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08 March 2009 @ 12:02 am
3/8/09 - Cashing Out  

Difficulty: Harder 9x9 (More like a Thursday in difficulty, despite the 9x9 size)

So, the (first) week of "Thomas Snyder Outdoes the NYT KenKen Puzzle" has come to a conclusion. You can believe this was a very well planned event that became necessary after the NYT announced it was starting a new puzzle, with a release of a set of puzzles starting from the April Fool's-like joke to today's $ puzzle (remembering my specific choice of $ as operator from Thursday). You can also believe this is an idea I came up with, and further developed, on a day-by-day basis by the seat of my pants. What's important to realize is that we've survived. (Exhales). What have we learned:

Me:
1. KenKen (with rule adjustments to appease my inelegance sensors!) can be surprisingly deep while easily constructed. The difficulty of making a specific theme in the numbers like "3" for 3/3/3*3 or a sequence as in Downward Spiral is very low because they are so easily constructed.

2. KenKen always felt "over-constrained" with lots of tiny boxes, in part because you have way too many clues. Without leaving unclued regions, this can be addressed and in an interesting way with larger region shapes which themselves can complement a visual theme at low cost. I did not write a single puzzle this week without a region larger than 10 cells (with 33 cells being my max), yet each puzzle was still sufficiently constrained to be solvable. By getting closer to a "one path through it" puzzle type, the puzzle is necessarily improved in challenge and likely fun. Dell never did remove those ~10 extra digits in Number Place or put in symmetry and look how that worked for them!

3. By allowing digit repetition, larger sets of sums/products/subtractions/divisions are available than in similar puzzles like Kakuro or Killer Sudoku which offers a new challenge to those both new to math puzzles like KenKen and those who have been doing Cross-Sums since approximately birth. Remember: 7+ = 1+2+4 normally, but with a bendy region, 1+1+5, 2+2+3, and 3+3+1 as well.

4. Commercial KenKen feels most natural at 5x5 or 6x6 in size. You can go larger, and appeal more to the "puzzle audience" of my blog/me, but I think the set of digits and operations in 1 to 5 and 1 to 6 is the right size with sufficient complexity for the majority of the puzzles. Better puzzle construction in this space should be highly commercial, with hard books venturing to 7 or 8 or even (gasp) 9.

You (I hope):

1. KenKen can be a good puzzle, but maybe not in the hands of those who control KenKen(TM).

2. Logic puzzles should be themed and written by human constructors. Unless you think all logic puzzles should be like the word search and lack character. Yes, some puzzles are diversions, but I like my diversions to be more artful than not.

3. Thomas Snyder is a very mean person - not only did he pick on Rex Parker, but he also introduced us to a fun "KenKen" puzzle for a week that we can't find anywhere else now, even if we wanted to continue solving them next week. I can't say I'm done with these - I have a couple "novelties" for another day or so - but I can't say this is going to be a daily thing for much longer.

Closing thoughts:
I answered a lot of my own questions through this exercise, and at least now have a section of my blog I can point to when people want the opinion of the 1st Greatest Solver of Sudoku Puzzles in the World! on this new thing called KenKen. I cannot really publish KenKen, as I'm not tied to the company with the rights, and fighting for space on the bookshelves with the Will Shortz name is very challenging. I would probably need a magic label like Mensa as in "Mensa Presents KenCubed: The Next Dimension of Puzzles" to even bother trying. Maybe there is room at Sterling, where this mark of "quality" exists, but I have other book promises to keep, and experiments to run before I sleep, and experiments to run before I sleep.
 
 
( 13 comments — Post a new comment )
[info]jrivet on March 8th, 2009 01:32 pm (UTC)
Hey, don't hate on the Word Search! Or you're going to have to post a week of those next.
motris[info]motris on March 8th, 2009 02:09 pm (UTC)
Dave Tuller mined a lot of the good space for the word search already, as I learned while others were solving playoff puzzles in India. But if the NYT starts a word search (or a wishing well or a jumble, etc.) I guess I can outdo those too.
Mike Selinker[info]selinker on March 8th, 2009 03:13 pm (UTC)
Good week. You have simultaneously proved the puzzle is good enough for a PuzzleCraft (clearly your overall point), and drained me of any desire to solve another one ever again. Importantly, that also only took about seven sudokus.

Mike
Fred Schneider: pic#84191436[info]grandpascorpion on March 8th, 2009 03:36 pm (UTC)
The Moneyed Set
Hey Tom,

Crazy week for me ... This is the first one I tried. On the surface, it didn't look possible that there was only solution, given one massive set and a lack of operators. Of course, the numerous 2-rooms make this possible.
Very clever.

That avatar is particularly hilarious.
motris[info]motris on March 8th, 2009 03:55 pm (UTC)
Re: The Moneyed Set
It certainly took some doing - and some very careful steering of digits at R2C19, R5C19, and R8C19 specifically (after working out a satisfying and useful center set of boxes) - but you can have such an incredible set of open rows and columns and resolve to a sudoku like solution at the end, even without the box constraint. It certainly makes the whole puzzle feel a bit different at the end, but that is probably a good thing.
[info]ericberlin on March 8th, 2009 03:44 pm (UTC)
At first glance, this looked way beyond me, but I'm glad I sat down to give it a shot, because it turned out to be an enormously satisfying solve. Thanks. I hope we do see more KenKens from you.
phat_joe[info]phatjoe on March 8th, 2009 06:46 pm (UTC)
"Mensa Presents KenCubed: The Next Dimension of Puzzles"

I hope you mean this literally... I can't wait to see the 3D version.

/joe
devjoe[info]devjoe on March 8th, 2009 09:40 pm (UTC)
1. Show the real potential of Kenken on your blog. 2. ??? 3. Profit! :-) Anyway, solution and stuff for the somewhat easier puzzle today.

The numerous 2-cell regions provide a lot of starting points.
17 can only be the sum of 8+9. 28 can only be 7x4. 36 can only be the product of 4x9; the known digits in the 17 and 28 allow both 36s to be filled in.

72 can only be 8x9. 40 can only be 8x5. These two block all the 8s in their two columns, so 15 in column 3 cannot be 7+8. It also cannot be 6+9 since the 17 and 36 block the 9s in these rows, so it must be 3x5 in some order. This allows the 40 and 72 to be filled in. The 13 in column 4 also cannot have an 8 or 9, so it is 6+7 in some order.

The 14 cannot be 2x7 (since the 28 uses the 7) and cannot be 9+5 (since we have a 9 in the column) so it must be 6+8, and the 40 forces the 8 to go on top. The 35 must be 7x5 and the 40 forces the placement of this as well.

Now the vertical 15 in column 7 cannot contain a 5, so it must be a sum. The upper digit cannot be 5, 6, 7, or 8, so it must be 9+6. This allows the 17 to be placed. The 18 in row 1 cannot contain a 9, so it can only be the product 6x3 which must go in that order. The 16 in this row cannot be the sum 7+9 since neither goes into the last cell, so it must be 8x2 (in that order).

There are two 11s in the last row, and neither can contain an 8 or a 9. One must be 7+4 and the other 6+5. The last digit in the row can only be 1, 3, or 5, so the 11 on the right is 6+5 in that order and the other one is then 7+4 in this order. That means the 4 in this row is 3+1 (in this order) and the one digit from the large region is a 2.

The horizontal 15 cannot contain a 3 or a 9, so it can only be 8+7 (in that order). This allows the 13 to be placed.

The 11 in the top row cannot be 2+9, 3+8, or 5+6 due to other numbers in the row, so it is 7+4 (in that order). The 8 now is blocked from having a 5, 6, 7, or 8, so it can only be the product 4x2 in that order. This allows the 28 to be placed.

The 13 in column 1 now can only be the sum 8+5 in that order. The 18 in column one must be 3x6 in that order. Then the 4 in row 1 is 1,5 in that order, and the 6 is 2x3 in that order. The last two 2-cell regions can now be filled in.

Now elimination can be used to complete all the rows except the ones with 7 cells in the large region. The center square can now be filled, as can the second square in its row. Column 4 can be filled from the top down, then column 8 starting from the middle, and then the rest becomes easy.

157496382
982164573
463759821
325618749
691372458
238547916
814235697
576981234
749823165

motris[info]motris on March 9th, 2009 01:40 am (UTC)
And the underwears gnomes link suggest a need to figure out how a KennyKenny puzzle might appear. 2. ??? is always the big thing which is too bad.
[info]ericberlin on March 9th, 2009 12:36 pm (UTC)
BTW, are you committed to only publishing books with Sterling? I see no reason why you can't pitch St. Martin's press on "Artisanal KenKen" or something like that.
motris[info]motris on March 9th, 2009 03:41 pm (UTC)
While you should never say never, St. Martin's never appreciated non-classic sudoku because they didn't believe it could sell.

My expectation is that until a valid market exists for Artisanal KenKen, they would not have any interest as their editorsr aren't as much puzzle people as Sterling's. Other publishers than these two would probably be options, but I'm not holding my breath on getting between NexToy and St. Martin's to find publication space.
(Anonymous) on March 10th, 2009 10:41 pm (UTC)
I've been away this weekend and have just managed to catch up on your latest set. This one in particular felt a lot like killer sudoku (minus the 3x3 box constraints, and - not applicable in this puzzle - the unique digits in a cage of course).

You've published a few enjoyable puzzles, however I'm not entirely sure I got a particular feeling during any of them that this is what a kenken should be (whatever that is). I guess puzzles of different sizes have slightly different characters - but this is true of more puzzles than simply kenken. The only thing setting it apart is (as you point out) the allowance of repeated digits in cages.

If you ask me, kenken has a bit of an identity crisis. As it was, it was a brain training exercise (i.e. mindless calculations). I've seen enough from your puzzles to grudgingly admit that this isn't necessarily the case - but in doing so you've introduced familiar ideas from kakuro and killer. You could possibly get some sudoku in there too I guess (this puzzle I spied a swordfish to quicken things up at the end, dunno if it was necessary though).

Anyhow, I like those 3 puzzles more than I do kenken (even these ones) - so I guess I'm still to be convinced...

Tom.C
motris[info]motris on March 10th, 2009 11:23 pm (UTC)
From the beginning of our discussions here (relating to the London Times introduction if I recall correctly) on KenKen, you've held the consistent position that it is a brain training exercise and I can understand this view, given what is out there, that this is exactly what KenKen is as a product. I don't buy into the brain training hype however, and I certainly see the value of puzzles being much different, so I'm exploring the potential of the concept of "KenKen" as a puzzle.

In addition to different rules in cages, let's not overlook that KenKen can involve thinking in 4 different operations where kakuro/killer are really + only. If anything, I'd say I am not yet very good at integrating all of these types into a single puzzle that will make it feel less like a Kakuro and more like a more general mathematical puzzle. Doing so likely requires both my adjusted rules, and my willingness to use them in puzzles, which I haven't done since Union Jack. Once I get better at isolating the interesting mathematical space of - and / and x, I can hopefully make a lot of KenKen puzzles that will feel nothing at all like addition-only puzzle types. You still may not end up convinced it is better than those other puzzles you named (preferences differ, and I honestly find many puzzles types much more fun than any of those three), but I actually enjoy constructing KenKen much more than any of the other three so you'll more likely see this project continuing a little longer than a daily Killer anytime soon.