How to play
A square frame holds numbered tiles and a single empty slot. The goal is to put the tiles back in reading order: 1 in the top left, counting along each row, with the gap ending up in the bottom right corner. On the 4×4 frame that means 1 to 15; on 3×3 it’s 1 to 8, and on 5×5 it’s 1 to 24.
Tiles can only move into the gap, so every move is really a move of the empty slot.
Tapping. Tap a tile next to the gap and it slides across. Tap a tile further away in the same row or column, and that tile plus every tile between it and the gap slide together in one go. A tile that isn’t lined up with the gap won’t move.
Keyboard. The arrow keys push a tile in the direction of the arrow. Pressing Left slides the tile on the right of the gap leftward into it, and so on.
Counting. Every tile that moves adds one to the move counter, so sliding three tiles at once counts as three moves. The status line also shows how many tiles are already in their home square, and those tiles get a green edge on the board.
Buttons. Size switches between 3×3, 4×4 and 5×5; the 4×4 frame is the default. New puzzle shuffles a fresh frame. Undo takes back moves, and the counter goes back with them. Hint plays one move for you. When you finish, the result shows your move count, your time and how many hints you used.
How the shuffle works
Not every arrangement of numbered tiles can be solved. If you prised two tiles out of a solved frame and swapped them, no amount of sliding would ever fix it: exactly half of all possible arrangements are unreachable, a fact that goes back to the puzzle craze of the 1880s.
This game sidesteps the problem. Instead of placing numbers randomly, it starts from the solved frame and makes a long series of random slides, 40 per square of the board. It then checks that the tiles are spread well away from home, and shuffles again if they’re not. Every puzzle you get was reached by legal moves, so it can always be undone.
For a sense of scale: any 3×3 position can be solved in 31 single-tile moves or fewer, and any 4×4 position in 80 or fewer. Those are the proven worst cases. Most real shuffles need far fewer, but nobody solves a 4×4 by hand in anywhere near the optimum.
Strategy
The usual human method breaks the puzzle into smaller copies of itself.
Finish the top row, then the left column. Get tiles 1, 2, 3 and 4 home across the top (on 4×4), then 5, 9 and 13 down the left. After that, never touch those tiles again. What remains is a 3×3 puzzle, and the same idea repeats until a small block is left.
Place the last two tiles of a row as a pair. Putting 1, 2 and 3 in place is easy; the 4 is where people get stuck, because the corner is hard to reach without disturbing 3. The standard trick: park 4 in the 3’s home square, bring 3 directly underneath it, then move the gap around so both drop into place together. The same pairing works for the last two tiles of a column.
Think in loops. Running the gap around a 2×2 block cycles three tiles one step. Running it around a 2×3 block cycles five. These rotations are how you move a tile into position without breaking anything you’ve finished.
Save moves with multi-tile slides. Tapping a far tile moves a whole line in one action. It doesn’t lower your move count, since each tile still counts, but it is much quicker than tapping one tile at a time.
Use the 3×3 frame to practise endings. The final 3×3 block of a bigger frame is solved exactly like the small puzzle, so practice on 3×3 pays off on 4×4 and 5×5.
Know what Hint does on each size. On 3×3 the hint follows a shortest possible solution. On 4×4 and 5×5 a full optimal search would be far too slow, so the hint follows a fast search that heads for the solution without guaranteeing the fewest moves. It’s a good nudge when you’re stuck, not a perfect line.
For other puzzles with a single clear target, try Tower of Hanoi or Peg Solitaire.
If you enjoy Sliding Puzzle, try Star Battle or Sudoku next.
