Who is lying?
James and Jonathan are liars, who lie on specific days. James lies on Fridays, Saturdays and Sundays, but he is honest on all other days. Jonathan lies on Tuesdays, Wednesdays and Thursdays, but he tells the truth on all other days. On what day of the week would they both say "Tomorrow, I will lie." ?
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7 solutions
This is simple logic:
Monday
James cannot say that he will lie tomorrow because he lies on Fridays, Saturdays and Sundays
Jonathan can say that because he will lie tomorrow, which is Tuesday.
Tuesday
Again, James cannot say that he will lie tomorrow, same reason as above.
Jonathan cannot say that he will lie tomorrow either, because if he says that he will be telling the truth, but he is lying on Tuesday.
Wednesday
James cannot say that he will lie tomorrow, the reason is still the same.
Jonathan cannot say that he will lie tomorrow either, because if he says that he will lie on Thursday, which he will, but that will be telling the truth, which is not possible since he is lying on Wednesday.
Thursday
James can say that he will lie tomorrow, because he is telling the truth today and tomorrow he will tell lies.
Jonathan can also say that he will lie tomorrow, because today he is still lying so he should be lying about what he will do tomorrow.
As you can see, the day that they will both lie is Thursday.