Tuesday 4 January 2011

Sudoku and Kakuro

On a recent plane ride I did one of The Guardian's Kakuro puzzles designated hard (in skills required it is similar to Sudoku, but the grid is no longer square, and the digits in rows and columns must add up to given totals). I was quite proud of myself for finishing, having found (in my estimation) several highly complicated arguments in order to fill in certain squares; I don't mention this just to boast. It led me to realise the futility of including yesterday's solutions to both Kakuro and Sudoku: it is trivial to check whether one's solution is correct without assistance, and seeing a solution gives no hint to a stuck reader beyond allowing her to peek at a square. (I once saw a lady on a plane do this, apparently not caring that the number she chose might be no help in cracking the backbone of the puzzle or -- worse? -- might render a tricky puzzle trivial.)

Like in good mathematics, I would prefer to have a simple solution than one that lets me show off (i.e. demonstrates my capacity to hold a large number of pieces of information in my head at once). Thus my aforementioned pride was tempered by frustration at (a) not being able to share my brilliance and (b) not knowing whether I had stupidly missed a simple alternative argument at one of the key stages.

The undergraduate math society at Bucknell held a Sudoku social event last year. I didn't attend, but I gather they had races to compete Sudoku puzzles. Where, I wonder, is the social aspect in that? (There was pizza, of course. There is always pizza.) Perhaps a social activity would have been to put up a puzzle on a projector at a key point and discuss possible strategies/observations, but that sounds horribly tedious and perhaps counterproductive. As an exercise in encouraging young mathematics students to be social and to collaborate, the whole event seemed terribly ill-conceived (and the speed/competitive element only made it worse).

There was a brief vogue for studying the mathematics of Sudoku (perhaps driven by the ongoing vogue demands for undergraduate research?) including attempts to codify strategies to solve them. I never saw anything interesting in that study (though each to their own...) and am pleased to see only one talk at this week's Joint Meetings mentions Sudoku, at least in its title. Why devote so much effort to something that a computer can be programmed to solve in milliseconds -- and which, as a former grad school colleague who refused to touch them pointed out, could easily be designed to have a unique solution yet be practically impossible to solve?

I much prefer crosswords, which are social (one can discuss clues and explain solutions), and so much more varied, forcing one to delve (albeit shallowly) into lists of Monarchs, wars, the oeuvres of great authors, and so forth. On which point, from my favourite crossword editor, the last word: anecdotal evidence that Sudoku rots your brain.