How to play
The board is filled with numbered tiles and exactly one empty square. That empty square is the only thing you really control. A tile can move only if it is directly above, below, left of or right of the gap, and when it moves it simply trades places with the gap. Nothing jumps, nothing rotates, and no tile ever leaves the board. The puzzle is finished when the numbers read in order from left to right and top to bottom, with the empty square back in the bottom right corner.
Every slide adds one to the move counter, and the timer starts on your first slide rather than on page load, so reading this page first costs you nothing. Each board size keeps its own best move count and best time on this device only, and a tile that is already sitting in its final square is tinted green. That green is the part worth watching: it turns a wall of numbers into visible progress, and it warns you the moment a finished area gets disturbed.
Controls
- Mouse or trackpad: click any tile that touches the empty square.
- Keyboard: arrow keys or W A S D pull a tile into the gap from that side. Pressing left brings the tile on the left of the gap into it.
- Phone or tablet: swipe on the board in the direction you want a tile to travel.
- Shuffle: deals a fresh scramble at the current size and resets the counters.
- Target hints: adds the destination row and column of each tile to its label for screen readers and hover tooltips, which helps on the 5 × 5 board.
The method that turns a 4 × 4 into routine work
Solve the top row and the left column first, then forget they exist. Once row one and column one are correct, every remaining tile lives in a smaller square, and you can treat a 4 × 4 as a 3 × 3 you already know how to finish. Repeat the trick and the 3 × 3 becomes a 2 × 2 that resolves with a handful of rotations. This layered approach is the whole reason experienced players look fast: they are not calculating a full solution, they are shrinking the problem one border at a time and never re-solving a finished area.
The awkward part of any row is its last two tiles, because the obvious approach traps you. If you place the second-to-last tile in its correct square first, the final tile has no way into the corner without pushing its neighbor back out. The fix is to stage them in the wrong-looking spots on purpose: put the second-to-last tile of the row in the corner square itself, and the last tile directly beneath that corner. Now walk the gap around to the square immediately left of the corner and slide twice — the corner tile moves left into place, then the tile below it lifts into the corner. The gap has traced a small three-square cycle, and that cycle is what rotates the pair into position without ever touching the tiles you already locked.
Pure improvisation works on a 3 × 3 and stops working above it, and the reason is arithmetic. A 3 × 3 board has nine factorial arrangements, half of them unreachable, which leaves 181,440 positions — small enough that nudging tiles toward where they look like they belong stumbles into a solution eventually. A 4 × 4 has sixteen factorial arrangements, so the reachable half runs into the trillions, and a 5 × 5 is unimaginably larger. In that space, moving the tile that is closest to home almost always costs you a tile that was already home, and you can spend twenty minutes cycling between two near-solutions. Method beats reflexes here: choose a border, finish it, protect it, shrink the board.
Reference figures from our own play testing, offered as estimates and not as records: a 3 × 3 usually falls in well under a minute once you stop guessing, a 4 × 4 tends to land near one hundred and fifty moves and a few minutes of clock, and a 5 × 5 is a comfortable ten-minute sit-down. Your shuffle decides how far each tile has to travel, so a fair run can be far above or below any of those numbers.
Where the puzzle came from
The four-by-four version, usually called the 15 puzzle, became a genuine craze in the 1880s, sold as a cheap wooden novelty and printed in newspapers alongside prize offers for arrangements that turned out to be impossible. That is the interesting part of its history: exactly half of all possible tile arrangements cannot be reached from the finished board, no matter how long you slide. A physical puzzle can be scrambled into one of those unreachable halves by lifting the tiles out of the tray, which is how the impossible newspaper challenges worked.
Our version cannot do that to you. Instead of shuffling the tile list, it starts from the solved board and applies a few hundred random legal slides, so the scramble is by construction a position you can walk back out of. The code and every word on this page were written from scratch for this site; only the rules are borrowed, because the rules are what makes it a puzzle.
Questions players ask
Is every shuffle solvable?
Yes. Half of all tile arrangements can never be reached from the finished board, so we never scramble the tile list directly. Each shuffle starts from the solved board and applies a few hundred random legal slides, which means the sequence can always be walked backwards.
How many moves should a 4 × 4 take?
Once the row and column method is a habit, our play testing lands near one hundred and fifty moves. Treat that as an estimate, not a target — the shuffle decides how far each tile has to travel, so two fair runs can differ by dozens of moves.
Do the arrow keys move the gap or the tile?
They pull a tile into the gap. Press the left arrow and the tile sitting left of the empty square slides into it, leaving the gap one square further left. On a touchscreen, swipe the way you want the tile itself to travel.