Two children with the same name in one class
Source: Germany 2016 - BWM Round 1, #4
November 12, 2016
combinatoricscombinatorics unsolvedpigeonhole principlegraph theoryGermanyblackboard
Problem Statement
There are children in a given class. Each child writes a number on the blackboard, which indicates how many other children possess the same forename as oneself. Afterwards, each child does the same thing with their surname. After they've finished, each of the numbers appear at least once on the blackboard.
Prove that there are at least two children in this class that have the same forename and surname.