Difference between revisions of "2007 IMO Problems/Problem 3"

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==Solution==
 
==Solution==
 
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==External links==
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* [http://sneezy.cs.nott.ac.uk/tmc/wp-content/uploads/2007/10/cliqueproblem.pdf Nottingham Tuesday Club solution]
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{{IMO box|year=2007|num-b=2|num-a=4}}
 
{{IMO box|year=2007|num-b=2|num-a=4}}
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[[Category:Olympiad Combinatorics Problems]]
 
[[Category:Olympiad Combinatorics Problems]]

Revision as of 16:23, 29 October 2007

Problem

In a mathematical competition some competitors are friends. Friendship is always mutual. Call a group of competitors a clique if each two of them are friends. (In particular, any group of fewer than two competitors is a clique.) The number of members of a clique is called its size. Given that, in this competition, the largest size of a clique is even, prove that the competitors can be arranged in two rooms such that the largest size of a clique contained in one room is the same as the largest size of a clique contained in the other room.

Solution

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External links

2007 IMO (Problems) • Resources
Preceded by
Problem 2
1 2 3 4 5 6 Followed by
Problem 4
All IMO Problems and Solutions