Alchemy Slide: how to solve a sliding puzzle

How to play

1. The goal is the tiles in order, 1, 2, 3 and onward, read left to right and top to bottom, with the empty slot in the bottom-right corner.
2. Only a tile in the same row or column as the empty slot can move. Tapping a tile further along that line slides it and every tile between it and the slot.
3. Each tile that moves counts as one move. The timer starts with your first move and pauses when you choose Pause or leave the tab.
4. A gold dot marks a tile that sits in its home square. Tile colours follow their home row, so a finished row reads as one colour band.
5. Every board is shuffled at random and then checked for solvability, so you never get a position that cannot be finished.
6. Solve the board to see your moves and time, then choose Play again for a fresh shuffle at the same size or New puzzle at any time.

Controls

Mouse

Click a tile in line with the empty slot to slide it, together with any tiles between.

Touch

Tap a tile in line with the slot, or swipe on the board to slide the tile next to the slot in that direction.

Keyboard

Arrow keys or WASD slide the tile next to the empty slot in the direction you press. Tab reaches each tile; Enter or Space slides it.

Score and progress

The move counter adds one for every tile that slides. The timer has no limit and stops when the board is solved. Fewest moves and fastest time are saved separately for 3×3, 4×4 and 5×5 in this browser when local storage is available.

Tips

• Move the empty slot, not the tile. To push a tile left, bring the slot to its left side without disturbing finished tiles, then slide the tile into it.
• Do not lock in the second-to-last tile of a row early. Placing it alone usually leaves no room for the last one.
• On 3×3, the first row plus the left column leaves a 2×2 square, which is quick to finish by cycling.
• Count moves only after you know the method. Speed comes from fewer wasted slot loops, not from faster tapping.

Stuck on a 3×3 or 4×4 board? The game opens your current position in the Sliding Puzzle Solver, which shows the fewest moves from there to the solved board.

How to solve a sliding puzzle by hand

You do not need to plan the whole board. Solve it in layers, and never disturb a finished row while you work below it.

1. Top row first. Bring tile 1 to the top-left corner, then 2 beside it, and so on. Move the empty slot around a tile to push it one square at a time toward its home.
2. Place the last two tiles of a row together. On a 4×4 board, put 4 where 3 belongs and 3 directly under it, then slide 4 right and 3 up into place.
3. Repeat for each row until only two rows are left. On a 4×4 board that is after two rows; on a 5×5 board, after three.
4. Solve the last two rows one column at a time from the left. Treat each column pair like the end of a row turned on its side: put the bottom tile where the top one belongs, the top tile beside it, then rotate both in.
5. When a 2×2 square is left, cycle its three tiles around the empty slot until they are in order. If they never line up, an earlier tile is out of place.

Why some sliding puzzles cannot be solved

Why can half of all arrangements never be solved? Count the inversions: pairs of tiles where a bigger number comes before a smaller one, reading row by row. A sideways slide never changes that count. On a board with an odd width, an up or down slide changes it by an even number, so its parity, odd or even, never changes; the solved board has zero, so only boards with an even count can be solved. On a 4×4 board, an up or down slide flips the parity while the empty slot changes row, so the inversion count plus the empty slot's row, counted from the bottom starting at 1, must be odd, as it is on the solved board (0 + 1). Swapping any two tiles breaks the rule, which is why a board with 14 and 15 swapped is unsolvable.