What is a 5x5 slide puzzle called?
The 5×5 slide puzzle is called the 24 puzzle, after its twenty-four numbered tiles. It plays by exactly the same rules as the 15 puzzle: slide a tile into the empty space until every number is in reading order.
24 puzzle · 5×5 board
5×5 slide puzzle
Twenty-four tiles. Big enough that the method matters more than luck.
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Tap or drag a tile next to the empty space to slide it. Arrow keys work too. Every shuffle is solvable.
About the 24 puzzle
How many moves does a 5x5 slide puzzle take?
Nobody knows the exact maximum. The hardest known 24 puzzle positions need at least 152 optimal moves, and it has been proven that no position needs more than 208. The gap has not been closed because the puzzle has 25!/2, about 7.8 × 10²⁴, solvable positions, far too many to search exhaustively.
Is a 5x5 slide puzzle harder than 4x4?
Yes, but only in length, not in kind. The layered method is the same: solve the top row, then the left column, then treat the rest as a 4×4 puzzle. A 5×5 solve by hand typically takes 150 to 300 moves, against 80 to 150 for a 4×4.
Can every 5x5 slide puzzle be solved?
Exactly half of all arrangements can. On a 5×5 board the test is simple: list the tiles in reading order, count the inversions (pairs where a larger number comes before a smaller one), and the position is solvable when that count is even. The row of the empty cell does not matter on odd-width boards.