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.”?
Answer
On Thursday.
They can only make this statement during the border days – on the border day they tell the truth and on the next day they lie, or vice verse. For James, his border days are on Thursdays and Sundays. For Jonathan, his border days are on Mondays and Thursdays. So, only on Thursdays can they both make the statement.