12 Counters on a Clock

1. Twelve counters are placed on the numbers of a clock face - white counters on one through six, and black counters on seven through twelve. Taking up one black counter at a time, pass it over two counters and place it on a third; in only six of these moves, repeat this operation until there is one black counter on each of the six white counters. Moves may be made in either direction round the circle and black counters may jump over either two individual counters, or one pile of two counters.
2. Same question with the black counters on the odd numbers.
3. Same question with the black counters on 1,2,5,6,9,10.
4. Same question with the black counters on 1,2,3,7,8,9. (Can this be done?)

Source: 1. Puzzlegrams, Pentagram Design Limited, 1989, #172. Used as Ken's Puzzle of the Day 8/15/94. 2-4:Original.