How to play Sliding Tiles
Slide tiles into the empty square, one at a time, until they are back in order with the gap at the bottom right. Also known as 15 puzzle, 8 puzzle, sliding puzzle.
The rules
- A move slides one tile that is next to the gap (across or up and down) into the gap.
- Tiles can’t be lifted out or jumped over each other.
- The puzzle is solved when the tiles read 1, 2, 3 … left to right, top to bottom, with the gap in the bottom-right corner (or the picture is complete).
Playing Sliding Tiles on Puzzle Solvers
- Choose 3×3 or 4×4, numbers or a picture, and a difficulty, then press New Puzzle.
- Tap a tile next to the gap to slide it in — or tap any tile in line with the gap to slide the whole row along. Arrow keys work too.
- Tiles in the right place get a green edge. Picture tiles show small numbers so you know where each piece belongs (you can switch them off).
- Hint shows the next move on the shortest way home, and the progress card shows the fewest moves possible.
Using the Sliding Tiles solver
- Choose 3×3 or 4×4 and set up your position (or press Sample).
- Press Solve: the first step explains the inversions check, then every move is shown — slide which tile, which way.
A worked example
3×3 board reading 1 2 3 / 4 5 6 / 7 _ 8: slide 8 left and it is solved in one move.
3×3 board reading 1 2 3 / 4 5 6 / 8 7 _: one inversion (8 before 7) — an odd count, so this position can never be solved, however you slide.
Strategies
- Top row first. Put 1, 2 and 3 (and 4 on a 4×4) in place, then never disturb them again.
- Last two of a row. Line up the last two tiles of a row together just below their spots, then rotate them in as a pair.
- Then the left column. Do the left column the same way; what’s left is a smaller puzzle.
- Finish with a cycle. The last 2×3 or 2×2 corner is solved by cycling tiles round until they click into place.
- Check solvability. Count inversions — pairs where a bigger number comes before a smaller one. On a 3×3 board the count must be even.
Common mistakes
- Breaking up a finished row to fix a tile below it — work around it instead.
- Trying to place the last tile of a row on its own; it nearly always needs the pair trick.
- Spending ages on an impossible position — check the inversions first.
Where it comes from
The 15 puzzle was invented in the United States in the 1870s and caused a worldwide craze around 1880. Mathematicians soon proved that exactly half of all arrangements can be solved — the famous ‘14-15’ swap is impossible.
Frequently asked questions
Why can’t some positions be solved?
Each slide changes the number of inversions in a fixed way, so a hidden ‘odd or even’ value never changes. Positions with the wrong value can never reach the finished board.
Is the hint the shortest way?
Yes — the hint and the solver search for the fewest moves. For very scrambled 4×4 positions the solver may give a short solution instead if the exact search runs out of time, and says so.
Can I download puzzles?
Yes — download a PDF of puzzles with the shortest solutions at the back. Sliding puzzles don’t work on the Slate whiteboard, so there’s no Slate file for this one.
How do I solve one from a book or a toy?
Open the Sliding Tiles Solver, set up your position and press Solve.
Keep going
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