50. 

On which days of the week can Leo make the following single statement: “I lied yesterday, and I will lie tomorrow.” Warning! The answer to this problem does not match the answer to the previous problem.

## B. TRALALALA AND TRULALALA

Once, for an entire month, Leo and the Unicorn did not show up in the Forest of Forgetfulness. They were somewhere else, engaged in an endless fight over the crown.

But Tralalala and Trulalala often visited the forest. One of them, like Leo, lied on Mondays, Tuesdays, and Wednesdays and told the truth all other days of the week. The other, like the Unicorn, lied on Thursdays, Fridays, and Saturdays, but told the truth all other days of the week. Alice did not know which one behaved like Leo and which one like the Unicorn. Moreover, the brothers were so similar that Alice could hardly tell them apart (the collars with their names embroidered on them, the brothers wore very rarely). Poor Alice had a hard time! Take, for example, the following cases.
50. The situation in this problem is quite different from the one we encountered in the previous problem. This example clearly shows the difference between two separate statements and one complex statement - their conjunction. Indeed, if any two statements $X, Y$ are given, then the truth of one complex statement «$X$ and $Y$» implies that both statements $X, Y$ are true. If the conjunction «$X$ and $Y$» is false, then at least one of the statements $X, Y$ is false.

After these preliminary remarks, let's proceed to solving the problem. The only day of the week when the statements «I lied yesterday» and «I will lie tomorrow» could both be true is Tuesday (since it is the only day that falls between two days when Lev lies). Therefore, the day when Lev made his statement could not have been Tuesday, because on Tuesdays his statement is true, and Lev does not make true statements on Tuesdays. Since it was not Tuesday, Lev's statement is false, meaning that on that day Lev is lying. Thus, the complex statement given in the problem could have been made by Lev either on Monday or on Wednesday.