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

  In the enchanted land, all tailors are gingers, and all gingers have green eyes. Is it true that every tailor who lives in the enchanted land has green eyes?

  Topics:

  Logic -> Reasoning / Logic

• Question

  Every student who prepared for the exam, indeed passed it. Students who worked while studying did not prepare for the exam. Shlomi worked while studying. Did Shlomi necessarily fail the exam?

  Topics:

  Logic -> Reasoning / Logic

• Question

  Three travelers need to cross a river. They have a boat that can hold a load of up to `100` kilograms. The travelers weigh `45`, `50`, and `80` kilograms. How should the travelers proceed to cross to the other side?

  Show hint

  Log in here to receive the hint
  Topics:

  Algebra -> Word Problems Logic -> Reasoning / Logic

• Question

  An apple is heavier than a pear, and an orange is lighter than an apple. Can you tell which is heavier: a pear or an orange? 

  Topics:

  Logic -> Reasoning / Logic

• Question

  When either Alice or Edith doesn't come to school, their friend Rosa is sad. Today Edith came to school, but Rosa is sad. Did Alice come to school today?

  Topics:

  Logic -> Reasoning / Logic

• Question

  In every forest with bears, there are no wolves, and in every forest with wolves, there are also foxes. In the magical forest, there are foxes. Is it possible that there are also bears there?

  Show hint

  Log in here to receive the hint
  Topics:

  Logic -> Reasoning / Logic

• Question

  Along the street are located `6` trees. One day, `6` parrots arrived and sat on the trees, one parrot on each tree. From time to time, two parrots each move to a neighboring tree of their choice. Can the parrots all gather on the same tree?

  Topics:

  Combinatorics -> Invariants Logic -> Reasoning / Logic Number Theory -> Division -> Parity (Even/Odd)

• Question

  In the following arithmetic puzzle, different digits have been replaced by different letters, and identical digits – by identical letters. Reconstruct the puzzle:

  `BAOxxBAxxB=2002`

  Topics:

  Arithmetic Algebra -> Equations Algebra -> Inequalities Logic -> Reasoning / Logic Number Theory -> Prime Numbers -> Prime Factorization Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Puzzles and Rebuses -> Reconstruct the Exercise / Cryptarithmetic

• Question

  Given `50` distinct natural numbers between `1` and `100`. It is known that no two of these numbers sum to `100`. Is it necessarily true that one of these numbers must be a perfect square?

  Topics:

  Number Theory -> Prime Numbers Arithmetic Combinatorics -> Pigeonhole Principle Combinatorics -> Matchings Logic -> Reasoning / Logic Proof and Example -> Constructing an Example / Counterexample Set Theory Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Proof and Example -> Proof by Contradiction

• Question

  Shlomi has a chessboard and a cube whose face size is the same as the size of a square on the board. Shlomi wants to paint the faces of the cube black and white, and then roll the cube across the board so that each time the face touching the board is the same color as the square it touches. The cube is supposed to pass through each square on the board exactly once. Can Shlomi do this? Justify or provide an example.

  Topics:

  Combinatorics -> Combinatorial Geometry Combinatorics -> Graph Theory Logic -> Reasoning / Logic Proof and Example -> Proof by Contradiction Combinatorics -> Colorings -> Chessboard Coloring