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Information on Pentomino Puzzles

A pentomino is an arrangement of 5 unit squares (or sometimes cubes) that are joined along their edges. Up to isomorphism (rotating and flipping), there are 12 possible shapes, which are illustrated below. Each piece is labelled by the letter that most accurately reflects its shape.

V T W X

U Z F P

I N Y L

The problem is to fit the 12 pentomino pieces into various shapes, often rectangles. The rectangle shapes that fit all 60 squares are of sizes 3x20, 4x15, 5x12, and 6x10. Here's a solution to the 6 by 10 puzzle using the letter encoding.

NFVVVYYYYI
NFFFVLLYZI
NNFXVLZZZI
PNXXXLZWTI
PPUXULWWTI
PPUUUWWTTT
Much better looking is the same solution using tables and gifs.

The algorithm used by COS is a clever backtracking algorithm, as described in the upcoming book "Combinatorial Generation."

Here is a page of more solutions to various pentomino puzzles.

Big List of Pentomino Related Links

The may get stale with time. Please send us any updated addresses or new ones that should be included.

For more information on pentominoes consult the classic book by Solomon W. Golomb, Polyominoes, Scribner's, New York, 1965, or the more recent book Polyominoes (A Guide to Puzzles and Problems in Tiling) MAA, 1991, by George E. Martin.


Programs available:
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