MathDB

Around a round table the people

P_1, P_2,..., P_{2013}

are seated in a clockwise order. Each person starts with a certain amount of coins (possibly none); there are a total of

10000

coins. Starting with

P_1

and proceeding in clockwise order, each person does the following on their turn:
[*]If they have an even number of coins, they give all of their coins to their neighbor to the left.
[*]If they have an odd number of coins, they give their neighbor to the left an odd number of coins (at least

1

and at most all of their coins) and keep the rest.
Prove that, repeating this procedure, there will necessarily be a point where one person has all of the coins.

Problem Statement