How many footballers and cricketers are present?

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There are 100 athletes (cricketers and footballers) gathered at a sports banquet.
Atleast one of them is a cricketer. Given any two athletes, one of them is a footballer.

How many footballers and cricketers are present?

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    Solution: 99 footballers and 1 cricketer

    Explanation:
    We are given that there is atleast one footballer in every given pair.

    Suppose we take one cricketer and pair him up with the remaining 99 athletes we will have 99 pairs with the cricketer as a constant.

    PAIR possibility-
    Cricketer + Footballer
    Footballer  + Footballer

    So in both cases there is atleast a Footballer

    So only possible solution that satisfies both the conditions is 99 footballers and 1 cricketer.

    Detective Expert Answered on 21st August 2015.
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