MathDB

At a conference there are

n

mathematicians. Each of them knows exactly

k

fellow mathematicians. Find the smallest value of

k

such that there are at least three mathematicians that are acquainted each with the other two.
[color=#BF0000]Rewording of the last line for clarification: Find the smallest value of

k

such that there (always) exists

3

mathematicians

X,Y,Z

such that

X

and

Y

know each other,

X

and

Z

know each other and

Y

and

Z

know each other.

Problem Statement