One day Alice meets the Lion and the Unicorn in the Forest of Forgetfulness. She knows that the Lion lies on Mondays, Tuesdays, and Wednesdays, and tells the truth on the other days of the week. The Unicorn, on the other hand, lies on Thursdays, Fridays, and Saturdays, but tells the truth on the other days of the week. Now they make the following statements to Alice:
Lion: Yesterday was one of my lying days.
Unicorn: Yesterday was one of my lying days too.
What day is it?

Thursday

The only days the Lion can say that he lied on the previous day are Mondays and Thursdays. The only days the Unicorn can say this, are Thursdays and Sundays. Therefore, the only day they both say that is on Thursday