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18 July, 14:02

Show that in any group of 101 people there are at least two persons having the same number friends (It is assumed that if a person x is a friend of y then y is also a friend of x and we are only considering the friends amongst the group of people). How would you modify your proof if the number of people were not 101?

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  1. 18 July, 14:28
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    Step-by-step explanation:

    Let us assume that if possible in the group of 101, each had a different number of friends. Then the no of friends 101 persons have 0,1,2, ... 100 only since number of friends are integers and non negative.

    Say P has 100 friends then P has all other persons as friends. In this case, there cannot be any one who has 0 friend. So a contradiction. Hence proved

    Part ii: EVen if instead of 101, say n people are there same proof follows as

    if different number of friends then they would be 0,1,2 ... n-1

    If one person has n-1 friends then there cannot be any one who does not have any friend.

    Thus same proof follows.
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