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Pentomino solutions

Pentomino 6×10 solutions: all 2,339

Every unique way to pack the 12 pentominoes into a 6×10 rectangle, plus the 5×12, 4×15 and 3×20 boards. Use Prev and Next, jump to a number, or roll a random solution.

6 × 10 solution #1 of 2,339

Pentomino 6x10 solution 1FFIIIIILZZVFFYLLLLZNVFYYYYXZZNVVVTWXXXNNPPPTWWXUNUPPTTTWWUUU

Solution counts at a glance

BoardUnique solutionsWith rotations & reflections
6 × 102,3399,356
5 × 121,0104,040
4 × 153681,472
3 × 2028
8 × 8, 2×2 centre hole65520

Every rectangle has 4 symmetries (itself, flipped left to right, flipped top to bottom, and turned 180°), so each unique solution appears 4 times among all placements.

The first 6×10 solution

Pentomino 6×10 solution 1FFIIIIILZZVFFYLLLLZNVFYYYYXZZNVVVTWXXXNNPPPTWWXUNUPPTTTWWUUU

The letters name the pieces: F, I, L, N, P, T, U, V, W, X, Y and Z. Each letter appears exactly once, covering 5 squares.

The two 3×20 solutions

The 3×20 strip has only two solutions, which makes it the hardest of the four rectangles to find by hand. Here is the first one; open the 3 × 20 tab above to see both.

Pentomino 3×20 solution 1UUXIIIIINNNFTWYYYYZVUXXXPPLNNFFFTWWYZZZVUUXPPPLLLLFTTTWWZVVV

Solve one yourself

FAQ

How many solutions does the 6×10 pentomino puzzle have?

2,339, counting each arrangement once (rotations and mirror images of a solution are not counted again). Including those copies there are 9,356 placements.

How many solutions do the other rectangles have?

5×12 has 1,010, 4×15 has 368 and 3×20 has just 2. The 8×8 square with a 2×2 hole in the centre has 65.

Where do these solutions come from?

We computed them ourselves with an exact-cover (Dancing Links) search and removed symmetric duplicates. The script is part of the PuzzlePave source code. The totals agree with the well-known published counts.

Can I link to a specific solution?

Yes. The address updates as you browse, for example #6x10-100 opens solution 100 of the 6×10 set.