49. 48 people {a1, a2,...... a48) meet and shake hands in a circular fashion. In other words, there are totally 48 handshakes involving the pairs, {a1, a2}, {a2, a3}, ...{a47, a48}, {a48, a1}. Then the size of the smallest set of people such that the rest have shaken hands with at least one person in the set is
O 16
O 24
O 17
O 15

• Ans: 16 (Quite popular and common question!)
  Thought process:
  It is said to form the smallest subset, look here:
  a2 shakes hand with a1 & a3.
  a4 shakes hand with a3 & a5.
  a6 shakes hand with a5 & a7.
  - - - - - - - - - - - - - -
  
  - - - - - - - - - - - - - -
  a48 shakes hand with a47 & a1 and likewise in circular manner.
  
  So the smallest possible selection would be to select from the set of these 3 elements, {a1,a2,a3}..and so on..
  This was just the analysis, now the trick!
  
  Trick:
  N/3 where N=Number of people in the meeting(and not the number of handshakes!)
  So, 48/3 = 16
  
• 10 years agoHelpfull: Yes(24) No(1)
• 16 ( a1,a2,a3) If we take in set of three persons. Since it is cyclic order.
  Therefore, at one person has handshaked with the other person.
  48//3= 16
  Ans is 16
• 10 years agoHelpfull: Yes(3) No(1)