How to play the heptomino puzzle
- 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.
- Drag a heptomino 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.
- 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.
- 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.
- 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.
How many heptominoes are there? All 108 shapes
A heptomino is seven squares joined edge to edge. Allowing turns and flips there are exactly 108 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 196; counting every turned and flipped position on a grid there are 760. 20 of the 108 look the same in a mirror. For comparison, our same enumeration code finds 1, 1, 2, 5, 12, 35 pieces with 1 to 6 squares.
■ most pieces (100) cover four of one chessboard colour and three of the other; ■ 8 pieces cover five of one colour and two of the other.
Heptomino puzzle strategy
- Start with the pieces that have the fewest homes. Long bars and skinny arms fit along edges; bulky ones need open space.
- 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 sevens: any closed-off region must have 7, 14, 21… squares. A pocket of 6 or fewer is already a dead end, so undo straight away.
- Use the chessboard colours. Seven is odd, so every heptomino leaves a colour imbalance of 1 or 3 — match that to the free squares left.
- 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.
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; fewer solutions usually means a harder level. From level 6 on, several levels have just one solution. Across the 15 levels, 62 of the 108 heptominoes appear at least once. Here is one solution to level 7, a 6×7 box with 6 pieces:
| Level | Board | Pegs | Heptominoes | Sol.Solutions |
|---|---|---|---|---|
| 1 | 7 × 3 | 0 | #6 #43 #107 | 4 |
| 2 | 4 × 7 | 0 | #7 #50 #102 #104 | 4 |
| 3 | 7 × 4 | 0 | #45 #53 #84 #103 | 4 |
| 4 | 5 × 7 | 0 | #1 #18 #38 #43 #84 | 8 |
| 5 | 7 × 5 | 0 | #12 #43 #50 #77 #103 | 8 |
| 6 | 5 × 6 | 2 | #3 #47 #72 #79 | 1 |
| 7 | 6 × 7 | 0 | #2 #8 #60 #76 #78 #108 | 8 |
| 8 | 7 × 6 | 0 | #2 #4 #44 #67 #81 #84 | 8 |
| 9 | 8 × 5 | 5 | #19 #47 #49 #62 #66 | 2 |
| 10 | 7 × 7 | 0 | #2 #50 #76 #84 #87 #95 #98 | 6 |
| 11 | 8 × 6 | 6 | #15 #27 #58 #75 #93 #103 | 1 |
| 12 | 7 × 8 | 0 | #7 #9 #10 #19 #61 #65 #84 #94 | 4 |
| 13 | 8 × 7 | 0 | #7 #9 #46 #52 #57 #62 #64 #91 | 4 |
| 14 | 8 × 8 | 8 | #4 #24 #44 #46 #55 #59 #71 #96 | 1 |
| 15 | 8 × 8 | 1 | #10 #11 #13 #14 #18 #33 #45 #92 #107 | 1 |
More shape puzzles
Prefer six squares per piece? Try the hexomino puzzle. For four, open the tetromino puzzle; for three, the tromino puzzle. The free 8×8 packing puzzle mixes many shapes, and polyomino tiling explains the exact-cover idea behind every level. Chinese readers can open 七格骨牌 — the same game with Chinese TDH and hreflang.