How to play 15 Puzzle

The 15 Puzzle is the classic sliding puzzle: fifteen numbered tiles in a four-by-four frame, with one space left empty. A tile next to the space can slide into it, and that is the only move there is. The tiles start shuffled, and your job is to slide them back into order - 1, 2, 3 along the top row, and so on to the last tile, with the space in the bottom-right corner.

It is a puzzle of planning as much as of patience. Anyone can solve it eventually; the skill is in solving it in few moves. On skill.games every shuffle comes with a target: for the smaller boards it is the fewest moves anyone can possibly solve that exact shuffle in, worked out by a computer search while you play.

How to play on skill.games

When you open the game, the settings popup appears. Pick a difficulty - Easy, Normal, Hard or Crazy, which sets the size of the board - and press PLAY. The level you chose is remembered for next time.

• Sliding a tile: tap a tile next to the space and it slides in. On a computer, click it.
• Sliding a whole row: tap any tile in the same row or column as the space. That tile and every tile between it and the space slide together, one step towards the space. It's one tap, but each tile that moves counts as a move.
• Swiping: swipe a tile towards the space to slide it (with the tiles between). A swipe anywhere else moves the tile next to the space in the direction you swiped.
• Keyboard: the arrow keys (or W, A, S, D) move the tile next to the space in that direction.

A tile in its home position wears a small green dot. The top of the screen shows your moves and your time; the clock starts with your first move, so you can study the board for as long as you like before it does. Under the board is your target (see below).

The menu button in the top-left corner pauses the game and the clock, starts a new game or switches the sound on or off. The game is saved as you play, so if you close the page you can press CONTINUE and carry on with the same board and move count.

Rules

The board. A square frame of numbered tiles with one empty space. The tiles are numbered from 1 up to one less than the number of cells.

Moves. A tile next to the space (above, below, left or right - never diagonally) can slide into it. Sliding several tiles in a line at once counts one move per tile, because that is what it would take one at a time.

The goal. All tiles in order, row by row from the top-left, with the space in the bottom-right corner.

Every shuffle can be solved. Half of all the ways to arrange the tiles can never be solved - the famous puzzle of 1880 whose last two tiles were swapped is one of them. Every shuffle here is drawn at random from the solvable half.

The target. On Easy and Normal the game proves the fewest moves that solve your shuffle. It shows "Fewest possible" when it has. On Normal that search can take a few seconds; until it finishes, and on Hard and Crazy where proving it is out of reach, the target is a computer solver's count - a good result to beat. Match the fewest possible and the results screen says PERFECT!

A board you leave unfinished for a new one counts as a loss in your statistics.

How to solve it

Anyone can learn to solve the puzzle by working in layers, so that solved tiles never have to move again:

1. Solve the top row, left to right. Bring 1 into the corner, then 2 beside it, and so on. Move the space around a tile to push it: the space goes to the side the tile should move towards, and the tile slides in.
2. The last two of a row go in together. Placing the last tile of a row directly is impossible without moving the one before it. Instead, put the last tile where the second-last belongs, the second-last tile just below it, and then slide both into place with one turn.
3. Repeat for each row until two rows are left. The board you still have to solve shrinks each time.
4. Solve the last two rows column by column, using the same pairing trick on each column's top and bottom tiles.
5. The final square of four cells is solved by turning the three last tiles round it.

That method always works, but it is far from the fewest moves. To get close to the target, you need to plan ahead.

Strategy tips

• Don't fix one tile at a time. Look for moves that bring several tiles closer to home at once. A tile moved away from home costs at least two moves to bring back.
• Steer the space. Every move moves the space. Plan where the space needs to go next and take the route that also helps tiles on the way.
• Watch for tiles in each other's way. Two tiles in their home row but in the wrong order must pass each other, which costs extra moves. Spotting this early lets you fix it while the board is still open.
• Use row slides for speed. Tapping a tile at the far end of the space's row moves the whole row at once: same moves, far fewer taps.
• Study before you start. The clock waits for your first move, so take a moment to look for the tiles that are already near home.
• Compare with the target. The fewest possible is a hard bar: a few moves over it is an excellent solve. Within about one and a half times the target on Normal is good play.

Difficulty levels

The difficulty is the size of the board.

• Easy: 3 by 3, eight tiles. Quick to solve; the target is always the proved fewest moves (at most 31 for any shuffle).
• Normal: 4 by 4, the classic 15 Puzzle. The fewest moves are proved for almost every shuffle, usually in under a second and sometimes after several seconds. Random shuffles need about 52 moves on average at best.
• Hard: 5 by 5, twenty-four tiles. The target is a computer solver's count, typically 100 to 140 moves.
• Crazy: 6 by 6, thirty-five tiles. The longest solves; the solver's target is typically 200 to 250 moves.

The results screen shows your moves, the target (Fewest possible or the solver's par), your best moves and best time at that difficulty (marked when you set a new one), and the board size. Your statistics - wins, losses, win rate and streaks - are kept separately for each difficulty.