode depending on the presence of any other digits/notes in the stack.
2. When returning to A mode, some effort is made to not perform redundant searches given a cache of what has been searched in the past.
3. If in A for a sufficient length of time n (n = 30 to 180 seconds), enter a bifurcation at a spot with a high density of notes to return to B mode. The value of n depends on the expected difficulty of the puzzle, which is often correlated to the "trust" the subject has in the organizers of a competition.

While this heuristic is powerful, the random nature of the A mode - which can also be described as "what catches his eye first" - is likely to vary from iteration to iteration on a single puzzle as observed in the data. Most of the observed differences in time is likely from total A mode time, and not total B mode time, although it is hard to accurately tally either value for this subject.

Appendix B:

Puzzles:
A - 000506017000901036000000000000200090059010800068000000000400020032000000076090400
B - 000800090000035706000021805092600070800009003047000000016200040400006001059000000
C - 000509000003801400060000002630000045570000089000000000004307200000105000010000003
D - 000803049000200010740000000000405061000600090150000000002030500003020100860000000
E - 000200800000500400000003007000470620907020030080000000000340910209060040010000000
F - 700030000080500000050100000018904000004006012000000600000000800061403000009005074
G - 000406509000501802000090030306080020090300100702000000070800400503000000408060070
H - 900410800010850009002000010006000050100980700070340006730000601690000304000000000
I - 400020061000000900760038000800060053000000800620093000040009000007100000030004000
J - 090700058700008096001050000320906000470302000000000000007040000030800065900005027
K - 800003059030700000009080036000000000601028000302041000050200000004030098200004061
L - 804093000072501000030800020080600090306024000027908000100080000000000104000000506
M - 000604000006000008805000063000902000040050300060070100000209000004000009503000027
N - 000000037070050096600800000020060013800200000000000048403605000000000000501903000
O - 001070004040902500000801000030000700504000061902000035020409800000607000003050006
P - 040070050000103000080090060400000300507000901000301000000408000800000200702000508
Q - 107000032000000000203000098040000600008405007500701080005104003090000800400208070
R - 600900000500200000010030000802601000003002140000000005407306000000000007006008420
S - 000000000608407000302601000003900000000000640020010750005200000000000560010090280
T - 000507803074000000000400006500010020800030060047000000000900002000302908026000000
U - 000007900000024108890000000002700040980000000001600030000052406000006500670000000
V - 000001050000720309000590804900070500043006080017000000100030200084009030026000000
W - 070608020600000500000703000000000000903000602204000803500000100000509000010304060
X - 000000045500007800070300026703095000602013000010800000100009300060400072000000098
Y - 000005800000600004000003500000097380001000000320010090490050070000069130008000000
Z - 000005060907080003603900800000008020108090006706400300000000000000820401000140907

Straight from my inbox

Mon, 23 Nov 2009 23:01:41 GMT

(I'm sure an official announcement on philly.com will come soon, but an email signed by Will Shortz qualifies for me even with the many typos. Here, for the sudoku community - whether advanced, intermediate, or beginner - is finally some justice; nothing can fully restore the finals, but this is something.)

Dear Thomas,

We are pleased to announce the final results for the Advanced Division of The Philadelphia Inquirer Sudoku National Championship, held on October 24, 2009, following an investigation regarding a possible violation of the Championship rules. First place and $10,000 was awarded to Tammy McLeod from Los Angeles, CA. Thomas Snyder from Palo Alto, CA. won second place and $4,000. Chris Narrikkattu was awarded thrid place and $3,000 as a result of the disqualification of Eugene Varshavsky.

Mr. Varshavsky's poor on-stage performance during the championship finals led to a thorough investigation of his qualifying round solving time, and ultimately resulted in his disqualification.

Over the last three years out Championship has established a reputation as the championship for everyone and has a strong following in the advanced, intermediate and beginner sudoku community. The integrity of this competition remains our highest priority and we hope you will join us again next year for our fourth annual Sudoku National Championship.

Will Shortz

ETA: Now the Inquirer's story is out: 3rd Place Winner Disqualified in Sudoku Scandal
EFTA: Philly.com/sudoku official statement

Upcoming

Mon, 23 Nov 2009 16:21:56 GMT

The year in competitive puzzles is over for me, but a couple upcoming events are worth mentioning here.

I've been asked by the Cupertino Libraries to give my "Art of Sudoku" talk on the evening of Wednesday, December 9th. As always, I'll talk about the history of the puzzle, how to solve, and how to construct.

On January 16-17 I will be the author for the 3rd SudokuCup. I will be using many of the styles from Mutant Sudoku and Sudoku Masterpieces as well as a couple originals. Writing these puzzles is the main puzzle-based thing I'll be doing the next month or so.

On January 30-31 I will be again speaking (I believe) and writing sudoku (I'm sure) for the 4th Silicon Valley Puzzle Day at the Morgan Hill library. They run seminars on Saturday and tournaments in crosswords and sudoku on Sunday.

Friday Puzzle #24 - Multi-Operation Calcu-doku

Fri, 20 Nov 2009 04:12:52 GMT

Last week I posted a Calcu-doku variant that I thought was pretty cool. The sudden motivation to explore this concept, which I'd been holding onto for awhile, was the discovery of a hilarious error with some official KENKEN(R) puzzles that couldn't even be corrected right. While I loved the text of my entry, in the rush to make a puzzle that fit a #23 theme I cut some corners and added in an extra constraint to the first 23-only grid I found to make it solvable; to restate your comments on this "fix" succinctly: the shaded cells were not appreciated.

Well, the very first Number Place puzzle had four circled cells that clued a small subset of numbers for those squares. We can agree that the proper form of a sudoku does not have circled cells just as the proper form of these calcu-doku should not have any extra constraints in shaded cells even if the first attempt at such a puzzle had this weakness. Since I really think Multi-Operation Calcu-doku offers some good challenges, I've tried to write some "proper" puzzles this week to reintroduce the concept. While "Parquet" should be rather approachable, the larger "Double Trouble" puzzle has some really fun deductions necessary to solve it.

18 = ((1+5)*3) or 1+5 ->6 *3-> 18

Rules: In each n x n grid, fill each cell with a number from 1 to n so that each number appears exactly once in each row and column. Each grid also contains several rectangular cages whose cells are labeled with either a number or a mathematical operation. Proceeding from the cell with the numerical value and going through the connected cells in order, performing operations as they are encountered, the digits placed inside the cells will evaluate to the indicated value (as in the example cage above).

What If...? #3 - Sudoku Editors

Wed, 18 Nov 2009 15:27:00 GMT

(This is the third entry in a series of essays exploring ideas in sudoku and sudoku competitions. The first entries on playoff puzzles and playoff videos are linked.)

I make a big fuss a lot of the time about the difference between "hand-crafted" and "computer-generated" puzzles, especially with sudoku, as if there is a clean separation between these two methods of construction. While the worst computer-generators are easy to identify (unpatterned asymmetric givens), the best ones (say Frank Longo's now, or in its era Pappocom's) are doing things with step-evaluation and rating that lead to interesting solving paths similar to many of the best hand-crafted ones. Of course, the best hand-crafted sudoku will have paths unlikely to ever be found by computer-generation, but I can think of only 50 or so of these I've solved in my 10,000+ sudoku lifetime.

There is actually a lot of space between full hand-crafting and computer-generation - a gap that I'll call computer-assisted construction - which is what my co-author onigame uses most of the time and where I have had the benefit, in puzzle types like Consecutive Sudoku, of using his scripts to accomplish particularly difficult themes like a consecutive sudoku with a smiley face and no other bars. I made my thermo-doku smile by hand, but it took so much longer to get right. Anyway, because we approach the puzzles with a theme in mind, and test the solving of them afterwards, tweaking as necessary, this computer-assisted construction is still making a human-inspired puzzle, and lies closer to hand-crafted than computer-generated in my opinion. Regardless of how these puzzles were made, they stand apart from anything a computer made entirely.

When it comes to classic sudoku, it has never been clear to me that my time is well spent writing more than a handful of puzzles each year. I cannot sell them for more than pennies in the States, so instead I contribute a couple every few months to Tetsuya Nishio in Japan and in return get several copies of the book they appear in, along with a hundred other brilliant but difficult sudoku to practice with. I also write 7 puzzles each year for the Silicon Valley Puzzle Day (here are puzzles from year 2 and year 3) and those tend to explore some themes but also be appropriate for competition and therefore deserve a special touch.

Even writing just these puzzles each year, I have a clearly developing concept for how books of classic sudoku should be put together. Its not completely new in name, as the best selling US sudoku books are apparently already "edited" by a puzzlemaster, but the goal of the process is original:

"What if talented sudoku solvers served as 'editors' for books of computer-generated puzzles, suggested patterns to generate interesting puzzles, and then tested 3-10x the number of required puzzles to pick out the ones with the best solving traits?"

We've already seen this process at work at the Sudoku National Championship. In year 1, Wei-Hwa certainly used computer-assisted design for the sudoku that appeared but he also made some extra puzzles that were not selected by puzzle organizer Nick Baxter and made adjustments to some, like "Q", to get them in the right solving range. In year 2, Nikoli authors provided ~50-80 hand-crafted puzzles but even they were tested and selected for particular rounds by Nick. In each year, the puzzles started on the good side of the construction spectrum and then the best were selected. Well, year 3 may have brought the first completely computer-generated puzzles into the mix. I believe Stefan Heine predefines some patterns for his generator to use, and then generates puzzles from these, but I have no details on his process and will just call it complete computer-generation for comparison. Stefan delivered 2-3x the number of puzzles needed for the tournament to Nick. Testing of these puzzles revealed some really neat ones, like the Round 3 Puzzle 3 void design (most void designs solve nice so this is not a surprise) and the Final puzzle on stage. There was even a themed round of just 17s that solve cleanly thrown in in the middle for variety. As "editor", Nick Baxter selected a good set of puzzles that pushed the competition puzzles closer to what the best hand-crafted puzzles would be like in terms of quality and memorability even though they were (for our discussion's purposes) close to completely computer-generated. I can certainly extol the virtues of the Super Franciscan rectangle puzzle (Round 1 puzzle 2) much more easily than the 10/18 Advanced practice puzzle even though they come from the same source, and the reason is puzzle selection.

During a sleepless night in Antalya, I wondered what a book of my classic sudoku would look like if I wrote one. I decided I would ideally find a good computer-generator that also lets a user define a pattern for the puzzles to be developed, and then throw a set of themed designs at them. In one extreme, I imagined what "Thomas Snyder presents Sudoku for the Coffee Break" or "Thomas Snyder presents Seaside Sudoku" might look like. Well, the classic sudoku would look like their themes: mug-shaped puzzles, or clocks, or a big sun, or a sand castle, or lots of puzzles with waves. I could imagine the Seaside book having a flip-book aspect to it. On the right hand side of each page would be a set of "sun" puzzles, starting with a rising sun, then a setting sun, as the book advances. About 30 patterns (maybe each used twice) would be fine. On the left-hand side of each page would be a set of "wave" puzzles - this design is much easier to conceive of and 30+ versions could also be made there. There is something to be said about how particular patterns with full triples in a box or voided rows and columns lead to fun solves so please consider that in making the patterns I would be using some of the years of experience I have here. Just giving predefined patterns to a computer-generator is a big step up from the worst of these algorithms.

Then, with the patterns going to the computer, I'd get back 3-5x the number of puzzles I need. I can solve 500 puzzles in less than a week (but cannot hand-construct 100 in the same time), and as can be seen from my nikoli.com solving comments, I can find interesting properties of a puzzle even when solving them very fast so let's say I can do this and mark times and fun properties. Now, in addition to already having some patterned sudoku that tell a story to fit the concept, I also have an above-average in quality set of puzzles for each of these patterns based on "editing" and puzzle selection. Just my puzzle rating should be closer to a human's experience from the editing process so the high variability of some sudoku books should be greatly minimized from actually test-solving the puzzles. This, to me, would be the cool book to try selling. Of course, I'd have to compete with "Will Shortz presents Coffee Break Sudoku" which already has his helpful hand in "editing", but I think Will is a talented crossword editor and understands what being a crossword editor means but does nothing with the sudoku books whatsoever. If someone actually did bother to be a sudoku editor, and I am certainly one of the highly qualified choices, then a better daily newspaper puzzle, or a better set of classic sudoku books, would likely result. But I'm not suggesting I'll ever do this, I'm just wondering "What If...". The best puzzles may still be fully hand-crafted, but "editing" computer-generated logic puzzles to improve their quality seems a great compromise with classic sudoku to me. "Hand-selected" may become the new "hand-crafted".

Inside the Mind of a Sudoku Master

Mon, 16 Nov 2009 15:06:36 GMT

TIME.com was following Wei-Hwa and me at the recent Sudoku National Championship and the video piece was just released. Aside from some minor factual flaws (I turned in my final puzzle at ~4:14, not ~7:30 for example), it captures the whole championship - even Eugene - really well. (Note: I'm not getting the embedded video to play right from lj so you'll likely need to click on the link above)

ETA: Some curiousities to add to the story: this video may actually show Eugene finishing the 3rd round (which is quite a weird moment to watch as he stares at the camera instead of just handing in). While the proctor does not collect his paper immediately after writing a time on it (leading me to initially speculate this could be an earlier round), I've been told a separate runner collects the papers so its not on camera. You'll notice that Eugene was not in this seat near Wei-Hwa during the round 1 filming so he wasn't competing then or wasn't competing there then, consistent with what we've heard about mid-competition registration. Still, there is no doubting Eugene's final puzzle board, shown here quite clearly after 8 minutes, with impossibly slow progress for an advanced solver. If he wasn't cheating on paper, he was certainly throwing the competition on stage.

Friday Puzzle #23 - #23

Fri, 13 Nov 2009 01:42:47 GMT

The number 23 is on strike!

While its been worn by many great athletes, features prominently in the numerology of human genetics as well as famous passages from the Bible, and has successfully driven Jim Carrey crazy, 23 still feels underutilized in puzzles (aside from that overused 3-cell entry in kakuro and killer sudoku which it does appreciate).

23 is tired of not existing as a BANG, for example.

23 is also tired of not being used as a common value in that "trendiest" of "puzzles", KenKen.

And 23 is hardly alone. A lot of possible numbers cannot be reached by simple operations of the same type. While there are reports of 4-cell 44s and other curiosities in KenKen products, these were not obtained by any cool means; there was simply a bug in "seven" of their 250 puzzles on "limited" wireless carriers (the linked page certainly shows 8 broken puzzles but who's counting? ... or at least doing error-checking of their error-checking). The unusual numbers resulted from 256 being subtracted from all values >= 128 it seems.

After writing a bunch of Calcu-doku puzzles myself for an upcoming book, my thoughts obviously drifted to considering how one could use more operations in each cage. I believe snake-shaped cages, that evaluate from the number (head) to the last cell (tail) with operations being used as encountered is an obvious way to do this. 44, for example, could be (((((5+3)/2)+1)+6)*4), as shown below. Going by order of evaluation: 5 +3= 8 /2= 4 +1= 5 +6= 11 *4= 44.

In a solving sense, what does this mean? Well, you have to almost work from the back to the front. As 44 = 2*2*11, the last cell (a multiplication) is most likely a 4 but possibly a 2. Three-cell cages would be great for this gimmick as something like [29][*][-] which is [5][6][1] or [6][5][1] in a 6x6 puzzle is not too hard to figure out, but shows one can spice up the math with more than just one operation at a time. If you are just doing one to three-cell cages anyway, the combinatorial confusion of big snakes and possibly unclear paths within certain region shapes won't be encountered at all.

With this example, I really had to appease the number 23 for a bit (at least until BANG 23 actually happens) which made the resulting puzzle a bit too hard. As large cages aren't always easy work-ins, I've also shaded five cells in the grid, which will together contain exactly 2 2's and 3 3's, and this knowledge should certainly get you to a satisfying conclusion.

Rules: Fill each cell with a number from 1 to 6 so that, in each row and column, each number appears exactly once. There are a series of snake-shaped cages starting with a target number followed by a series of adjacent, connected cells each with an indicated operation. Proceeding from the cell with the value through the connected cells in order and performing operations as they are encountered, the digits placed in the cells will evaluate to the indicated value. Numbers may repeat in a cage, but cannot otherwise repeat in a row/column. In this puzzle, five cells are shaded and these cells will eventually contain the set of digits {2,2,3,3,3}.

Breaking...

Wed, 11 Nov 2009 15:02:04 GMT

Sudoku contest competitor to be retested - so, maybe someone found Eugene after all (or his not showing will make a choice easier?). This could get weird and I'm not sure what this extra step means in terms of how the investigation is leaning. Also of note, Phil Irwin from the chess community is the first to publicly associate the chess "player" from 2006 with the sudoku "solver" in 2009.

What If...? #2 - Solving Videos of Championships

Wed, 11 Nov 2009 01:32:35 GMT

(This is the second entry in a series of essays on ideas about things that should be done with sudoku and sudoku championships. The first, on playoff puzzles of increasing difficulty, is here.)

The 2nd World Sudoku Championship in Prague, Czech Republic web-cast the entire championship, including the playoffs. While watching solvers focused squarely on papers at their desks for hours could not have been that exciting, watching the four simultaneous solutions of grids during the four playoff rounds certainly was for those following in the audience and at home. However, now two and a half years after the event, none of this video that was web-cast live, especially of the playoffs, has ever been released. Two "telephone videos" from Simon Anthony of the UK which show me checking puzzles with my finger are the only digital record I have of my first and most memorable championship.

The 3rd World Sudoku Championship in Goa, India similarly used cameras to display the final puzzles of the four finalists but no video from those organizers was ever made available either. The German team posted some clips from the final toroidal puzzle and another earlier one where I'm already done and doing a word find, and I have a commentated (and time-edited) version of the "goes to 11" classic final puzzle #4 from the preview copy of the Sudokumentary, but the latter cannot be made publicly viewable. Still, what I do have suggests that the finals are compelling theater if any organizer would ever put together a full clip of the finals. (Note: the Germans also posted video from Zilina including this underwatched gem, the infamous 6...4...5...3...2...1... start to the non-sudoku final puzzle, which speaks for itself about the bumbling nature of this "sudoku" "championship" quite well.)

For three years, the US National Sudoku Championship has also had videographers covering the event, as well as a wealth of photographers from various outlets assaulting the stage during the playoff rounds. It has never affected me much as a solver (unlike the press in Lucca at WSC1), but it certainly keeps the audience from seeing everything. There has also always been a camera platform in front of the main stage where at least two tripod-stabilized cameras have recorded video, sometimes for the purpose of displaying the finals to the audience - although only one board at a time is shown and this is still not in an easy to follow format as you need to simultaneously assimilate where three solvers are, not just one. Regardless, none of this video - aside from say 3 seconds of me starting a grid, or declaring finished (for better or worse) is available anywhere online. Some of the unreleased tape from 2009 may be being used as "evidence" in an investigation that is "still ongoing" but undecided on whether Eugene Varshavsky, aka the "Sudobomber", legitimately qualified as a finalist in the advanced division two weeks ago.

With the past as preface, my question this week is: "What if organizers, realizing digital media and venues like YouTube can be used to tell stories about an event, actually bothered to show the finals of these tournaments in a compelling way?" Watching any athlete performing at their best can be very thrilling to those with limited and with great experience (the better you are at golf, the more you can appreciate Tiger Woods). Seeing top sudoku solvers approach a puzzle, particularly a challenging one with 10,000 dollars on the line, would be interesting to enthusiasts and possibly encourage both future participation and increased media coverage. Since organizers are in complete failure on providing a video story of the final puzzles of past US and World events, I've taken advantage of my loving parents who videotaped my finals performance to show you a third of what could be done. Here is this year's 2009 Sudoku National Championship Advanced Final for one of the three competitors, which shows me going from hero to goat in about 3 seconds. I've cut the last 3 minutes of the video I have, which is basically me sitting, smiling, and talking to camera people, as I still think I've won during this time as do the judges. I do not have tape of Tammy's last few minutes of finishing her puzzle, or of me congratulating her and pointing out my error, or of me telling Tournament Director Will Shortz that there are three errors on my grid, although the Inquirer's news piece gave some of that. I also do not have any more tape of Eugene standing still, but you get the feel for that from this already.

Reviewing the video establishes three things:

First, I was well ahead of Eugene's 8 minute point after just ten seconds, with almost all the 9's and 3's placed. Extrapolating progress and relative difficulty of placements, he might be finishing about now.

Second, while Eugene does gets the 9 in R1C3 quickly, he does not chain another 9 immediately into box 7 (and then another in box 8) which any experienced solver of sudoku would eventually think to do. He never gets this 9 at all, in fact. Watching carefully, you should see both me (and during the pan Tammy) do the 9 to 9 to 9 relay right away which each and every other advanced solver would likely do as well.

Third, and certainly news to me, my error in the puzzle was almost certainly caused by sloppy handwriting accentuated by the white board format. The rate at which I write the 8 followed by a 6 in box 6 tells me I was reading the two markings in R5C78 as a 6 note, when it actually was an 8 note. My duplicated notes are written a bit faster than usual on the white board (I normally just write once on the gridlines on paper) and this sometimes leads to clarity errors (see for example the 7 note in column 9 I go back and fix earlier when my first mark did not end up being a 7). Here, in my haste, I didn't close my 8's. Since I would have taken a longer fraction of time to search the box and at least one of the row/column if I was checking for what was missing there, what the video clearly tells me I was doing when I made my error was propagating digits by reflex off of notes and not thinking or scanning at all. Penmanship, on the large board, cost me 6,000 dollars and a spot on the US team.

You may wonder why I posted the unedited video (with just the audience/competition sound and no extra commentary or unnecessary use of the first/last movement of the Carmina Burana). First, I wanted to demonstrate the current sterile environment in which the finals go on which is sadly nowhere near as compelling as the American Crossword Puzzle Tournament where I watch the finals every year afterwards online. Stage control is much worse in Philadelphia; my parents were filming from the front row and you can tell, with judges and camera people circling, that the observation of these puzzles is hardly ideal for the audience. Second, commentary during the finals is a deserving future topic of another What If? so I only wanted to post an unedited story this time and then go further into the realm of what could be in the future, maybe with the 2008 advanced finals or beginner/intermediate finals from this year.

Mon, 09 Nov 2009 05:10:26 GMT

Back home after a very long "day" of traveling (29 hours from leaving the hotel at 2 AM to hitting my doorstop) with a real race to the gate after a customs delay with baggage in Chicago.

The most surreal experience of this year's WPC was having other competitors pinging my blog (spotted at least 4 teams having it up at different times on their laptops) and even was asked whed I'd update as we sat in the Delphin Diva lobby. Apparently, my stories are part of their in-event experiences too and not just for the readers at home.

The hosts were good about posting score updates online where we found them first before they were printed out but this isn't always the case for all hosts (which is why I now blog all events on-site so that partial results can be found by my friends and family) and having a good online site is important for any WSC/WPC host but then so many things are and each year different ones will be missed. Even if I listed standard concerns here, I no longer hope that they will be addressed since there is not even enough agreement that Slovakia had issues to do something meaningful to codify sudoku rules and standards, not just "meet in a subcommittee" to discuss. In my opinion, the quality of a competition is often well-correlated with the amount of competitive experience of the organizers - not just puzzle-solving experience but actual competition experience. The puzzles and the puzzlers should always come first, and five hour delays because instructions were not handed out is simply not acceptable by any means to me. The solution key error and its effect on Ulrich (or whichever other solver would have gotten there first if not for him) only added onto these problems, and was another unfortunate result of not testing the format/puzzles carefully for the all-important "playoff" if you are running one. This kind of problem happened in Bulgaria as well, so its not that its a new thing and its not that it couldn't be avoided.

So, after this trip, I feel I've got lots of new puzzles ideas I want to write (can you say Tapa variations?), some "What Ifs" about competition/sudoku ideas I'd love to see here, and other energy on the construction side after seeing fun puzzles in Antalya. I am 80+% committed to writing a SudokuCup for next year's pre-WSC period (in part to cover the fact I am 80+% sure I will not be constructing for the next world tournament).

But I just do not have any energy to solve puzzles competitively at this moment. After a year with a challenging Mystery Hunt experience, the disaster that was Slovakia's world sudoku "championship" where nonsensical "rules" and unsolvable "sudoku" reigned supreme, my first discovery of the direct plagiarism of my puzzles on the French national championship just before the USPC and my first discovery of blatant cheating at the USSC that combined to destroy any sense of "innocence" puzzles might have had for me, and continued unfair and disrespectful treatment of solvers at the WPC because of the need for some kind of a "secret" playoff (foreign competitors must see WRITTEN rules and well before-hand since they do not all speak English; the documents we got certainly seemed to have been typed formally after the rounds were meant to start during the many hours of delays, and then further amended as we went on), I'm still wondering where the future of competitive puzzling will lie if I don't put on a different hat for awhile and establish standards others can't be bothered to put in place. I still await some resolution on the cheating scandal at the National Sudoku Championship and will certainly report on that here. But I'm honestly beaten down after a long year with a ton of frustration, and just need a break right now.

WPC - final update

Sun, 08 Nov 2009 00:14:03 GMT

Short version: WPC happened.

Longer version:
Today did not get off to a good start as we battled a mosquito or two in our room at night - basically without working AC, we had the windows open at night to sleep and at 3-4 am the likely bug problem arose. So not restful sleep, and not a quick start to the day. As already stated, there were about 5 hours from the announced start of the team finals at 10 am and when they actually started; the late start also meant no break between team finals and individual finals.

I already commented before, after the disastrous WSC in Zilina, that the rules for the playoffs should not be a super privileged secret and here the organizer's first flaw - after two days of incredible puzzles and mostly sound round design aside from the unavoidable timing issues - was not just delaying the rules meeting from last night, but not having printed rules when they started. Even with an unclear top 12 or top 4 teams the night before, there were only a handful of extra people in the running and a meeting could be held with all potentials so that the actual event could get started on time. Here, even after the delay, not having a printed copy of a complicated set of rules was further problematic as it led to a lot of competitor questions and further unclear answers. So, after several more hours of waiting, we finally got a printed list of 28 puzzle types that would occur in both playoffs and a list of the timing and tiebreaking rules for the event. Still, we'd never receive info on what puzzles would appear in any round before it started - it was a mystery revealed in the packet - and this did not help me either strategize or mentally prepare for the type of challenges I should do. Having to instantly react to seeing 5 types and remembering what some of them were and knowing which ones to solve, when already not in my best state of mind, led to some poor decisions.

The team playoffs finally started at ~2:45, when the individual finals were initially intended to be finished. First, the Czech Republic faced Japan and we learned some about the desk matching format which let us figure out how we would play the next team. When Japan prevailed, to maintain their ranking over 4th, we decided to match the Japanese competitors at their desks in alphabetical order (for various reasons such as to match their strongest Hideaki Jo with Zack and the rest of us against fairer match-ups). I had my best of the playoff rounds I was in today, getting through 3 of the 5 challenges in 18 minutes before stalling and breaking the Magnets. The 5th puzzle was a challenging "puzzle" about finding the lowest unreachable positive integer (LOUPI) using a set of 4 numbers and any operations (with some other rules). It would actually appear in all the team rounds, and never go solved to my knowledge by any member of any team in any of its iterations as it takes way too long to sort through so many possible numbers and even when you think you have an answer you can't know (and didn't, for just this type, get a second entry chance).

So, with H.Jo beating Zack, and the rest of us winning our desks, the US team held its spot in 2nd for the moment at 3-1.

The Germans then had the desk control and time edge, with Ulrich as 3rd alphabetically being kingmaker with the option to pick either me or Wei-Hwa (the 3rd and 4th alphabeticaly on our team with an empty seat meaning me and Wei-Hwa's table the other choice). Their first players matched desks and then Ulrich set-up the "dream match-up" against me leaving Philipp Weiss as Wei-Hwa's opponent. I was glad to have the chance to face Ulrich in this setting, but not glad to be solving like I was brain-dead and without much sleep in 5 days. After my one good solve of a latin-square/shape Ikebana puzzle where I made back some time on Ulrich, I broke (and never finished) the Scale Sudoku several times. Even knowing the main 3-cage to 1-cage comparison to use, and how it applied to some of the cages, I missed the possibility in column 8 I needed to fill it. I really wonder if the sudoku grid size (and the puzzle grid size in general) was not helping my scanning or thinking. It should be noted, as no one but us could see the puzzles we were solving, that I found it odd every grid was now 2x the size we had seen in past days when solving and in the sudoku at least I know this affected me. I switched to the pentomino packing puzzle instead of the sudoku after 2 attempts, and despite checking all 12 shapes, had managed to tweak an X to an F and not fix an easily satisfied 1 constraint. So, a 1 minute penalty followed by a 3 second fix. As time ended, still with a hopeless scale sudoku, Ulrich had soundly demonstrated his ability at 4-2. The match-ups had actually worked out for the Germans in all cases so a clear new world champion team was here on display in Antalya.

All this action brings to mind the question of why a 2-hour long team playoff was needed to not change the rankings at all. It at least showed the team playoff style was a good means of proving team depth and strength as already awarded after day 2 where gaps between all rankings were already established.

After a quick transition to the individual rounds, Wei-Hwa competed in the first heat but failed to advance with problems in puzzle selection and solution execution being his downfall. I was in the 4th desk in the second heat, with Zoltan Horvath and Peter Hudak moving up to join our group of Hideaki Jo, Nikola Zivanovic, and Philipp Weiss. As I've mentioned before we did not know the puzzle types in an individual round until we opened the envelope and here at least the Anglers jumped out as a good choice. I was a bit rusty at getting the checkerboard constraints matched quickly but the solution was found somewhat efficiently. I then went to another latin-square like puzzle with row/column constraints called Range and despite seeing the way through, wrote a 36 instead of a 35 early on the right path to get an answer with all but 1 cell. I erased and started again and apparently made a similar error again. The third time through I finally solved it, but this certainly was my first fatal mistake since "banking" puzzles soonest would win tiebreakers if no one finished the round (and in general no one was finishing any round in the team playoffs or here). I then went to a corral-like variant (I forget its name), solved it in about 90 seconds which was nice, checked the constraints, somehow counted a 6-sized region as 7, and turned in another error. Again, my paper came back for a 1 minute penalty. 3 seconds later it was back to the judge. In a 30 minute round I could not stand to lose this time or momentum. With my Japanese Arrow solution interrupted, I think I lost the path. I got close to an answer but tweaked for 5 minutes and got farther and farther from it leaving me with just 3 done and what I think is 7th place. Again, fatigue and errors from day 2 forward compromised the skills I know I can show in a single 2.5 hour tournament at home like an OAPC or USPC.

So I left to drop off some things and was frankly tired (it being nearly dinner time now before the finals started) and eventually came back to observe great controversy (again! - can any competition conclude cleanly?). Ulrich, with a large head-start, had gotten to a good start in the round when, about midway through, he turned in a solution that was adjudicated as wrong after a minute. When this happened to me, it was easy to check and find the mistake and turn it back in. Getting a wrong paper is itself really discouraging, but you can often find the mistake. Here, Ulrich spent time and energy looking over his puzzle and could not find the mistake because there wasn't one. The answer key itself was wrong, and the judge - just checking one grid against another - did not spot the issue in the key and therefore could not prevent the complete round problem from unfolding. Ulrich raised his strong concern of incorrect grading (he similarly had to do this when encountering the error in Bulgaria's semi-final Star Battle). His distress at the mistake, and how it would affect the final if it was allowed to continue (it had been stopped) was clear. What to do was not. A long meeting was held with many captains. A decision was announced to continue with a 2 minute restart time for Ulrich (after 15 minutes of the announcement) was made. An additional error - Peter Hudak had not been given the right time for his start - was also mentioned which led to me rolling my eyes once again at playoff incompetency unfolding in an unreal way. After continued discussion of Ulrich with organizers, more huddling happened, and it was eventually decided that a new set of finals puzzles, mostly of the same types, would be used in a rerun. At dinner, Wei-Hwa and I would join some other solvers in testing these extensively and I was tasked with going through a Kropki Sudoku which needed some tweaking and fixing to get simpler which Wei-Hwa and I helped with. In the end, now as we sat at dinner tables, the finals reran and Ulrich clearly repeated as WPC champion so a fair resolution to another potential disaster happened here.

I'm still left with a lot of doubts about the ability of the WPF to organize a fair competition when so much is left on the host nation's themselves and standards are not being enforced (if they even exist, which is honestly not clear to me after recent events). Some of the simple issues I mentioned in my open letter after this years 'WSC', like the unclear rules for these playoffs that were not given to competitors in advance leading to 5 hours of delays shows me that there are serious problems with competition standards that are not being addressed by organizers. I'm honestly still really angry about the WSC fiasco and am currently not enthused to perform in any puzzle competition next year outside of the 94306 zipcode or a 1 hour drive. I also continue to persist that I should start my own online puzzle site, and possibly also start to contribute - as the OAPC team did for nine months this year - to online contests to rank top solvers and constructors in the world. The WPC community grasped onto the excellent OAPC puzzles and I'd hope they would similarly welcome anything I could offer for solvers in the coming year.

So, all in all, a WPC with phenomenal puzzles and a lot of great additions like the run up of monthly OAPCs to introduce a lot of the new Turkish types in a competitive context, but still consistent and disappointing flaws in playoff execution that leads to both increased and possibly needless stress for the finalists. If there is no doubt after the individual standings that one solver is the best, and if there are few in the audience (at least during the team playoffs), given a format that is hardly interactive and frankly way way too long, what is the point of these playoffs? After 2 days, the Germans were clearly first as was Ulrich. They both ended up winning. If only any considerations were given to order of finish at a WSC.... I do not believe the board frankly wants or can address my concerns with that event, so I don't know when I will see many of my foreign friends again, but for now goodbye and safe travels.

Instructionless part deux?

Sat, 07 Nov 2009 11:41:06 GMT

Following a weird round without instructions, we are now 3.5 hours late at even starting the team finals as the instructions are late and not printed - the oral English descriptions are neither perfectly fair for all teams nor perfectly clear. We do have over two dozen puzzle types that might show up, and a slight idea what will occur during the team rounds (4 individual head to head matches will occur with 3 versus 4, winner versus 2, winner versus 1) but that will take two hours and be tiring before the individual playoffs start which will also take two hours and be tiring. I'm at least 6th individually, so I only have 2 heats to get through although a huge time advantage to overcome in the finals if I make it.

Friday Puzzle #22 - Color Puzzle Sampler 2

Sat, 07 Nov 2009 07:57:43 GMT

So I'm not sure what day it actually is, except I have a feeling I have 3 minutes to post, to hit Friday in the west coast. These three combined puzzles were first written as part of a birthday hunt for Wei-Hwa last summer; there is a solution "word" but it is not a further instruction so when you have it you are done. If Four Winds/Nurikabe are not instantly familiar, use Google.

(This jpg is the best image format I can do while on the road from the files I have - an updated form may be here next week.)

WPC - day 2

Fri, 06 Nov 2009 22:07:33 GMT

We'll do this in fake stream-of-consciousness at the time style even though this was written well after the events.

8:00 - wake up after a tiny bit of sleep in a stupor, likely from being interrupted during a dream. I manage a shower and a trip down to breakfast and see the latest standings with all of day 1 posted - 2nd place, 89 behind Ulrich and 95 ahead of 3rd, right where I don't mind being if I can't be in 1st. I had made some more errors on papers, including my favorite of writing 8*(1-7) = 48 in the puzzle as I was giving the clear product to get a common largest number. Just tired I guess. It was an amusing loss of some 17 points but not too costly. My battleships were clean which was my worry given placement and time bonuses. A bowl of ChocoChamps and some yogurt later and we are ready for round 1.

9:45 - Screen Test 2 - a bit delayed start, but the standard quick puzzle round which covers a lot of observational puzzles. However, the new twist this year, which I found really brilliant, is that the test organizers had a clicker-type technology to log competitors' answers. This system was actually used in other rounds where you logged your finished time which digitally time stamps your set of puzzles (a brilliant change that would affect proctoring elsewhere, add second-level data at other competitions, etc.) and allowed the organizers to post a list of finishers during the round to know your competition's results (for better or worse). The system was also used for attendance before rounds started - again a nice touch. They gave live results after each 5 of the 15 puzzles here. I got a 3/4/4 split which left me unhappy to be one behind the pace at the first break but back where I wanted to be at the end, in 2nd in the round with 6 gained on Ulrich. My one criticism - having failed to log an answer in a puzzle after knowing I could not change a button press later - is that the "disappearing digits" was not as clear a time indicator as a progress bar or actual clock.

10:25 - Now thirty minutes behind schedule due to delays in changing the lighting in the testing room after the screen test, we come to the round I was waiting for - Tapa (a painting/path/minesweeper type puzzle). Its my newfound specialty. Its a 35 minute round with 2 "standard", 2 hex, a tapa distiller with 4 puzzles that must extract clues from a single grid to form four valid answers while spending all clues, and a TAPA LOGIC which is basically a super-large Tapa with encrypted numbers. I blaze through the TAPA LOGIC, get a good number of reasonable solutions to the Distiller but decide to come back to finish it off, whip through the hex, and the standard, clean up the distiller, check that all cells in all grids are marked filled or empty as the common error is to miss the whole chain constraint with a single unshaded square, and tap my clicker to be finished. 1st with 11+ minutes on the clock - should be worth 20+48 bonus on the 200. Ulrich finishes second with 6 or so minutes left so I figure I got 19 more points back given his placement and time bonuses. Still, my best round to this point where everything clicked.

11:10 - Matchmaker - this round had 7 grids and 8 puzzle instructions all based around grid/number puzzles such that, in principle, any of the puzzles could work on any of the grids. But, some puzzles have particular constraints (like islands not having unlike numbers touching) or other reasons why they aren't valid. Our goal is to find the 6/7 grids that can be solved by 6/8 of the puzzle instructions. It seemed a high variance round where the order you searched things might pay off quickly or slowly. It was also an hour long and a likely source of huge time bonuses and large losses if mistakes were made. (This is not, at this point, a sign of impending doom since I just crushed the Tapa round. Just mentioning.)

I start with the Islands and show all 7 fail for it, then do the masyu and see 2 of the 6 work for it and after 3 minutes I'm already getting somewhere. I go through and try the Kuromasu next, which is a good choice, as it is also easily provable, since I've solved tons of these with Nikoli, that there are none of those. So I think I now have 7 grids and 6 puzzle types. The tetro minesweeper is the next type to go (you can see some of these I wrote in a recent GAMES PuzzleCraft). All but one are provably false. The last feels close to a solution, but does not yield for a long long time. I jump off of it, thinking I now have 7 grids and 5 puzzle types which is a problem. I focus on grids and prove 2 isn't anything but maybe Hamle. I spend 5 minutes solving it as a Hamle, get all but 1 number placed, and see the contradiction. Worried I'm making errors, I solve it again and find the same contradiction. So 2 is not a Hamle, I guess, but I still don't have 6 puzzles types even if I'm down to 6 grids now. 5 more minutes and Tetro Minesweeper is indeed the grid I felt it was which is encouraging but I wish I had that 15 minutes ago. I fill some top heavy number place puzzles for awhile - getting two of them working, then realize I should just force the remaining types to any grid instead of oversolving the types I have left. The pill sum comes fast, then I decide the 7 which isn't the hamle is likely the top heavy number place I still have written there. I try 4 as a hamle, get it, then check the rest of my work. I spot my fatal error (or so I think) by correcting a 122 pill sum entry to a 132 where it is obvious what I meant from what cells are actually touching but wrote too fast - broke "the speed limit" I guess - and had a problem. I have 16+ minutes on the clock, but the best finishers took only 30 minutes of the hour. I figure I've lost 50-75 points to Ulrich who finished around ~5th but should still be comfortably in second overall.

12:30 - Four by Four for the Four
After a great morning, I figure I should change our team's original plan where I'd knock off black and white and instead do the Half-Life which starts with a Tapa and then transfers info to a corral, which transfers into a japanese sum, which transfers into an islands. The tapa and corral go really fast, and then the roadblock comes which is the japanese sum. I get a lot of the grid in, fit the extra info from the corral, and then get Roger who has finished the minesweeper to help on the sum and he is as good checking my thinking as doing the solving and we get it done together. The islands is trivial afterwards, particularly with a clear transfer of data. As I finish, the Mr. Universe and black and white are done and being checked and after a full round of checks we turn in first.

13:00 - So, a good morning and off to lunch. We decide to try one of the many other restaurants/food services at the hotel and go for Doner which is incredible. Much like my favorite non-Pinocchio's Pizza option in Harvard Square whose name I am forgetting, but now closer to its source. We talk briefly about the upcoming instructionless round (thinking maybe 3 new types, 2 of each type) and the OAPC puzzles. We also played some Tichu.

14:00 - Instructionless - the "Guess What I'm Thinking" round. I thought this round could be interesting - I enjoy the Nikoli magazines section where I start with no clue what an experimental puzzle is doing and then figure out what to do by looking at some of the puzzles and solutions and making sense of it. The issue I have is that the typical "example" is a tiny grid with a lot of subtle things going on that needs the text to work. I typically break in with a larger, deeper puzzle and then wipe the memory of the physical solution to be able to solve it. Here, two of the six examples (puzzles 4 and 6) seemed obvious from the small instructions. The other 4 fit into some general genres but were pretty much WTF?!? I came up with thoroughly consistent rules like "if the 1-4 gappy skyscrapery-puzzle is not giving a skyscraper clue, the clue is telling the distance of the 2 and 4 from each other." This sounds crazy, but it is fully consistent with the example and solves the grid (maybe 2-6 choices, but whatever). Its likely not what was going on, but without "guessing" exactly what the designer is thinking, its intractable to find the global maximum of thought space. No one feels really confident after the round and it was a bit exhausting to get 2 in 3 minutes and then in 22 more get no perfect clue sets on any of the others. Still, have to refocus for the OAPC round.

14:35 - OAPC 10 - I'd been eyeing this round for awhile as I tend to do well on many of these puzzle types. It was the longest round, at 130 minutes, and the highest valued, at 750 points. I get going ok, with the sigma snakes done in about 8 minutes, and get the first 2 of the next part before I hit quicksand for the first time. I jump between the two but don't get the answers. I move on. Polygraph is next. I get almost all of the first but one corner that trips me up for an unknown reason, so skip to 2,3,4 and get all of those and then come back to the first and clean it up. I go forward and intuit the slash packs well too. Then I start to hit some curious weaknesses. On my first pass, I could do none of the 4 tripod sudoku. Sudoku problems? I move on. I reach the four squares and somehow manage to break it early, not realize, and then try to tweak for a long long time. 20 minutes I bet, then I move on without an answer. +- 1 is a quick breeze, and so are the first 3 magic fences, but after spending 10 minutes with another almost solution of the 4th that I felt was good until checking, found the mistake, fixed, checked and found another mistake, I abandoned it. With 20 minutes left, I had to choose between the kakuro and returning to where I'd banked time but not finished like the four squares. I go back to the four squares. In 10 minutes I do clean it up, and then knock off two tripods before time ends. I never look at the kakuro! This would anger me as it seemed an easy type given how well I'd done the kakuro on day 1; the scores were high to boot. So, a good round without errors and with better puzzle choices and I get those 4 with what I basically have for all but 4 puzzles. As is, I'm down 224 or so points (before errors) from full marks.

16:45 - minutes after leaving the room frustrated at not doing well enough in the OAPC round to catch up to Ulrich, I catch a brief glimpse at the scores just posted. Hmm. Why is my tapa score 175 (an error on the second hex)? Second hmm. Why is my matchmaker score 250 (an error on one of the 6 puzzles). The first cost me 25 (puzzle)+20(place)+33(time)=78 points (39% of round value) I figure. The second cost me 65 (puzzle) + likely 1 or 0 place + 48 time = 113 points (36% of round value) I figure. No papers to see why I'm suddenly sick to my stomach but, yeah, ugh. I'm now in 6th and miles back of where I felt I would be.

I try my best at these tournaments to act like the travel and fatigue from work and other things aren't bothering me but it is clear the jet-laggy Thomas of today is not just making errors on puzzles but making errors in checking as well as points are slipping away. I now routinely check puzzles in a "quick" way after finishing, looking at the most likely ways I have an error and circling clues I've spent to confirm all constraints are met. Still, in some situations the adrenaline of finishing a round might make me declare finished before I spot what will ruin my score or worse, incorrectly confirm a constraint is met when a trivial fix is there if I find it. Still, the low feeling after these massive point losses that happen to me at each and every championship (I feel a photo gallery of my favorites will be here after the tournament) is often too much to bear. If not for a rejudging in Brazil, I would never have qualified in the top 3 after two days of a WPC, and in the Eastern Hemisphere I've dropped from 1st/2nd every year after some point in day 1 to much lower after day 2. 10 hours of jet lag has a way of catching up to you.

I'm steaming through the coffee break and head to the last individual round - Upgrade - with a goal to survive and maybe pull a miracle with a finish.

17:10 - The round involves placing dice on a 3x3 skyscraper to make a 5x5 skyscraper using sides and top faces to "upgrade" the smaller version. An interesting concept certainly. Three each of two chirally opposite but otherwise standard dice (with a "dead" 6 side that cannot be shown in a solution) are awaiting us. I suffer through the easy one for awhile but learn how to solve it/notate after 10 minutes. The second is much quicker, now knowing the type, at 4 minutes. The last 16 minutes are spent trying a lot of things that could work on the much less constrained and much much harder to try logic third grid. I don't get a solution.

Afterwards, I tell Nick (who has been advised by Husnu that I might need "consoling" when I see my papers from the morning rounds) that I never ever EVER EEEEEVVVEERRR!!!! want to see them.

18:00 - WPF - a team round to end things. I just want the day to be done still. Fortunately, Wei-Hwa is solid at manipulative puzzles and this one, a box puzzle with hinge-y blocks like the four winds variant I saw in Brazil, is solvable as we talk through the steps. We finish about 3rd, and leave the room to go to the lobby and play some Tichu. I eventually get the papers I never ever want to see (thanks Nick). Somehow, having a straight flush bomb waiting and two different people trying for tichu can let me handle a simple tapa error where I'd marked a blank in place of a full in a clear isolated side. If I'd seen (or not circled incorrectly) the 2 constraint filled, I would have trivially fixed the error. My check - of filled cells - can't account for complete idiocy. In the other round, in my Hamle, I did not write a single of the digits that transferred. Given the grid to grid writing, I'd tried some checking and circled the digits I moved. Somehow the 2 got circled in the upper-left and wasn't written two spots to the right. Again, two "obvious" and fixable mistakes. I might have just copied the grid from my scrap paper wrong - its hard to know. Its hard to come to this kind of competition, knowing how well I can solve in my time-zone in online competitions in various disciplines, to then perform so much worse than I could and to make so many "speed-limit breaking" violations that lead to lost points. Epic fail!

19:40 - Dinner brings more food (50%+ of desserts given my mental state) and a discussion of the puzzle spectrum (STDs are apparently the opposite of Sudoku) and the Sudoku spectrum in particular with Roger and others, in part framed about what "variants" should be allowed at a WSC. I rate different kinds of variants as being close or far from the sudoku end of the puzzle spectrum, touched closest by Latin Square puzzles which should not be confused with three constraint puzzles (Sudoku) even though many (skyscrapers, easy as, kenken, etc. are common). Anyway, Roger believes just classics should be at a WSC - he doesn't even allow 6x6 or 8x8 or 12x12 in his world - maybe relays, certainly not diagonals, etc. His opinion is wrong, but he is a sit-out noncompetitor in WSC matters despite some fast solving times. Nick mentions the next WSC will go "back to basics" and I say what does that mean and apparently it means lots of classics which means my interest will be low. I pull out the Turk's sudoku magazine to practice before the competition and before I get started we decide to just go to the testing room. On the way I spot a cool Yurekli variation that achieves an unknown regions that builds together jigsaw bits with unclear borders to form a jigsaw sudoku. Basically, a 6x6 sudoku with 12 three-cell regions with 6 pairs needing to be made considering numbers, geometry, etc. Really cool and I can't wait to try it. Much more fun than any classic.

20:20 - I want to get to the test room for the evening's sudoku cup and get 5-10 puzzles practice with the conceptis classics beforehand to relearn their feel when I'm pulled out to do another team photo - the 20 minute session the night before was without our guests so we needed to do it again. The photographer again acts like he's photographing a head of state or at least something for a book cover but honestly 30 shots in 4 poses aren't needed. I lose my cool a bit with the whole process much as I would after all the Prague videography a couple years ago.

20:30 - 2 practice sudoku and then a round of 6 to do to qualify. I finish in around 14 minutes, but as I warned others, I'd check for a long time. 4.5 minutes it seems (I timed). 3 full passes. I still eventually turn in for first (and clean). The top 8 again make the finals like last night's Karala cup and so I'm 1st against 8th (Frederique Rogeaux of France) in a single puzzle and run through it, check quickly, turn in simultaneous to the other first finisher at another table and am in the semis. Jan Novotny is my next opponent, the Czech champion and a talented sudoku-ist who similary was dealt a cruel Slovakian punishment in April. The large grid format of the playoffs is unfriendly with my scanning, as is all the flash photography going on. I bifurcate unluckily, but used a perfect spot so the right answer falls immediately from the other as well. Onto the finals, or so I think. A big controversy arises as seems to be the case in every sudoku tournament I'm in, half the time because of format. My prospective co-finalist, Salih Alan of Turkey, has turned in his paper with 80 cells filled, and a tiny tiny tiny note in the 81st cell. It was certainly written earlier in the solve process as an either-or choice, but it is the only thing in the otherwise empty space so it would technically be a correct number if you were searching for a number there instead of looking at the face of a solution for the big numbers that are what he means everywhere else. Lots of team captains are consulted on the result, and when Byron Calver of Canada finally finishes he is shown the paper and agrees to let Salih move on even though there is a case for an incorrect grid being turned in 5 or so minutes earlier.

The final breaks in several ways for me, and I spot some naked singles I normally suffer at to fill the 7th column as a quick break-in. After some slower progress and being seemingly stuck with 25 numbers to go, I again bifurcate to finish first. Looking at the puzzle later, I simply had not propagated a 3rd 7 into a column after I'd filled the second and couldn't see it for the size of the grid. I'll need to practice not only on whiteboards for the future but on 6x6 or 7x7 inch grids since organizers vary sudoku sizes so often. Can we agree on 3-4 inches (7.5-10 cm) square?

So a long and dispiriting day ended with one piece of hardware to bring home. I'm certainly still in the playoffs tomorrow, as is the team, but with a round to go I'm in 4th and probably falling below a magic cutoff at 6 when the OAPC comes in. There are 12 going in, with the bottom 6 playing in a choose your poison format like Belarus last year. The top 2 in that round face 3rd-6th in the same format, with the winners there joining Ulrich and whoever winds up in 2nd in the Final Four for the trophy. Without my "big" errors I'd be in that 2nd spot - probably without just the Matchmaker one certainly - but with both of them I'll likely be around one of the bubbles at 6th or 7th. The good part of this might be that having seen my sudoku speed, I doubt anyone else will choose this kind of type (if it occurs) for a round with me. If I don't choose them either, they'll remain if I get to face Ulrich. If I can find my tired adrenaline style like in Goa (or even the 1st of my playoffs in Belarus) I could have a shot. If I find my tired muddle-headed style like in the second Belarussian playoff round where I couldn't even do a kakuro, I won't. Ulrich is certainly the favorite and will have a head-start. A team playoff with unknown rules awaits as well as the US in second tries to catch up to a 1st place German team with a solid Ulrich and a similarly solid Philipp Weiss currently at 1/2 with one round to be reported. I've typed enough. Now to post.

WPC Day 1

Thu, 05 Nov 2009 21:12:53 GMT

Mostly fun puzzles, although all rounds seemed to have a "new type" or an optimizer, not a puzzle, that stymied me from finishing. Getting 90% done in 2/3 of the time, and 5% done in the last 1/3 was the story of the day. Still, I've been checking things and scoring ok so about where I want to be. After 2 rounds, in third behind Peter Hudak and Ulrich Voigt.

Summary of the day:
Part 1 - Team - this round involved wrapping a set of green paper according to somewhat standard snake rules onto a grid that turned out to be a 4x4x4 cube sitting in the middle of an 8x8 platform. Some cells were marked and had to be avoided. It was fun to work with, but I never got the feeling we were really optimizing more than solving a corner/quarter and combining progress. There was a trick move not in the booklet (but apparently in the instruction session where I don't really pay attention) that we could have used to get an even better score but oh well.

Part 2 - Individual - Sprint - with a Saint Nick theme given his connection to Antalya - 16 puzzles, 20 minutes, and 13-14 of them were legitimately sprint puzzles. I did them with 15 minutes; two - an optimizer based on "How many solutions" a broken battleships puzzle had - seemed to take too long and also had a 5 point penalty leading to a skip. I stared at the OpHoop for too long and the combination of bad math skills under little sleep led to no more progress. So, at 20 minutes, 14 puzzles done (although 1 had an error).

Part 3 - Individual - Classics - a WPC should have a classics round with just classics puzzles. About 3 of each type for the standards would be fine. Brazil was the last host to do this perfectly and the Hungarians were reasonable about it too in '05. New designs or weird designs should be elsewhere. There were 2-3 suspects here. I took much longer than the score allowed on a german? slitherlink variant I call gessundheit. I got through the Hex Slitherlink but I'd argue the classics form of a slitherlink should be neither a variant, nor on a non-standard grid. I apparently forgot how to solve Black and White puzzles (Ying-Yang) which slowed me up, and almost got the harder magnets at the end but posted another 3rd-5th place score. Getting a lot of these is how to make the finals.

Part 4 - Individual - Optimizers - I like the concept of optimizers having their own round. So this round was fine. Having pseudo-optimizers like the "how many solutions" in the sprint, or a numerical maximization problem in the next round, should be removed from puzzle rounds and kept in this kind of round. The three challenges here went fine for me - pretty solid scores on all three but none perfectly maximal. One was a strict math puzzle which I misread the scoring slightly but I got the maximum of 6 of the 8 products formed. Then a Boggle-like puzzle involving placing letters to spell PEACE and EARTH which lead to a lot of P's on top of a couple EARTHs. Also, a path puzzle with either ANTALYA or ANATOLIA entries to draw the longest path.

Lunch - the restaurant here is phenomenal as already mentioned with tons of dessert choices to go with many meal choices, grill, etc. However, there is now a great overabundance of melon art which made its first WPC/WSC in Prague but here is just apparently a thing the hotel does every day with 6 carved melons of people or nature or quotes everyday.

Part 5 - Innovative - another 90 minute round where the non-classics should be - although here another different slitherlink on octagons was used. So, my one puzzle type that the Turks used was Diagramless Kakuro. While I've only written the one, I have a kind of mental synergy with the constructor of these and grasped the essential symmetry likely at play with little work and blazed through those puzzles. I blazed through all but 4 of them actually. Then the tweaky - try and try until you get them - puzzles were there. The harder of a pair that involved drawing multiple lines in a circle to split groups of numbers into common sums was one offender. With a couple choices of sum and tricky line placements, it took me a lot of time. A rectangle hanging puzzle had me stuck for awhile too - should have planned better what rectangles/squares could exist so I wasn't inventing a wheel/gimmick while solving the puzzle for the first time. Then those math optimizers again; ugh. I don't do math well when very tired and certainly only got the first of these. So, 45 minutes and 3 more pushed through but that's not what half the round time after ~15+ others solved in the first 45 should be like.

Part 6 - Screen Test 1 Matches - two screen tests this year. This was clearly the hardest for me. Puzzles involved identifying a match/two matches to add/subtract/move to make an equation that was false into one that was true. You either explored the right thought space or didn't before time was up. I might have barely gotten over half.

Part 7 - Last individual test of the day and the highest variance round left with a 140 point puzzle that could easily be 0 with errors. It involved 4 sheets of paper with battleships grids with holes in the layers that would see info (ships/numbers) below. Figuring out how to stack them, and then solving the puzzles, was the challenge. A lower grid might reveal a square shape in this spot, but that doesn't mean the higher grid uses the same ship below, just the same square shape. My default battleship notation of shading in used cells lost the necessary shape information which confused me. Still, I finished the puzzle with 3 minutes left just out of individual bonus unless there were errors. Assuming I'm clean (I checked all 4 layers I'm pretty sure), I made my goal of not repeating last years cards round and losing hundreds of points to a lot of other solvers.

Part 8 - Team - Weakest Link - so, Weakest Link rounds fail for many reasons, including too hard entry puzzles. The biggest issue though is that it is impossible to predict the timing of these rounds. I'd prefer a "we'll run extra time until 5 teams finish" kind of plan, particularly for the last round of the day, as it is a failure if no team finished this round in my opinion. So, as the entry puzzles were 4 crypted kakuro variations that I solved fastest. Another team was already at the desk but they'd left after 10 minutes to just work on it together. It was an ORu Kakuro, which can be solvable without extra help but in this case was maybe closer to a busted version of my Siamese Twins Kakuro where the options are really close in a lot of spots. Each new team member would get a sheet giving certain clues in particular places. After 8 minutes on the puzzle, and many others coming to other desks, I was 20-30% done in various parts but otherwise stuck. Roger was next to the table and we added his clues and solved forward, catching a slight error I'd made and tweaking to fix it. Zack arrived thereafter but time was running out. When Wei-Hwa arrived with 3 minutes left in the round, to give us just a single clue of a 4 (which was valuable, but also revealed the lower-left was just directly solvable), we got where we could but were still a couple minutes short of finishing. No team did. So, run the round for 60 minutes and we finish, possibly the Germans, Japanese, or others, and teams would gauge the round as more of a success. So, a sour taste in our mouths as we could not get it worked out in time, but we should gain some by just getting a whole team to the desk. Given tomorrow's last round has this +15 minute idea, I wish there was one today as well.

Dinner, and then an evening activity of Karala puzzles (the Turkish magazine for Paint-by-Numbers). I decided (unwisely?) to compete at a type I rarely solve. After a 15x15 and 20x20, I was one of 8 finalists to make a playoff. I eliminated my first rival Pal from Hungary but was soundly crushed by Hideaki Jo in the semifinals. Michael Ley pulled a mini-upset in my mind to win over Hideaki in the finals. An interesting non-official activity, and it had a simple trophy too. Tomorrow's activity is a Sudoku Cup and maybe I can win a sudoku tournament again for the first time in a long while. The rounds beforehand will be rough, although I'm eyeing the OAPC round, where I've already proven I can get in a good groove, as my big ground-gainer. The "Instructionless" is more frightening - is "Solutionless" a better name? - but we'll see.

Tue, 03 Nov 2009 20:53:24 GMT

Arrived in Antalya safely after ~24 hours in transit. Hotel has a good range of facilities and at least 40 desserts on the buffet line which is nice. The organizers here also look to be really on the ball and their intro had high production values, animation, and by far the best trophies at any WPC I've attended - maybe not for size, but its quite a light show of a spinning cube for the winners. Since they only go to 1st, I'm now extra motivated so watch out world. Still two nights before the competition starts so hopefully I can get some sleep, which I will go try for now.

quick post

Sat, 31 Oct 2009 04:07:16 GMT

No real further developments in the Sudobomber story over the last few days; the latest word is that the intermediate and beginner prizes will be released but no word on any changes in the advanced division.

I should be getting ready for the WPC, making instruction/preview posts here or something, but I have not had any time. I skimmed the instructions and saw that one thing I hypothesized the Turks would do from past discussions (a team playoff) is indeed happening. No details on the individual playoff besides a dozen go in, but their national championship used a belarussian-like set of weighted heats which might be what they do again. The OAPC round will use OAPC like grading/entry without marking full papers which feels right. A future "What if?" will likely revisit the concept of what/how much such be graded to confirm an answer to a puzzle at a competition.

The lack of more detail in my WPC thoughts when I normally share a ton of thoughts here is in part due to my being on a really interesting and fast developing project at work; I have been doing extra hours for the last month to get this data ready for public view. Sleep has been irregular and inconsistent and I can't tell you what time zone my body is in right now, but it won't be any more out of whack when I land in Turkey I guess. I just really worry I'll have another late day 2/day 3 shutdown but will certainly try my best to win the one title I want to win before I run out of opportunities to compete.

Friday Puzzle #21 - Extra Region Sudoku

Fri, 30 Oct 2009 03:27:50 GMT

My favorite current variation of Sudoku is Arrow Sudoku. Outside the realm of mathematical variants, my favorite geometric variant is the topic of this week's entry: Extra Region Sudoku. In addition to the standard 1-9 constraint in rows/columns/3x3 boxes, in these puzzles there are 4 more regions which also obey the 1-9 constraint and these are the contiguous groups of peach cells. I'm posting so many this week as I wrote these a long time ago and am unlikely to revisit this topic in the future; it should be noted that the last geometry is sometimes given its own name of Windoku and is syndicated in Dutch newspapers (and possibly elsewhere). The geometry of Windoku is less interesting to me than the others, but it has some hidden constraints to find if you've never looked at one before.

What If...? #1 - Sudoku Three Ways

Thu, 29 Oct 2009 02:51:50 GMT

I'm a big fan of Top Chef and the concept of presenting a protein or other component multiple ways (ie Pork Three Ways) has come up a few times recently. Well, Sudoku Three Ways is my first entry in a new "What If ...?" series about concepts that might be interesting to explore further for competitions or other settings. These will not always include puzzle-based examples, but should be fun to discuss.

The ACPT uses the same crossword solution but with different clues for three on-stage finals. The finalists are sequestered until their round starts so that the same solution is not compromised during the tournament itself. In addition to a question about why we can't get commentary at a sudoku tournament (Will doesn't think it possible, but he is in my opinion wrong), I've been wondering: "What if variations in the number of givens could produce three satisfying puzzles for each level with common steps seen by the audience as the finals play out?" Certainly, as fewer digits are in the grid, new ripples/challenges will emerge but some comfort zone about how "this column" or "this pair" or "this first digit with the 2's" are important will be set-up and could be discussed to the audience.

Here, since I write themed puzzles, I began with the idea to start with a smiley face and then turn it into something that looked like a sad face by removing digits and then turn that into an even harder "themeless" puzzle with more removals. I then started the construction around the hard puzzle, embedding a couple nice starting points of different styles (its probably two notches easier than the actual advanced final in last weekend's tournament, but would be a good stage solve). Restoring digits to make a frown and remove a particularly challenging use of C1/C9 information leads to the intermediate puzzle which is easier but not tremendously so. Making the full smile then led to a very easy puzzle that is perfectly appropriate for a Beginner final. I'm not sure playoff puzzles should be created this way, but then I'm only asking "What If ...?" You can choose the puzzle at your level and then solve it, or go in order if you can forget what numbers were where, or something else entirely.

And it keeps on growing and growing and growing...

Wed, 28 Oct 2009 14:36:37 GMT

Sudoku prizes frozen in cheating probe - the Inquirer is still incorrectly reporting that the second and not the third qualification round is critical here, but they are also mentioning that "After the competition, the blogosphere quickly began buzzing with skepticism and outrage. Chief among the bloggers was second-place finisher and former champion Thomas Snyder, who wrote competition officials a scathing 'open letter' that went viral." I'm not sure its exactly viral, but my presentation seems effective and, more importantly, incredibly public, given all those who enjoy what my blog should be about which is sharing tips and puzzles. (To those who are here just to follow the story but enjoy puzzles, please take some time to explore some of the links on the left of my blog-page, such as Puzzles I've Written or Thomas Snyder Outdoes the NYT KenKen as this blog is meant to demonstrate innovation, creativity, and beauty in logic puzzles - its The Art of Puzzles - and not just reveal details of a sordid cheating scandal.)

While the hold on prizes applies to the finalists in other divisions, I do not expect any changes anywhere else - I watched 4/6's of those boards from my position to the left of the stage and spotted nothing odd on the ones I saw - just true sudoku solving styles (two heavily candidate-based, one entirely noteless until he got stuck, ...) slowed down due to format and nerves, as would be expected. Still, its certainly worth reviewing everything because this championship's integrity, and this host's integrity for next year's WSC, is really at stake to me. This at least shows the organizers are taking things seriously. There will also need to be a real addressing of other concerns of the sudoku solving community before the next championship, but this "scandal" must be addressed right now.

This whole incident brings back to me the funniest part of my first championship win, on Yahoo's front page, with one option, right under the link to the story, for how others might catch up to me. That search then was frankly useless, but finding "ways to cheat at Sudoku" will hardly be a novel concept anymore.

The Sudobomber story develops...

Tue, 27 Oct 2009 13:54:50 GMT

From the Philadelphia Inquirer: Possible Cheating Probed at Sudoku Tournament (they get a fundamental point wrong - its round 3 not round 2 that matters) - let's hope the evidence (such as the appearance of his test papers and whether it looks like a grid someone would have when solving a puzzle, versus a grid someone would have when copying/being read an answer) leads to a fairer resolution here. There is still no way to restore a final with three advanced competitors, but not rewarding someone who gamed the system is a good start.

[ETA: NPR is reporting on it as well as standard AP wire. While indeed the Weekend Edition's Will Shortz is an organizer leading an investigation, I believe my contributions to exposing this cheater should not go unmentioned as they also borrow the frame I gave the story and the quotations around this person's name here on this blog.]

[EFTA: I've been interviewed a couple places now, including Philly's WHYY, for developing coverage tomorrow. Will Shortz has already been interviewed about this on All Things Considered and a couple new details are emerging from the cone of silence around this investigation. Most significantly, Eugene registered not just the day of as a walk-on, but also in the middle of the tournament and he only competed in Round 3. This is quite significant IMO. My observations of him after he finished 2nd is so far the only eyewitness account of this solver during the general qualification.)

The Sudobomber aka Eugene Varshavsky, in "action" (or I guess, inaction). The big headset bulge is expected in the finals, but who knows what was under the hood earlier.

Dr. Sudoku aka Thomas Snyder, in action and motion-blurred, before his mistake.

To think the next four minutes would take me through the whole range of OMG!!! I Won! to (gulp) two sixes to Congrats Tammy to No, Will, there are three errors on my grid to WTF is going on over here with "Eugene". Nothing is simple in the world of puzzles.

Some Picture Evidence for the Sudobomber

Mon, 26 Oct 2009 19:06:08 GMT

I'll place "evidence" here as solvers or others send it to me of the likelihood something fishy was happening with Eugene Varshavsky at Saturday's tournament. These are screen captures from the Inquirer's own edited video. The first is the grid, as it was during the awards ceremony which was certainly after he stopped, and at increased contrast difference. It has 2 observable placements in it, both in row 5, and a suggestion that the 9 in R1C3 may be there too (eta: confirmed from other images now). It is however not the most focused image and does not tell how this grid got to this state, if erasing happened, etc. Still, having this for 8 minutes of work on the puzzle after demolishing 3 hard ones in 12-13 minutes to qualify is simply not possible.

The second is the only picture of the Sudobomber minus the hood from the video as well; I ask that anyone who knows members within the chess community who may have been at the World Open in Philadelphia three years ago to see if he is recognizable, with a large bucket hat over his head and ears or not.

The Cat in the Hat Strikes Back?

Mon, 26 Oct 2009 06:50:55 GMT

I never thought, given the level of distaste left in my mouth by serious organizational mistakes, bad puzzles, and other controversy at the World Sudoku Championships in Zilina, Slovakia, that I would ever again spend most of a trip back from a puzzle event in the midst of another serious controversy and with such serious disappointment at many parties. We'd laugh before the tournament about my declaration on my blog, in answer to a question from a competitor about music that popped up over here, that my opinion that "[d]uring the rounds I cannot imagine any listening devices ... are allowed", was trumped by a facebook organizer post basically saying "yes, you are :)" with that extra friendly smile. I'm betting at least one other competitor is wishing now that basic steps taken during any other testing situation (no cell phones or electronic devices for example) were in the considerations of these organizers when in reality a lot seems to be missed, in part because of either failed imagination or limited experience competing in (not just running) a tournament.

So, here I am again, with a different controversy that needs addressing. Again I am left sitting on a plane writing a letter in my head to the organizers of a sudoku tournament to hopefully correct basic mistakes now and in the future in the organization, proctoring, and ranking of sudoku competitions. I do not believe I am a lone voice in my concerns that impropriety has occurred at the 2009 Sudoku National Championship, but I am a respected member of the puzzle community and so I am speaking out in hopes that this concern is addressed. I encourage feedback from other observers who may have additional memories or photographic or video evidence of this competitor to help solidify an understanding of what was going on with the "man under the hoodie." I've done my best to report what I know and what I saw as someone who also had a lot else on his mind.

Open Letter to the Sudoku community and the organizers of the Sudoku National Championship about the potential cheating of Eugene Varshavsky during this Saturday's tournament:

It is with a heavy heart and with the fullest consideration of the seriousness of these allegations that I am writing today. As a past US and World Sudoku Champion, a person who has solved (and watched others solve) enough puzzles to know a lot about the art of solving a sudoku puzzle, I have significant suspicions about the performance of a contestant in this Saturday's Sudoku National Championship.

Just as in college exams, sports, or other venues, intellectual competitions are certainly not free of people trying to use technological assistance or other cheats to gain an edge on more formidable competition. In 2006, for example, a suspected incident of cheating occurred in the World Open Chess Tournament. Against Grandmaster Smirin, a relatively unknown player wearing a hat the whole time performed well beyond expectations and ranking to beat the Grandmaster. After some suspicion was raised, this unknown disappeared to a bathroom where after ten minutes he was searched and nothing was found. Under closer watch, without the possibility of using unallowed assistance, the performance of this player returned to more expected levels and he lost the following matches, coming nowhere near to the mastery he had demonstrated earlier.

The city this chess tournament was held in: Philadelphia; the name of this suspected cheater: Eugene Varshavsky.

In 2009, in a different intellectual sport of sudoku, two established solvers from past years and a complete unknown, who was solving his qualifying round puzzles under a hooded sweatshirt, made the finals of the Sudoku National Championship. As competitors were (unfortunately) allowed to wear headphones to listen to music and could have electronic devices such as ipods as timers on their desks, the opportunity for something unknown to be hidden under this "hoodie" such as a camera/transceiver that would allow a person outside of the room to use a computer solver to relay a solution back to a competitor, was great. While much drama occurred in the finals between the two established solvers, it did not go unnoticed by some (ok, me, but not just me) that the "unknown", who was now forced to wear sound-shielding headphones over otherwise bare ears and under much more careful watch to eliminate potential advantages, performed well below the standard of any solver who would have been capable of being on stage at the time.

The city this sudoku tournament was held in: Philadelphia; the name of this suspected cheater: Eugene Varshavsky.

Only in Hollywood. Except it happened.

I first noticed this solver after I had finished Round 3 of the tournament. I had already turned in my paper, which did not matter for the competition as I had qualified for the Finals in Round 1, when I turned to look at each of the finishers that followed. Well, the second place finisher who handed in shortly after me was dressed in a black sweatshirt, hood up and fully covering his hair and a lot of his head, with a nametag reading "Eugene" that was handwritten indicating he was a walk-in contestant who had not preregistered. Given his attire, unfamiliarity, and the fact "Eugene" left the room so soon after he turned in his paper, my Snyder-sense was tingling. Still, I chalked it up to possibly being nerves at having an unknown facing me on stage at the time.

I next observed Eugene much later as he came to the front of the room after being announced as the round 3 winner in the advanced division. He was not speaking to anyone - instead having a phone to his ear the whole time - and while I did congratulate him and shake his hand, he did not seem interested in much conversation with me. Again, fully explainable for other reasons - who would want to be intimidated by a world champion? - although I tend to offer friendly advice to solvers for how to deal with the whiteboard format since it is a big change from standard solving. I lost sight of him during the Beginner and Intermediate finals and frankly had my mind on other things as I stepped on stage to begin my own final puzzle.

The results of my attempt at this puzzle are now well reported: I raced through the final puzzle but by going too fast ended up making a transposition error in the last few digits I placed leading to my turning in an incorrect grid. While my errors were unknown to me and the judges for a couple minutes, when I finally stood up and looked back I got a quick bulge in my throat as I saw two sixes in the 5th row and saw for myself that my fate was sealed. So, instead of congratulating Tammy McLeod on finishing 2nd as she completed her puzzle in seven and a half minutes, I was the first to tell her she was the champion. The organizers would learn this fact from me too, which is unfortunate. Regardless, the rules of the tournament state that a second place finisher who is clean within twenty minutes would trump my boneheaded error, so I was concerned about the state of the third finalist's grid because he had stopped, similar to an apparent error in the first beginner final, when a finalist seemed to me to have been better off continuing solving as another solver had turned in an unfinished board with notes instead of givens.

At this time, in this advanced puzzle, with a thousand dollars extra on the line, Eugene also stopped solving as the round would be over and he would get the third place prize money. But I was not correctly finished, and the rules would allow him to continue for the full twenty minutes to try for a correct grid and in this confusion organizers were trying to figure out if it would be fair to give him more time (I would quickly have countered that he had seen two basically completed grids in the interim as he was standing near us when I was explaining to Tammy my problems, check the video). But I did take a chance to peek at his board to see if he had a decent claim to finishing second with more time and was beyond shocked to see that there were very very few numbers written in. He also had absolutely no notes or other markings as would be typical of every other advanced solver I have met in the US and overseas who could have qualified as a solver on stage.

While there are many assumptions made about sudoku, such as that the puzzle is originally from Japan, or that computers create the best puzzles, these assumptions are incorrect. Yes, computers create most of the available puzzles, but the best sudoku challenges, including those used in this tournament, are hand-crafted and all the memorable hand-crafted ones like this final puzzle or Wei-Hwa's "Q" puzzle will have very tight solving paths with very specific sticking points that slow down a solver. Signatures of the designer's thought process, such as the type of sticking point, where it happens in the grid, if the same kind of sticking point is used multiple places, ..., are often a sign that can be used to tell if a puzzle is at least partially hand- versus completely computer-crafted.

A tight solution path also means that almost all solvers going logically through it without guessing will place numbers in a similar order and get stuck at similar/identical spots. On this puzzle, that path starts with placing at least a dozen digits in very quick succession - all of the 9s and all of the 3s and possibly a couple others - before hitting a stopping point where two sets of locked triples in boxes 1 and 9 are identified to lead to further progress. The evens are the key to the puzzle, hinted in part by having none of the evens in box 5 where progress is impossible for a long time, but the big triple for me was the one in box 9 with just evens. After these nice breakthroughs on opposite corners of the grid (the symmetrical placement another sign of the designer's hand at work here), a race to the finish will result as all the remaining digits are relatively "easy" singles. In fact, the trail of these final digits should be somewhat narrow and I'd bet that Tammy ended close to where I ended but wrote 46 and 4 instead of 64 and 6. The point of this aside is that on a difficult, well-crafted sudoku, the top solvers will certainly follow a similar series of moves and be stuck in the same spots. Just as a grandmaster in chess could look at a game and analyze inconsistently strong or weak plays and smell something funny, a grandmaster in sudoku (no such rating exists, but I'll suggest I probably qualify for consideration) can analyze a board and see a huge inconsistency in the level of progress a solver at the advanced level would have after 8 minutes even given the large whiteboard format. Indeed, in many online sudoku communities, the order and speed with which a player enters his digits is a very strong consideration for making a claim that a solver is cheating with computer assistance when solving a puzzle. So, being stalled at one of the triple-identification stopping points in this final puzzle would have made sense if at least ten more digits were in Eugene's grid. Having some notes or other markings on the board that speed solvers use to help find the way through the stopping point would have made sense too. It would at least show he was trying. Having a basically empty board missing several of the "easy" placements after 8 minutes does not.

As I was working through a complex mixture of disappointment and disgust with myself at the time I first observed these facts, I did not bring up all of these concerns with the organizers immediately which leads to this letter. Its probably not my role as a competitor to make sure the competition is run fairly, but it doesn't take a Dr. Sudoku to diagnose something is not right here. I did mention afterwards, and certainly that evening to Nick Baxter, that I thought the "Eugene" under the hoodie was possibly not the same "Eugene" on stage as the ability of the two solvers was so different from expectation. I'd barely seen any of his face when he qualified given the hoodie over it, so it was hard to rule out my wild speculation of two competitors. I began referring to the person(s) as "Eugene" with quote marks and this got into my initial posting on the tournament. Thankfully, the curiousity of that construction led to a foreign friend in puzzles, Johan de Ruiter, to post that he tracked this suspicion further and found a link to the past story about questionable behavior at a chess tournament in the exact same city by a competitor with the exact same name. Not caught red-handed, but with enough questionable signs that something certainly was up.

These suspicions are therefore rather serious and require some investigation. It would certainly be helpful for the Inquirer's film and photography coverage to be reviewed for pictures of this competitor before the finals and on stage, and specifically that the state of his final puzzle after various amounts of time and certainly after eight minutes when he stopped be made publically viewable for the community of sudoku solvers to see as, just like an odd sequence of chess moves, it will be prima facie evidence of this claim I am staking some of my reputation on that this is not the kind of filled-in board a person who supposedly can finish 3 hard puzzles in 12 minutes on paper could have by any stretch of the imagination. Even with all my ranting about the difficulty and problems of the stage format, it simply is not possible. Rather, in my mind, cheating of some form must have occurred.

What to do?

As I do not believe Eugene fairly qualified for the stage, and therefore only two true sudoku solvers were in the finals, it unfortunately brings the championship of Tammy McLeod under a cloud of uncertainty which she does not deserve as she did beat me fairly after I certainly helped beat myself. As the rightful third finalist would have a very reasonable chance of finishing this puzzle within twenty minutes cleanly and beating me out for second place given the scoring method of the finals where accuracy counts first, if a decision to disqualify the current third place finisher is made, I believe the only fair decision is to declare us both runners-up to Tammy and split the difference in the prizes to each receive $3,500. I ask that the checks for both my prize and Eugene's be held until this suspicion is addressed, perhaps by establishing through various means in the chess community that this Eugene Varshavsky is the same person at the World Open. While I will reluctantly accept the $4,000 second place prize if no change in the results is made, I would much more gladly receive less money and see a deserving sudoku solver who should have been on stage claim the prize he'd won (yet still have to deal with wondering what could have been, short this malfeasance). I ask that we at least take some time to make sure the so-called "Cat in the Hat" did not strike back here this past weekend in Philadelphia.

I am sending this letter to the organizers of the tournament, and posting it for all to see on my blog (motris.livejournal.com), because I do not believe this matter should be dealt with entirely in private for the future health of the competitive sudoku community.

-Thomas Snyder

Cheating in a sudoku tournament?

Sun, 25 Oct 2009 12:58:52 GMT

The breaking story from Philly (at least on my blog) as seen in my comments section on the last post from Johan de Ruiter:

"When you search for his name as mentioned in the Inquirer, first hit will be this:
http://www.avlerchess.com/chess-misc/The_Man_with_the_Hat_beats_Grandmaster_Smirin_at_World_Open_221891.html"

So, "Eugene" (at least a person with the same full name) had presumably used a transceiver/camera set-up at the 2006 World Open in Philadelphia three years ago but was not officially caught. Yesterday, having seen his finals board after ten minutes, I was convinced the man in the hoodie I saw qualify in round three was not the same one who eventually showed up on stage. I was dealing with my own issues at the time, but I was still super curious about this man who finished just behind me in round three, then quickly left the testing room. A simpler explanation than a new person, with some sleep and with this potential link, is that it is quite likely we have the same cheater and he has just found a way to expand the areas he can use technology to punk. What was under that hoodie, and will the organizers of this tournament care? I'd hold his check until he can sit in a room and solve three sudoku puzzles in a day. No hoodie and no headphones of course.

You call this a quick place-filler post?

Sun, 25 Oct 2009 00:14:24 GMT

Short Version: USSC happened.

Longer Version:
The US National Sudoku Championship was very much similar to past years' with 3 sprint rounds each consisting of three puzzles used to qualify for the stage (winner takes the spot in each individual round), then a single white board puzzle on the stage with the big prizes on the line. Its hardly my favorite format as it doesn't really rank more than a handful of solvers well, fails to select a US team, and times aren't reported for solvers after the event (Wei-Hwa, for example, was 4th in all three rounds and certainly a consistent solver, but that is not valued in the race for 1st in a round) but it has at least gotten good solvers on stage consistently including both me and Tammy McLeod the last two years. Most of my time today was spent solving puzzles and then answering interview questions as I do as a kind of ambassador for sudoku for different people including a TIME magazine video reporter who interviewed me and onigame the night before as well. I look forward to the piece. I also showed off my book a lot.

The puzzles, still printed too large at ~6" square, were for the most part similar to the others we saw online before the championship with one cool exception happening in the second round. So all D4 puzzles, boxes 2/4/6/8 important, solutions with pairs and triples which I really believe is the right level of hardest step for a competition sudoku since it won't reward bifurcation, and I did okay on the rounds. I broke and fully erased at least one puzzle on each round but finished the first set of three puzzles in 9:29 and clean for 1st. The second round had a secret theme; I'd commented here before about disliking asymmetry in puzzles and how I'd accept it with minimal puzzles and here was a round of just 17s that were rather fun to solve but which I broke entirely (2 with duplicated digits, one with my classic pitfall of writing a pair of notes on the grid, not seeing a forcing given in a row/column, and then trusting my note assignment for too long without relooking at for a deduction). Finished that round 7th (Tammy McLeod was the 1st). Third round went well, with the first two puzzles done in 6 minutes total and the last in a little under 6 more (it was another memorable void design), but while I finished first, it was apparently not clean with a 6 instead of a 9 or something (too much Hendrix?). Still, I'd already qualified and the mysterious late registrant "Eugene" was the third finalist (this is all I ever saw on his name tag; I'm sure he has a last name).

A lot of time passed before the critical moments, while age rounds and geography rounds happened (I still find it entirely inappropriate to give an on-stage finalist like me 50 dollars for my age group and not to the second place in the group since the concept of these extra prizes should be to spread the wealth). thedan, who finished second for 27-29, can pick up 50 dollars minus taxes when I next see him....

The finals were unchanged in format from last year: large whiteboards which Will Shortz/organizers may be the only people who like. Certainly no solver likes them, although I practiced for it and feel comfortable there now, but its unclear if it "benefits" the audience when many other options seem to have worked better. This format has in the past always tripped up different solvers and made a 2x time result pretty typical (round qualifying tends to be in 10 mins for 3 puzzles and a similar challenge on stage averages 7+ in all levels in this format which is silly). I practiced to get better at this, and set breaking 7 minutes as a goal. I proceeded to not just break the goal, but to absolutely crush the puzzle, which was an incredibly fun solve and which I won't spoil but can be found on philly.com/sudoku sometime I hope, in ~4:14. I checked for blank squares, saw none, said done. Tired, I didn't check my grid and instead sat facing the audience for awhile relieved at beating the whiteboard and winning. News of an error never came to me - the judges didn't see it but many in the audience did. I actually noticed it for myself two minutes later when I finally looked back at my grid and saw a problem. Basically, with a few numbers to go, I made a transposition error of a 46 pair which trickled one other wrong number up so a 46 and another 4 was entered 64 and another 6. An Epic Fail in a sense. If I had done anything close to my patented checking in the time I did not realize I would have, I would have found it. But as I felt the puzzle was easier than past finals, and the competition strong, I did not check and thus did not win. While this drama developed as the audience caught on to my error, Tammy continued and finished in 7:41 for what she thought was second place, a typical experience solvers have had in recent years at the ACPT tournament where the fastest solver has finished, left the stage even, and you know they are done but you cannot know they've made an error. As Tammy turned to congratulate me, I informed her that no, there are three wrong numbers on my grid, and you are the new champion. (Aside: the confusion was not later helped by Will Shortz announcing Tammy as second which I also helped correct since she had deservedly won.) "Eugene" had only 3 or 4 numbers filled in and this made no sense to anyone in the room.

So, I guess the story of this championship is that I found a new-gear for my on-stage solving and hit one out of the park. However, I missed third base on my way to score. I'm still unsure what my WSC plans (construct/solve) are - I'll think about it after the WPC. Lots to do before the championship I care most about in a week in Antalya....

[ETA: Here is the detailed Philly Inquirer piece - not sure what "pots of puzzle gold" I'm missing but I've never brought any of them back from overseas.]