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Pentomino solver

Pentomino puzzle solver

Choose a board, press Solve, and step through solutions for the 12 pentominoes. Everything is computed on your device, in a background worker that keeps the page responsive.

6 × 10 pentomino board

Pick a board and press Solve.

What the solver does

The 12 pentominoes (F, I, L, N, P, T, U, V, W, X, Y, Z) have 5 squares each, 60 squares in total. That fits exactly into four rectangles: 6×10, 5×12, 4×15 and 3×20, or into an 8×8 square with four holes.

Pick a board size and the solver finds a complete tiling. Press Next solution to keep searching from where it stopped. On the 8×8 board you can tap squares to move the four holes.

How many solutions are there?

  • 6×10: 2,339 unique solutions (not counting rotations and reflections)
  • 5×12: 1,010 unique solutions
  • 4×15: 368 unique solutions
  • 3×20: only 2 unique solutions, which makes it the hardest rectangle to solve by hand
  • 8×8 with the 2×2 centre removed: 65 unique solutions

Tips if you want to solve it yourself first

Place the X early, since it fits in the fewest spots. Use the edges for U, V and L, and check that every empty region still has a size that is a multiple of 5. Read the full how to solve pentomino puzzles guide, or browse all 6×10 pentomino solutions.

FAQ

How does the pentomino solver work?

It treats the board as an exact-cover problem: every square must be covered once and each of the 12 pentominoes used once. A Dancing Links search (Knuth’s Algorithm X) runs in a background Web Worker in your browser, so the page never freezes and nothing is sent to a server.

Which boards can it solve?

Any board with exactly 60 open squares: the 6×10, 5×12, 4×15 and 3×20 rectangles, and an 8×8 board with any 4 squares blocked (the classic version blocks the 2×2 centre).

Why does “Next solution” sometimes show a mirror image?

The live solver lists every placement it finds, including rotated and mirrored copies of the same arrangement. Our 6×10 solutions page lists only the unique ones: 2,339 for 6×10.

Some 8×8 boards say “No solution”. Is that a bug?

No. Many choices of 4 holes cannot be tiled, for example when the holes cut off a region whose size is not a multiple of 5.