Prove that any group of six people contains either 3 mutual friends or 3 mutual strangers.

(For the purpose of this problem any pair of people must be either friends or strangers.)

(In reply to possible solution? by calla tah-n)

also... forgot to add this lah...
if there are three groups...
say:
2-2-2 or 1-2-3
then there will be three mutual strangers, in the second case possibly 3 mutual friends...
if four groups (1-2-1-1) than there are 3 mutual strangers, person A does not know B, C, and D; person E will also not know persons B, C, and D
if all are strangers then obviously by the above way they will be several sets of mutual strangers
for example: A and B: C,D,E
A,C: B,D,E
A,D: B,C,E... so on and so forth

Posted by calla tah-n on 2003-05-22 20:59:50