motris (motris) wrote,

Thomas Snyder Does the Nikoli Hitori

Until we get an English language forum, I think I'm going to take up a discussion of their puzzles here from time to time. Certainly after today's big puzzle:

5/15/10 - 17x17 by Casty - 15' with error, then 6'44"

Of course I'd like to believe that in response to my negative post yesterday Nikoli pulled out an impressive puzzle in its Hitori arsenal. The truth is I'm more like a tiny fly in their world and this was in the queue for awhile. Still, do the puzzle and then join in the commentary that follows from yesterday's discussion.

So this is a perfect example of a Nikoli Hitori, and one of the better ones I've solved. I think the theme kept it from being hard, as it had a self-correcting feature to any missed digits you had, and again the "hard" steps were more observational than logical. Still, I stumbled in my first try out of the gate with a mistake halfway through. I'll often jump into morning Hitori before I've truly woken up just to get them done with. Just like you can ruin a good movie by watching it at a bad time in your life, I bet I partially ruined a good hitori by solving it when I was error-prone and therefore botched it up the first time.

I don't know if it is one of Nikoli's unwritten design rules [maybe all the rules are written, I just can't read Japanese], but this one really follows the "start low, go high" concept. In fact, that is 90% of the puzzle, which is amazing as "start low, go high" tends to only finish the first 30-40% of shading steps. Here, this actually works for almost all of the grid, with an explosion in the top and left sides that eventually converges when you deal with the 15s, 16s and 17s in the mid-right. It is truly an impressive puzzle.

Unlike Rex Parker (and I don't know how he gets away with it), I don't think I can fairly post a solution to this puzzle or the puzzle itself. But I can post this. This is the digit location in the "minimal" puzzle, colored like a checkerboard. White cells are "noise", red and black are filled in and are digits that have a repeat in a row or column. This is certainly the constructor's entire grid when he was done laying out the logic in the puzzle, before adding in digits to the other >50% of the cells to make his theme not stand out so instantly.

So, what to make of it? First, as discussed yesterday, there are a ton of paired digits with numbers between them. All imbetween digits (almost 60) are useless. Why? Because the non-noise digits are almost exclusively on the same checkerboard color when looking at the grid. The outliers? The 4 1-1-1 triplets (which I've said tend to be the digit used for a triplet), the 11-triplet (why 11? because you'd spot it as six 1's in a row?), the 678 edge rectangle, and a singleton 1 needed to give uniqueness which is that lone black square surrounded by white on the left side. In the minimal version, you could instantly shade this digit in by uniqueness, but most of the time I guess you don't see the signal from the noise. Still the checkerboard pattern gives you a sense to the constructor's vision and also redoubles a second point from yesterday - white cells near black cells tend to be useless in Nikoli (but not computer-generated) hitori. There are only 9 potential spots touching the red checkerboard squares, and all but 1 of them are resolved by triples/edge constraints and not adjacency of that number elsewhere to a shaded square.

The puzzle starts with marking the 1-1-1 triples and then using the 2-2 pair at the top, pinned by a 3-3 pair on the highest row, to mark off a two and some other threes. The first digit I missed was that fourth 3 in the top row, since it was well removed from the first nucleus of digits that spring forth (and could be edited to be a 4 and closer to the site of action later on). My second time through I missed the third 4 in the second row, but obviously got the two close 4's. This suggests I undersearch the prime numbers even knowing how Nikoli puzzles go. I also missed one of the many 6's when I did that step the first and the second time through as well, I guess because marking rows missed one in a column. The vertical 12s were a problem one of the times too. But the thing with this puzzle is that because you know you need to be able to mark 7's after getting through 1-6, if you can't do this you have missed something. I actually got the whole top going in 1-14 order before I had problems getting anything done with 15, 16, and 17. I could see where action would occur, but had no reach over there because of bookkeeping mistakes. Still, the minimal form, which I created to study later (and which you have the pattern of above), while fun to look at, is an absolute piece of cake to solve. This kind of theme is destroyed for difficulty without the noise of other digits and missed shadings. The logic isn't so involved, besides basic steps, so simplifying the flow without the noise leaves it too bare. So maybe this is the pinnacle of Hitori (which values observation/bookkeeping more than deduction). I'm waiting for the pinnacle of Minimal Hitori (which values deduction more than the tedious stuff). Unlike with the TomTom v. KenKen wars, I care much less about fixing Hitori, so I may not explore this peak myself. Still, great puzzle Casty, as its led to some fun analysis!
Tags: hitori, nikoli


Comments for this post were locked by the author