300 parliament members are divided into 3 chambers of 100 each
Source: 2010 Indonesia TST stage 2 test 1 p4
December 16, 2020
combinatorics
Problem Statement
parliament members are divided into chambers, each chamber consists of members. For every members, they either know each other or are strangers to each other.Show that no matter how they are divided into these chambers, it is always possible to choose members, each from different chamber such that there exist members from the third chamber so that all of them knows these two members, or all of them are strangers to these two members.