Logical Games

1987/06/01 Goñi, Jesus Mari Iturria: Elhuyar aldizkaria

• Matematika

In this number we have decided to present to a very skilled author in the creation of Mathematical Games. The author is the North American Raymond Smullyan. Raymond Smullyan has focused on the creation of Logical Games, being the bibliography that has illuminated witness of his work.

The bibliographic records of the books published in Spanish by Raymond Smullyan are shown below:

The lady or the tiger? and other logical pastimes Editorial Professor - Theorem Collection ISBN 84-376-0414-1 Alice in Guessing Country Publisher Professor - Theorem Collection ISBN 84-376-0479-6
• How is this book called? Editorial Professor - Theorem Collection ISBN 84-376-0297-1

We have chosen the first of the books mentioned to propose some games as the problems that appear in it.

The book tells that the daughter of a king was so beautiful that the whole of the boyfriends was far greater than the king's patience could bear. (The book does not say that, but neither does the opposite, and we prefer to think that).

The king, being rich, did not want a rich husband for his daughter, was not; he preferred a man who was going to be intelligent. Therefore, with the help of a minister who was a little macaveral, he prepared hard tests to expel the boyfriends. They were hard tests, as they were risky, as we will see later. They were tough and difficult, as we will see below.

The contracting parties were taken to a room with a variable number of doors. In each of the above mentioned doors there was a card, and in the room that was hiding behind those doors, a tiger or a slender princess desired. If they understood well what these cards said, and thanks to the reasoning made with a proper combination of the messages that appeared there, it was possible to guess what the princess's classroom was. But if they did not act clearly and the conclusion was erroneous, they had prepared death in the claws of the tiger. The winner needed courage and intelligence to participate. That was the proof the king had prepared.

Of all the proofs that appear in the book, we have selected three to bring them. Whoever wants more knows where to go.

First Trial Test

I put it on the cards of the classrooms:

The king made a warning: the two cards tell the truth or both are false. What is the door that has to open the pretender to get the princess? I or II?

Second test: Second test

Here is what I put on the cards of the rooms.

The king made a warning: if in the left room there is a lady, his card says the truth, and if there is a tiger, lie. In the right room things go wrong, that is, if inside there is lady card lying and if there is tiger the truth. You, if you are single, what door would you open?

Third test: Third test

Here is what I put on the cards of the nine rooms. Yes, you read well, had nine rooms, one to choose from, pretending sick.

The lady is in an odd room I

This Room II is empty

Card III V is fine or the VII is wrong

IV First bad card

V II. card or IV in good condition

VI III. incorrect card

Lady VII is not in class I

In this Room VIII there is a tiger and IX. room empty

In this Room IX there is a tiger and the VI is wrong

The king said:

The princess is in one of these nine rooms, and the card corresponding to this room is certain. The other rooms are empty or equipped with a tiger (je, je! ). If in a room there is tiger, your card lies, if it is empty it is not known whether what it says is true or false.

Look, I have forgotten one thing: VIII. The room is not empty.

In what room is the princess?