In sumoku puzzles, the arrangement of the tiles must resemble a crossword puzzle, with each row and column adding up to a multiple of the provided key number. A sumoku is the name of the pattern that is produced. The first thing to consider is the several ways in which two different integers can be divided.

For instance, a sum of 3 can only be divided in one way (1+2) at one extreme, but a sum of 10 can be divided in four ways using the digits 1 to 9 (1+9, 2+8, 3+7, and 4+6) at the other.

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