Difference between revisions of "2007 IMO Problems/Problem 3"
m (→Solution: template) |
|||
| Line 3: | Line 3: | ||
==Solution== | ==Solution== | ||
| − | * [http://sneezy.cs.nott.ac.uk/tmc/wp-content/uploads/2007/10/cliqueproblem.pdf Nottingham Tuesday Club solution] | + | * [http://sneezy.cs.nott.ac.uk/tmc/wp-content/uploads/2007/10/cliqueproblem.pdf Nottingham Tuesday Club solution] <-- dead link :( |
{{alternate solutions}} | {{alternate solutions}} | ||
Revision as of 06:44, 8 February 2009
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
- Nottingham Tuesday Club solution <-- dead link :(
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
| 2007 IMO (Problems) • Resources | ||
| Preceded by Problem 2 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 4 |
| All IMO Problems and Solutions | ||
