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The hypercube is one of the most versatile and efficient interconnection networks for parallel computation. Let Fv (respectively, Fe) be the set of faulty vertices (respectively, faulty edges) in an n-dimensional hypercube Qn. In this paper, we show that Qn - Fv - Fe contains a fault free path with length at least 2n - 2|Fv| - 1(or 2n - 2|Fv| - 2) between two arbitrary vertices of odd (or even) distance if |Fv| + |Fe| les n - 2, where n ges 3. Since Qn is bipartite of equal-size partite sets, the path is longest in the worst case. Furthermore, since Qn is regular of vertex-degree n, both the number of faults tolerated and the length of a longest fault-free path obtained are worst-case optimal.