Number Sliding Puzzle

Overview

One square of the grid is always empty, and that single gap is the only way anything moves. The number sliding puzzle — best known as the 15-puzzle when it ships as a 4×4 of tiles numbered 1 through 15 — hands you a scrambled board and asks you to restore the tiles to ascending order with the gap in the lower-right corner. Each move slides a single neighboring tile into the empty space, so progress is indirect: you cannot lift a tile, only coax it through the grid one step at a time. Multiple difficulty levels set the grid size and how badly scrambled the start state is, while a move counter and a timer track the cost of your solution. Half the puzzle is figuring out the algorithm, the other half is executing it without disturbing the rows you have already locked in. A well-known result from the mathematics of the 15-puzzle is that exactly half of all possible arrangements are reachable from any given start — parity is fixed — so a correctly generated board is always solvable.

How to Play

Press an arrow key to slide the tile adjacent to the empty space into that gap — Up moves the tile below the gap upward, and so on. Click any tile orthogonally adjacent to the empty space to slide it in. On touch, tap an adjacent tile to slide it into the gap. The move counter ticks up with each slide and the timer runs until the tiles sit in order with the empty square in its home corner. Multiple difficulty levels change the grid size and scramble depth, so pick an easier preset to learn the method before tackling a larger board.

Tips & Strategy

Solve the puzzle top row first, then the left column, then the next row, then the next column, working inward until only a 2×2 corner remains — which is small enough to fix by feel. Positioning the final two tiles of a row is the standard bottleneck: drop the tile that belongs in the corner into the space one cell to its right, place the next tile directly below its target, then rotate the pair into place. Never go back to fix a solved row, because every move you make above or to its left disturbs tiles below and to the right; commit to solving in strict order. Keep the empty square close to where you are working rather than dragging it across the board, since long slides cost moves and invite mistakes. The move counter is your efficiency gauge — a clean solution on a 4×4 sits in the low hundreds of moves, and anything drastically higher usually means you backtracked. If the timer is running long, stop and restart rather than grind, because the algorithm is much easier to execute from a fresh scramble than from a tangled middle state.