people at party

Algebra Level 1

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


The answer is 12.

Aditya Raj by Aditya Raj , 22, India

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4 solutions

Since n(n-1)/2 = 66, n=12

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Simple . if there are n people the total number of shakehands will be n combination 2.. so n*(n-1 /2 =66 so n=11.)

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Supathat Sukaiem
Jun 10, 2014

I don't know any formula but I know the number of handshakes by...

If n is number of people, the number of handshakes is just

n + (n-1) + (n-2) + ... + 1

Then I try to guess and finally get n = 12

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Aditya Raj
Mar 16, 2014

Solution: 12 In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n. Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66. This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.

Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.

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