MathDB

Let a regular polygon with

p

vertices be given, where

p

is an odd prime number. At every vertex there is one monkey. An owner of monkeys takes

p

peanuts, goes along the perimeter of polygon clockwise and delivers to the monkeys by the following rule: Gives the first peanut for the leader, skips the two next vertices and gives the second peanut to the monkey at the next vertex; skip four next vertices gives the second peanut for the monkey at the next vertex ... after giving the

k

-th peanut, he skips the

2 \cdot k

next vertices and gives

k+1

-th for the monkey at the next vertex. He does so until all

p

peanuts are delivered. I. How many monkeys are there which does not receive peanuts? II. How many edges of polygon are there which satisfying condition: both two monkey at its vertex received peanut(s)?

Problem Statement