Slide the tiles into order from 1 to 15, using the one empty square. Play the daily shuffle, or pick a 3×3, 4×4 or 5×5 board. Every shuffle can be solved.
How to play
Tap a tile in the same row or column as the gap; it (and any tiles between) slides into the gap.
On a keyboard, the arrow keys slide the tile next to the gap: ← moves the tile on the gap's right to the left, and so on.
Tiles on their home square get a ✓. Finish with 1 to 15 in order and the gap at the bottom right.
Why some shuffles can't be solved
Count the pairs of tiles that are in the wrong order relative to each other (inversions). Each slide changes that count in a predictable way, so on a 4 × 4 board the inversions plus the gap's row (counted from the bottom) always stay odd or always stay even. A solved board makes that total odd. Swap just the 14 and 15 of a solved board and the count becomes 1 inversion with the gap on row 1: an even total, so the puzzle code reports it as unsolvable. This rule was proved in 1879, when the puzzle was new. The shuffles here are always checked against it.
Tips
Work row by row from the top; once a row is done, don't disturb it.
For the last two tiles of a row (like 3 and 4), place 4 where 3 should go and 3 just below it, then slide both up together.
Finish the last two rows column by column from the left, the same trick turned sideways.
Start with 3 × 3 to learn the moves; it needs far fewer moves than 4 × 4.
The board has numbered tiles and one gap. Tap a tile next to the gap to slide it in, or tap any tile in the same row or column as the gap to slide that whole line at once. Put the numbers in order, left to right and top to bottom, with the gap in the bottom-right corner.
Can every shuffle be solved?
Every shuffle here can. Only half of all arrangements of the tiles are reachable by sliding, and the game checks this before you start. Swap any two tiles of a solved 15 puzzle and it can never be put back by sliding.
What's the best way to solve it?
Solve the top row first, then the left column, and you're left with a smaller puzzle of the same kind. Repeat until a 2 × 3 corner is left, which you finish by cycling tiles around it. The last tile of each row usually needs a short detour: park it below its place, then bring it up with its neighbour.
What counts as a move?
Each tile that slides one place counts as one move, so sliding a line of three tiles counts as three. Your fewest moves for each size is saved on this device.
Is the daily puzzle the same for everyone?
Yes. Everyone gets the same 4 × 4 shuffle on the same date, so you can compare moves and times. A new one arrives at midnight where you are.
