Logic

Logic is the study of reasoning and valid inference. It involves analyzing statements, arguments, and deductive processes. Questions may include solving logic puzzles, evaluating the truth of compound statements, using truth tables, and identifying logical fallacies.

• Question

  Everyone on Ginger Island is a ginger unless they are a tourist. I met someone there with ginger hair. Is he necessarily a local?

  Show hint

  Log in here to receive the hint
  Topics:

  Logic -> Reasoning / Logic

• Question

  When Alice and Edith drink tea together, Mary always joins them. Alice is drinking tea now, and Mary is not. Is it possible that Edith is drinking tea now?

  Topics:

  Logic -> Reasoning / Logic

• Question

  My father always tells the truth, and my son always lies. Is there a question you can ask them both, so that they will give identical answers to that question?

  Topics:

  Logic -> Reasoning / Logic Logic -> Truth-tellers and Liars Problems

• Question

  A tourist arrived at an island inhabited by truth-tellers and liars. Truth-tellers always tell the truth, and liars always lie. The tourist is traveling with a local guide, and they see a farmer working in the field. The tourist asked the guide to find out if this man is a truth-teller or a liar. The guide spoke with the farmer and then said to the tourist: "He said that he is a truth-teller."

  A. What can be deduced about the farmer?

  B. What can be deduced about the guide?

  Topics:

  Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Logic -> Truth-tellers and Liars Problems
  Sources:
  • problems.ru web site

• Question

  On Alice's birthday, her friends are asked how old she is. The Mad Hatter says that Alice's age is greater than `11`, and the Cheshire Cat says that her age is greater than `10`. It is known that exactly one of them is wrong. How old is Alice now? Explain!

  Show hint

  Log in here to receive the hint
  Topics:

  Number Theory Algebra -> Inequalities Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures

• The broken chain

  There are five segments of a broken chain, each segment having three links. Moses wants to repair the chain. What is the minimum number of links he needs to open and close again to join all these segments together?

  Note: The chain is not circular!

  Topics:

  Algebra -> Word Problems Logic -> Reasoning / Logic Proof and Example -> Constructing an Example / Counterexample Minimum and Maximum Problems / Optimization Problems

• Question

  There are two coins in a wallet, and their sum is `15` shekels. One of the coins is not a `5` shekel coin. What are the coins in the wallet?

  Topics:

  Arithmetic Algebra -> Word Problems Logic -> Reasoning / Logic

• Question

  a. The apple is heavier than the peach, and the peach is heavier than the pear. Which is heavier – the apple or the pear?

  b. The orange is heavier than the pear, and the plum is lighter than the orange. Which is heavier – the pear or the plum?

  Topics:

  Arithmetic Algebra -> Inequalities Logic -> Reasoning / Logic
  Sources:
  • problems.ru web site

• Question

  There are `85` balloons in a room, red and blue. It is known that:

  - At least one of the balloons is red,

  - In any pair of balloons we take, at least one of the balloons must be blue.

  How many red balloons are in the room?

  Topics:

  Logic -> Reasoning / Logic Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures
  Sources:
  • problems.ru web site

• Question

  One-seventh of mathematicians are philosophers, and one-ninth of philosophers are mathematicians. Which are there more of – philosophers or mathematicians?

  Show hint

  Log in here to receive the hint
  Topics:

  Algebra -> Word Problems Logic -> Reasoning / Logic Arithmetic -> Fractions
  Sources:
  • problems.ru web site