The Pond

In a pond, 6 stones are arranged in a circle. A frog sits on one of the stones. It jumps clockwise, first 2 stones forward, then 5, then 3, then 1, and finally 4 stones forward. In doing so, the frog visits each stone exactly once, never lands twice on the same stone, and has jumps which are all of different sizes.

If the frog had jumped in the order 1, 2, 3, 4, 5, it would have landed back on its starting stone after the third jump. And with the order 1, 4, 5, 3, 2, the fourth jump would land on the same stone as the first jump.

The jump sequence 2, 5, 3, 1, 4 can be written as 25314. We call this a ‘frog jump number’ for 6 stones. Note: the frog cannot jump further than a full circle.