Consider $n$$(>1)$ spots created around a circle. A man jumps from one spot to another in the following manner. He starts from some selected spot. From there, he skips exactly one spot in the clockwise direction and jumps to the next one. Then skips two spots and jumps to the next and then three spots and so on. He is allowed to visit the same spot more than once. Suppose that after some time he ends up visiting all the spots. Is it possible for the value of $n$ to be odd?
Well, the answer is obviously no. I tried to assume that it is odd and then take "$\mod n$" to prove that all possible remainders will not come. Though that seems to be the right path, I am not able to conclude. Please help!
