Each of Abner, Berenice, Calvin and Dolores is either a knight who always tells the truth, or a liar who always speaks falsely, or a knave who alternates between lying and telling the truth in any order.
They say:
- Abner: Berenice is a liar.
- Berenice: I am a knight.
- Calvin: If asked, Berenice would say that she is a knight.
- Dolores: I am a knight.
Given that each of the four individuals being any of the 3 types is equally likely, and all the four statements are simultaneous and independent, determine the probability that:
- Abner is a knight, Berenice is a liar and each of Calvin and Dolores is a knight.
*** For an extra challenge, solve this puzzle without taking resort to a computer program/excel solver aided methodology.
(In reply to
Extra Challenge Accepted (spoiler) by Steve Herman)
While Calvin's statement cannot depend on what Berenice said, it could in fact be dependent on Berenice's previous statement, whatever and whenever that was, and therefore was a prediction of what Berenice would be saying this time. That actually can be, as he did correctly predict this outcome as she did claim to be a knight, as he predicted.
In fact, if he had made the prediction after knowing Berenice's answer, that would have ruled out Berenice's being a knave, as Calvin would have predicted the opposite of what Berenice had said (i.e., admitted to being a knave), in that case.
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Posted by Charlie
on 2023-09-13 06:58:04 |
re: Extra Challenge Accepted (spoiler)
