motris (motris) wrote,

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,

Tags: fridaypuzzle, hitori, nikoli

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