perplexus.info :: Logic : Not a clear cut

Not a clear cut (Posted on 2012-11-18)

I have slightly rephrased a problem found on the web (Steve Miller's page):

begin **

The police rounded up Jim, Bud and Sam yesterday, following the robbery of the local bank.
The three suspects made the following statements under intensive questioning:

• Jim: I'm innocent.
• Bud: I'm innocent.
• Sam: Bud is guilty.

If only one of these statements turns out to be true, who robbed the bank?

Communicated by G. Mejia.
**end

Apparently, there are several solutions.
Find them.

No Solution Yet Submitted by Ady TZIDON

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Solution Comment 4 of 4 |

If Jim's comment is the truth:
Jim is innocent.
Bud is guilty
Sam is either guilty or innocent, and Bud is innocent.

If Bud's comment is the truth:
Jim is guilty.
Bud is innocent
Sam is either guilty or innocent, and Bud is innocent.

If Sam's comment is the truth:
Jim is guilty.
Bud is guilty.
Sam is either guilty or innocent, and Bud is guilty.

Jim's comment cannot be logically correct.
If Bud's comment is the true one, Jim is guilty and Sam could be guilty.
If Sam's comment is the true one, both Jim and Bud are guilty and Sam could be guilty.

So there are four solutions:
-Jim robbed the bank.
-Jim and Sam robbed the bank.
-Jim and Bud robbed the bank.
-Jim, Bud and Sam robbed the bank.

Posted by Kell on 2013-01-18 21:02:27

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