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