Dusk Mountains

Serene sunset glow reflecting across tranquil alpine waters

Select Art Scene6 Gallery Canvases

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Click a tile next to the gap to slide it · Or use Arrow Keys / WASD

The Mathematics of Sliding Tile Puzzles

Sliding tile puzzles (like the classic 15-puzzle invented by Noyes Chapman in 1874) are deeply tied to permutation group theory and inversion parity. Randomly rearranging tiles creates unsolvable states 50% of the time! Our game uses a guaranteed-solvable shuffle algorithm by executing valid sliding steps directly from the solved state.