At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?

Guest Mar 10, 2019

#1**0 **

To see this, imagine that just 4 people were at the party

The first person shakes 3 hands

The second person shakes 2 hands

The third person shakes 1 hand

The last person has already shaken hands with everybody

So...the number of handshakes between 4 people = (4)(3) / 2 = 6

So....it appears that the number of handshakes between n people is just n(n - 1) /2

So.....we can solve this

n(n - 1) / 2 = 66 multiply both sides by 2

n(n - 1) = 132 simplify

n^2 - n = 132

n^2 - n - 132 = 0 factor

(n - 12) ( n + 11) = 0

Setting each factor to 0 ans solving for n ives n = -11 (reject) or n = 12 (accept)

So....there wqere 12 people

CPhill Mar 10, 2019