Question

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 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.
Which of the following is the correct order of batsmen who got the top score, second best and third best score respectively?

• A. Brian, Ricky, Sachin
• B. Brian, Sachin, Ricky
• C. Ricky, Sachin, Brian
• D. Sachin, Brian, Ricky

Hint:

Test the case where Sachin is first; it forces both of Brian's statements to be false, which is not allowed, so that case can be ruled out immediately.

Answer 1

The Correct Option is A

Another way to solve this is to directly test each of the four given options against the "one true, one false" rule for every batsman, instead of deducing the order from scratch.

1. Option (1): Brian first, Ricky second, Sachin third. Sachin's statements: "I am top" is false, "Ricky is second" is true, one true one false, OK. Brian's statements: "I am top" is true, "Sachin is second" is false, one true one false, OK. Ricky's statements: "I am top" is false, "Sachin is third" is true, one true one false, OK. This option satisfies all three conditions.
2. Option (2): Brian first, Sachin second, Ricky third. Brian's statements: "I am top" is true, "Sachin is second" is true, both true, which breaks the rule. This option is invalid.
3. Option (3): Ricky first, Sachin second, Brian third. Ricky's statements: "I am top" is true, "Sachin is third" is false since Sachin is second, one true one false, OK. Sachin's statements: "I am top" is false, "Ricky is second" is false since Ricky is first, both false, which breaks the rule. This option is invalid.
4. Option (4): Sachin first, Brian second, Ricky third. Sachin's statements: "I am top" is true, "Ricky is second" is false since Ricky is third, one true one false, OK. Brian's statements: "I am top" is false, "Sachin is second" is false since Sachin is first, both false, which breaks the rule. This option is invalid.

Only option (1), Brian first, Ricky second, Sachin third, satisfies the "one true, one false" rule for all three batsmen, confirming it as the correct answer.