A pentomino is a shape made of five squares joined edge-to-edge. There are 12 distinct ones, named after letters: F, I, L, N, P, T, U, V, W, X, Y, Z.
Quick check
How many distinct pentominoes are there (shapes from 5 squares, rotations/reflections counting as the same)?
Why pentominoes are a great puzzle
- Just 12 pieces, but tiling a rectangle with all of them is a real challenge (the 6×10 board has 2,339 solutions; the 3×20 has only 2).
- They're a gentle introduction to tiling / packing problems and to thinking about symmetry.
- The video game Tetris uses *tetro*minoes — the 4-square cousins (there are 5 of those, or 7 if you count reflections separately).
Your turn
All 12 pentominoes have area 5. What's the total area, and which square board (minus a small hole) can they exactly cover?
All 12 pentominoes together cover 60 squares — exactly enough to fill a 6×10, 5×12, 4×15 or 3×20 rectangle. The 8×8 square minus a 2×2 hole works too!