Please comment your solutions, questions and remarks..
This one I learned from Sam Hardwick.
Show that the number of those, who have shaken their hands with others an odd number of times, is even.
Level 1/5
P.S. This lemma has deep applications. I’ll get back to it!
This wording is slightly different and potentially misleading: “all of whom shake hands with each other” doesn’t mean eg. that everyone has shaken hands with everyone else. I think the problem is most elegant with the first sentence simply omitted.
You are right. Thanks. I guess I wanted to emphasize that the size of the group doesn’t matter.