Mathematical problem: the algorithm of building blocks filling boxes.

Fill in from the big one:

12x 12 1 9x 9 0 6x 6 2

12x 12 1 9x 9 0 6x 6 1 4x 4 0 3x 3 4

12x 12 1 9x 9 0 6x 6 1 4x 4 1 3x 3 0 2x 2 5

12x 12 1 9x 9 0 6x 6 1 4x 4 0 3x 3 0 2x 2 9

12x 12 0 9x 9 2 6x 6 0 4x 4 0 3x 3 6 2x 2 0

12x 12 0 9x 9 1 6x 6 0 4x 4 0 3x 3 15 2 x2 0

12x 12 0 9x 9 1 6x 6 2 4x 4 0 3x 3 7 2x 2 0

12x 12 0 9x 9 1 6x 6 1 4x 4 1 3x 3 7 2x 2 5

12x 12 0 9x 9 1 6x 6 1 4x 4 0 3x 3 7 2x 2 9

12x 12 0 9x 9 1 6x 6 0 4x 4 3 3x 3 7 2x 2 6

12x 12 0 9x 9 1 6x 6 0 4x 4 2 3x 3 7 2x 2 10

12x 12 0 9x 9 1 6x 6 0 4x 4 1 3x 3 7 2x 2 14

12x 12 0 9x 9 1 6x 6 0 4x 4 0 3x 3 7 2x 2 18

12x 12 0 9x 9 0 6x 6 6 4x 4 0 3x 3 0 2x 2 0

Each 6x6 can be replaced by a group (4 3x3), a group (4 4x4 and 5 2x2) or a group (9 2x2). There are 15 combinations.

12x 12 0 9x 9 0 6x 6 0 4x 4 12 3x 3 0 2x 2 6

One set (4 2x2) can be changed every 4x4. There are 1 1 species of this combination.

12x 12 0 9x 9 0 6x 6 0 4x 4 0 3x 3 24 2x 2 0

Every 4 pieces of 3x3 can be replaced by a group (9 pieces of 2x2) or a group (1 pieces of 4x4 and 5 pieces of 2x2). There are ten kinds of this combination.

12x 12 0 9x 9 0 6x 6 0 4x 4 0 3x 3 0 2x 2 54

There are 53 kinds in all.

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