Senators are arranged in 10 parties and committees
Source: Romanian IMO Team Selection Test TST 2003, problem 13
September 24, 2005
combinatorics proposedcombinatorics
Problem Statement
A parliament has senators. The senators form 10 parties and 10 committees, such that any senator belongs to exactly one party and one committee. Find the least possible for which it is possible to label the parties and the committees with numbers from 1 to 10, such that there are at least 11 senators for which the numbers of the corresponding party and committee are equal.