MathDB
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

300300 parliament members are divided into 33 chambers, each chamber consists of 100100 members. For every 22 members, they either know each other or are strangers to each other.Show that no matter how they are divided into these 33 chambers, it is always possible to choose 22 members, each from different chamber such that there exist 1717 members from the third chamber so that all of them knows these two members, or all of them are strangers to these two members.