33 students
Source: ARMO 1997, 9.6
April 20, 2013
combinatorics proposedcombinatorics
Problem Statement
A class consists of 33 students. Each student is asked how many other students in the class have his first name, and how many have his last name. It turns out that each number from 0 to 10 occurs among the answers. Show that there are two students in the class with the same first and last name.
A. Shapovalov