MathDB

3

Part of 2011 Flanders Math Olympiad

Problems(1)

18 students in a class

Source: Flanders Math Olympiad 2011 p3

12/24/2022
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.
combinatorics