I have a weird logic like problem that doesn't entirely make since...?!


Question:

I have a weird logic like problem that doesn't entirely make since...?


Okay,

there are three suspects in a bank robbery case, Pat, Sam, and Danny. At least one of them is guilty. Either Danny is innocent, or Sam is guilty. If Sam is guilty, Danny is innocent. Pat and Danny never work together, and Pat never does a job on his own. If Sam is guilty, so is Pat.

Who's guilty?

Additional Details

21 hours ago
I sortof think it's sam and pat, but I have doubts for two reasons:

1) In the beginning, it says EITHER

2) I have a hard time believing that they would put the answer in the last line


Answers: 21 hours ago
I sortof think it's sam and pat, but I have doubts for two reasons:

1) In the beginning, it says EITHER

2) I have a hard time believing that they would put the answer in the last line There are eight possibilities:

1. Pat guilty, Sam guilty, Danny guilty
2. Pat guilty, Sam guilty, Danny innocent
3. Pat guilty, Sam innocent, Danny guilty
4. Pat guilty, Sam innocent, Danny innocent
5. Pat innocent, Sam guilty, Danny guilty
6. Pat innocent, Sam guilty, Danny innocent
7. Pat innocent, Sam innocent, Danny guilty
8. Pat innocent, Sam innocent, Danny innocent

"At least one of them is guilty."
This eliminates possibility #8.

"Either Danny is innocent, or Sam is guilty."
Then it cannot be that Danny is guilty and Sam is innocent. Thus, possibilities #3 and #7 are eliminated.

"If Sam is guilty, Danny is innocent."
Then it is not true that both Sam and Danny are guilty. So we can eliminate possibilities #1 and #5.

"Pat never does a job on his own."
This eliminates #4.

"If Sam is guilty, so is Pat."
Then it is never true that Sam is guilty and Pat is innocent. This eliminates #6.

The only remaining possibility is #2 -
Pat is guilty, Sam is guilty, and Danny is innocent.

You are right! And this shows why! Sam. Sam and Pat Pat Sam and Pat end of.

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