₦airaland Forum

Got this question in an interview recently that got me puzzled
"If everybody at a party shook hand with each other and there are total of 66 handshakes, How many people attended the party ? Am sure there are gurus in the house

12 people

Godwin0420:
12 people

please how come

Godwin0420:
12 people

correct, oga boss na you o

caljulator:
please how come

I really want godwin0420 to explain how he got the answer. I know for a fact that he is right, you can confirm by solving it backwards.
I also solved it myself but it took me a whole lot of time and I don't know how to explain it well, I sha developed this method and i'm pretty sure it works for all cases though it is a bit cumbersome and lengthy
1+2+...+(x-1) = y,
where x is the number of people in the party and y is the total number of handshakes. assuming the total number of people shaked each other just ones.

so therefore we have, 1+2+3+4+5+6+7+8+9+10+11=66,
from this you can infer that (x-1)=11,
so therefore x = 12,
it works for all cases,
e.g if we had 6 hand shakes in all it means
1+2+3=6,
so therefore (x-1)=3, then x =4,
e.g2 if we had 10 handshakes in all it means
1+2+3+4=10,
so therefore (x-1) = 4, then x = 5.

I know there must be an easier way to this, oga godwin show us the way. This method above took me time to develop.

so just keep adding starting consecutively from 1till you get the total number of handshakes, keeping in mind that the last number is equal to x-1. or simply just add 1 to the last number.

there definitely has to be an easier way, maybe through combination and permutation.

The total number of handshakes= n(n-1)/2 where n is the number of people involved.

I really want godwin0420 to explain how he got the answer. I know for a fact that he is right, you can confirm by solving it backwards.
I also solved it myself but it took me a whole lot of time and I don't know how to explain it well, I sha developed this method and i'm pretty sure it works for all cases though it is a bit cumbersome and lengthy
1+2+...+(x-1) = y,
where x is the number of people in the party and y is the total number of handshakes. assuming the total number of people shaked each other just ones.

so therefore we have, 1+2+3+4+5+6+7+8+9+10+11=66,
from this you can infer that (x-1)=11,
so therefore x = 12,
it works for all cases,
e.g if we had 6 hand shakes in all it means
1+2+3=6,
so therefore (x-1)=3, then x =4,
e.g2 if we had 10 handshakes in all it means
1+2+3+4=10,
so therefore (x-1) = 4, then x = 5.

I know there must be an easier way to this, oga godwin show us the way. This method above took me time to develop.