Logic puzzles

Paradoxes

Simply put, a logical paradox is a sentence, statement, or argument that contradicts itself. A well-known example of a paradox is the following sentence:

This is a false statement.

If the statement is true, it is false, but if it is false, then it is true?!

Another famous paradox is the ‘barber’s paradox’.

A barber is known to shave all the men in the city who do not shave themselves. Who then, shaves the barber?

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Smullyan’s knights and knaves puzzles

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One such puzzle involves two cities: one, a city of “knights”, and the other of “knaves”. The residents of the two cities like to visit each other. One day, a man enters one of the cities, but doesn’t know which. He decides to ask the first person he meets where he is. The answer he receives is that he is in the “knaves” city. A few seconds later, the visitor realizes that he still doesn’t know where he is. He may be in the “knaves” city, and the person he met was a “knight” visiting there, but he also may be in the “knights” city and the person he met was a “knave” visiting there! Therefore, the visitor decides to ask another question. What question can he ask in order to know definitely which city he is in? A possible answer to this problem is that he should ask: “Do you live here?”

If the visitor is in the “knights” city, then a “knight” will answer YES, and a “knave” (visiting there) will also answer YES. On the other hand, if the visitor is in the “knaves” city, both a “knight” and a “knave” will answer NO. So, if the reply is YES, he is in the “knights” city, and if the reply is NO, then is in the “knaves” city.

Answering logic puzzles can be pretty puzzling. A good trick is to realize that there are some statements that a liar cannot possibly make, for example, “I am a liar”. These are the sort of statements that we look for so that we can distinguish between liars and truth tellers.

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