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.”?
Check your answer:-Explanation
Lets say if the person is speaking truth then he must be lie on next day, but if he is lying while saying “Tomorrow i will lie” then he will speak truth on next day.
So they can say the statement only when they change their behavior on next day.
Lets prepare a table for James and Jonathan for all days
From above table
James can say the statement on Thursday and Sunday
and Jonathan can say it on Monday and Thursday.
As both of them say the statement on same day, so it must be Thursday only.
Cut Circular cake puzzle