# 2010 IMO Problems/Problem 5

## Problem

Each of the six boxes , , , , , initially contains one coin. The following operations are allowed

Type 1) Choose a non-empty box , , remove one coin from and add two coins to ;

Type 2) Choose a non-empty box , , remove one coin from and swap the contents (maybe empty) of the boxes and .

Determine if there exists a finite sequence of operations of the allowed types, such that the five boxes , , , , become empty, while box contains exactly coins.

*Author: Unknown currently*