Fifteen
Slide the tiles back into order using the one empty square.
The maths Permutation parity
No moves yet. 1 of 8 tiles in place.
How to play
One square is empty. Click any tile sharing a row or a column with it and the whole run of tiles between them shifts one square along. You are done when the tiles read 1 upward in order with the empty square last.
A tile that can move right now is outlined and carries a small triangle pointing the way it would travel. A tile already standing on its finished square is shaded and carries a dot. The move count adds one for each tile that shifts, so pushing a run of three counts three.
Keyboard: arrow keys move the highlight around the board, and Enter or Space slides the highlighted tile. Hold Shift with an arrow key to slide a tile in that direction without moving the highlight first. Home jumps to the top left square, End to the bottom right.
About parity, honestly: exactly half of all the ways you could lay these tiles out can never be slid into order. Swapping just two tiles on a finished board produces one of them, and no sequence of slides will ever repair it. That is why every puzzle here is built by starting from the finished board and making hundreds of legal slides, rather than by shuffling the tiles into a random arrangement.
Why this is mathematics
Exactly half of all possible tile arrangements can never be solved, no matter how long you slide. Each move swaps the blank with a tile, which flips a hidden even/odd quantity, so the puzzle can only ever reach arrangements of one parity. Every puzzle here is generated solvable on purpose.