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

  A vendor has two rolls of fabric, each `36` meters long. He sells the fabric in pieces of `3` meters. How many times will the vendor need to cut the fabric?

  Topics:

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

• Question

  Samuel has three sons, and each son has one sister. How many children are there in this family?

  Topics:

  Algebra -> Word Problems Logic -> Reasoning / Logic

• Question

  Two workers pave two kilometers of road within two days. How many workers are needed to pave `20` kilometers of road within `20` days?

  Topics:

  Arithmetic Algebra -> Equations Algebra -> Word Problems Logic -> Reasoning / Logic Number Theory -> Division

• Question

  In Danny's class there are `30` students. Danny claims that the number of boys is greater by `3` than the number of girls. Is it possible that Danny is right?

  Topics:

  Arithmetic Algebra -> Equations Algebra -> Word Problems Logic -> Reasoning / Logic Number Theory -> Division -> Parity (Even/Odd)

• Question

  If it is raining in Tel Aviv at `12` noon, is it possible that in `36` hours there will be sunshine in Tel Aviv?

  Topics:

  Logic -> Reasoning / Logic

• Question

  When it rains, Alice always drinks tea. Alice is currently drinking tea. Does it necessarily mean it is raining now?

  Topics:

  Logic -> Reasoning / Logic

• Question

  On the circle, there are blue and red points. It is allowed to add a red point and change the colors of its neighboring points or remove a red point and change the colors of its neighboring points (it is not allowed to leave fewer than 2 points on the circle). Prove that it is impossible to move, using only these operations, from a circle with two red points to a circle with two blue points.
  K. Kaznvosky

  Topics:

  Combinatorics -> Combinatorial Geometry Combinatorics -> Invariants Algebra Logic -> Reasoning / Logic Number Theory -> Division -> Parity (Even/Odd) Set Theory Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Combinatorics -> Colorings -> Chessboard Coloring
  Sources:
  • Tournament of Towns, 1979-1980, Main, Spring Question 1

• Question

  Alice eats ice cream only when it is not raining. It is not raining now. Is Alice necessarily eating ice cream right now?

  Topics:

  Logic -> Reasoning / Logic

• Question

  Alice has three friends – Edith, Rose, and Mary. When Alice is sick, at least one of her friends comes to visit. Alice is sick, and Edith comes to visit her. Is it possible that Rose and Mary also came?

  Topics:

  Logic -> Reasoning / Logic

• Question

  When Rosa and Edith come to visit Alice, Alice's mother bakes a cake. Edith came to visit Alice today. Is Alice's mother necessarily going to bake a cake? Is Alice's mother necessarily not going to bake a cake?

  Topics:

  Logic -> Reasoning / Logic