Solutions to Problems 1371 - 1380

Q1371 Consider shuffles of a standard 52-card pack.  (See the article in volume 47 number 3 for terminology and basic information.)  Let rev be the shuffle which reverses the pack - that is, the first card is swapped with the last, the second with the second last, and so on.  As in the article, out denotes the outshuffle.
(a) Write a formula for rev(k) in terms of k; also, write rev as a product of cycles.