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Problem of the Week 1051

Very Mini Sudoku

Many of you are familiar with the Sudoku puzzles found in newspapers, books and online. The goal is to fill in a 9 × 9 Latin Square with the digits 1-9 so that each of the nine 3 × 3 subsquares also contains all nine digits. When properly created, often with about 20 of the 81 spaces filled to start, there is only one possible answer.

Nothing stops us from doing this problem for any n2 by n2 array: What is the minimum number of filled-in squares to totally determine a 4 × 4 Sudoku? That is, how sparse can it be and still allow only one filled-in array?

© Copyright 2006 Stan Wagon. Reproduced with permission.

14 February 2006