Difference between revisions of "2007 IMO Problems/Problem 3"
(New page: <h2>Problem</h2> 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 particul...) |
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| + | The Nottingham Tuesday Club members solved this problem and published their solution in their website. The solution is a PDF document. | ||
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| + | <ul> | ||
| + | <li><a href="http://sneezy.cs.nott.ac.uk/tmc/wp-content/uploads/2007/10/cliqueproblem.pdf">TMC Solution to Problem 3, IMO 2007</a></li> | ||
| + | <li><a href="http://sneezy.cs.nott.ac.uk/tmc">TMC webpage</a></li> | ||
| + | </ul> | ||
Revision as of 09:01, 28 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
The Nottingham Tuesday Club members solved this problem and published their solution in their website. The solution is a PDF document.
- <a href="http://sneezy.cs.nott.ac.uk/tmc/wp-content/uploads/2007/10/cliqueproblem.pdf">TMC Solution to Problem 3, IMO 2007</a>
- <a href="http://sneezy.cs.nott.ac.uk/tmc">TMC webpage</a>
