Professor Armstrong suggests the following procedure for generating a uniform random permutation:

PERMUTE-BY-CYCLIC (A)

1. n = A.length
2. let B[1. . n] be a new array
3. offset = RANDOM (1, n)
4. for i = 1 to n
5. dest = i + offset
6. if dest > n
7. dest = dest – n
8. B[dest] = A[i]
9. return B

Show that each element A[i] has a 1/n probability of winding up in any particular position in B. Then show that Professor Armstrong is mistaken by showing that the resulting permutation is not uniformly random.