Problem 8
A Halloween Puzzler:
Last night, I went to a Halloween Party dressed as Zorro, with the hopes of amazing my friends with my excellent swordsmanship.
Much to my chagrin, my costume was not unique! Four others had come with the exact same costume. Without removing any masks (as that would take the fun out of the problem), can it be determined whether, in the group of 5 Zorros, there exist either a group of 3 mutual acquaintances
or a group of 3 mutual strangers?
To generalize, true or false: in a group of 5 people, there
must be a group of either 3 mutual acquaintances or a group of 3 mutual strangers.
Provide justification for your answer! If you believe it is true, provide justification. If you believe it is false, provide a counter-example.
Hint:
With a problem like this, drawing a picture helps. I've started you off. If you choose to give examples, use the picture as a basis (e.g. - the graph where A knows B, B knows C, and C knows A produces 3 mutual acquaintances).
