## IMC 2011 Day 2 Problem 2

An alien race has three genders: male, female and emale. A married triple consists of three persons, one from each gender who all like each other. Any person is allowed to belong to at most one married triple. The feelings are always mutual ( if likes then likes ).

The race wants to colonize a planet and sends males, females and emales. Every expedition member likes at least persons of each of the two other genders. The problem is to create as many married triples so that the colony could grow.

a) Prove that if is even and then there might be no married triple.

b) Prove that if then there can be formed married triple ( i.e. everybody is in a triple).

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I think this problem is not the case in question a), may be k> = n / 2 rather than k> = 1 / 2. Be sure to check back and see more here http://www.mathdoi.com/2011/07/de-thi-olympic-toan-sinh-vien-quoc-te-nam-2011-imc-2011-problems-of-2st-day/

Yes, you are right. There was instead of . Thank you for your correction.