Jack and Rose speak lies on some particular days.
While Jack speaks lies on Fridays, Saturdays and Sundays, Rose speaks lies on Tuesdays, Wednesdays and Thursdays. On all other respective days, they speak truth.
If you know about this behavior, can you find out a day in the week when both of them will say "Tomorrow, I will lie."?
Solution:
They can say this line only on Thursday.
Explanation:
Let us analyze the statement. If the person who is speaking this line is speaking truth, then the person will have to speak a lie on the next day. But if the person is lying, the next day, that person must speak truth on the next day.
If you notice here, the behavior is changing on the next day no matter what the person speaks. If we create a response table for both Jack and Rose, it will look like this:
Jack Rose
Monday Truth Truth
Tuesday Truth Lie
Wednesday Truth Lie
Thursday Truth Lie
Friday Lie Truth
Saturday Lie Truth
Sunday Lie Truth
Now as you can clearly see, Jack can say this statement on Thursdays and Sundays while Rose can say this statement on Mondays and Thursdays.
Since they are saying on the same day, the required day is Thursday.