## 75. The Next Round

- In this round, said one of the brothers, the rules remain the same, but the question you need to answer is different. Instead of determining who among us is Trulala and who is Tralala, you need to find out who among us is lying and who is telling the truth.

Both brothers entered the house, and when they came out, they declared the following:

First brother. The cards are of the same suit.

Second brother. The cards are not of the same suit.

Who among the brothers is telling the truth?

## The Third Game - Two Additional Rounds

Both brothers warmly congratulated Alice: she had won all the rounds in a row!

- Before you continue, said Trulala with a mischievous smile, my brother and I want to offer you two extraordinary games, each with one round. We won't need the cards anymore; we will play with signs. Here's how it works. My brother and I go into the house. Then one of us comes out first, and the other follows a bit later with a large sign (like a road sign), on which the question will be written in such large letters that both you and the one who came out first can easily read it from a distance. After reading the question, the one who came out first answers with a sign, drawing a square or a circle in the air. One of these signs means "yes," the other means "no," but we won't tell you which is which. The sign that means "yes" is drawn on the back of the sign with the question, but we won't show you that side until you tell us who is Trulala and who is Tralala. Of course, the one who came out first (who is to answer the question) has seen what is drawn on the back of the sign and therefore knows which sign means "yes" and which means "no." However, when answering the question in the language of signs, he can either tell the truth or lie!
- I'm afraid I don't quite understand, said Alice.
- I mean that if, for example, a circle means "yes," then the one who tells the truth will draw a circle in the air in response to the question, and the one who lies will draw a square.
- Now I understand! Alice was delighted.
- Excellent! Then let's begin! By the way, I want to warn you about one more thing. My brother and I have agreed that if Tralala answers the question, he lies, and if Trulala answers, he tells the truth.
75. The Sixth Round (Orange and Purple). The brothers contradict each other, so one of them is lying, and the other is telling the truth. Therefore, their cards (the same principle applies!) must be of different suits.

Thus, the first brother is telling the truth (his statement is true).