Hexomino puzzle online

How to play the hexomino puzzle

1. Look at the board. Each level is a wooden board, sometimes with dark pegs that cannot be covered. The pieces in the tray cover exactly the free squares, and no piece appears twice in a level.
2. Drag a hexomino onto the board. Touch or click a piece and drag it over the board. With a finger, the piece floats just above your fingertip. A green outline shows where it will snap; red means it overlaps something.
3. Turn and flip. Tap a selected piece (or press Turn) to rotate it 90°, and press Flip for its mirror image. On a keyboard, R turns and F flips.
4. Move or take back pieces. Drag a placed piece to a new spot, or drag it off the board to return it to the tray. Undo steps back one move and Reset clears the board.
5. Fill every square. The level is solved when every free square is covered. Stuck? Hint places one piece where it fits in a real solution of your current board.

What are hexominoes? All 35 shapes

A hexomino is six squares joined edge to edge. Allowing turns and flips there are exactly 35 of them, numbered below the way this game numbers them (longest first). Counted as one-sided pieces, where a mirror image is a different piece, there are 60; counting every turned and flipped position on a grid there are 216. 10 of the 35 look the same in a mirror. For comparison, our same enumeration code finds 1, 1, 2, 5, 12 pieces with 1 to 5 squares, so six squares is where the family really grows.

■ balanced pieces (24) cover three dark and three light squares of a chessboard; ■ unbalanced pieces (11) cover four of one colour and two of the other. marks the 11 hexominoes that fold into a cube.

Hexomino puzzle strategy

• Start with the pieces that have the fewest homes. Long, thin pieces (#1 to #4) fit along edges; bulky ones need open space, which disappears quickly.
• Fill corners and the squares next to pegs early. A peg splits the board, and the squares around it accept only a few shapes.
• Count in sixes: any closed-off region must have 6, 12, 18… squares. A pocket of 5 or fewer is already a dead end, so undo straight away.
• Use the chessboard colours. If the free squares left have more dark than light ones, you will need an unbalanced piece to fix it.
• Try a piece in a few spots before letting go: the green outline tells you it fits, but not that the rest still can.
• On the hardest levels there is only one solution. Place a hint, then think about why that piece had to go there.

Why the 35 hexominoes can’t make a rectangle

All 35 hexominoes together cover 210 squares, so a rectangle such as 2×105, 3×70, 5×42, 6×35 looks possible. It is not, and the proof is the classic chessboard argument:

1. Colour the rectangle like a chessboard. Every way of writing 210 as width × height has an even side, and a rectangle with an even side has exactly as many dark squares as light ones: 105 of each.
2. Wherever you put a hexomino, its colour split stays the same. Our script checked all 35: 24 always cover 3 dark + 3 light, and 11 always cover 4 + 2 (either way round).
3. Every balanced piece adds 0 to “dark minus light”; every unbalanced piece adds +2 or −2. With 11 unbalanced pieces the total is a sum of 11 terms of ±2, which is twice an odd number — never 0.
4. But a filled rectangle needs “dark minus light” to be exactly 0. So no rectangle can be filled with one of each hexomino.

That is why our levels use a different subset of the 35 pieces each time (35 of the 35 appear somewhere across the 20 levels). Here is one solution to level 7, a 6×5 box with 5 pieces:

All levels at a glance

Every level was built from a random wooden board and then checked with the same Dancing Links search that powers our pentomino solver. The solution count includes every arrangement, so on an open rectangle a turned or mirrored copy of a solution counts separately; fewer solutions usually means a harder level. From level 15 on, several levels have just one solution.

More shape puzzles

Want something gentler? The tetromino puzzle uses 4-square pieces, and the 8×8 packing puzzle mixes many shapes. For five squares per piece, learn the 12 pentomino shapes or try the 8×8 pentomino puzzle. Playing with children? See our logic puzzles for kids.