The 12 pentomino shapes
A pentomino is five squares joined edge to edge. There are exactly 12 different shapes, 60 squares in all, which is why 6×10, 5×12, 4×15 and 3×20 are the classic boards.
Step-by-step strategy
- 1
Learn the 12 shapes
Name each piece by the letter it looks like: F, I, L, N, P, T, U, V, W, X, Y, Z. Knowing the names helps you plan: “the U goes on the edge, the X goes inside”.
- 2
Place the X first
The plus-shaped X fits in the fewest spots and can never touch a corner. In a 6×10 rectangle, start with the X near one end, then build around it.
- 3
Fill corners with friendly pieces
Corners are the hardest squares to cover. The V, L, P, U and N cover a corner cleanly, while the X can never reach one. Settle all four corners early.
- 4
Count empty regions in fives
Every piece covers 5 squares, so every enclosed empty area must have 5, 10, 15… squares. If a region has 7 squares, undo straight away. This one check removes most dead ends.
- 5
Avoid one-square gaps and narrow slots
A single trapped square, or a 1-wide corridor that is not exactly 5 long (for the I), means the board is lost. Keep the remaining space chunky.
- 6
Save the flexible pieces for last
P and Y can squeeze into odd leftover spaces, so keep at least one of them back for the final gap.
- 7
Check your work with a solver
If you are stuck, open the pentomino solver, choose your board and compare. Then try to reach that solution in a different order.
Common mistakes
- Leaving the I for last. It only fits a straight 5-long gap, so place it along an edge early. In 2,328 of the 2,339 6×10 solutions the I touches the border
- Building from both ends at once. Grow one solid block of pieces from one side instead
- Not flipping pieces. N, P, Y, L, F and Z each have a mirror image that is easy to forget
Practice online
Pick a rectangle in the pentomino solver and compare your attempt with a computed answer, or browse all 2,339 6×10 solutions for ideas. The same habits (hard spots first, keep space chunky) also help in the free packing puzzle and the daily calendar puzzle.