Difference between revisions of "2007 IMO Problems/Problem 3"
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==Solution== | ==Solution== | ||
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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 15:23, 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 | ||
