Notes on this puzzle
Fifteen #5210 is a 4×4 board with 15 numbered tiles and one gap, which starts in row 4, column 4. 1 tile starts in its home square.
Add up how far each tile is from its home square and you get 20, so no solution can be shorter than 20 moves. The shortest possible solution is exactly 26 moves. Matching it is a real achievement. Solving it row by row, the method from our guide, takes 56 moves on this board. Tile 11 has the longest trip home: 3 squares.
Where to beginTiles are not far from home after this short shuffle; fix one corner, then grow outwards from it.