True or ...

[Buck Mulligan]

Tell me whether the following statement is TRUE or FALSE "In a group of
five persons there will always be three persons who know each other, or
three persons who do not know each other."

Before that first tell me whether this statement "In a group of five
people there always exist a person who knows at least three or there
always exist a person who does not know at least three" is TRUE of
FALSE.

[Himanshu Saini]

The second statement sounds true to me.
The first one sounds true too.
Answers please!!

[Buck Mulligan]

Both are false. Try pentagon.

[Balaji Gopalan]

are these called Ramsey numbers??


On Fri, 07 Jan 2005 08:58:50 -0800, Buck Mulligan <subh...@gmail.com> wrote:
>
> Both are false. Try pentagon.
>
>

[Buck Mulligan]

"The Ramsey number R(m,n) gives the solution to the party problem,
which asks the minimum number of guests R(m,n) that must be invited so
that at least m will know each other or at least n will not know each
other. In the language of graph theory, the Ramsey number is the
minimum number of vertices such that all undirected simple graphs of
order v contain a clique of order m or an independent set of order n.
Ramsey's theorem states that such a number exists for all m and n".