MathDB

22

mathematicians are meeting together. Each mathematician has at least

3

friends (friends are mutual). And each mathematician can pass his or her information to any mathematician through the transfer between friends. Is it possible to divide these

22

mathematicians into

2

-person groups (that is, two people in each group, a total of

11

groups), so that the mathematicians in each group are friends?
[hide=original wording in Chinese]仃22位数学家一起开会.每位数学家都至少有3个朋友(朋友是相互的).而且每位数学家都可以通过朋友之间的传递.将门已的资料传给任意一位数学家.问：是否一定可以将这22位数学家两两分组(即每组两人,共11组),使得每组的数学家都是朋友？

Problem Statement