Play the sliding tile puzzle online, free

How it works

Tiles numbered 1 to 15 sit in a four-by-four frame with one empty square. Slide a tile next to the gap into it, and keep going until the numbers run in order. Choose a 3 by 3, 4 by 4 or 5 by 5 board. Tiles glide smoothly, a move counter and timer track your attempt, and your best result for each size is saved on your device. You can tap a tile or use the arrow keys.

Every shuffle is made by playing legal moves backwards from the solved board, so every puzzle can be solved.

Why that last point matters

The puzzle became a craze in 1880, after a postmaster named Noyes Palmer Chapman was credited with inventing it in the 1870s. A famous puzzle maker, Sam Loyd, later offered a prize for solving a version with just the 14 and 15 swapped. Nobody could collect, because the position is impossible: only half of all random arrangements can ever be solved. A shuffle that ignores this gives you a puzzle that can't be done, which is why ours doesn't.

How to solve it

1. Solve the top row, left to right, then the second row. Don't touch them again.
2. Do the same with the leftmost columns, so the problem keeps shrinking to a smaller square.
3. Leave the last two-by-two or so for last, and rotate tiles around the gap until they fall into place.
4. The trickiest move is the last tile of each row. Park it a square away, then slide it in as a pair.

Why half of all shuffles are unsolvable

Every slide swaps the empty gap with a neighbouring tile, and that changes the arrangement in a way mathematicians call parity. Starting from the solved board, you can only ever reach half of the possible arrangements. Swap two tiles by hand and you land in the other half, where no sequence of slides will ever fix it. That's exactly what happened with the swapped 14 and 15 prize puzzle.

Bigger boards

The 3 by 3 board is a nice warm-up with eight tiles. The 4 by 4 is the classic. The 5 by 5 board has 24 tiles and takes patience, but uses the same method: finish the top row and the left column, shrink the problem, repeat. Watch your move counter and see if you can beat your best.

How fast can it be done?

Even the very worst four-by-four arrangement can be solved in at most 80 single-tile moves with perfect play, a result worked out by computer. Most people solve a typical shuffle in far more than that, and a move counter on the screen makes a good target: write down your best, then shave it down. Speed solvers rarely think tile by tile. They solve the top two rows in pairs and treat the last two rows as a column puzzle.

From a prompt

You can read the brief behind the game, including the shuffle rule, on its page.