Question

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

Answer 1

66?

Answer 2

idk

Answer 3

33?

Answer 4

idk

Answer 5

@jc17 A handshake is when two people shake hands. So just divide 66 by 2 and you have your answer.

Answer 6

Ohhh okay thank you

Answer 7

I think I didd that backwards hold on

Answer 8

33?

Answer 9

i think your right because we want to find out the people

Answer 10

@Razor would it be 33 because of to find out how many people we need to divide. Right?

Answer 11

There were 66 handshakes... a handshake should be one thing. A joined component, so.

Answer 12

it's not as simple as dividing by 2

let's suppose you only have 3 people (A, B, and C)

step 1: A shakes hands with B and C ---> 2 handshakes
step 2: B shakes hands with A and C ---> 2 handshakes
step 3: C shakes hands with A and B ---> 2 handshakes

which is 6 so far, however, if you actually look at the hands being shaked, there are duplicates (in the first step, A shakes hands with B and C, which means that B doesn't need to shake hands with A again in step 2
and C shaking hands with A and B is already accounted for in steps 1 and 2

in total, there are only 3 unique handshakes (A+B, A+C, B+C)

Answer 13

extending this logic
for n people, each of those n people shakes hands with (n-1) people, and then you must divide by 2 to eliminate duplicate handshakes

so # of handshakes, for n people = (n)(n-1)/2

since your # of handshakes is 66, (n)(n-1)/2 = 66, and you can solve for n

Answer 14

Ok thank you