In a group of 267 people how many friends are there who have an identical number of friends in that group?
A. 266
B. 2
C. 138
D. 202
Answer:B
In a group of 267 people how many friends are there who have an identical number of friends in that group?
A. 266
 B. 2
 C. 138
 D. 202

Explanation: Suppose each of the 267 members of the group has at least 1 friend. In this case, each of the 267 members of the group will have 1 to 267-1=266 friends. Now, consider the numbers from 1 to n-1 as holes and the n members as pigeons. Since there is n-1 holes and n pigeons there must exist a hole which must contain more than one pigeon. That means there must exist a number from 1 to n-1 which would contain more than 1 member. So, in a group of n members there must exist at least two persons having equal number of friends. A similar case occurs when there exist a person having no friends.
