The $$ sliding$-$tile puzzle $$ consists of three black tiles, three white tiles, and an empty space in some order. The goal is to arrive at the

goal configuration shown below by legal moves $[$B$-$ Black tile, W$-$White tile$].$

B

B

B

W

W

W

The puzzle has two legal moves with associated costs

Move #$1$ : A tile may move into an adjacent empty location. This has a cost of $1.$

Move #$2$ : A tile can hopover one or two other tiles into the empty position. This has a cost equal to the number of tiles

jumped over