"2λ + 1 puzzle" - I variant:
Tile puzzle has 2λ+1 cells. Each cell can be have none or one tile.
In initial state, the most left λ cells contain white tiles, most right
λ cells contain black tiles, and the cell in the middle is empty.
The goal is all white tiles to be moved left of the black ones.
THe position of the empty cell is not important.
Each tile can:
- move to adjacent empty cell (the cost of the action is 1), OR
- jump one or λ-1 cells (the cost of the action is equal to the number of the tiles, that have been skipped).
Note: Suggest solution for the problem when λ=3.