Notes on this puzzle
Fifteen #5302 is a 4×4 board with 15 numbered tiles and one gap, which starts in row 2, column 3. 2 tiles start in their home squares.
Add up how far each tile is from its home square and you get 33. 2 pairs of tiles already sit in their correct line but in the wrong order, which pushes the minimum to at least 37 moves. Solving it row by row, the method from our guide, takes 77 moves on this board. Tile 4 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.