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

(Solution)
(Solution)
 
Line 4: Line 4:
 
==Solution==
 
==Solution==
  
{{alternate solutions}}
+
{{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