How many ways can the 12 pentominoes tile a 6 x 10 rectangle?

2,339, counting tilings that are turns or mirror images of each other once, and 9,356 if every placement counts separately. Load the 10 × 6 rectangle example and press Count all: the search needs about 4 million nodes, well inside the default budget of 50,000,000, and takes several seconds on a typical computer. The same search gives 1,010 for a 5 x 12 rectangle (4,040 counting every placement), 368 for 4 x 15 (1,472) and 2 for the 3 × 20 strip (8).

Why does it say Unknown or At least instead of no solution?

Because a search that stops early has not ruled anything out. When the node budget, the solution limit, the time limit or your Stop press ends a search, the solver reports the tilings it found as a lower bound, such as At least 12 tilings, or Unknown if it found none. It says No tiling exists only after it has finished every branch. Raise the limits and search again: the node budget goes up to 1,000,000,000 and the time limit to 120 seconds.

What does up to rotation and reflection mean in the count?

Many tilings are the same arrangement turned or mirrored. The second number counts each such group once, using only the symmetries of your board: 4 for a rectangle and 8 for a square, counting the one that changes nothing, and fewer when blocked squares or fixed pieces are not symmetric. With flipped pieces not allowed, only turns are used, because a mirror image would need flipped pieces. The first number counts every placement, so the 3 × 20 strip shows 8 tilings, 2 up to rotation and reflection.

Can I make my own shape instead of a rectangle?

Yes. Set a width and height up to 20 by 20, then block the squares outside your shape; on a big board, Block every cell and then opening the squares you want is quickest. The usable squares must number exactly five times the pieces in the set, and at most 60, the area of all 12 pieces. Take pieces out of the set with their letter buttons to make a smaller puzzle, and the page says whether the two areas match.

How do I fix a piece in place before solving?

Choose Place pieces, pick a piece in the tray, turn it with Rotate and mirror it with Flip (or press R and F while a board square has focus), then click a cell, or move there with the arrow keys and press Enter. The piece's first square in reading order, top row first, lands on that cell. Clicking a fixed piece lifts it off again. The solver keeps fixed pieces exactly where they are and fills the rest, and a piece that would overlap another, run off the board or cover a blocked square is refused with the reason.

Are flipped pieces allowed?

By default, yes: each piece can be turned and mirrored, which gives 63 distinct orientations across the 12 pieces. Turn off Allow flipped pieces for a one-sided puzzle, where each piece may only be turned from its drawing in the tray, 41 orientations in all.

Can I save a puzzle and print the solution?

Download puzzle JSON saves the board size, blocked squares, piece set, fixed pieces and flip setting, plus the tiling on screen if there is one. Load puzzle JSON reads it back and checks all of it, including that a saved tiling still fits, before it replaces your board; a file that fails leaves your board as it was. Download SVG gives a printable picture: the puzzle with its blocked squares and fixed pieces, a dot marking each fixed piece, or the whole tiling once one is shown. This browser also remembers your last board.

Does it solve Kanoodle or 3D pentomino puzzles?

No. It works on flat boards with the 12 standard pentominoes, each used at most once, so it has no three-dimensional pyramids, no branded piece sets and no built-in commercial levels. You can still enter a flat puzzle from a book by drawing its board, choosing its pieces and fixing any pieces the puzzle gives you.

Pentomino Puzzle Solver

Draw the board, choose the pieces, and the solver treats the puzzle as exact cover: every usable square covered once, every selected pentomino used once. The board can be up to 20 by 20 with at most 60 usable squares; block squares with a click or the keyboard, and fix pieces where you want them, turned and flipped from the tray. Solve stops at the first tiling. Count all keeps going and, once it has finished every branch, gives the exact number of tilings and how many remain when turns and mirror images of the board are counted once. Searches run in a background worker under a node budget, a solution limit and a time limit you set, and a search that stops early says so: it reports a lower bound or Unknown, never that the puzzle is impossible. Every tiling shown is checked again square by square, and you can step through it piece by piece, copy it as text, or download it as a printable SVG or as a puzzle JSON file to load later.

Board

Arrow keys, Home and End move the cursor. In Block cells, Enter, Space or a click blocks or opens a cell. In Place pieces, it puts the chosen piece with its first square there, or lifts a fixed piece. On the board, R turns the chosen piece, F flips it and Delete lifts a fixed piece.

Piece to place

F, as drawn. 5 squares.

Puzzle and search

WidthHeight

Pieces in the set, each used once

12 pieces cover 60 squares; the board has 60 usable cells, so the areas match.

Allow flipped pieces

Node budgetSolution limitTime limit, seconds

Node budget 0 to 1,000,000,000; solution limit 1 to 1,000,000,000; time 1 to 120 seconds. A search that reaches a limit reports a lower bound, never an impossibility.

Load puzzle JSON

Ready

Solve finds one tiling. Count all counts every tiling and the classes up to rotation and reflection.

Example board: a 10 × 6 rectangle for all 12 pieces. Press Solve, or edit the board to set your own puzzle.

Pieces placed: 0 fixed of 12
Cells covered: 0 of 60
Independent check: not run
Status: ready

Board as text

Rows top to bottom. Letters are pieces, # is a blocked cell and . is an open cell.

..........
..........
..........
..........
..........
..........

Common questions

How many ways can the 12 pentominoes tile a 6 x 10 rectangle?: 2,339, counting tilings that are turns or mirror images of each other once, and 9,356 if every placement counts separately. Load the 10 × 6 rectangle example and press Count all: the search needs about 4 million nodes, well inside the default budget of 50,000,000, and takes several seconds on a typical computer. The same search gives 1,010 for a 5 x 12 rectangle (4,040 counting every placement), 368 for 4 x 15 (1,472) and 2 for the 3 × 20 strip (8).
Why does it say Unknown or At least instead of no solution?: Because a search that stops early has not ruled anything out. When the node budget, the solution limit, the time limit or your Stop press ends a search, the solver reports the tilings it found as a lower bound, such as At least 12 tilings, or Unknown if it found none. It says No tiling exists only after it has finished every branch. Raise the limits and search again: the node budget goes up to 1,000,000,000 and the time limit to 120 seconds.
What does up to rotation and reflection mean in the count?: Many tilings are the same arrangement turned or mirrored. The second number counts each such group once, using only the symmetries of your board: 4 for a rectangle and 8 for a square, counting the one that changes nothing, and fewer when blocked squares or fixed pieces are not symmetric. With flipped pieces not allowed, only turns are used, because a mirror image would need flipped pieces. The first number counts every placement, so the 3 × 20 strip shows 8 tilings, 2 up to rotation and reflection.
Can I make my own shape instead of a rectangle?: Yes. Set a width and height up to 20 by 20, then block the squares outside your shape; on a big board, Block every cell and then opening the squares you want is quickest. The usable squares must number exactly five times the pieces in the set, and at most 60, the area of all 12 pieces. Take pieces out of the set with their letter buttons to make a smaller puzzle, and the page says whether the two areas match.
How do I fix a piece in place before solving?: Choose Place pieces, pick a piece in the tray, turn it with Rotate and mirror it with Flip (or press R and F while a board square has focus), then click a cell, or move there with the arrow keys and press Enter. The piece's first square in reading order, top row first, lands on that cell. Clicking a fixed piece lifts it off again. The solver keeps fixed pieces exactly where they are and fills the rest, and a piece that would overlap another, run off the board or cover a blocked square is refused with the reason.
Are flipped pieces allowed?: By default, yes: each piece can be turned and mirrored, which gives 63 distinct orientations across the 12 pieces. Turn off Allow flipped pieces for a one-sided puzzle, where each piece may only be turned from its drawing in the tray, 41 orientations in all.
Can I save a puzzle and print the solution?: Download puzzle JSON saves the board size, blocked squares, piece set, fixed pieces and flip setting, plus the tiling on screen if there is one. Load puzzle JSON reads it back and checks all of it, including that a saved tiling still fits, before it replaces your board; a file that fails leaves your board as it was. Download SVG gives a printable picture: the puzzle with its blocked squares and fixed pieces, a dot marking each fixed piece, or the whole tiling once one is shown. This browser also remembers your last board.
Does it solve Kanoodle or 3D pentomino puzzles?: No. It works on flat boards with the 12 standard pentominoes, each used at most once, so it has no three-dimensional pyramids, no branded piece sets and no built-in commercial levels. You can still enter a flat puzzle from a book by drawing its board, choosing its pieces and fixing any pieces the puzzle gives you.

Each pentomino covers five orthogonally connected squares. Solver can time out without establishing solvability or impossibility; count is exact only after exhaustive completion under the displayed symmetry convention. No commercial puzzle levels, branded Kanoodle piece set or three-dimensional pyramid support.