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Maths - So who's up for sudoku?

What it's all about

I once knew a fellow teacher who was convinced that he hated maths and enjoyed sudoku, writes Jonny Griffiths. The only possible conclusion was that sudoku and maths did not overlap. I remember him telling me earnestly, "You see, Jonny, you could replace the numbers with colours and sudoku would work just as well". I was speechless at the narrow view of maths.

The argument thickens

Maths is about pattern, structure and reasoned argument as well as arithmetic, and these areas are tested by sudoku. We can argue about how profound the maths required to solve a sudoku is. Many mathematicians I have spoken to over the years say that they enjoyed the first few puzzles they tried, but the pleasure became superficial in the long run. Compare the thrill of polishing off a routine sudoku with the thrill of doing real maths, of coming up with a fresh conjecture and finding a proof for it that may not be straightforward. There is not much competition.

Proof by contradiction

I do use the occasional sudoku with my pupils. It is a good way to demonstrate, for example, proof by contradiction. A particular square could be, let's say, a 5 or a 1. Suppose the right choice is the 5, but then this square here must be a 4, and this a 3, and this must be a 7, but then we have two 7s in the same row. So our initial choice of 5 must be wrong and we must choose the 1 instead. If anyone knows of a simpler demonstration of proof by contradiction, I would like to hear it.

And there's more

Get pupils warmed up for bigger maths problems with squidley's array of sudoku problems.

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