Count The Number of People From Handshakes

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

Skip to the count!

Getting Count of Number of Peoples From Handshakes

Want to read question first? Click here!

Let's suppose that there are 'n' number of people in the party.

The first person will shake hand with (n-1) people, the second person will shake hand with (n-2) people, the third will shake hand with (n-3) people.

In this way, (n-1) th person will shake hand with n-(n-1) = 1 person i.e. last person.

Adding all the number of handshakes,

(n-1) + (n-2) + (n-3) + ..... + 3 + 2 + 1 = n[(n-1)/2]

But total handshakes given are - 66

n[(n-1)/2] = 66

n(n-1) = 132

n^2 - n - 132 = 0

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

n = 12 or n = -11

Since number of people can't be negative, n = 12.

Hence there are 12 people in the party.

Simple Logical Mathamatical Problem

There are 5 people who can build 5 houses in just 5 days.
 
How long would it take 100 people to build 100 houses?

100? Really? Check back or click here!

Answer Of Simple Logical Mathematical Problem

Want to read the question first? 

Did you answer 100?

"There are 5 people who can build 5 houses in just 5 days."

The above statement suggests that 1 man takes 5 days to build 1 house & not 1 man take 1 day to construct 1 house.

So 100 people will make 100 houses in only 5 days as each one completing the task in 5 days!