In Classic Slide, every move exchanges a tile with the empty space beside it. The aim is to restore the picture. A useful first habit is to plan where the empty space needs to go, rather than repeatedly tapping the tile you want to move.
This guide starts with a single move, then shows how to protect completed sections and place the awkward last pair in a row. In the numbered diagrams, each tile's number marks its position in the finished picture, starting at the top left. The blank belongs at the bottom right.
Move a tile by moving the space
A tile can slide up, down, left, or right into an adjacent empty cell. It cannot move diagonally or jump over another tile. If the tile you want to move has no empty neighbor, first move other tiles to bring the space beside it.
Try that move in The Copley Family 3×3 challenge. Notice that bringing the space closer to one tile may move another tile farther from its goal. That is often necessary. Distance to the goal can guide you, but some useful moves temporarily increase it.
Solve a row, then a column
For a first solution, reduce the board in layers. This gives you a smaller problem after each completed section.
- Complete the top row, working from left to right and placing its final two tiles as a pair.
- Complete the leftmost column below that row, treating its final two tiles as a pair too.
- Leave the completed row and column alone. Repeat within the remaining rectangle.
- When only a 2×2 region remains, cycle its tiles around the blank until they match the goal.
On a 4×4 board, completing the first row and column leaves a 3×3 working area. Repeating the process leaves the final 2×2. Avoid solving row after row until you have only one unfinished row. A one-cell-wide strip gives you no room to move tiles around each other.
Keep completed rows and columns intact. A tile that happens to be correctly placed in the unfinished area may still need to move, so do not treat it as fixed.
Place the final two tiles together
The last two positions in a row need preparation. If you put the next-to-last tile directly into its goal too early, it can obstruct the final tile's approach.
For the top row of a 4×4 board, first finish tiles 1 and 2. Then arrange tile 3 in tile 4's goal, with tile 4 immediately below it and the blank immediately to its left. Once those three cells are arranged, the row finishes in two moves.
The diagram begins at the prepared position, not at an arbitrary scramble. Use the unfinished rows to bring 3 and 4 into this arrangement. If one is trapped, move it back into the working area before trying again. For a column, turn the same idea through a right angle.
For a longer illustrated walkthrough of the setup, use the Fifteen Puzzle Solution Guide. Its numbered stages make a useful companion while practicing on a larger board.
Route the blank around a tile
Suppose a tile needs to travel left twice. After its first slide left, the blank is on its right. Sliding the tile right again simply undoes your move. Instead, route the blank through the unfinished area until it reaches the tile's left side, then slide the tile left again.
Before starting that route, check that there is enough room to go around. Near a completed edge, you may need to approach from the rows below. If the blank cannot get around without disturbing a completed row or column, move the tile into a better position before trying again.
Recognize a linear conflict
Two tiles can both be in their correct row but appear in the wrong order. For example, 2 followed by 1 in the top row is a conflict even though neither tile needs to finish in another row. They cannot pass each other while both remain in that row.
Move one of the conflicting tiles into the unfinished area, make room for the other, and return the first tile afterward. The same reasoning applies to reversed tiles in a column. Treat the coaching overlay as a prompt to inspect the order of the tiles, rather than as a complete move sequence.
Finish the remaining 2×2
Once the other layers are correct, move the blank around the perimeter of the final square. Three tile moves carry it past all three numbered tiles; continue the cycle if needed. If the original board was solvable and the rest is correctly placed, the remaining tiles can be finished this way.
If you seem to have only two tiles swapped, check the larger picture before dismantling your solved rows. Two similar-looking image tiles may be in each other's positions. A true two-tile swap with everything else fixed is not reachable from the standard solved board by legal slides.
What makes a sliding puzzle solvable?
For the standard numbered goal, read the tiles row by row and omit the blank. An inversion is a pair in which the larger number appears first. In 1, 3, 2, 4, only the pair 3 and 2 is inverted.
- On an odd-width board, the inversion count must be even.
- On an even-width board, the inversion count plus the blank's row counted from the bottom, starting at 1, must be odd.
These rules assume the goal runs in ascending order with the blank at the bottom right. They are explained in Princeton's sliding-puzzle assignment. For picture tiles, use each tile's intended position as its number.
Puzzuzu's randomizer starts from a solved board and makes legal moves, which preserves solvability. Counting inversions is more useful when checking a manually arranged puzzle than when starting a random game here.
Additional resources
- Fifteen Puzzle Solution Guide gives a staged visual solving method, including the difficult row and column pairs.
- Princeton's sliding-puzzle assignment explains Manhattan distance, search, and solvability with numbered examples.
- Cut the Knot's history of the fifteen puzzle examines the early puzzle craze and Sam Loyd's later claims.
- The Puzzuzu glossary explains the terms used here, including heuristic, parity, and state space.
For your next Classic Slide game, practice completing just the first row and column without undoing either. Once that feels reliable, repeat the same process inside the smaller board you have left.