15 boys and 15 girls
Source: Russian 2007
September 6, 2007
linear algebramatrixinductiongraph theorycombinatorics proposedcombinatorics
Problem Statement
In the class, there are boys and girls. On March , some boys made phone calls to some girls to congratulate them on the holiday ( each boy made no more than one call to each girl). It appears that there is a unique way to split the class in pairs (each consisting of a boy and a girl) such that in every pair the boy has phoned the girl. Find the maximal possible number of calls.