If the positions are marked like the numbers of the clock: "0 1 2 ... 11" Then with n = 5, the bags are placed like: "0 5 10 15 20 25 30 ..." which modulo 12

If the positions are marked like the numbers of the clock: "0 1 2 ... 11" Then with n = 5, the bags are placed like: "0 5 10 15 20 25 30 ..." which modulo 12 becomes: "0 5 10 (15-12) (20-12) (25-2*12) 6 ..." = "0 5 10 3 8 1 6 ..." As 5 and 12 have no common divisors, all positions will be occupied. Cheers