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.
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.
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.
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.
The arrow keys ←↑↓→ push the neighboring tile from the given side into the empty cell — handy for precise single moves.
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".
Set the last two tiles of a row using the special "rotation" technique, keeping the bottom-right corner reserved for the empty cell.
The "✨ Hint" button highlights which tile to move. "↺ Reset" solves the board manually, and "🔀 Shuffle" starts a new game.
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.
Solve the top rows and left columns first, then leave them alone while working on the rest.
Set the last two tiles of a row together with a "rotation" around the corner, not one at a time.
Every slide disturbs the neighbors. Plan how to bring them back into place before you move.
A small board helps you get a feel for the "rotation" mechanic before taking on 4×4 and 5×5.
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.
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.
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.
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.
The top row 1–4 and left column 5–9 are already locked in (in gold) — only the lower remainder is left to solve.
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.
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.
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.
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.
Corner staging: 4 sits above 8 in the right column — one rotation of the gap closes both tiles.
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.
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.
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.
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.
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.