MathDB

1

Part of 1993 Flanders Math Olympiad

Problems(1)

easy combinatorics

Source: flanders '93

9/27/2005
The 20 pupils in a class each send 10 cards to 10 (different) class members. [note: you cannot send a card to yourself.] (a) Show at least 2 pupils sent each other a card. (b) Now suppose we had nn pupils sending mm cards each. For which (m,n)(m,n) is the above true? (That is, find minimal m(n)m(n) or maximal n(m)n(m))
pigeonhole principle