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

• 12 people.
  n=11 (when there are 12 people, there will be only 11 hand shake)
  For checking it=n(n+1)/2=11*12/2=6*11=66 shakehands
• 10 years agoHelpfull: Yes(1) No(0)
• If there are 4 people the number of hand shakes will be:
  3 (first person shakes hand with every one except with himself) +
  2( second person shakes hand with every one except himself and the first 1)=
  1(third person shakes hand with only last person )+
  0 (as last person has already shook hands with every 1)
  so total number of hand shakes=3+2+1+0=6=3*4/2=n(n+1)/2 (Sum of natural number)
  Substitute n(n+1)/2=66, you get 11.
  Now add 1 as for the last person as person.
  So the answer is 12.
• 10 years agoHelpfull: Yes(1) No(0)
• n(n-1)/2=66
  n(n-1)=132
  then n value is 12.
• 10 years agoHelpfull: Yes(0) No(0)