Question

There is a Congressman from Texas who lives in my neighborhood. He always introduces himself and shakes hands with everyone he meets-that's a politician for you! He went to a party and encouraged everyone to shake hands with everyone else. I was there and observed the following: when there were two people, they shook each others hand, so that was 1 handshake. When three people shook hands, there were three handshakes. When four people shook hands, there were six handshakes. Suppose that this was a big fundraiser for the Congressmen, and 105 people were there.
How many handshakes were there am

Answer 1

*among those 105 people?

Answer 2

5460 handshakes.
How? lets see this:
The number of handshakes is equal to the sum of the digits from 1 to n when n +1 is the number of people involved. You can see this from:

If there are 105 people:
1st person shakes with 104 people
2nd person shakes with 103 other people because they've already shook with the first person.
3rd person shakes with 102 other people because they've already shook with the first two people.
.
.
.
103rd person shakes with 2 other people
104th person shakes with 1 other person

So the total handshakes is the sum of 1 + 2 + ...+ 102 + 103 + 104 = 104(105)/2 = 5460

Answer 3

got it ? :)

Answer 4

Omg thank you. Yeah that makes sense. (:

Answer 5

my pleasure :)