# Maths - Sudoku, anyone?

I once knew a fellow teacher who was convinced of two things: first, that he hated maths, and second, that he enjoyed sudoku. 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 struck speechless by the narrow view of maths this revealed.

To be fair to my colleague, one national newspaper advises sudoku fans that "no mathematics is required". What the paper means is that "no arithmetic is required". Yes, the numbers can be replaced with colours, but is the logical thinking that ensues not at least partly mathematical in nature? Maths is about pattern, structure and reasoned argument as well as arithmetic, and these areas are tested by sudoku.

As with any good puzzle, sudoku has spawned myriad variations and I must confess to loving the "killer" sudoku: a deeper logic is needed for this that feels more like real maths to me.

We can argue about how profound the maths required to solve a sudoku is. Many mathematicians I have spoken to say 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.

I do use the occasional sudoku with my students. 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 that 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.

When one starts a sudoku, there is a belief that the compiler has produced something consistent - they write "gentle" or "fiendish" at the top. When one begins work on a mathematical proof, however, there is no telling how easy it will be or even whether a proof exists. The easiest thing to state may be a devil to get anywhere with; the twin prime conjecture, for example.

And if you do get somewhere with that? Ah, then you will be remembered, not for solving the same sudoku as millions of others, but for doing something unique.

Jonny Griffiths teaches at Paston College in Norfolk

What else?

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

Or try clairemooneyuk@yahoo's "Monday Mars Bar Challenge".

Stimulate logic with some lateral thinking questions shared by fkahlaoui.

Find all links and resources at www.tes.co.ukresources023

In the forums

Check out the "Maths Games Ideas" thread on the TES maths forum - it has lots of ideas for games and challenges for starters and plenaries.

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