The Frog Problem
Five points on a circle are numbered 1, 2, 3, 4, 5 in clockwise order. A frog jumps in the clockwise order from one number to another as follows: If it is at the odd number it moves one place. If it is at even number it moves two places. If the frog is initially at 5, where it will be after 2010 jumps?
The answer is 4.
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1 solution
First step takes it to 1. From there it repeats: 2, 4, 1, 2, 4, 1, etc. So there are only three locations per circle and there are 2009 jumps going round and round this circle. The remainder after 2009 is divided by 3 is 2, so the last circle is only 2, 4. The last location being 4 .