How to Solve a Sliding Puzzle (15 Puzzle): Step-by-Step

What Is a Sliding Puzzle?

A sliding puzzle is a grid of numbered tiles with one empty space. Any tile next to the gap can slide into it, and by making a series of these slides you rearrange a scrambled board back into numerical order. The most famous version is the 15 puzzle: a 4×4 grid with fifteen tiles and one empty square, which caused an international craze in the 1880s. You can play the 3×3, 4×4, and 5×5 versions on our free sliding puzzle.

Why Half of All Scrambles Are Impossible

Here is a surprising fact: of all the ways you could arrange the tiles, exactly half are unsolvable. Whether a board can be solved depends on a mathematical property called parity — the number of tile inversions combined with the blank's position. This is why a puzzle that shuffles tiles completely at random can hand you an impossible board. Our version avoids that entirely by scrambling from the solved state using legal slides only, so every puzzle you get is guaranteed solvable — you will never waste time on an impossible one.

The Layered Method

The reliable way to solve any sliding puzzle is to work in layers, permanently locking in tiles as you go rather than trying to arrange everything at once. Here is the full sequence for a 4×4 board; the same logic scales to any size.

1. Solve the top row (1, 2, 3, 4) in order. Place 1, then 2, then 3. The last two tiles of the row — 3 and 4 — need the special corner trick below.
2. Solve the left column (5, 9, 13). With the top row done, work down the left edge. Again, the bottom two need the rotation trick.
3. Shrink the puzzle. The top row and left column are now permanent. Ignore them — you are left with a smaller 3×3 puzzle in the corner.
4. Repeat. Solve the new top row and new left column of that smaller area.
5. Finish the last 2×2. Eventually only a 2×2 block remains, which you simply rotate until the three tiles fall into place.

The Corner Rotation Trick

The one genuinely tricky part is placing the last two tiles of any row or column. If you try to slot them in directly, you end up knocking the row apart. The trick is to set them up as a pair and rotate them into place together. For the top row, position the final tile (4) directly below where it belongs and the second-to-last (3) to its left, then rotate the pair into the corner. Learn this one little manoeuvre and every “stuck” moment in the layered method disappears. It feels like magic the first time it works.

Cutting Your Move Count

Once you can reliably solve the puzzle, the next challenge is efficiency — solving in as few slides as possible. The biggest waste of moves is shuffling the blank back and forth without a plan. Instead:

• Position the gap first. Before moving a target tile, route the empty space to exactly where it needs to be, then slide the tile in one clean sequence.
• Never disturb solved tiles. Once a row or column is locked, keep all your moves inside the unsolved region.
• Plan two or three slides ahead. Reacting one tile at a time almost always costs extra moves.
• Practise on 3×3 first. The 8-puzzle teaches the whole method quickly; then scale to 4×4 and 5×5, where the steps are identical.

For reference, the hardest possible 15-puzzle position takes 80 moves to solve, and a typical random scramble falls somewhere in the 40–80 range. Your best move count for each size is saved so you can keep beating it.

Frequently Asked Questions

What is the fastest way to solve a sliding puzzle?

The layered method: solve the top row, then the left column, then repeat on the smaller remaining grid until only a 2×2 block is left. Master the corner rotation trick for the last two tiles of each row and column.

Why does my puzzle seem impossible?

Half of all random tile arrangements genuinely cannot be solved due to parity. Our puzzle scrambles using legal moves from the solved state, so it is always solvable — if a physical puzzle seems impossible, it may have been reassembled into an unsolvable state.

How many moves should it take?

For the 4×4 15 puzzle, skilled solvers usually finish in roughly 40 to 80 moves depending on the scramble. The hardest possible position needs exactly 80.

Is the 8-puzzle the same as the 15 puzzle?

They are the same game at different sizes: the 8-puzzle is 3×3 (eight tiles), the 15 puzzle is 4×4, and the 24 puzzle is 5×5. The layered solving method works on all of them.

Start Playing

Practise the method on our free sliding puzzle. Choose 3×3, 4×4, or 5×5, watch your moves and time, and beat your best score. Every scramble is guaranteed solvable and it runs entirely in your browser — no download, no signup. Start on 3×3, learn the corner trick, and work your way up to the 5×5.