Arrange tiles 1 through 15 in reading order with the empty space at the lower-right corner.
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Arrange tiles 1 through 15 in reading order with the empty space at the lower-right corner.
Complete guide
The Fifteen Puzzle slides numbered tiles through one empty space on a four-by-four board. Every generated position is created from legal moves, so it is solvable without swapping tiles or relying on an impossible permutation.
Select a tile directly above, below, left, or right of the empty space. That tile slides into the gap. The goal is reading order from 1 through 15 with the empty space in the lower-right corner; diagonal moves and arbitrary swaps are not legal.
Not every random permutation of fifteen tiles can be solved. This generator begins from the completed board and performs legal seeded moves, preserving the puzzle's parity class. A daily or numbered seed reproduces the same verified position.
Place the top row from left to right, then the next row, while avoiding moves that disturb completed areas. The last two tiles of a row usually need to be positioned as a pair rather than forced independently.
Move the empty space around a small loop to rotate nearby tiles. Manhattan distance is a useful direction signal, but the locally closest move may trap the final row. Undo lets you compare a cycle without losing the original layout.
Yes. Positions are produced by applying legal moves to a solved board, so they remain in the solvable parity class.
No. Each move slides one tile adjacent to the empty space.
Placing one without arranging the other can force a cycle that breaks the completed row, so the pair should be planned together.
