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How to Play the 15 Puzzle

A complete guide: how to slide tiles in the frame, arrange the numbers in order, and solve the puzzle in the fewest moves. Controls on muta.pro and solving strategy.

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In brief

Goal
Arrange the numbers in order
Players
1
Game
3–10 min
Difficulty
Medium
Randomness
None

Goal of the game

The 15 Puzzle is a single-player perfect-information puzzle: there is no randomness, everything is solved by logic. In a 4×4 frame there are fifteen numbered tiles and one empty cell. The board is shuffled, and your task is to arrange the numbers in ascending order from left to right and top to bottom (1–2–3–4 in the first row and so on up to 15), leaving the empty cell in the bottom-right corner. The game counts the number of moves and the time.

Setup

On launch the board is immediately shuffled with a set of random but always solvable slides. You can change the size in the "Board size" block: 3×3, 4×4, or 5×5. On the right you'll see the move and time counters and the record for the chosen size, and on the left the record table and game statistics. The timer starts on your first move.

How to solve

Sliding a tile

Click a tile that lines up with the empty cell — it (and the whole row between it and the gap) slides into the free space. A single click can move an entire line.

Keyboard controls

The arrow keys ←↑↓→ push the neighboring tile from the given side into the empty cell — handy for precise single moves.

Build row by row

Place the numbers in order: first the top row 1–2–3–4, then the next one. Tiles already in place are highlighted as "correct".

Corners last

Set the last two tiles of a row using the special "rotation" technique, keeping the bottom-right corner reserved for the empty cell.

Hint and reset

The "✨ Hint" button highlights which tile to move. "↺ Reset" solves the board manually, and "🔀 Shuffle" starts a new game.

When it's solved

The puzzle is solved when all tiles are in ascending order and the empty cell is in the bottom-right corner. The timer stops and a "Solved!" screen appears with the number of moves and the time. If you beat your previous result for this size, "★ New record!" is noted. The competition is with yourself — for the fewest moves and the best time; your result goes into the record table.

Controls on muta.pro

🖱️
Click a tile
A tile lined up with the empty cell slides into the free space; a whole row moves in one click.
⌨️
Keyboard arrows
←↑↓→ push the neighboring tile into the empty cell — for single precise moves.
🔀
"🔀 Shuffle" · "↺ Reset"
Shuffle starts a new game; Reset returns the board to the solved state.
"✨ Hint" and size
The hint points out the next move; the "Board size" block offers 3×3, 4×4, and 5×5.

Tips for beginners

Top down

Solve the top rows and left columns first, then leave them alone while working on the rest.

Corners by technique

Set the last two tiles of a row together with a "rotation" around the corner, not one at a time.

Think one move ahead

Every slide disturbs the neighbors. Plan how to bring them back into place before you move.

Start with 3×3

A small board helps you get a feel for the "rotation" mechanic before taking on 4×4 and 5×5.

Solving strategy

The 15 puzzle isn't solved by brute force but layer by layer. The key idea: never touch the part of the board that's already solved, and do all your work in the remaining "live" rectangle. First you lock in the top row and left column — after that the board effectively shrinks, and the same logic repeats on the remaining 3×3, then 2×2.

Row by row, top down

Solve the entire top row in order, then the left column. The finished "L" of a row and column isolates the lower part — from then on you work only within it.

The empty cell is your tool

Tiles don't move on their own: the empty cell pushes them. Think not "where does the tile go" but "how do I lead the gap around it" to slide the needed piece in without breaking what's solved.

The 2×2 finale is solved by rotation

When a 2×2 square remains, all three tiles fall into place with one circular movement of the gap. If the order doesn't come together after the circle, the position simply wasn't set up correctly on the previous step.

1
2
3
4
5
7
6
8
9
10
11
12
13
14
15

The top row 1–4 and left column 5–9 are already locked in (in gold) — only the lower remainder is left to solve.

Advanced techniques

The main challenge is the last two tiles of a row (for example 4 and 8 in the right column of the top row). You can't set them one at a time: the second always pushes out the first. Experienced players use a staging setup and the rotation technique around the corner.

Stage the pair in the corner

Place tile 4 not in its spot but in the top-right corner, and tile 8 right below it. Then a single rotation sets both into place at once.

Count the parity

A position is solvable only if the parity of permutations matches. Muta shuffles the board with real slides, so there are no dead ends — but understanding parity explains why an "almost solved" board sometimes requires a full rebuild of the corner.

Fewest moves over haste

Both moves and time go into the record table. Extra "shuttle" slides of the gap back and forth inflate the counter — lead the gap to its goal along the shortest arc.

4
8

Corner staging: 4 sits above 8 in the right column — one rotation of the gap closes both tiles.

Variants and records

On muta the board size is switched in the "Board size" block, and these are essentially three different games. Records for moves and time are kept separately for each size, so it makes sense to level them up one at a time.

3×3 — the eight-puzzle

Eight tiles, perfect for practicing rotation. The optimal solution of any position is no more than 31 moves; it's a good place to hunt for a short record.

4×4 — the classic

The very "fifteen". It's solved layer by layer; a good result is a confident solve with no getting stuck, rather than the absolute minimum of moves.

5×5 — 24 tiles

The hardest mode. The same "row + column" method, but with more layers, and the cost of a corner mistake is higher — plan several moves ahead.

Grow gradually: hone your rotation on 3×3, carry the method over to 4×4, and only then take on 5×5. That way each record rests on an already-practiced technique rather than on luck.

Common mistakes

Almost every snag in the 15 puzzle is destroying what's already solved for the sake of one tile. Below are the typical traps and how to avoid them.

  1. Breaking a finished row. When sliding a new tile in, the player leads the gap straight through the solved top. Route the empty cell around the locked zone, not through it.
  2. Placing the last pair one at a time. The two end tiles of a row can't be closed one after another — the second knocks out the first. Always use corner staging and rotation.
  3. Racing the clock while piling up moves. Chaotic quick slides improve your seconds but ruin the move counter. Both metrics matter for a record.
  4. Jumping straight into 5×5. Without a practiced rotation, the big board feels unsolvable. Start with 3×3 and work up in size.
  5. Deeming a position a dead end. Every deal on muta is solvable. An "impossible" corner means the pair needs to be re-staged, not that the board is broken.

Frequently asked questions

Is every board solvable?
Yes. Shuffling is done with a series of real slides from the solved state, so every deal is guaranteed to have a solution.
Can I move several tiles at once?
Yes. If you click a tile with a row of tiles between it and the empty cell, that entire row slides in a single move.
How does the difficulty change?
Through the board size: 3×3 is easy, 4×4 is the classic, and 5×5 is the hardest. Records are kept separately for each size.
What counts as your result?
The number of moves and the solving time. The fewer moves and the faster you go, the higher your place in the record table.
How many moves does solving a 4×4 take in the worst case?
Any position of the classic 15 puzzle can be solved in no more than 80 moves — that is the proven maximum. In practice, a careful layer-by-layer solve fits into a noticeably smaller number.
What is the "rotation" technique in simple terms?
It is when you lead the empty cell in a circle around two or three tiles, and they fall into place one after another. This circular move is the basis for solving the last tiles of a row and the final 2×2 square.
Why can't you place the last two tiles of a row one at a time?
When you slide the second tile into its place, it inevitably pushes out the first. That's why the pair is set up together via a staging spot in the corner and closed with a single rotation.
Does the strategy differ between 3×3 and 5×5?
The method is the same — first a row, then a column, layer after layer. The only difference is the number of layers: on 5×5 there are more, so you have to plan further ahead.
What matters more for a record — time or number of moves?
On muta both metrics count, and records are kept for them together. A perfect game means both few moves and a fast time, so don't sacrifice one for the other.
Does the hint button help solve the whole board?
The hint points out one sensible next move rather than solving the puzzle entirely. It's useful for getting out of a jam, but solving the board and holding the record is still up to you.
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