MathDB

3

Part of 2022 JBMO TST - Turkey

Problems(1)

29 peoples attending a party, replacing a hat of a person

Source: 2022 Turkey JBMO TST P3

3/15/2022
Each of the 2929 people attending a party wears one of three different types of hats. Call a person lucky if at least two of his friends wear different types of hats. Show that it is always possible to replace the hat of a person at this party with a hat of one of the other two types, in a way that the total number of lucky people is not reduced.
combinatorics