🧩 Pentominoes

How to Play

The idea

A pentomino is five squares joined edge to edge. There are exactly twelve ways to do that — no more have ever been found because no more exist — and each is named after the letter it looks like. Fit them all into the box with no gaps and no overlaps.

Placing a piece

Tap a piece in the tray, then tap a square. You do not have to aim carefully: the piece slides into the first place it fits. Or drag it straight out of the tray and drop it where you want it.

Moving one you have already put down

Tap it and it is chosen — it stays exactly where it is, outlined in black. Tap it again and it turns, right where it sits. Drag it to move it, or tap an empty square to send it there. To take it off altogether, tap it in the tray below.

Turning and flipping

Tapping a chosen piece turns it, and the Turn and Flip buttons do the same thing — a quarter turn, or held up to a mirror. A piece on the board turns where it stands, staying over the squares it was using. If a quarter turn will not fit it keeps going until it finds one that does, and if no way up fits at all it goes back exactly as it was rather than vanishing. Both count as the same piece: an L flipped over is still an L. The X looks the same however you turn it, which is why it is the easiest piece to place and the hardest to place well.

Where people go wrong

Leaving a gap of one, two, three or four squares. Nothing can ever fill it, so the moment you make one you have already lost — you just do not know it yet. Watch the edges and corners.

A good tactic

Start with the piece that has the fewest choices, not the one you like best. In a narrow box the I and the X barely fit anywhere, so put them first and the rest follows more easily.

Hints

A hint works out the rest of your board and places one piece that genuinely belongs there — it is never reading from an answer sheet. If your board cannot be finished at all it will tell you that instead, which is worth knowing. A puzzle solved with hints does not go on the best-times board.

How many answers there are

All twelve pieces fit a 6 by 10 box in 2,339 genuinely different ways. A 5 by 12 box has 1,010, a 4 by 15 has 368 — and a 3 by 20 has exactly two. That last one is one of the hardest puzzles on this whole site.

Finishing one

Fill the box and the next puzzle comes along by itself after a moment. If you have made the best-times board it waits until your name is in first — and Next puzzle moves you on straight away whenever you like.

Keyboard

R to turn, F to flip, H for a hint.