\input zb-basic \input zb-matheduc \iteman{ZMATH 2007b.00419} \itemau{Thorup, Anders} \itemti{The Josefus permutation. (Om Josefus' permutation.)} \itemso{Normat. Nord. Mat. Tidskr. 55, No. 1, 25-36 (2007).} \itemab Summary: It is well-known that any permutation can be presented as a composition of cycles. In fact every permutation has a unique representation, up to order, as a product of disjoint (and hence commuting) cycles. It turns out that the composition $c_n,c_{n-1},\dots,c_2$ where $c_k = (1, 2, 3, \dots, k)$ has a nice and easily found such representation, but surprisingly if the order of the cycles is reversed the problem becomes almost intractable. The elementary nature of the problem gives a good exposure to students, and it has in fact been studied by students over the years. The article is in the nature of a progress report, and the cases of $n = 2^m, 2m-1$ are treated in detail. Surprising connections to other parts of combinatorics are highlighted. \itemrv{~} \itemcc{K20 N70} \itemut{combinatorics; fixed points; cycle types} \itemli{} \end