Bloody narwhal

I am not convinced that puzzle 8H on Picross DS is solvable without recourse to a case split. (Since neither Wikipedia nor Google produce useful output on this matter, I should explain here. Case splitting is a technique used in deciding by machine whether Boolean formulae are satisfiable. If you have a formula that your other techniques can't decide, you pick one of your variables, and produce two new formulae: one assuming the chosen variable is true, one assuming it is false. Iff at least one of these new formulae is satisfiable, the original is. The term is sometimes appropriated by computer scientists and logicians for similar constraint-solving techniques when performed by humans. In Picross, it means hypothetically filling an uncertain square in and following all the implications of that square on its row and column, to other rows and columns they affect, and then back to the original row and column, in the hopes of finding a contradiction. It's the sort of thinking you might do a lot of to solve non-trivial sudoku puzzles, but because you can't note down your hypothetical filling-in, and because all reasonable-sized boards are far too big to fit in working memory, it's infeasibly hard to do for Picross, so puzzles are constructed so as to not require it.)

I think Picross DS fails somewhat, though as I am currently very addicted to it I am hardly qualified to judge. The developers, Jupiter, really wanted to take advantage of the touch-screen interface to fill squares in and to place crosses (which mark impossible squares). On the small puzzles, this is quite good, though switching between the filling-in tool and the cross tool takes far too long. But when the puzzle size exceeds 10×10, the squares are too small to poke, so they won't let you edit the grid without zooming into it. Zooming in lets you see about 7×7 squares on the screen at a time, with the numbers for the middle three rows and columns superimposed, and the upper screen showing an overview of the whole grid. The screen scrolls automatically as you fill squares in (which is really annoying as it makes me lose count) or when you drag using the pan tool (which, again, takes too long to switch to). Thus I find it easier to fall back to the traditional method of using the D-pad with buttons A and B, just like the old days.

Picross DS does go one up on its Game Boy predecessor by offering eye-destroying 20×20 puzzles. Some of them are ridiculously easy, but I find playing while listening to Orson Welles radio plays to be quite relaxing. But at a certain time of the evening, I stop being able to count above five, which makes it much less entertaining, and I maintain that this is why I had to resort to a guess to solve 8H tonight. I will try it again in the morning and see if it is solvable then.


Last modified: Sat Mar 1 00:28:53 2008

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  • solved

    Written by Daniel Hulme (828438da885b170d) on Sat Mar 1 10:58:18 2008

    Yeah, I tried it again this morning and have now convinced myself that it is in fact doable in under 17min, so I must have been just failing to spot something obvious last night.