n names of candidates, elections - All-Russian MO 1999 Regional (R4) 10.7
Source:
September 25, 2024
combinatorics
Problem Statement
Each voter in an election puts names of candidates on the ballot. There are at the polling station urn. After the elections it turned out that each ballot box contained at least at least one ballot, for every choice of the -th ballot, one from each ballot box, there is a candidate whose surname appears in each of the selected ballots. Prove that in at least one ballot box all ballots contain the name of the same candidate.