### Getting Count of Number of Peoples From Handshakes

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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.

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