SOLUTION: A lies on mon, tues, wed and speak truths on other days, B lies on Thurs, Fri, Sat and speaks truths on other days. One day a said I lied today and B said I too lied today. What is

Question 487775: A lies on mon, tues, wed and speak truths on other days, B lies on Thurs, Fri, Sat and speaks truths on other days. One day a said I lied today and B said I too lied today. What is the day?
Found 2 solutions by josmiceli, solver91311:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
A and B both agree
If I was telling the truth, then both
A and B were lying.
---------------
But there is no day that both
A and B are lying, since:
A is lying on
Mon, Tues, Wed
B is lying on
Thurs, Fri, Sat
-------------
Therefore, I must have been lying
and both A and B were telling the truth
-------------
There is only 1 day when both A and B
are telling the truth, so today
must be Sunday
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

There are two ways to interpret your sentence containing A's and B's statements:

One day A said, "I lied today," and B said, "I too lied today." Where each of A and B were referring to themselves, then it is impossible for either of them to make these statements.

If it was Monday, Tuesday, or Wednesday, then A's statement would be the truth, but that cannot be because A lies on Monday, Tuesday, and Wednesday. If it is any other day, then A's statement would be a lie, but that cannot be because A tells the truth on the other days. Same logic for B's statement.

On the other hand, if you truly meant: One day A said I lied today and B said I too lied today. Where "I" is a third party who is telling the story about A and B, then if you presume that the storyteller is telling the truth on the "One day" mentioned, then there is no day when both A and B's statements are true. But if you presume that the storyteller is lying (and the "One day" must be a day other than the day on which the storyteller told the story) then it is a day when both A and B told the truth, namely Sunday.

John

My calculator said it, I believe it, that settles it

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