Notes on this puzzle
Fifteen #5406 is a 5×5 board with 24 numbered tiles and one gap, which starts in row 2, column 5. 1 tile starts in its home square.
Add up how far each tile is from its home square and you get 89, so no solution can be shorter than 89 moves. Solving it row by row, the method from our guide, takes 233 moves on this board. Tile 5 has the longest trip home: 8 squares.
Where to beginOn 5×5, peel off the top row and left column twice; only then does the board become a familiar 3×3.