Alice in Puzzle-Land by Raymond Smullian

Alice in Puzzle-Land is one of my favorite books... at least is the book that I have open the most. I recommend this book... not only for the beautiful drawings in it... but for the mathematics and logic... Sadly, there is not a movie yet... - Alicia en el país de las adivinanzas es uno de mis libros favoritos... al menos es el libro que he abierto más veces. Recomiendo este libro tanto por sus bonitas ilustraciones como por las matemáticas y lógica... Una pena que no hayan hecho una película todavía.



This is a example...


Game III: Two Extra-Specials

Both brothers congratulated Alice warmly for having won every round.

"Before you leave," Tweedledee said with a grin, "we have two extra-specials for you! We will play two extra games, one round each, only the games will now be in sign language. We won't use colored cards this time. What we'll do is this: We will both go into the house, and one of us will come out first. The second one will come out soon after, carrying a large sign with a question written on it which both the first brother and you will be able to read clearly. Then the first brother will answer the question in sign language:

He will draw either a square or a circle in the air. One of those two figures means yes and the other means no, but you will not be told which figure means what. However, the figure which does mean yes is already drawn on the back of the sign, but you will not be allowed to see it until after you have guessed which of us is Tweedledee and which is Tweedledum. The first brother (the one who answers the question) will, of course, have already seen the back of the sign, so he will know which of the square and circle means yes and which means no. However, he might lie when he gives his answer in sign language."
"I'm not sure I understand that," said Alice.

"Well, if, for example, the circle means yes, and the correct answer to the question is yes, then if he tells the truth, he will draw a circle in the air; if he lies, he will draw a square in the air."
"Oh, I understand!" said Alice.

"Good! Then we'll play the first game. One last thing: My brother and I have already agreed that if Tweedledee answers the question, he will lie, and if Tweedledum answers, he will tell the truth.


76- WHO IS WHO? The brothers then went into the house. Almost immediately, one of them came out and stood in silence. Shortly after, the other one came out bearing a sign, on the front of which was written


IS THE FIGURE ON THE BACK OF THIS SIGN A SQUARE?


The other brother answered by drawing a circle in the air. Which one was Tweedledum?


77- WHAT QUESTION SHOULD ALICE ASK? "Congratulations, you did it again!" both brothers cried. "Now comes the best game of all, and if you win it, you also win a prize!" said Tweedledee.

"This time," he continued, "we have not agreed which of us lies and which tells the truth. What we do is this: we go into the house, and each one comes out, each with either a red or a black card in his pocket. Again, red signifies truth-telling and black signifies lying. Now, just one of us has a prize in his other pocket. If you can guess which one of us has the prize, you get it. It now is not important which of us is Tweedledee and which is Tweedledum; your job is to find out which one has the prize. Now, when we come out of the house, you point to one of us and ask him a question—a question answerable by yes or no. But instead of answering yes or no, he will again answer in sign language: He will draw either a square or a circle in the air. Now, the important point is this: if he is carrying the prize, then by a square he means yes and by a circle he means no. On the other hand, if he is not the one who is carrying the prize, then by a square he means no and by a circle he means yes. On top of that, he might tell the truth or he might lie—this is determined by whether he is carrying a red card or a black card."
"But what question am I supposed to ask him?" inquired Alice.

"Ah, that is for you to figure out!" he triumphantly replied. "That's the hardest part of the game, and if you can figure out the right question, you certainly deserve a prize."

"Well," said Alice, "I'm afraid I can't do this without pencil and paper, and I forgot to bring my memorandum book in this journey into the Looking-Glass."  Tweedledee quickly went into the house and returned with a pencil and a pad of paper.

"We'll be in the house while you are figuring out your question, and when you are ready, call us and we will come out. Take as much time as you like."

The brothers then went into the house, and Alice worked quite hard on the puzzle. After a while, she shouted, "I'm ready." The brothers then came out, Alice asked one of them a question, and he replied by drawing either a square or a circle in the air. Alice pointed to one of the two brothers and said, "You're the one who is carrying the prize," and Alice was right. How, in one question, could Alice find out which one has the prize?
"Congratulations again!" said both brothers. "You have certainly earned your prize!"
Alice was then given her prize, all nicely wrapped and tied together. The more she tried unwrapping it, the tighter it got!
"Have you forgotten that you're in the Looking-Glass?" asked one
of the brothers.

"Oh, of course!" remembered Alice, who then tried wrapping it and making the string tighter. This worked like magic; the parcel almost immediately unwrapped itself. The prize consisted of a pencil and a beautiful brand-new memorandum book.