A bank theft has been committed and, after due investigation, the police has detained four suspects.
During the course of verbal questioning, the four suspects recorded the following statements.
- Al: The thief was Bud.
- Bud: The thief was Dax.
- Cal: I am innocent.
- Dax: When Bud said that it was me, he lied.
Determine the perpetrator, whenever:
(I) Precisely one of the suspects is lying, and the others are speaking the truth.
(II) Precisely one of the suspects is telling the truth, and the others are speaking falsely.
As Dax explicitly accuses Bud of lying, exactly one of them must be lying and the other telling the truth. If Bud is telling the truth, then Dax is guilty. However, in this case, Al would be lying and Cal would be telling the truth, leading to 2 true statements and 2 false statements. As this violates both (I) and (II), this is impossible. Therefore, in both (I) and (II), Bud is lying and Dax is telling the truth.
For (I): Bud is the only liar, and therefore Al, Cal and Dax are all telling the truth. Al directly implicates Bud as the culprit; this is consistent with Cal and Dax's statements also being true. So Bud is guilty if exactly one person is lying.
For (II): Dax's statement is the only true one. Cal is therefore lying when he claims to be innocent; this is consistent with both Al and Bud making false statements. So Cal is guilty is exactly one person is telling the truth.
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Posted by H M
on 2022-10-10 07:56:00 |
Solution
