I said on an ILX thread yesterday that the main problem I have with Sudoku is the unacceptable difficulty of doing a filthy version. Andrew Farrell suggested the elegant solution of only using the numbers “6” and “9” but this still seems somehow limited.

The key of course is in understanding that Sudoku is not a maths puzzle. This is actually the heart of its appeal. It’s a simple and easily grasped logic game (though individual puzzles can be very difficult) which happens to use numbers. Except it doesn’t just *happen* to use them. Numbers = maths. Maths = hard. Therefore I = clever if I do a Sudoku puzzle. But the numbers could actually be any 9 different symbols: numerals are just easy to remember.

So for Dirty Sudoku all that needs to happen is to think of an obscene phrase made up of nine discrete letters. “O WIDE ANUS” say. This gives you the letters A,D,E,I,N,O,S,U and W. Take an existing solved Sudoku puzzle and write your phrase on one of the lines to allocate letters to numbers, then take the starting grid and replace the starting numbers with the allocated letters. The joy of the puzzle lies in unconvering the sliver of filth within!

Sudoku is most certainly a mathematical puzzle. It does not deal with numbers, but graphs. A graph is just a collection of dots joined by lines. Consider a collection of dots, one for each cell of a sudoku puzzle (so 81 dots). Join two dots by a line if:

(1) they lie in the same horizontal line or

(2) they line in the same vertical line or

(3) they line in one of the nine standard 3×3 grids in the game.

Then the problem of Sudoku is simply to label each dot by a number from 1 through 9, but in such a way that two dots joined by an edge never bear the same label. This is called a graph colouring problem, and it is a very common mathematical problem indeed.

Look for graph theory on the web and you’ll find tons of information. There is lots more to math than numbers.