Here's a problem I recently saw (not my own):

In a group of 20 people, each person bears a grudge against exactly one other person in the group. No matter how these grudges are arranged (multiple people can bear a grudge against the same person), is it always possible to break the 20 people into three smaller groups such that no one bears a grudge against anyone in their own group?

Note: I will give the source of this problem after a correct (and hopefully a well-explained) answer has been given. I haven't got a proof myself.

Here's a problem I recently saw (not my own):

In a group of 20 people, each person bears a grudge against exactly one other person in the group. No matter how these grudges are arranged (multiple people can bear a grudge against the same person), is it always possible to break the 20 people into three smaller groups such that no one bears a grudge against anyone in their own group?

Note: I will give the source of this problem after a correct (and hopefully a well-explained) answer has been given. I haven't got a proof myself.

Source (where I found this problem): Grudge Problem