In 2009 James Crook, emeritus professor of mathematics from South Dakota, published on the website of the American Mathematical Society a formula for solving every Su Doku grid. It runs to 9 pages & involves concepts & techniques such as pre-emptive sets, completion chromatic polynomials & hidden tuples.
Spoil sport.
When Su Doku first hit The Times in 2004 I thought: How boring – no laughs there, unlike the cryptic crossword.
But when I could no longer see to do the crossword on the bus going home I tried the numbers thing – larger print, more white space & greater contrast; easier to read in the dim light.
It was OK, but I thought it might be more interesting to look at the mathematics of it – simple permutations or combinations of a mere 9 digits – even though I used to hate all those problems in Feller about the probability of husbands & wives sitting next to each other at dinner.
I soon gave up on that idea – no wonder really in the light of the illumination provided by Professor Crook.
I did however persevere with the puzzles & a strange thing happened – I found it much easier to do those at the higher levels of difficulty as these were introduced. In fact I sometimes find Super Fiendish laughably easy, & certainly less tedious than the Easy ones.
This must in part be a simple case of practice & familiarity, of knowing what to expect &, perhaps subconsciously, remembering techniques & tricks which have worked on earlier occasions.
The techniques are tremendously difficult to describe in words – as the introductory explanations & instructions provided in some of the books of collected puzzles show only too well. I can only describe the method as ‘seeing the pattern.’
There are physical factors which make it much easier for me to successfully complete one of these problems – notably lots of white space around the puzzle & smooth paper which does not get scuffed up by the eraser; I especially like those books with a spiral binding which you can open out flat, a single puzzle per page of smooth white paper. I do not like a grid much larger than the size normally adopted by newspapers.
I also find it essential to use a Paper Mate non-stop 0.7mm HB pencil.
I never enter possible alternatives in an empty square, except occasionally just two – never (like at least one previous winner of The Times National Championship) all possible candidates, to be eliminated & erased one by one - & is essentially Professor Crook’s method.
I find it much harder to complete puzzles where the numbers already inserted form a zig zag pattern; the first step on the way to a solution is to fill in the cells which will straighten up the layout. The pattern is at least as important as the individual numbers – something which was made startlingly clear in a post by David Speigelhalter on Randomness in Art: he asked us to spot the fake piece of random art from a set of 4 Su Dokus-type grids with colours rather than numbers – in that case it was the pattern formed by squares coloured in a particular shade of acid green which immediately gave the game away.
All this solipsism has a wider point. Ultimately we, each of us, have only our own experience & reflective cogitation to go on, even if we have the resources & ability to design & conduct psychological or neurological experiments on a wide variety of ‘subjects’ under laboratory conditions.
The older I get, the more faculties begin to fade, the more we hear how brain scans show up ‘real’ differences between the way different brains perceive or respond to the world, the more I realise that the old idea, that the world simply IS, with ‘I’ its flawed observer & interpreter, is not true.
Each one of us inhabits a different world, one described & limited by our own perceptive abilities – mine are different from yours; that world out there is different.
We overlap enough however. Like a kind of multi-dimensional stereo vision bringing the parts together to make a whole.
The world is a kaleidoscope.
And Su Doku is only a pastime.
