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Introductions all around (Posted on 2013-06-14) Difficulty: 4 of 5
The town of Friendville has an interesting property. Given any two people in the town, they either know each other or they don't. If they don't know each other, then they can be introduced to each other. One single introduction will work for both people. That is, "Tom this is Phil, Phil this is Tom" counts as one introduction.

The other interesting property that this town has, is that if any group of n people get together, the number of introductions that must be made in order that everyone in the group knows everyone else is at most n-1.

Problem: Prove that the town can be divided into two groups (A and B) such that everyone in group A knows each other, and everyone in group B knows each other.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 3.0000 (1 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(3): SolutionDan Rosen2013-06-22 12:55:03
re(2): SolutionDan Rosen2013-06-22 12:51:32
re: SolutionDan Rosen2013-06-22 09:10:40
SolutionSolutionDan Rosen2013-06-22 07:26:56
Some ThoughtsIt's not who you know, but who you don't know, that's important.broll2013-06-16 13:14:42
re(2): Possible solutionbroll2013-06-15 11:46:30
Some Thoughtsre: Possible solutionSteve Herman2013-06-15 11:05:08
Possible solutionbroll2013-06-15 08:42:22
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