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The Independent Culture
GONE ARE the days when football was played on the village green and it wasn't done to question the ref's decisions, no matter how daft. Ours was not to reason why.

Actually, ours is very much to reason why. Nowadays, absolute authority is yielding to accountability. Fair challenges to authority should be welcomed as they are the only way we have of testing its validity.

Soccer has changed. Big money is now involved. Most of us watch rather than play. May body contact be reduced so we can enjoy dribbling, shooting and passing skills without expensive, talented legs being hacked down by moronic foulers. But, above all, let's see this art form freed from the vagaries of poor refereeing.

During Man United vs Inter Milan, the commentators expressed delight at the quality of refereeing, which is, of course, tantamount to admitting that its quality is variable. And at this level it ought not to be. Bring on the technological revolution in refereeing.

Ditto with Lewis vs Holyfield. I am no fan of boxing but even I could see that by any sane measure, Lewis won, and that the scoring was neither objective nor accountable. But it was interesting to see the media arguing over who had won in terms of numbers of punches landed. You see: something we can measure. Something all sane folk can agree on. The basis of science. Maths makes an art of the demonstrable. It replaces unstated beliefs by explicit axioms. No matter how much 2+2 may wish to be, other than 4, it is stuck with it. Facts is facts as surely as x is x.

That is the point of mathematics and the sciences that rest on logically conducted proofs. It opens factuality up to scrutiny. It does not "assume these things to be self-evident", nor does it assume the existence of reasonable men. But it does assume rational process. The rest is up to you.

Take Uncle Tadek's problem (last week, see diagram A). The mountain road BG and the road along BP are impassable. Colour the towns as shown. Then every black town is connected to white towns only and every white town is connected to black towns only. So any route from O to T passes black and white towns in alternation. So any route at all from Omsk to Tomsk traverses an even number of towns. Get out of that without moving. Maths is a test of our often irrational standpoints. The more life is brought under its civilising influence, the better.

Points to ponder

Prove that no matter how resourceful you are feeling, or how much rearranging of pieces you do, there is no way to slice a 3 x 3 x 3 cube into 27 cubelets each measuring 1 x 1 x 1 without making at least 6 cuts (see diagram B). Solution next week.

Comments to: indy@puzzlemaster.co.uk