How to play 15 Puzzle
The 15 Puzzle is fifteen numbered tiles in a four-by-four tray with one empty slot. Slide tiles into the gap until they read 1 to 15 in order, left to right and top to bottom, with the gap in the bottom-right corner.
Pick a 3×3 board for a one-minute warm-up, the classic 4×4, or the 5×5 when you have a whole coffee to finish.
Rules
- Only a tile next to the gap can move, and it moves into the gap. Clicking a tile further along the same row or column slides the whole line of tiles between it and the gap in one go.
- The puzzle is solved when the tiles are in order with the gap last.
- Every shuffle here is solvable — half of all possible arrangements are not, and we never deal one of those. Shuffles are also never nearly solved already.
- The clock starts on your first move and stops the moment the last tile lands. Moves count tiles moved, so sliding a line of three counts as three.
- Best times and fewest moves are kept separately for each board size.
Controls
- Click / tap a tile
- Slide it, and any tiles between it and the gap, towards the gap
- Arrows / WASD
- Move the tile next to the gap in that direction
- Swipe
- The same as the arrow keys, on touch screens
- P
- Pause (the board is hidden while paused)
- N
- New shuffle (press twice if you have started)
- Enter / Space
- Shuffle again after a solve
Tips
- Solve the top row first, then the left column, and you are left with a smaller puzzle of the same kind. Repeat until only a 2×2 corner is left.
- The tile faces are patterned by the row they belong in, so you can see at a glance which tiles still need to go up or down.
- For the last two tiles of a row, park the final tile below its spot, then rotate the pair in together.
- Arrow keys move one tile at a time, which is precise; tapping a far tile moves a whole line, which is fast.
15 Puzzle strategy
Move the gap, not the tile
A tile only travels when the gap is next to it, so every manoeuvre is really about steering the gap. To shift a tile one square along a row, the gap must loop round to its far side first, which takes several moves. Choose routes where the gap travels through tiles you have not yet placed. If the gap has to pass through a finished row, you will be repairing it a moment later.
Finish with columns
Once only the bottom two rows are left, stop working in rows. Set the two tiles of the leftmost column as a vertical pair, using the same park-and-rotate trick you used on row ends, then the next column, and so on. On 4×4 that leaves a final two-by-two block in the bottom-right corner. Every deal here is solvable, so if the earlier tiles are correct, the last three tiles always come right by cycling the gap round that block.
Plan before the clock starts
The clock waits for your first move, and pausing hides the board, so the planning time that matters is at the start. Find where the first few tiles are and work out the gap’s route to them. The sum of every tile’s distance from its home is the least number of moves the solve can take, so a deal with tiles scattered far from home will be long however well you play it.
Fast hands on the timed board
Your time is the score; moves are only a statistic. Clicking a tile several squares from the gap slides the whole line in one action, which saves time even though each tile still counts as a move. Use line slides for long straight runs of the gap and the arrow keys for fiddly rotations near finished tiles. On 5×5, solving the top row and left column turns it into a 4×4, so practise that size first.
About 15 Puzzle
The 15 Puzzle was made by Noyes Palmer Chapman, a postmaster in upstate New York, in the mid-1870s, and swept America and Europe in 1880 in one of the first puzzle crazes. Newspapers ran columns on it, employers complained about it, and the famous challenge to swap only the 14 and 15 back into order turned out to be impossible.
That impossibility was proven in 1879 by William Woolsey Johnson and William Edward Story: every slide changes the parity of the arrangement in a fixed way, so exactly half of all arrangements can never be solved. It is the same check this game uses to make sure every shuffle can be finished.
Questions
Is every shuffle solvable?
Yes. Exactly half of all tile arrangements can’t be solved, so each shuffle is checked with the parity rule and fixed by swapping two tiles if needed, which keeps every solvable arrangement equally likely.
When does the clock start?
On your first move, not when the board appears — take as long as you like to plan. It pauses when you switch tabs.
How are moves counted?
One per tile moved. Clicking a tile three places from the gap moves three tiles, so it counts as three moves.
Can you swap the 14 and 15?
Not by sliding. That position is in the unsolvable half, which is why the famous 14–15 challenge of the 1880s was never beaten.