MathDB

10.7

Part of 1999 All-Russian Olympiad Regional Round

Problems(1)

n names of candidates, elections - All-Russian MO 1999 Regional (R4) 10.7

Source:

9/25/2024
Each voter in an election puts nn names of candidates on the ballot. There are n+1n + 1 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 (n+1)(n + 1)-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.
combinatorics