The shortest solution consists of 31 moves.*
When the tiles are numbered from 1 through 8 as it is shown in the Start position above, then the solution sequence can look like (U-up, R-right, L-left, D-down):
7D, 6L, 5D, 4DR, 2R, 3RU, 8UL, 3D2, 2L, 5U2, 6RU, 7UR, 3RD, 2D, 5L2, 1DR, 5RU, 2U, 7L2, 6DL, 4LD, 1DR, 2R, 7U2, 6LU, 4L2, 2D, 7R2, 6U, 5D, 8R.
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*The minimal number of moves has been proved with the help of Taniguchi's
Sliding Block Puzzle Solver.
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