Pentomino solutions
Answers for the well-known shapes filled with all 12 pentominoes. Puzzle Lounge's own program searched for every answer and checked the counts. Answers that match when turned or flipped count as one.
Shapes and number of answers
| Shape | Answers |
|---|---|
| 6×10 rectangle | 2339 answers |
| 5×12 rectangle | 1010 answers |
| 4×15 rectangle | 368 answers |
| 3×20 rectangle | 2 answers |
| 8×8 square (2×2 hole in the middle) | 65 answers |
The longer and thinner the rectangle, the fewer the answers. The pieces in the diagrams carry their usual letter names. If your pieces are different colours, compare by shape.
- F
- I
- L
- N
- P
- T
- U
- V
- W
- X
- Y
- Z
1The 6×10 rectangle
There are 2339 answers. No single one is the answer; any of them is right. Here are 4 of them.
2The 5×12 rectangle
There are 1010 answers. Here are 2 of them.
3The 4×15 rectangle
There are 368 answers. Here are 2 of them.
Oni No.1 on Puzzle Lounge is this 4×15 too. You can play it right in your browser. Play Oni No.1
4The 3×20 rectangle
There are only 2 answers, which makes it the hardest rectangle. This shape is also a puzzle in the Puzzle Lounge game, so its answers are not shown.
5The 8×8 square
The 8×8 square has 64 squares, 4 more than the 60 of the 12 pieces, so you fill it around a 2×2 hole. With the hole in the middle there are 65 answers. Here are 2 of them.
The 2×2 hole doesn't have to be in the middle. Wherever you put it, the square can still be filled.
6What the answers tell you
Go through every answer and you find clues for solving on your own.
| Shape | Answers with the I along an edge | Pieces most often in a corner |
|---|---|---|
| 6×10 | 2314 of 2339 | I, V, L |
| 5×12 | 1009 of 1010 | L, I, V |
| 4×15 | 368 of 368 | V, L, U |
| 8×8 | 65 of 65 | I, L, V |
- In almost every answer the straight I lies along an edge of the frame. In the 6×10 that's 2314 of 2339, and in the 8×8 it's all of them.
- In the 6×10, the pieces most often in a corner are I, V and L. Try those first in the corners; it's the quick way.
- The cross-shaped X can never cover a corner. Still, in 60% of 6×10 answers the X touches the edge of the frame.
If you can't solve your own set
- Lay the I along a long edge, put the V or L in the remaining corners, then work out the middle.
- When comparing with the diagrams, go by shape, not colour. You may flip pieces.
- Copy one answer from the diagrams, then swap just 2–3 pieces. Sometimes that turns up a different answer.
There are more placing tips in the How to solve section of How to play.
Questions
Do pentominoes have only one answer?
No. A 6×10 has 2339, and the diagrams on this page are only some of them. If yours differs from the diagrams but fills the frame with no gaps, it is right.
How many are there if turns and flips count separately?
Turning and flipping a rectangle gives each answer 4 orientations, so a 6×10 has 9356. The 8×8 square gives 8 orientations, so it has 520.
Which shape is the hardest?
The 3×20, which has the fewest answers: only 2. The 6×10 has many, so an answer is that much easier to find.