Notes on this puzzle
Fifteen #5102 is a 3×3 board with 8 numbered tiles and one gap, which starts in row 2, column 3. 1 tile starts in its home square.
Add up how far each tile is from its home square and you get 15, so no solution can be shorter than 15 moves. The shortest possible solution is exactly 25 moves. Matching it is a real achievement. Tile 1 has the longest trip home: 4 squares.
Where to beginOn the small board, think two or three moves ahead and look for short cycles that bring two tiles home together.