Lotus leafs and a frog
Source: ISI Entrance 2014, P8
May 11, 2014
modular arithmeticcombinatorics proposedcombinatorics
Problem Statement
lotus leaves are arranged in a circle. A frog jumps from a particular leaf from another under the following rule:
[*]It always moves clockwise.
[*]From starting it skips one leaf and then jumps to the next. After that it skips two leaves and jumps to the following. And the process continues. (Remember the frog might come back on a leaf twice or more.)
Given that it reaches all leaves at least once. Show cannot be odd.