Question

At a business meeting each person shook hands with every other person exactly once. If there were fifteen handshakes, can you tell how many people attended the meeting?

Answer 1

6 people

Explanation:

15 is the sum of the series from 1 to 5.

What we're doing is finding the sum of 1 to n-1, where n is the number of people. The sum is equal to `(n(n-1))/2`
So we can solve for n.
`15 = (n(n-1))/2`
`15 = (n^2 - n)/2`
`30 = n^2 - n`
`n^2 - n - 30 = 0`
`(n+5)(n-6) = 0`

So n can equal -5 (not possible) or 6.