Solve relative-truth cat puzzle
Logic Puzzle: Directed Truth/Lie Rule and Cat Counts
This problem involves three individuals, Asta, Bronya, and Clara, each owning a unique, positive integer number of cats. A specific rule governs their communication:
- A speaker tells the truth if the listener has fewer cats than the speaker.
- A speaker lies if the listener has more cats than the speaker.
Based on the following statements, determine the number of cats Asta owns.
Statements
- Bronya to Clara: "You have the most cats."
- Asta to Bronya: "I have exactly 30% more cats than you."
- Asta to Clara: "Your number of cats is the average of Bronya’s and mine."
- Clara to Asta: "You have at least 4 more cats than me."
Question
How many cats does Asta have?
AI interview prep
Core dilemma
Systematically navigating a complex, interdependent set of logical constraints to converge on a unique solution, where each piece of information can flip the interpretation of others. The core challenge is managing the combinatorial explosion of possibilities while ensuring all constraints (truth/lie rule, distinct positive integers) are satisfied.
3 tradeoffs and 3 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Solve relative-truth cat puzzle
Logic Puzzle: Directed Truth/Lie Rule and Cat Counts
This problem involves three individuals, Asta, Bronya, and Clara, each owning a unique, positive integer number of cats. A specific rule governs their communication:
- A speaker tells the truth if the listener has fewer cats than the speaker.
- A speaker lies if the listener has more cats than the speaker.
Based on the following statements, determine the number of cats Asta owns.
Statements
- Bronya to Clara: "You have the most cats."
- Asta to Bronya: "I have exactly 30% more cats than you."
- Asta to Clara: "Your number of cats is the average of Bronya’s and mine."
- Clara to Asta: "You have at least 4 more cats than me."
Question
How many cats does Asta have?