A circle is divided into 13 segments, numbered consecutively from 1 to 13. Five fleas called A,B,C,D and E are sitting in the segments 1,2,3,4 and 5. A flea is allowed to jump to an empty segment five positions away in either direction around the circle. Only one flea jumps at the same time, and two fleas cannot be in the same segment. After some jumps, the fleas are back in the segments 1,2,3,4,5, but possibly in some other order than they started. Which orders are possible ? combinatorics unsolvedcombinatorics