🚀 go-pugleaf

X-Orig-MsgId: <848v1u$9up$1@news1.bu.edu>


1. Prove that the number of people in the world, at any given time,
who have shaken hands with an odd numer of people (1,3,5,..)
is even (0,2,4,..)
 
2. Prove that in a group of six people there exists either a) a
group of three who dont know each other or b) a group of three 
who all know each other or c) both a and b.

3. prove that in a group of n people (n=1,2,3,..) there are atleast
two people who are acquainted with the same number of people within the
group

4. given 2n people (n=1,2,3,..) where each person knows atleast n-1 people
show that there can be an arrangement of four people on a round table where
each person does not know the person at his side but knows the person 
on the opposite side.

happy puzzling!