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NO. 01 / SPATIAL LOGIC
Fifteen tiles. One empty space.
A small challenge that falls into place,
one thoughtful move at a time.
1 to 15, left to right.
Leave the last space empty.
BEFORE YOUR NEXT MOVE
No clock to beat. No rush to finish.
Just you and the next move.
Arrange the numbers from 1 to 15 across the rows, starting at the top left. The empty space belongs in the bottom-right corner. Only a tile directly above, below, left, or right of the gap can slide into it. Diagonal moves and jumps are not allowed.
On a phone or tablet, tap a neighboring tile. On a computer, click inside the board and use the arrow keys: each arrow is the direction the numbered tile moves. You can also click tiles with a mouse.
The timer starts on your first move. Pause hides the board and stops the clock; switching tabs also pauses an active attempt. Restart returns to the same starting board. New puzzle gives you a different shuffle. Undo reverses the last move and counts as another move.
Need a nudge? Click Hint to highlight a tile and see which way to slide it. Follow successive hints for a verified route to the finish, though not necessarily the shortest one. A tile may need to move away from its destination first. Hint does not move the board or start the clock.
Once a hint is shown, this attempt is Assisted. Restarting the same shuffle or undoing a move keeps it Assisted. New puzzle or a difficulty change starts a fresh Solo attempt. Solo and Assisted bests are kept separately; open Best scores below the board to compare them.
Start with 1 and 2 in the top-left corner. Treat 3 and 4 as a pair: bring 3 to the top-right corner, place 4 directly underneath it, and bring the gap to the left of 3. Slide 3 left, then 4 up. Filling the last two positions independently often traps the final tile.
Once the top row is complete, work on the next row without moving the first. For the bottom two rows, solve the leftmost pair as a column, then move right. Keep the last 2×2 square free to cycle into order.
THE MATH BEHIND THE MOVES
Swap just two tiles in a solved board and it becomes impossible to finish. Half of all random arrangements are unreachable. That’s why we shuffle by making legal moves from the solved position.
For a 4×4 board, count inversions: pairs of numbered tiles in the wrong order when read left to right, ignoring the gap. Add the gap’s row counted from the bottom. The board is solvable exactly when that sum is odd. Our shuffles preserve this parity, so a tricky position never means an impossible one.
FIND YOUR PACE
Ten legal shuffle moves from the finish. A gentle starting point for learning how the gap moves around a pair of tiles.
Fifty shuffle moves, with the tiles farther from home. Practice finishing a row without disturbing the one above it.
A deeper, 180-move shuffle. Leave space to circulate the bottom tiles and think in pairs, not individual numbers.
Shuffle length is not the shortest solution length. Best scores are saved on this browser, separately for each difficulty and for Solo or Assisted play, ranked by fewest moves and then time. The current board is 4×4.
A COUPLE OF GOOD QUESTIONS
Swapping only those two tiles changes the board’s parity. A board generated here cannot end with just 14 and 15 swapped while everything else, including the gap, is correct. If the ending feels stuck, check the other tiles: an earlier pair is likely out of order. Work backward to the last unfinished row or column.
Yes. “15 Puzzle,” “fifteen puzzle,” and the classic 4×4 sliding number puzzle refer to the same arrangement: fifteen numbered tiles and one gap. The smaller 8 Puzzle uses a 3×3 board and a different solvability rule.
A sliding puzzle needs room to circulate tiles. The hint follows a complete, verified route that fixes rows and columns in stages. Temporary detours can open the gap needed for a pair of tiles. The route reaches the goal when followed, but it is not a promise of the fewest possible moves. You can ask for a new hint after trying a different move.
Completed personal bests remain in this browser’s local storage unless you clear site data or use a private session. An unfinished board is saved for this browser tab. Reload or visit the collection and return to resume the same shuffle, paused, with your active time and Assisted status intact. Closing the tab normally ends that session; a browser may restore it when reopening tabs. Completing a board clears its unfinished session. If your browser blocks storage, you can still play, but records will not persist.
A LITTLE SPACE TO THINK