At the party everyone shook Hand with everybody else. There are 66 handshakes. How many peoples were at the party
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Let there be 'n people.
Since everyone shook hand with everybody else, there would be n*(n-1)/2 hand shakes.
Total hand shakes = 66
66 = n*(n-1) /2
66*2 = n(n-1)
11*6*2 = n(n-1)
12*11 = n(n-1)
on comparing, n=12, n-1=11
Hence, n= 12 = Number of people
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