Tile a Rectangle With All Twelve Pentominoes
A pentomino is any shape made from five equal squares joined edge to edge — there are exactly twelve distinct ones, once you rule out rotations and reflections as duplicates. The challenge: fit all twelve into a single rectangle with no gaps and no overlaps. Several rectangle sizes are known to work. Can you find one?
Reveal the answer
All twelve pentominoes (60 unit squares total) tile rectangles measuring 6x10, 5x12, 4x15, and 3x20 — the 6x10 case alone has 2,339 distinct solutions. Solomon Golomb named and formally studied pentominoes in the 1950s, and Martin Gardner introduced them to the public in his December 1957 Scientific American column, launching a recreational-math craze.
— Solomon W. Golomb (Martin Gardner, popularizer), Pentomino — Scientific American, "Mathematical Games," December 1957
Go deeper: get the book →