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In a cricket team, three batsmen Ricky, Sachin and Brian are the top three run-scorers in any order. Each of them gives two replies to any single question; one of which is true and the other is false, again, in any order. When asked about who the top scorer was, following were the replies they gave:

Sachin: I got the top score. Ricky was second.
Brian: I got the top score. Sachin was second.
Ricky: I got the top score. Sachin was third.

Can you identify the correct order of batsmen who got the top score, second best and third best score respectively?

From the given replies we can conclude that only one of the first statements given by the players can be true as the top score can only be achieved by one person.

From the given 2nd statements, maximum two can be corret. So letâ€™s find who is saying the truth.

Let us suppose that Sachin is right for his first statement and Brain and Ricky both are right for their 2nd statement. That means Brain and Ricky both are wrong for their first statement as Sachin is the top scorer. We get the following chart (x stands for a lie):

PlayerÂ Â Â  Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  SachinÂ Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â  BrainÂ Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â  Ricky

Statement 1Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Â Â Â Â  Sachin (T) Â  Â  Â  Â  Â  Â  Â  Â  Â xÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â Â Â  x

Statement 2Â Â Â  Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â x Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â Sachin(T) Â  Â  Â  Â  Â  Â  Â  x

Statement 3Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  x Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â xÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â Â Â Â  Sachin Â (T)

It is not possible as in this case, the position of Sachin cannot be different. He has to be first according to every player and this is not the case. Â The true statements in the three different statements lead to three different solutions.

So letâ€™s try for another combination: Assuming the first statement by Brain was true. Brian said that I got the top score. This means Sachin was not second, he has to be third.

Player Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â BrainÂ Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â Â Â  SachinÂ Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â  Ricky

Statement 1 Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â Brain(T)Â Â  Â  Â  Â  Â  Â  Â  Â  x Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  x

Statement 2Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  x Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Ricky(T)Â Â  Â  Â  Â  Â  Â  Â  Â x

Statement 3Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  xÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â Â Â Â Â  x Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Sachin(T)

From this table shown above, we can see that we obtain consistent results in terms of the positions of the players as we had assumed. Hence the correct order is: Brain , Ricky, and Sachin

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