In a group of 26 people, is it possible for each person to shake hands with exactly 3 other people?

Question

In a group of 26 people, is it possible for each person to shake hands with exactly 3 other people?

Does anybody know how to solve this?

Answer 1

If you imagine forming a ring of all 26 people such that they form a regular 26-gon; then each person can shake hands with exactly three other people by shaking hands with the person opposite them and to either side of them.

Note that this is the case for any $n$-gon where $n\equiv 0\pmod{2}$ and $n>3$.