The puzzle that went viral in 1880
The 15-Puzzle consists of 15 numbered tiles in a 4×4 frame, with one cell empty. Sliding an adjacent tile into the empty space is the only legal move. The goal: arrange the tiles in numerical order, 1–15, with the empty space back in the bottom-right corner.
In 1880, the puzzle sparked a global mania — businesses posted "no puzzle-solving during working hours" signs, and unsolvable configurations were a recurring source of frustration. The mathematics of which configurations are solvable was worked out during that craze and remains the puzzle's most elegant feature.
The solvability rule
A 15-Puzzle configuration is solvable if and only if the permutation parity of the tiles matches the Manhattan distance of the empty space from its solved position. Concretely: count the number of "inversions" (pairs of tiles in the wrong order). For a 4×4 board, the puzzle is solvable when inversions + the row number of the blank (counted from the bottom) is even.
This is why randomly shuffling the tiles by hand can leave you with an unsolvable board — and why every digital implementation worth its salt shuffles by performing random moves instead.
How to play
- The board has 15 numbered tiles and 1 empty space, in a 4×4 grid.
- A move consists of sliding a tile adjacent to the empty space into that space.
- Goal: arrange tiles 1–15 in order, with the empty space in the bottom-right corner.
- Tiles can only move horizontally or vertically — never diagonally.
- The puzzle is solved when every tile is in its correct position.
Strategy tips
- Solve row-by-row, then column-by-column. Solve the top row first, then the second row, then the left column, then the second column. The bottom-right 2×2 resolves last.
- The last tile of each row is the trick. To place tile 4 in the top-right corner, you must place it temporarily in position 3, then rotate.
- Never disturb a solved row. Once a row is locked, restrict yourself to moves in the rows below.
- For the final 3×2 region, memorise the rotation pattern — it's the same every time.
- Move count, not time. Aim to solve in fewer moves; speed comes naturally with move efficiency.
Play now
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