Imagine the six people. Of them, some person X either has at least three friends among the other 5, or at least three strangers.
If X has at least three friends, (call them A, B and C), then either the three of them are all mutual strangers (and satisfy the condition), or at least two of them are friends, and then the these two plus X are the three people that satisfy the condition.
The above paragraph applies likewise to the case where A, B and C are strangers to X. |