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I hope that my fellow programmers will find this question intriguing!

Say we have a blank N x N grid, and a list, W, of N-digit words (ie. some subset of the N! valid numbers).

The aim is to form a Latin Square (or Sudoku grid) using only words from the list. That is, the words corresponding to each row (from left to right), and for each column (from top to bottom), must match a value in W.

My question is this - how many words must W contain in order to guarantee that at least one valid LS can be formed?

My rather limited progress to date can be viewed over at math.stackexchange (here).