Notes on this puzzle
Fifteen #5308 is a 4×4 board with 15 numbered tiles and one gap, which starts in row 4, column 3. Not a single tile starts in its home square.
Add up how far each tile is from its home square and you get 41, so no solution can be shorter than 41 moves. Solving it row by row, the method from our guide, takes 91 moves on this board. Tile 14 has the longest trip home: 5 squares.
Where to beginSolve the top row, then the left column, and treat what remains as a 3×3 puzzle.