Logic

Let us begin with the following puzzles.

1. (Wason’s Card Game) You see 4 cards on a table.

Suppose each of these cards has a letter on one side and an integer on the other side. How many cards do you need to flip to verify the statement that “Any card that has a consonant on one side has an odd number on the other side”?

2. In the Island of Knights and Knaves, there are certain inhabitants called knights who always tell the truth and others called knaves who always lie. Every inhabitant of this island is either a knight or a knave.

You meet 3 inhabitants A, B and C. They make the following statements.

• A: B is a knave.
• B: A and C are of the same type.

What type is C?

3. In the Island of Knights, Knaves and Normals, there are certain inhabitants called knights who always tell the truth, some others called knaves who always lie and rest are normal people, who sometimes lie and sometimes tell the truth. Every inhabitant of this island is either a knight or a knave or a normal person.

You meet 3 inhabitants A, B, C and one is a knight, one is a knave, one is normal (not necessarily in that order). They make the following statements.

• A: I am normal.
• B: That is true.
• C: I am not normal.

What are A, B and C?

4. The Caskets Challege 1: Consider 3 caskets of which exactly one of them has a gem. Each of these caskets has an inscription.

At least one of the 3 statements is true and at least one of them is false. Which casket has the gem?

5. The Caskets Challege 2: Consider 2 caskets of which exactly one of them has a gem. Each of these caskets has an inscription as follows.

Which casket has the gem?

References

1. What is the name of this book? by Raymond M. Smullyan.
2. Reasoning by P. C. Wason.