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Logic Warmups

Sharpen your deduction skills with a variety of puzzles, ranging from basic reasoning up to some serious mind-benders. See more

Truth-tellers and Liars

Suppose you are visiting an island with knights, who always tell the truth, and knaves, who always lie.

You come across two islanders named Arnav and Bella.

Arnav says, "Bella is a knave."

Bella says, "Arnav is a knave."

How many of them are knights?

Suppose I make the claim:

\[ \color{purple} { \text{If it's raining, I have my umbrella.} } \]

If I am lying, which of these must be the case?

Honest men always tell the truth and liars always lie. What are these men? Both honest? Both liars? Or one of each, and, in that case, who is who?

You are in a dungeon and come across three doors; one contains a treasure, and the other two lead to bottomless pits.

The doors have signs. You know the door that leads to treasure has a sign that is false and the other signs are true.

Door 1: The treasure is behind door 2.

Door 2: The treasure is behind door 3.

Door 3: The treasure is not behind this door.

Which door should you take to get the treasure? (Remember, the sign on the door that has the treasure is false.)

\[ \text{This statement is false.} \]

Is the sentence above a logical contradiction?

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