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A pentomino is made up of five squares where two squares are joined along an entire side. Two pen- tominos are the same if they can be matched by turning or flipping. How many different pentomino shapes are possible?

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sqdancefan

There are 12 such shapes. One can start with two squares, adding squares around the edge and rejecting shapes that have been previously seen. Repeating until you have 5 squares results in 12 distinct shapes.

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2 shapes are possible with 3 squares: L, I

5 shapes are possible with 4 squares: L, I, N, T, O

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