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