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14 May 2010 @ 12:14 am
Friday Puzzle #49 - "Sorry, Thomas"  
In any given week, I hit or I miss with my audience.

This week will be no different.

This week, I think I even manage to miss myself, at least initially.

I titled this week's entry in the same way I thought to dedicate a book of the same type several years ago. When the US team in Rio found ourselves with 3 Turkish puzzle books and four team members, we needed some fair way to distribute the books. Since not having any of the books was probably as good (or better) than the situation of having some of them, we played a game to determine who would distribute the books to the other three. I won, and then solved a page of each book and signed that page before giving them out to my teammates. Wei-Hwa got the Sudoku title with Dr. Sudoku's signature, Roger got a joking adoration on a heart-shaped Kakuro, and Zack got a book on which I simply signed the page "Sorry, Thomas". I think Zack knew what I was apologizing for. A lot of puzzle solvers probably do too.


It was a book of Hitori.

I have a fair bit to say, some of which is ranty and some of which is spoilery, so I'll probably start with the puzzles as generally presented and put the rest behind a cut. It might be worth using this new "Minimal Hitori" format of the puzzles though, as that might be the single immediate improvement I can offer.

Rules: See here












So the puzzles above are as Hitori have always appeared in publications. The first puzzle was written to feel like computer-generated puzzles. The second and third to feel like Nikoli creations. None are probably that memorable. No hitori in my mind have been, at least with numbers in logic magazines. The Hitori Meta in the 2008 MIT Mystery Hunt by Mark Halpin is the most memorable use of the style by far, and solving it with only half the words was one of my bigger meta achievements of that Hunt (of which I had several, which led to another year of work and subsequent retirement from Mystery Hunts, although no longer having a team helped on that account).

Why no love for this style? I've tried to think of the possible reasons a lot, to come up with tweaks that would make it better. The puzzle is based on Japanese crosswords and uses black/white square rules common to that type. I don't speak Japanese; I don't solve Japanese crosswords. Maybe this leads to a lack of translation of the rules to a form that makes sense to me. But Heyawake is another type of puzzle built around Japanese crossword rules and I have no problems with it (although strict rectangular rooms are not really necessary in modern architecture or in Heyawake).

The puzzle is sort of an observational puzzle, and that's generally a style of puzzle that I like. Sudoku is a very observational puzzle, with some logic too, and it's a magic mix of my skills I guess. Word searches are an observational puzzle, and I am quite good at them. I fight to keep them appearing on the USPC. I solve them in between sudoku at the WSC when the playoffs run for 3 hours. Spot the Differences (STDs) are also observational puzzles that I practice on, play webgames with, and tend to enjoy. None of these types frequently appear at WPCs, to my detriment. Still, I'd rather solve a Spot the Differences puzzle than a Hitori any day of the week. Heck, I'd rather do the Jumble.

Some of this may be that the observational elements of Hitori are more monotonous than fun, much more hit-or-miss and unrewarding than the instant gratification of finding that 10th difference in the mouse on the left corner in the USPC STD. Almost every Hitori puzzle starts with finding three of the same number in a row and shading in the two outer boxes. On a computer-generated puzzle, this could be three of any number; on a Nikoli puzzle it tends to be three 1s. If there is more than one triplet on a Nikoli puzzle, the next ones are likely three 2s, then three 3s, and so on (although this is not hard and true but frequently the case). I guess this shows the human element. I find it redundant and uninteresting. But these are "simple" break-ins and puzzles don't need them. Mine don't have them anywhere. So the question is what next? While there are some edge rule things to look for, things with touching pairs of digits, and so on, the first area you might be tempted when solving a Hitori for the first time is with that simplest of extensions to the triplet: looking for any digit surrounded on left/right or top/bottom by a repeated digit. This digit must be white! Yes! And on a PC-generated puzzle, this will likely be useful. But on a Nikoli Hitori, it's almost never useful. And because it is almost never useful you stop looking for it. Except sometimes there are one or two occasions you must spot such a thing amidst dozens of useless spots and good luck finding them. Most of the time you don't find gold - there may be no gold to find at all. To me the search feels like a puzzle equivalent to that hay bale unrolling challenge the Amazing Race has now painfully done two times. It's no joy to do. It's no joy to watch being done. It's just clumsy, repetitive, mostly fruitless, and the only relief - not joy - comes when the task reaches an end.

And it's not just failing to find (or wasting time when useless) digits from a search for numbers between numbers that gets me. A corollary to this principle is in an even more fundamental step: "cells touching black squares must be white". You can certainly mark them all as white, and carefully search the row and column to see if that digit is there. Even if you do this you sometimes miss it. Again, in PC-generated puzzles, marking white cells is really useful as black squares chain together in this way in random grids. Nikoli puzzles focus more on larger geometry effects and connectedness I guess; it's very rare for cells immediately adjacent to "obvious" black squares to be useful. It's the one or two white cells off of them forced by connectivity that end up giving more black squares in a Nikoli puzzle. So, on Nikoli puzzles you don't search the numbers around the blacks you mark very often. You wish there was an "automark" feature because you oftentimes search for hundreds of other things before coming back to something this basic that is 99.5% of the time useless. So it's frustrating.


Let me represent my three puzzles in a different style. These are still the same puzzles, and are still perfectly valid to solve from. I actually wrote these three puzzles to present them in just this style, to encourage solution on them.












These are "minimal" Hitori. These are functionally the puzzles with all digits that are unchecked (do not have a duplicate in a row or column) removed. They are therefore fundamentally the same puzzle logically, just with the "number noise" removed. A minimal form makes the puzzles a ton less frustrating (and easier), because all the missed connections mentioned above will not occur.

All Hitori must have at least a quarter to a third of their digits, oftentimes more, be completely unchecked and useless. Just "number noise", because a larger fraction of cells must be white compared to black for all cells to be connected and each white cell must have a unique number in its row and column which requires a lot of singletons. You might notice that the digits 7, 8, and 9 completely disappear in the Nikoli style B puzzle. This is by design, as it sometimes happens in their puzzles too. Why Hitori seem to require the digits 1 to N all appearing in puzzles, when this is clearly not necessary, is unclear to me. Still, you'll learn that in Nikoli Hitori the meaningful numbers tend to be smaller (and the first steps tend to involve the 1s) and the high numbers are often singletons. This may oftentimes get you a head start on your searching, but not all Nikoli style puzzles are like this and larger ones, like my third puzzle, still require shading digits from 1 to 12.

So, why is solving on these minimal styles better? Well, if you mark a black cell and there is a number next to it, then it is always worth considering. If the cell is blank, then it isn't. Similarly, if you see two identical numbers that have a single cell between them with a number in it, then that number is important. If not, it isn't. Look back at the first 9x9 puzzle. It has 8 such pairs. 7 are useful. Look back at the second 9x9 puzzle. It has over a dozen such pairs. Only 2 are useful. All of the 2's in row 3 and column 3 are useless in "between" space but are a critical part of the design. Nikoli Hitori are like this all the time. That there is a pinned 6 on one side of the middle 1-1-1-1 square is a sign I'm not a great designer, at least of perfectly archetypal Nikoli Hitori. But still, the times when digits are useful or not are instantly clear in this form. You might say - yes Thomas, but the white cells now let you use uniqueness and other constraints in other ways. And I'd say you are correct. But on any hitori you are given, you first step can effectively be to make this minimal puzzle by highlighting the useless cells. I don't do this when solving because it's tedious and uninteresting. It's why I don't write in all the candidates when I start solving a hard sudoku because it's tedious and uninteresting. It may be useful, but I'd rather have code do it, or just eliminate the step. Puzzle formatting to remove tedium is an important thing for me.

At the recent World Sudoku Championship, we took a puzzle like Comparative Sudoku, sometimes called Greater Than/Less Than Sudoku, and changed the formatting to be easier to start solving on. While the gradient may have been over the top, identifying the locally min and max cells is a basic step that is tedious for the solver at the start but always necessary. So let's just start with them shaded. Now you're done preparing for the meal, and can actually eat. We're not the only authors to have thought of this. It's clear right on the cover of Naked Sudoku, for example, a book of numberless sudoku variants. Their >/< sudoku have blue and pink cells.

So I'd really like to see minimal hitori in the future, or at least some code/an intern that can perform this step for me when I have to solve the large ones. But the question remains, even with minimal hitori to remove unfriendly steps and common mistakes, is the logic that remains compelling enough to solve as a puzzle? And here I still think Hitori comes up short. But then it may just not be a fully explored space. All the triple to locked pair to new shading to new locked pair starts are tired. The 2x2 squares in the corners, tired. I'd like to see new patterns and other new rules explored, like authors do for other Nikoli puzzles. I tried in the 12x12 puzzle to take a fairly simple to deduce set of break-ins that may be less common to appear. They just might be too hard to spot in the noise. This look at the puzzle might be helpful.



The center region is rather defined, if you spot how 4 pairs of digits form a 4x4 box of sorts. With the 2x2 center, only one outer possibility can be made. Then the 2x2 middle waits for the global constraint to steer it one way or the other. The 4 3x2 outer rectangles with a checkerboard pattern of two digits though were where I started this puzzle. Each hides a kind of deduction that works elsewhere in the row/column the rectangle is in. Unlike a typical Nikoli hitori, I made this deduction work for each digit from 1-8 since I wanted people to eventually stumble onto this theme element. But with so much noise, you might have missed it. I don't have much practice making Hitori beautiful. I'm not sure I want more. But this is what I could do. It's a start, but the puzzle still feels like it's missing something.

So I'm left with a lot of ideas which I guess I can eventually explore, and maybe here as a Friday Puzzle after I've left enough gap from this entry for you to forgive me. I've got a dozen ideas at least.

I'd love to try an adaptation with American crossword rules, which would fundamentally change a lot of parts of the puzzle. Black squares could touch but mirror symmetry would be needed. Other changes in the rule space would be necessary.

I'd love to put in sudoku-like region constraints. Consider a 16x16 puzzle where you are shading boxes to leave behind a grid that is functionally an Extra Space Sudoku solution. Heck, in a minimal form it could even become an Extra Space Sudoku. That already sounds to me like a lot more interesting combination of elements, but it makes it less of a Hitori I suppose.

Hitori end up with a random collection of digits in each row. What if each row ended up with 1 to xi, with a different xi possible in every row/column? This sort of reduces the noise problem, as every row and column will need a 1. So start by looking at them and resolving issues, or at 2's or 3's. At the higher numbers it won't be as clustered anyway. It may make them much harder to construct, but I'd gladly see the computer-generators build in such a constraint rather than churn out the garbage in those "Japanese puzzle books", even for Hitori. The additional 1-x rule might have to serve as a replacement to the all connected rule, thinking about constraints, but black squares not touching would still be the right logic-forcing requirement to keep in place.

I'd love a Hitori-word search hybrid. Maybe finding a string of numbers gives you some black cell positions. This would reward observation in ways the current format generally feels it doesn't.

I'd love Hitori that use English letters and possibly leave behind words or fill-ins or something fun after solving like a message. Word searches have lame messages all the time, but it's a way to reward the "noise" of unneeded letters.

And Hitori crossed with other shape-placement puzzles might work out ok too. Battleships might be hard, but Tetrominoes with Hitori seems a definite match. Or Triominoes. Shapes might get a single number labeled on them which defined a spot they must pivot around. That would lead to more global thinking and variety I guess.

Or maybe hitori is a total loss. As I said at the start, either I hit or I miss each week. Wait for Puzzle #50, and I probably won't be apologizing from the start. But from time to time I have to scratch an itch and barring ever doing this for a PuzzleCraft (and I won't), I had to see if I could fix Hitori. Minimal presentation is the best I've got, but it may be enough to restore some elegance with an inelegant format to a puzzle that tends to look and feel inelegant whenever I solve them. The minimal form certainly represents how my hitori look when I first constructed them, long before I added in all those extra numbers and then triple checked that I did that right. Not having numbers in all cells may not look as good, but if it feels even slightly more fun to solve, it's certainly the right thing to do.

So until next time ... Sorry,

Thomas
 
 
( 25 comments )
(Anonymous) on May 14th, 2010 11:30 am (UTC)
Excellent! If there's anything I enjoy more than reading a classic Snyder rant, it's replying provocatively to a Snyder rant! :)

Still, standing in defence of the beating hitori takes here is a bit trickier than when kakuro got the treatment a few weeks back. I guess I don't have anything against hitori, but it's certainly not my favourite nikoli variant. Indeed, I find the solving experience a bit hit and miss - perhaps the best analogy I have is a sudoku with lots of naked singles. Some days you spot the steps you need very quickly and the solve flows very nicely, and indeed enjoyably. Other days you miss them, and the solve turns into a frustrating hunt for a tantalising clue that you need to spot before progressing further.

I'm not sure about the grids with useless digits removed; your most interesting idea to me was the mutation with extra-space sudoku. That might just be because I'm a sudoku sort of guy - everything else just seems a little too much of a one-off to me. Perhaps the best thing for hitori is to simply leave it as a take it or leave it puzzle, depending on your mood...

Tom.C
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(Anonymous) on May 14th, 2010 12:57 pm (UTC)
Although for what it's worth, I thought the third of your puzzles was pretty good - even by nikoli standards!

Tom.C
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motrismotris on May 14th, 2010 04:49 pm (UTC)
Thanks for liking the third puzzle. It was my first real go at an interesting one. Still a lot to learn.

I'm not sure all the other ideas are one-offs. I think just changing numbers to letters and keeping rules as is can make the presentation more fresh at times. Not all letters have to perfectly spell a message. Still, you ask, "Should I write hitori puzzles with sudoku kind of steps?"

or,


SHOULD
IWRITE
HITORI
PUZZLE
SWITHS
UDOKUK


and that works, if the message is shortened. That kind of thing made the MIT meta fun, as a crossword-based logic puzzle actually felt word puzzle-like. The numbers feel forced to me, and are very hard to scan when they become double digit numbers (my same problem with 16x16 sudoku that use 1-16 instead of 0-F or something else).

Edited at 2010-05-14 04:59 pm (UTC)
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(Anonymous) on May 14th, 2010 10:02 pm (UTC)
Very cute - I like that a lot!

Still, I'm not totally convinced. If you were to give me a whole book of wordy hitori in larger sizes I'm not sure I'd like it any more than a good book of standard hitori (which is not to say I'd dislike either by the way); although there's certainly an excellent novelty factor in the word puzzles.

Tom.C
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motrismotris on May 14th, 2010 10:25 pm (UTC)
I'm hardly saying letters or words should be the only next step for Hitori (it does remove language neutrality) but I can say it is an option for something different thematically and certainly tying in some word puzzle elements too would create a good niche hybrid.

I may not be a great designer of new puzzle types, but I'm a fervent believer in innovation of design, and would say a lot of what I've done in puzzle construction is to try to identify the best parts of any style and improve them within the style or resynthesize them as hybrids in interesting ways. So this entry is my first dissection of my least favorite Nikoli type. Hitori is one of the older Nikoli mainstays, written since 1990, so its reasonably mature in a design sense for Nikoli. My lingering question is what is the next natural step for the puzzle to take, to make it even better. I've made some suggestions here, and certainly intend to try to solve puzzles in minimized form from Nikoli for awhile to see if it improves my response, but I've appreciated reading your perspective and others' today as well.

Edited at 2010-05-14 10:33 pm (UTC)
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stigant on May 15th, 2010 04:43 pm (UTC)
How about a skyscraper type of rule. White cells could be a skyscraper with height and no skyscrapers of the same height can see each other, but taller skyscrapers may block the view so that you could have 2 skyscrapers of the same height in the same row/column, provided that there was a taller skyscraper between them.
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motrismotris on May 15th, 2010 05:56 pm (UTC)
Well, there are a bunch of other "seeing" rules that could work too, using the properties of the digits. Consecutive digits could not be anywhere in the same white-space connected row or column. There was a Turkish shading puzzle very much like this in the OAPCs last year. Removing the white-cells connected constraint but keeping the shaded cells from touching worked out really well. Its actually another favorite in the Hitori genre that outdoes Hitori. Of course it only ever had 8x8 sized grids if I recall correctly so it never got too grungy.

The Skyscraper idea you propose may or may not work. The role of black squares is similar to that of a very tall building? I like Skyscrapers puzzles for adding in numbers; Hitori is a puzzle that is about subtracting information and so it may not match as well. Still, I'd be convinced by any example (not to suggest anyone should spend time just to do this if other things are more compelling).

Edited at 2010-05-15 05:57 pm (UTC)
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stigant on May 14th, 2010 12:40 pm (UTC)
Amen! What I've always found frustrating about Hitori (or as I fondly refer to it, "HATEori") is that tedious scanning up and down a row/column every time I mark a square white. The problem is that there is so much information because all the cells start out with digits in them. The other thing that bugs me is that it's usually an advantage (for me anyway) to take some time to use uniqueness (if an 11, say, is the only non-white 11 in its row and column, then it must be white) to eliminate "clues" that have no effect on the solving of the puzzle just so I can concentrate on things that might be helpful. When the style of the puzzle actively encourages you to cheat, that's a problem.
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(Anonymous) on May 14th, 2010 01:57 pm (UTC)
I'd go one step further on the "encouraging you to cheat" meta nature of Hitori. If you see a cell with no duplicates in its row and column, nothing will ever force it to be black, so it must be white (as noted by stigant). But more strongly, something must FORCE it to be white in order for the solution to be unique, and you can sometimes actually exploit that to figure out significant bits of logic. "If the puzzle goes this way, then really it doesn't matter whether this square is black or white ... so it must go this other way where it must absolutely be white...".

And amen to the tedious scanning aspect of Hitori. I do actually like some of the logic in the better Nikoli puzzles, but it's very similar to the logic in Heyawake and Heyawake is way less annoying.

- Jack
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motrismotris on May 14th, 2010 03:32 pm (UTC)
I've got no way to eliminate the "cheating" aspect from Hitori with meta-solution thinking. Excluding the extra digits makes some of the spots easy to see (like the upper-left of puzzle A forces the 4 in row 2, column 2 to be black as otherwise the whole grid has 2 solutions. But this is true in all presentation of the form. If anything, it encourages a constructor to put extra digits (you sometimes have extra constrained digits to place) into such spots to block immediate realizations. Still, its one of the things that has always felt "off" in hitori.
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MellowMelonMellowMelon [wordpress.com] on May 14th, 2010 05:10 pm (UTC)
I have a fondness for the concept of Hitori, and there's a lot of wonderful things that can be done with it. On nikoli.com the Hitori time trials and Botsu Bako puzzles are some of my favorite puzzles on the site. Yet I do find the same problems with the type as you and everyone else does. I think it's mostly the fact that getting unstuck in a Hitori is often a disgusting facepalm moment, when in other nikoli puzzles it's usually an enjoyable "Aha!" Really good Hitori have the latter too, but they often get shadowed by the gruntwork in between.

Anyways, my personal response to this conflict was to try to scrap the disgusting part of Hitori and leave in the good stuff. This was the result:
http://mellowmelon.wordpress.com/category/puzzle-types/out-of-sight/
I don't think it was a 100% success, but I think it worked reasonably well. It could be that Hitori would be mostly salvaged if done in color, each number getting a different one. Same colors are a lot easier to spot than same numbers.
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motrismotris on May 14th, 2010 05:12 pm (UTC)
Yes, color can help. And in the vein of Hitori variants, I meant to point to your Out of Sight puzzles. They have some of the "minimal" feel I think works well, with some extra elements that give it a more complete logical set. If only we could get more Out of Sight authors - or other fresh versions - and get the regular Hitori out of sight. Maybe I'm being too harsh, but your point on the facepalm and not the "Aha" is a well crystallized summary of how this puzzle fails with the solver's general experience.

Edited at 2010-05-14 05:18 pm (UTC)
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(Anonymous) on May 14th, 2010 09:40 pm (UTC)
I agree with MellowMelon; I think you're being too harsh on Nikoli's brand of Hitori. The rules of Hitori are rich enough for some very elegant and creative logic (unlike, say, Kakuro). I don't judge Hitori by all its shovelware incarnations; I judge it by how elegant the best examples can get. Which is, after all, the theme of your blog! :)

Yes, you need to trust that the puzzle designer isn't just relying on a boring, cheap, computer-friendly and human-unfriendly trick... but I have that same trust issue with other puzzle types, including Sudoku.

And yes, there are some powerful, dubious meta-solving techniques, but it's hardly the only puzzle type with those. Heck, in Dominos and Numberlink puzzles you're pretty much expected to use uniqueness constraints while solving.

- Derek
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motrismotris on May 14th, 2010 09:47 pm (UTC)
I think I'm arguing that both computer-generated ones and Nikoli ones fall into different regimes of being unsatisfying. I'm proposing a change to the puzzle that would make either form much more solvable and allow the interesting logic to spring forward, instead of most often running into a puzzle where my bookkeeping was the sticking point instead of something fundamentally interesting.

Still, while my opinions may not match yours, Hitori is far and away my least favorite Nikoli type. (25x25 Sudoku wins the next spot, but that's just a needlessly unfun variant of a type that I avoid twice a year, not a type that appears much more frequently.) I prefer the mechanical nature of their Kakuro much more, maybe as a test of pattern recognition more than math, maybe for the "race" aspect to it. I've bought maybe 100 nikoli books - 10 of which being kakuro pencil puzzle books. I've bought 0 Hitori books. So for me, it has problems. And I should be its audience as an observational logic puzzle solver.

Edited at 2010-05-14 09:47 pm (UTC)
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garethmoore on May 15th, 2010 12:09 am (UTC)
I agree pretty much entirely. And it's worth noting further that Hitori is a particularly special case where computer-generated versions are almost ubiquitously appalling, much more so than with any other puzzle type. They're either pointlessly easy, with nothing other than the obvious (and yet often hard to spot) deductions mentioned, or alternatively requiring such torturous 'what-if' guesswork that there is no pleasure in them.

I did try to write a 'better' Hitori generator than average (which is not hard, given that average = utterly awful) back in 2005 when a publisher decided I should write a book of Hitori for them, and whilst some of the puzzles I made were actually okay (because I deliberately searched for a list of usually-interesting configurations and required deductions) there's no doubt that the majority were much inferior to Nikoli's puzzles, which in turn I agree still have all the problems you highlight.

I do think it's entirely possible to write a computer generator which would make puzzles just like those on Nikoli.com, albeit no better - you could program a long list of explicit rules gained from experience solving the hand-made puzzles, and then search for puzzles that packed as many as possible in, perhaps using the idea that you want the 'white forcing black' implications to be as local in the grid as possible. You could force certain symmetries into the design, and you could easily renumber afterwards for the 1,2,3 etc solving that Nikoli often has. However there would be no point anyone bothering, since Hitori is in such little demand and the puzzle is weak anyway.

That Book of Hitori I got commissioned to do in 2005 sold just 1% of the number of UK copies that my first book of Kakuro sold, which is pretty amazing. Of course, the pathetic computer-made Hitori that briefly featured in some UK newspapers was probably one reason Hitori never took off, but I do think it still gives some idea of how popular the puzzle is(n't).

You can of course use computer solving aids to remove some of the grunt work when solving, although the information overload you highlight is still an issue (I haven't tried your sparse grids yet, but I like the idea). On Nikoli's site I often make random selections so I can keep hitting 'check' until I spot a missed implication (then undo my random selections), and always use the ability to press down on the numbers on the left to highlight unshaded squares of that value - very useful. On my own puzzlemix site I have the option to highlight the forced blacks, which is helpful (and would be great on Nikoli, with the better puzzles!). However on the Conceptis site their player doesn't just do that but auto-places any forced whites too, which in turn reduces most of their puzzles to about 4 or 5 clicks - which in a very weird way makes a very different puzzle with its own peculiar charm. Have you tried it? (I've no idea how good their Hitori puzzles are in general; not very, I'd imagine!)
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motrismotris on May 15th, 2010 01:06 am (UTC)
I haven't played on the Conceptis site in about 9 years (in college, pre-USPC/Nikoli/informed knowledge era) so I have no idea how their system works. I did play with your puzzlemix version for a little bit when you referred it to me and the forced blacks option is nice. I think the paper-puzzle equivalent is the "minimal" grid but I'm willing to hear other opinions. Thanks for your sharing your insight and background again on this puzzle.
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grandpascorpion on May 15th, 2010 12:34 am (UTC)
Heyatori
Here's a hybrid I was quite happy with:

Heyawake + Hitori = Heyatori:

http://grandpascorpion.livejournal.com/4872.html

The Heyawake constraints help to solve the noise issue.

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motrismotris on May 15th, 2010 01:08 am (UTC)
Re: Heyatori
I remember playing those awhile ago. The sparse grid in the second one worked well as I recalled, and certainly maintains more of the Heyawake feel where fewer numbers are wanted but also serving this "enough digits to do Hitori but not every digit" goal I seem to be offering.
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grandpascorpion on May 15th, 2010 11:02 am (UTC)
Re: Heyatori
And, I think the full grids can work as well because (depending on the Heyawake-ness) the clues that would be noise in a plain Hitori puzzle might be key to the hybrid solution.

Re: #2, I remember wondering at the time why the full set of numbers was necessary. The sparse grid of course enables one to have a nice theme or symmetry to the clue set (as well as the room layout).

Interesting post.
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motrismotris on May 15th, 2010 03:45 pm (UTC)
Re: Heyatori
Indeed. And if I make more Minimal Hitori, I will try to experiment with where white cells end up to see if symmetry can be achieved.
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mathgrant.blogspot.com on May 17th, 2010 06:20 pm (UTC)
I feel lonely.
I agree that your first puzzle felt very much like a computer-generated puzzle -- I wouldn't have known it wasn't made by a computer had you not told me. The other two were better than the first one, and showed signs of being handmade. I noticed the 121/212, 34/43/34, etc. blocks in the third one -- that was nice. :)

I can't say Hitori's my favorite Nikoli puzzle, but I give it much more love than a lot of people do, and actually enjoy solving and making them with no empty cells (not to say that the puzzles with empty cells automatically suck). In fact, I have purchased and completed all three Hitori volumes in the Pencil Puzzle Book series -- and thoroughly enjoyed them. Every time I see someone bash Hitori, I'm rather tempted to pull a Chris Crocker and make a YouTube video of me sobbing and crying, "LEAVE HITORI ALONE!" Feel free to ignore my opinion, though -- I like all kinds of things that no intelligent person should like. :P
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https://www.google.com/accounts/o8/id?id=AItOawnSiEsFOdFZTIoL6hJE2c5H-ZCRNoZT76s on May 18th, 2010 09:13 pm (UTC)
Explicit line/links would be too busy?
I agree that I don't look forward to Hitori. I haven't tried mocking this up, but what would you get if you indicated the connections using lines connecting cells that are linked, and omitted the numbers altogether? The result might be intolerably busy, but I'd be interested to see it. Perhaps someone's already done this.

John Clements
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motrismotris on May 18th, 2010 09:36 pm (UTC)
Re: Explicit line/links would be too busy?
That's an interesting suggestion. I was going to circle cells with lines between to show my point with in between numbers in the above puzzles, then just did it in text form only, but the thought of graphically showing some connections might work. The problem is not all connections are local and therefore catching them all within some scheme is probably impossible. Maybe each cell gets a symbol over a 4-direction arrow. Only directions with connections are filled in with arrowheads?

Edited at 2011-07-29 12:55 am (UTC)
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lunchboylunchboy on May 20th, 2010 07:28 pm (UTC)
I love this idea. I actually like hard Hitori even though they invariably involve me, essentially, manually finding the unchecked squares and whiting them out to filter the noise. (And even so they still make for visual clutter.) As it happens, the pink/blue squares in the greater-than puzzles in Naked Sudoku (and Color Sudoku) were one of my editing suggestions, so clearly we see eye to eye on these "let's get the bookkeeping out the way" topics.
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motrismotris on May 20th, 2010 07:41 pm (UTC)
The only thing I like about bookkeeping is those three repeated double letters in a row. Glad to see we agree on what are the fun parts of a puzzle and I guess I must push Minimal Hitori to its limits in future weeks to see if there is a there there.
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