Slide numbered tiles into order with the gap in the last corner. Play 3×3, 4×4 (the classic 15 puzzle) or 5×5; every shuffle can be solved.
What is a Sliding Puzzle?
A Sliding Puzzle is a puzzle in which numbered tiles sit in a square frame with one empty space, and you slide tiles into that space until the numbers are back in order. On the 4 by 4 board, with tiles 1 to 15, it is the famous 15 puzzle.
No tile can be lifted out. Every move pushes a tile into the gap, which leaves a new gap behind it, so putting one tile in place often means moving several others out of the way and back again. The skill is in solving the board in a fixed order so that finished tiles stay finished.
How to play the Sliding Puzzle
The goal: arrange the tiles in order, 1, 2, 3 and so on, from left to right and top to bottom, with the gap in the bottom-right corner. On the 3 by 3 board that is tiles 1 to 8, on 4 by 4 tiles 1 to 15, and on 5 by 5 tiles 1 to 24.
Moving tiles: tap any tile in the same row or column as the gap. It slides toward the gap, and every tile between them slides along with it. You can also swipe, or use the arrow keys, to push the tile next to the gap in that direction.
Counting: every tile that moves counts as one move, so sliding three tiles in one tap counts as three. The timer starts with your first move.
Feedback: a tile turns gold when it is in its final place, which makes it easy to see which part of the board is finished. When the last tile is in place, the game shows your moves and time next to your best for that size.
How to solve the 15 puzzle and other sizes
Work in layers. Solve the top row first, then the left column. What is left is the same puzzle one size smaller, so repeat: top row, left column, until only a 2 by 2 corner remains. That last corner can be turned into place by moving the gap round in a circle. On 4 by 4, after the top row and left column you are left with a 3 by 3 board, and on 5 by 5 with a 4 by 4.
Most tiles of a row are easy. Bring each one into its place from below or from the side, moving the gap around it, and do not touch the gold tiles already done.
The last two tiles of a row need a trick, since putting one in place blocks the other. On 4 by 4, for the top row: put the 3 in the corner where the 4 belongs, and the 4 directly under it. Then move the gap into the 3's place, slide the 3 left and slide the 4 up. Both drop into place together. The same idea works for the last two tiles of a column, turned on its side.
If the 4 lands in the corner while the 3 is not next to it, do not fight it. Move the 4 away, down into the unsolved area, and set the pair up again. Trying to force it usually breaks the finished part of the row.
Mind the gap. Most moves go into bringing the gap to the right place. Plan the gap's route so it goes around the tile you are placing, on the side away from the finished area.
Fewest moves is a different game. The layer method always works, but it uses more moves than the minimum. For the record, any 3 by 3 position can be solved in at most 31 single-tile moves, and any 4 by 4 position in at most 80, but finding such short solutions by hand is very hard. Lower your move count by planning the gap's route and avoiding back-and-forth slides.
Board sizes in our Sliding Puzzle
Our Sliding Puzzle has three sizes: 3 by 3 with 8 tiles, the classic 4 by 4 with 15 tiles, and 5 by 5 with 24 tiles. 3 by 3 is a short warm-up and a good way to learn the last-two-tiles trick. 5 by 5 takes the most moves; once you solve its top row and left column, the rest is a 4 by 4 puzzle.
Every shuffle can be solved. Exactly half of all possible arrangements cannot be, for example the 15 puzzle with only the 14 and 15 swapped. The game checks each shuffle with the standard parity test and corrects it before you play. Other variants exist that use a picture cut into pieces in place of numbers; ours uses numbers only.
Where the 15 puzzle comes from
The 15 puzzle became a craze in the United States and Europe in 1880. It is credited to Noyes Chapman, a postmaster in New York State, who made it in the 1870s. The puzzle maker Sam Loyd claimed for years that he had invented it, a claim that historians have shown to be false.
Mathematicians soon looked at it closely. In 1879, William Johnson and William Story published a proof that only half of the starting positions can be solved. That is why the famous challenge of solving the board with the 14 and 15 swapped has no answer.
Play the Sliding Puzzle on Hevagames
Our Sliding Puzzle runs in the browser on phones, tablets and computers, with nothing to download. Tap or click tiles, swipe on a touch screen, or use the arrow keys. The Shuffle button deals a new board, and you can switch size at any time.
The game in progress is saved in your browser, so you can close the page and come back to it. For each size, the game keeps your fewest moves and your best time. A solved board scores 1000 points on 3 by 3, 2000 on 4 by 4 and 3000 on 5 by 5, minus one point per move and one per second, with at least 10 points.
How to play
- 1Tap a tile in the same row or column as the gap. It slides toward the gap, together with any tiles in between.
- 2You can also swipe or use the arrow keys to push the tile next to the gap.
- 3Order the tiles 1, 2, 3 and so on, left to right and top to bottom, with the gap in the bottom-right corner.
- 4Tiles turn gold when they are in their final place.
Controls
Tips
- Finish the top row first, then the left column, and repeat on the smaller square that is left.
- Place the last two tiles of a row together: line them up under their spots, then turn them in.
- The timer starts with your first move.