One fellow (A) lies only on Mondays, Tuesdays, and Wednesdays, and tells the truth on other days, and his friend (B) lies on Thursdays, Fridays, and Saturdays, and tells the truth on other days.

At noon, they have the following conversation:

A: I lie on Saturdays.

B: I will lie tomorrow.

A: I lie on Sundays.

On which day of the week does this conversation take place?

Adapted from Crux Mathematicorum.

A's first statement is a lie, so we know it's either Monday, Tuesday or Wednesday.  B tells the truth on those days, so his claim that he'll lie tomorrow means it must be Wednesday.  We don't need A's second statement (though of course it is also a lie, which is consistent with the answer).  

Posted by tomarken on 2016-04-21 08:10:49