Ben from Victoria College, Jersey sent this solution to the first part of the problem:
For a steady drum beat there are four possible ways: 1, 2, 3 or 6 drums equally spaced.That's a very clear way of describing it, Ben, thank you.
For the second part of the problem, some of you may have worked out that a rhythm will sound the same forwards as backwards only if you arrange the drums symmetrically. There are only two ways of placing 3 drums symmetrically on 6 points:
Finally with 5 drums, there is only one rhythm that you can make, as moving the drums around just creates the same sequence with only one empty space. However this arrangement is symmetrical so it does sound the same forwards as backwards:
