At a party, everyone must shake the hand of the other. If the total number of handshakes is 66, there are ----people at the party.

To find the number of people at the party, we can use the following formula for calculating the total number of handshakes in a group:

Total handshakes = (n * (n - 1)) / 2

Where "n" is the number of people at the party.

Given that there were 66 handshakes, we can set up the equation:

66 = (n * (n - 1)) / 2

Now, let's solve for "n." First, multiply both sides by 2 to remove the fraction:

2 * 66 = n * (n - 1)

132 = n^2 - n

Now, rearrange the equation:

n^2 - n - 132 = 0

We have a quadratic equation, and we can factor it:

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

Setting each factor equal to zero:

n - 12 = 0 n = 12

n + 11 = 0 n = -11

Since the number of people cannot be negative, we discard the negative solution.

Therefore, there were 12 people at the party.

The correct answer is 12.