How to Play the 15 Puzzle
The 15 Puzzle is a four-by-four grid holding fifteen numbered tiles and one empty space. Any tile directly next to the empty space can slide into it. That is the only move in the game. Your goal is to shuffle the tiles until they read 1 to 15 in order, left to right and top to bottom, with the empty square finishing in the bottom-right corner.
It sounds trivial. It is not. The puzzle has been sold, published and obsessed over for nearly 150 years precisely because the rules take five seconds to learn and the solution takes real technique.
Controls
Tap or click any tile that shares an edge with the empty square and it slides across. Tiles that are diagonal from the gap, or further away, cannot move. On a touchscreen you can simply tap the tile you want to move.
Think about the blank, not the tiles
The first mental shift that makes this puzzle solvable is realising you are not moving tiles — you are moving the empty square. Every tile movement is really the gap swapping places with a neighbour. Strong solvers plan a route for the gap: "I need the blank to come around the left side of this tile without passing through the row I have already finished." Once you think that way, the puzzle stops feeling random.
The layer method
Almost everyone who solves this reliably uses the same approach, which is to lock the puzzle down in layers and never disturb a finished layer.
Step one — the top row. Place 1, then 2, then 3. Leave 4 for last, because getting the final tile of a row into place requires temporarily moving the tile next to it.
Step two — the second row. Same idea with 5, 6, 7 and 8. You now have the top half finished and you must not break it. From here on, the blank square is only allowed to travel through the bottom two rows.
Step three — the bottom two rows together. This is where beginners get stuck, because the last two rows cannot be finished one row at a time. The bottom six squares work as a single block, and you solve them with a repeating rotation: move three tiles in a small loop until the numbers cycle into position. It feels like you are undoing your work at first, and then suddenly everything lands.
The last-tile trick
The hardest moment in each row is the final tile. If you try to slide it straight in, you will find the tile you just placed gets pushed out. The standard solution is to deliberately park the last two tiles of the row in a rotated position — the second-to-last tile in the corner and the last one directly beneath it — and then rotate the pair into place with one three-move loop. Learning this single trick is the difference between solving the puzzle sometimes and solving it every time.
Not every arrangement can be solved
A genuine mathematical curiosity of the 15 Puzzle is that exactly half of all possible tile arrangements are impossible to solve. Swap just two tiles on a finished board and no sequence of legal moves will ever fix it. This is what made the puzzle famous in the 1880s, when a prize was offered for solving an arrangement that had been rigged to be unsolvable. Our version always deals a solvable board, so if you are stuck, it is the method rather than the puzzle.
Plays on any device
The 15 Puzzle runs in your browser with HTML5 — nothing to install, no signup, and it works on phones, tablets and computers alike.
