Boys and Girls from Nordic Math Contest 2005
Source: Nordic Mathematical Contest, April 2005, problem 3
April 11, 2005
combinatorics proposedcombinatorics
Problem Statement
There are young people sitting around a large circular table. Of these, at most are boys. We say that a girl has a strong position, if, counting from in either direction, the number of girls is always strictly larger than the number of boys ( is herself included in the count). Prove that there is always a girl in a strong position.