1. One day, Alice found herself in a magical forest where two amazing twins, Tra-la-la and Tru-la-la, lived. Tra-la-la always lied on Mondays, Tuesdays, and Wednesdays, but told the truth all other days of the week. Tru-la-la always lied on Thursdays, Fridays, and Saturdays, but told the truth all other days of the week. One day, Alice met both brothers (it was impossible to tell who was who just by looking), who declared:

First: “I lie on Saturdays”

Second: “I will lie tomorrow”

First: “And I also lie on Sundays”

Determine which day of the week this meeting could have taken place.
Answer: only on Wednesday.

Solution. The statement "I lie on Sundays" is false for either of the brothers, so the first one was definitely lying. This means his first statement is also false. Thus, the first brother does not lie on Saturdays, so the first one is Tralala. Then the second one is Trulala, and on the day of the meeting, he was telling the truth (if he were lying, both brothers would be lying, which never happens on any day of the week). So on the day of the meeting, Trulala was telling the truth, but the next day he would lie. The only such day is Wednesday.

Criteria. Only the answer - 1 point. Answer with verification that the situation is possible on Wednesday, but other days are not considered - 2 points. Correctly proven that the first one is Tralala and the second one is Trulala, but there is no conclusion or an incorrect conclusion about the day of the week - 3 points. It is stated without justification that the first one is Tralala and the second one is Trulala, and the rest of the solution is correct - 4 points.