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I have a chess board that has 13 squares on a side.

I want to break it [along the borders of the individual squares] into smaller square pieces.

I could make a 12x12 square and 25 1x1 squares - 26 in all.

I could make a 7x7 square, 3 6x6 squares and 12 1x1 squares - 16 in all.

What is the fewest I could make?

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12

8x8, 3- 5x5's, 2 - 3x3's, 2- 2x2's, 4- 1x1's

12 is the smallest number, although I did it with 1 7x7, 2 6x6, 1 5x5, 5 2x2 and 3 1x1 squares.

I've quickly come to learn that the next question will be: what is the optimal solution for a board of dimensions nxn, where n is odd.

(n+11)/2, for n > 3. The division consists of 1 ((n+1)/2)x((n+1)/2) square, 2 ((n-1)/2)x((n-1)/2) squares, 1 ((n-3)/2)x((n-3)/2) square, (n-3)/2 2x2 squares, and 3 1x1 squares.

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