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Pairs of opponents in a parliament !!

Source: Romania TST 2015 Day 3 Problem 4

June 4, 2015
combinatoricsRomanian TSTgraph theory

Problem Statement

Given two integers h≥1h \geq 1 and p≥2p \geq 2, determine the minimum number of pairs of opponents an hphp-member parliament may have, if in every partition of the parliament into hh houses of pp member each, some house contains at least one pair of opponents.
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