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A crime has been committed with four people at the scene of the crime. You are responsible for finding out who did it. You have recorded the following statements from the four witnesses, and you know one of them has committed the crime.

1. Anuj says that Binky did it.
2. Binky says that Anuj did it.
3. Chacko says that Binky is telling the truth.
4. Desmond says that Chacko is not lying.

You know that exactly three of the statements recorded are FALSE. Who committed the crime?

1. $\text{Anuj}$
2. $\text{Binky}$
3. $\text{Chacko}$
4. $\text{Desmond}$
5. $\text{Either Anuj or Binky; the information is insufficient to pinpoint the criminal}$

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option B)?
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Out of 4 statements, exactly $3$ are false and $1$ is true.

• If statement 4 is true then it implies statement 3 is also true (but only 1 statement can be true).
• If statement 3 is true then it implies statement 2 is also true (again only 1 statement can be true).
• If statement 2 is true then all other statements are false including statement 3 which states "Chacko says that Binky is telling the truth". This means Binky is not telling the truth, so statement 2 can not be true.

Thus statements $2,3$ and $4$ cannot be possibly true implying statement $1$ is true.

Statement 1 states "Anuj says that Binky did it", so Binky is the culprit.

Option (B).

by Active (2.1k points)
selected by
Statement 1 by Anuj can be true while others can be false making system of statements consistent. But If statement 2 by Binky is true then statement 3 can't be false because if it is false it will contradict statement 2. See this - "Chacko says that Binky is telling the truth". If this statement is false then Binky is telling lie because Chacko is telling lie. So here is contradiction so correct system is 1 statement is true while others are false. i.e Binky committed the crime. So option B.
by Loyal (6.2k points)

+1 vote