For x, y ∈ {0, 1} n , define d(x, y) as the length of the longest consecutive run of differing bits in corresponding positions of x and y—that is, d(x, y) := max {j − i : for all k = i, i + 1, . . . ,...

For x, y ∈ {0, 1} n , define d(x, y) as the length of the longest consecutive run of differing bits in corresponding positions of x and y—that is, d(x, y) := max {j − i : for all k = i, i + 1, . . . , j we have xk 6= yk} . For example, d(01000, 10101) = 3 and d(00100, 01010) = 3 and d(01000, 10000) = 2 and d(11010, 01000) = 1. Is d a metric?