Shakehands!

Probability Level 2

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

6 8 33 12

Δημήτρης Μάνος by Δημήτρης Μάνος , 34, Greece

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3 solutions

The first person shakes hand with 11 people. The second person with 10 people. (he already shook hand with the first.) The 3rd person with 9 people and so on.

So we have:

11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 66 11+10+9+8+7+6+5+4+3+2+1= \boxed{66}

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Sarthak Rath
Sep 13, 2015

( n 2 ) {n \choose 2} = 66

so, by solving this,

n(n-1) = 132

n 2 − n − 132 = 0 n^2 - n - 132 = 0

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

n=12,-11

-11 isn't possible as no. of handshakes can't be negative,

hence, n = 12 \boxed{n=12}

1 Helpful 0 Interesting 0 Brilliant 1 Confused

Solved it exactly the same way. :)

P.S. No. of people can't be negative.

Tapas Mazumdar - 4 years, 8 months ago
Fox To-ong
Jan 13, 2015

that's a quadratic eq. where a = 1,b= -1 and c = -132 the root = 12

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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