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18 students in a class

Source: Flanders Math Olympiad 2011 p3

December 24, 2022
combinatorics

Problem Statement

There are 1818 students in a class. Each student is asked two questions: how many other students have the same first name as you and how many other students have the same surname as you. The answers 0,1,2,...,70, 1, 2, . . ., 7 all occur. Prove that there are two students with the same first name and last name.
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