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15 May 2010 @ 10:07 am
Thomas Snyder Does the Nikoli Hitori  
Until we get an English language Nikoli.com 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!
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MellowMelon MellowMelon [wordpress.com] on May 15th, 2010 08:46 pm (UTC)
I agree about the quality of this puzzle, and I think my comment last post about how Hitori has a lot of potential (even if it's not realized often) is vindicated by it. :)
zundevil zundevil on May 16th, 2010 12:14 am (UTC)
I thought this one was all well and good but not terribly noteworthy. There were fewer triples than usual, it seems, and a bit more extensive logic than normal -- more than just the usual pairs around the outer two of a triple sort of stuff.

I got stuck for a while and probably missed something with the 17 in the lower right. But then I've never had an acceptable time at 17x17...

You're our only hope against halca, Melon. And I've already put a hundy down (to win 85) for you to win the next (Shikaku) Time Trial.
MellowMelon MellowMelon [wordpress.com] on May 16th, 2010 05:42 am (UTC)
Heh, halca. That guy makes me laugh. I wouldn't bet on any time trial victories in the near future; I've noticed my performance on nikoli.com is highly correlated with how well-rested I am. And if I want to win a time trial, I have to solve at 6:00 in the morning. Still going to take a shot at it though.

As for the lower right of the Hitori, I suppose I missed whatever was down there too, because after a brief bit of staring I clicked Try, guessed my way to a possible finish, and was lucky enough to be right.
MellowMelon MellowMelon [wordpress.com] on May 28th, 2010 01:25 pm (UTC)
Two weeks later: turns out I _did_ win...
(Anonymous) on May 16th, 2010 01:36 am (UTC)
It strikes me that there are two different sorts of feel of hitori puzzles: ones that are very much latin square puzzles, working almost like akari in eliminating squares; and ones that are "wall" puzzles where you try and avoid walling off a corner of the puzzle. More like heyawake.

The former type to me are a bit boring - its the type a computer generator can cook up with no trouble - but I swear that the nikoli.com offerings are entirely in the second category. There's a bit more interest there - the solve flows better whilst you are keeping an eye on a wall that doesn't want to get too big.

With regards to the the ascending start to nikoli hitori, I think it's a really nice convention. It immediately helps with the scanning and gets you into the puzzle - meaning you can have more interesting larger puzzles without requiring the solver to have a code-breaker's level of pattern-spotting. To say something relevant to the puzzle in question, it's pretty cool that you could get to the end without having to restart, but there are other fun hitori puzzles, where you get to that 30-40% stage, hit 12/17 and then you start thinking: "ah-ha - the puzzle really starts here, I should be on the lookout for something nice" - something that has become plausibly apparent thanks to the start.

Not a hugely coherent reply, but it's a bit late and there are at least some points there. Finally - lets not save all the love for hitori, the heyawake this evening was also pretty good!

Tom.C