Notes on this puzzle
Fifteen #5408 is a 5×5 board with 24 numbered tiles and one gap, which starts in row 4, column 5. 2 tiles start in their home squares.
Add up how far each tile is from its home square and you get 79. 4 pairs of tiles already sit in their correct line but in the wrong order, which pushes the minimum to at least 87 moves. Solving it row by row, the method from our guide, takes 197 moves on this board. Tile 15 has the longest trip home: 6 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.