Party shakes

Probability Level 1

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

33 19 12 6

Intisar Hassan by Intisar Hassan , 24, United Kingdom

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1 solution

The total number of handshakes must be equal to ( n 2 ) \binom{n}{2} , so we can make an expression, ( n 2 ) = 66 ⇒ n ( n − 1 ) 2 = 66 ⇒ n 2 − n − 132 = 0 \binom{n}{2} = 66 \Rightarrow \frac{n(n-1)}{2}=66 \Rightarrow n^2-n-132=0 Solving which we get the answer as, n = 12 n = \boxed{12}

1 Helpful 0 Interesting 0 Brilliant 1 Confused

It's 12 not 2.

Pi Han Goh - 5 years, 9 months ago

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Thanks for telling my error.Ive edited my solution.

Athiyaman Nallathambi - 5 years, 9 months ago

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