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Consider first-passage percolation on the square lattice. Hammersley and Welsh, who introduced the subject in 1965, conjectured that the expected minimum travel time from (0, 0) to (n, 0) along paths contained in the cylinder 
is always non-decreasing in n. However, when the bonds have time-coordinate 1 with probability p and 0 with probability 1 – p (0 < P < 1), then, for p sufficiently small, we get a counterexample.
