Difference between revisions of "2008 USAMO Problems/Problem 6"

(create template)
 
(Fixed link)
Line 12: Line 12:
 
{{USAMO newbox|year=2008|num-b=5|after=Last Problem}}
 
{{USAMO newbox|year=2008|num-b=5|after=Last Problem}}
  
* <url>Forum/viewtopic.php?t=202908 Discussion on AoPS/MathLinks</url>
+
* <url>viewtopic.php?t=202908 Discussion on AoPS/MathLinks</url>
  
 
[[Category:Olympiad Combinatorics Problems]]
 
[[Category:Olympiad Combinatorics Problems]]

Revision as of 19:58, 1 May 2008

Problem

(Sam Vandervelde) At a certain mathematical conference, every pair of mathematicians are either friends or strangers. At mealtime, every participant eats in one of two large dining rooms. Each mathematician insists upon eating in a room which contains an even number of his or her friends. Prove that the number of ways that the mathematicians may be split between the two rooms is a power of two (i.e., is of the form $2^k$ for some positive integer $k$).

Solution

Solution 1

Solution 2

Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.

Resources

2008 USAMO (ProblemsResources)
Preceded by
Problem 5
Followed by
Last Problem
1 2 3 4 5 6
All USAMO Problems and Solutions
  • <url>viewtopic.php?t=202908 Discussion on AoPS/MathLinks</url>
Invalid username
Login to AoPS