Difference between revisions of "2007 IMO Problems/Problem 3"
m (restore extlink) |
(→Solution) |
||
| (5 intermediate revisions by 3 users not shown) | |||
| Line 3: | Line 3: | ||
==Solution== | ==Solution== | ||
| + | |||
{{solution}} | {{solution}} | ||
| − | == | + | ==See Also== |
| − | |||
{{IMO box|year=2007|num-b=2|num-a=4}} | {{IMO box|year=2007|num-b=2|num-a=4}} | ||
[[Category:Olympiad Combinatorics Problems]] | [[Category:Olympiad Combinatorics Problems]] | ||
Latest revision as of 00:06, 19 November 2023
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
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
| 2007 IMO (Problems) • Resources | ||
| Preceded by Problem 2 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 4 |
| All IMO Problems and Solutions | ||
