Question

At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?

Answer 1

132 people.
A handshake takes two people, so therefore:
$$66 \times 2 = 132$$

Answer 2

there aren't 132 people

Answer 3

Did I mess something up?

Answer 4

yeah, it's not 66x2. for example 2 people have 1 handshake, 3 people have 3 handshakes, 4 people have 6

Answer 5

Say we had 4 people: A, B, C, D

We can write up a table like so

Answer 6

Cross out the cells along the diagonal (since A can't shake hands with him/herself, B can't either, etc etc)