11 persons who were attending a meeting shook hands with each other. What is the total number of hand shakes that took place?

When thinking about complex problems, it’s useful to scale down.

Let’s imagine that there are 5 people at the conference.

Person #1 can shake hands with #2, #3, #4 and #5. Person #2 can shake hands with the latter three (they can’t shake with #1, as they’ve already shaken hands.) Person #3 can shake with #4 and #5, and Person #4 can only shake with #5.

That means that with five people, the number of handshakes is 4 + 3 + 2 + 1 = 10 handshakes.

Now we’ll scale it up.

12 people shaking hands, so 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 66 handshakes. This is less than you might expect, but otherwise, people would be shaking hands with the same person more than once.

But wait! The question says that they shake hands after the meeting as well!

This bit’s easy to take into account. Just multiply 66 by 2, and you get 132 handshakes, and that’s your answer.