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ANSWER


While there may be longer, more redundant paths, the shortest path requires 44 moves by the king. Note that all moves involving a capture are indicated by an "x" in front of the square.

Ka8 - b7 - c6 - xd5 - c6 - xc7 - c6 - d5 - e5 - f4 - g5 - h6 - xg7 - f7 - xe8 - f7 - g7 - h6 - g5 - xf5 - e4 - d3 - e2 - d1 - c1 - xb1 - xc2 - d1 - xe1 - d2 - c3 - b4 - xa5 - a6 - b7 - xc8 - b7 - xa7 - b6 - c5 - d4 - e3 - f2 - g1 - h1