Logic, Reasoning / Logic

This category emphasizes general logical reasoning skills, often applied to puzzles or scenarios not strictly formal. It involves deduction, inference, identifying patterns, and drawing sound conclusions from given information. It overlaps with formal logic but can be broader.

• Question

  When it rains, Rosa always takes an umbrella with her and wears a coat. Today, Rosa wore a coat and took an umbrella with her. Is it necessarily the case that it is raining today?
  Topics:

  Logic -> Reasoning / Logic

• Question

  When there is snow and a strong wind, Alice doesn't meet her friends. Today there is snow. Is it possible that Alice meets her friends today?

  Topics:

  Logic -> Reasoning / Logic

• Question

  A disheveled soldier named Shlomi flees when he sees the regimental sergeant major (RSM) or the base commander. Shlomi is walking across the plaza and sees the base commander and the RSM walking together. Does he flee?

  Topics:

  Logic -> Reasoning / Logic

• Question

  When it's dark outside and there are no buses, Yossi and Danny always hang out together. Currently, there are no buses, and Yossi is walking alone to the park. Is it true that it is daytime now?

  Topics:

  Logic -> Reasoning / Logic Proof and Example -> Proof by Contradiction

• Jack the Cat

  My cat Jack purrs when he is happy and sitting in a warm place. Currently, Jack is cold.

  A. Is it possible that he is purring now?

  B. Is it possible that he is happy now?

  Topics:

  Logic -> Reasoning / Logic

• 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