description 15 Puzzle Overview
The 15 Puzzle is a sliding-tile puzzle consisting of fifteen numbered square tiles arranged in a four-by-four frame with one empty space. Players move adjacent tiles into the gap to restore a specified numerical order, and only half of all apparent arrangements are mathematically reachable from any given starting position. The puzzle became an international craze around 1880 and remains a standard example in combinatorics, algorithms, and heuristic search.
insights Ranking position
15 Puzzle ranks #1 of 85 in the Number Game ranking, ahead of Mancala.
help 15 Puzzle FAQ
How can you tell whether a 15 Puzzle position is solvable?
Solvability depends on the parity of the tile permutation together with the blank square's row in the four-by-four grid. As a result, exactly half of the apparent arrangements can be reached legally from a solved position.
Why can swapping just 14 and 15 make the puzzle impossible?
A single swap reverses the permutation parity without making the corresponding change required by legal blank moves. That is why the famous arrangement with only tiles 14 and 15 exchanged cannot be solved by sliding pieces normally.
Who popularized the 15 Puzzle?
The puzzle became an international craze around 1880 and was strongly associated with American puzzle promoter Sam Loyd. Loyd later claimed he had invented it, but the puzzle's earlier manufacture is generally linked to Noyes Palmer Chapman.
What is the usual strategy for solving a 15 Puzzle?
A practical method is to complete the top row, then the second row, before solving the remaining lower section without disturbing finished tiles. The final two tiles of a row often need to be positioned as a pair rather than inserted independently.
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