If there are 15 people at a meeting and they all shake hands with each other how many handshakes will occur?

Question

If there are 15 people at a meeting and they all shake hands with each other how many handshakes will occur?

Answer 1

15 * 15= 225

Answer 2

Assume person #1 starts, by shaking hands with people #2-15. That's 14 handshakes.

Now move on to person #2. He's already shaken hands with person #1, so he just has to shake hands with #3-15. That's 13 handshakes.

Person #3 shook hands with #1 and #2 already, so he just has to shake hands with #4-15. That's 12 handshakes.

Get the pattern?

14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 105.

Edit- since this answer has popped up twice now, I'll explain why it's incorrect: The answer is NOT 15² (225). That would mean all 15 people would each have to shake hands 15 times each... which would involve everyone shaking hands with everyone else twice, as well as shaking hands with himself! Ever tried to shake your own hand? It's pretty awkward. :<

Answer 3

225 is obviously the answer!

Answer 4

One person shakes hands with everyone; then "remove" that person mentally.

So 14

Plus 13

Plus 12

-- you can probably see where I'm going with this.

Answer 5

i need to get my super dynamic speed calculator ahaha ^_^

Answer 6

15!

Answer 7

Mayyybbee I'm wrong, but 15*2, which equals 25. Because, ( Well, my reasoning) Each person has to have one handshake. Oh well, rely on another answer.