15 Puzzle
The sliding classic, always solvable, with moves and time tracked.
About this puzzle
Fifteen tiles, one gap: slide to order them 1โ15. Click any tile in the blank's row or column to slide the whole run at once (arrow keys work too); correctly placed tiles tint as you go, and moves, time and your best game persist on this device.
Solvability, and history's greatest puzzle hoax
Half of all random tile arrangements are IMPOSSIBLE โ permutation parity divides positions into two families, and no legal slide crosses between them. This build shuffles by random walks from the solved state, so every board is guaranteed solvable; that guarantee matters because the gap is where Sam Loyd built the 1890s' greatest hoax, offering $1,000 for solving a board with just the 14 and 15 swapped โ a provably impossible position, prize money perfectly safe, nation successfully obsessed. Technique: solve the top row, then the second (last two of each row go in together with a rotation), then the final two rows column by column from the left. Under 120 moves is solid; optimal solutions average around 53, and finding THE optimum is NP-hard โ genuinely difficult for computers too. Sudoku and Minesweeper carry on the logic-puzzle shelf.
Frequently asked questions
Are these shuffles always solvable?
Yes โ boards are scrambled by legal moves from the solved state, so a solution path always exists. Half of RANDOM arrangements aren't solvable, which is why honest shuffling matters.
What was the Sam Loyd hoax?
An 1890s $1,000 prize for solving a board with only the 14 and 15 swapped โ mathematically impossible (wrong parity), so the prize was never at risk while the puzzle sold wildly.
What's the solving strategy?
Top row first, then second row (placing each row's last two tiles together with a rotation), then the bottom two rows in vertical pairs from the left. The last six tiles are one practiced manoeuvre.
What counts as a good solve?
Under 120 moves shows real technique; optimal play averages ~53 moves. Time matters less than moves โ the best games are calm ones.