15 Puzzle
Use the one empty space to slide the numbered tiles back into order. Half of all possible arrangements can never be solved — no matter what you do.
Slide a tile in the same row or column as the gap.
How to play
Tap a tile in the gap’s row or column, or drag it toward the gap. The tiles between them move together; each slide counts as one move. Focus the board and use arrow keys to move a neighboring tile in that direction. On 3×3, hints follow a shortest route using this move count. On 4×4, hints first try a shortest route, then fall back to a method that completes rows and columns in turn. Each hint says whether the route is shortest.
Learn more
Half of all arrangements cannot reach the goal. Exhaustive search of the 3×3 board finds 181,440 reachable states and a maximum distance of 31 single-tile moves. That differs from the grouped slides counted during play.
Background and mathematics