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Jumping Isn't Everything
The applet above helps you experiment with the problem. Click on the counter you wish to move and then click on the empty space where you want to place the counter. 
SolutionThe task is impossible for an N×(N + 1) board with N odd as becomes clear from the following diagram
The counters originally located on the black spots will always stay on the black spots. The problem is there are six of them on the left and only three on the right. Observe that removing up front one or two counters on the left still would not allow one to move the remaining ones to the right. What happens when N is even I do not know yet? Reference
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