Name of the Old Sliding Square Puzzle Game: The 15-Puzzle

It's the 15-Puzzle (also called Sliding Tile Puzzle, Gem Puzzle, Boss Puzzle, or Game of Fifteen).

• Mechanic: 4×4 grid, 15 numbered tiles + 1 gap. Slide tiles to order 1–15.
• Origin: Noyes Chapman, 1874 (craze 1880).
• Variants: 8-puzzle (3×3), 24-puzzle (5×5), picture versions (no numbers).
• Math: Only half of random starting positions are solvable (parity).

Modern apps: 15 Puzzle - Sliding Puzzle (Android/iOS), Sliding Puzzle on web.