At a party, everyone shook hands with everybody else. There were 66 handshakes.
How many people were at the party?  Choices.
A) 15	B) 18	C) 11	D) 12	E) 19
D   12   If there are n people,   the first person will shake hand with n-1 persons,   the second with n-2,   the third with n-3,   and   the (n-1)th person with n-(n-1)=1 person means the last person.   Hence, total handshakes are (n-1)+(n-2)+(n-3)+….+3+2+1   Which can be equated using n(n-1)/2 -( -1)= 
<gadget id="calculator"> -( -1)</gadget>
<output>1</output>
1 person means the last person.   Hence, total handshakes are (n-1)+(n-2)+(n-3)+….+3+2+1   Which can be equated using n(n-1)/2=66   Hence, n=12
<result>D</result>
At a party, everyone shook hands with everybody else. There were 66 handshakes.
How many people were at the party?