5 people {a1, a2, ..., a5} are invited to a party. The host and the hostess shake hands with each invitee and also with each other. The invitees shake hands in a circular fashion, i.e. the pairs {a1, a2}, {a2, a3}, ..., {a4, a5}, {a5, a1} shake hands. So, in all there are 16 handshakes. Let S be a set of people such that every pair in S shake hands. The size of S is at most

• ans: 11
  sol: no. of handshakes = no.of people in a group
  total handshakes = 16
  5 hand shakes are given
  so left no. of hand shakes =16 - 5 = 11
  therefore no. of people in s group is = 11
  
  
• 8 years agoHelpfull: Yes(2) No(0)
• ans : 2
  no.of handshakes in circular fashion for a group = no. of person in that group : (condition when person is more than 2)
  total handshakes = 16
  1st group (group of 5 people) handshakes = 5
  left no. of handshakes = 16 - 5 = 11
  suppose: x person in group 's'
  case 1 : when no. of person in group > 2
  total no. of handshakes b/w two group is = 5 * x
  and hand shake in same group is = x
  so, 5*x + x = 11
  6*x = 11
  here x is fraction (impossible )
  so , no. of person in 's' group is
• 8 years agoHelpfull: Yes(0) No(1)