Question

During a party a total of 78 handshakes occurred. If each person shook hands once with each of the other people , how many people were at the party?

Answer 1

`n=13`

Explanation:

Lets say we have `n` people. The first one can shake hands with `n-1` people (everyone, except himself). The next person can shake hands with `n-2` (everyone, except person 1 and himself). The one after that with `n-3` and so on. So the sum would be:
`1+2+3+4...+(n-2)+(n-1)="total sum of handshakes"`
This can be expressed by:
`((n-1)n)/2="total sum of handshakes"`
`((n-1)n)/2=78|*2`
`(n-1)n=156`
`n=13`