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Problem of the Month (September 2015)

This month we pack unit squares into small polyominoes. The problems of packing squares into squares, dominoes, and L-triominoes have been studied before. This month we pack squares into straight triominoes and the non-square tetrominoes. What is the smallest of these polyominoes that contains n non-overlapping unit squares? For example, some solutions for the T tetromino are shown below.

1.

s = 2√2/3 = .942+
4.

s = 1
5.

s = 4/3 = 1.333+
6.

s = 3/2 = 1.500
7.

s = 5/3 = 1.666+
8.

s = 1.850+
16.

s = 2
18.

s = 7/3 = 2.333+


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