Deduce Cat Counts from Conditional Truth Rules
Company: Sig
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Online Assessment
# Deduce Cat Counts from Conditional Truth Rules
Three people, A, B, and C, own distinct positive integer numbers of cats. A speaker tells the truth when speaking to someone with more cats and lies when speaking to someone with fewer cats. They make these statements:
1. C to B: “You have an even number of cats.”
2. B to C: “You have exactly 40% more cats than I do.”
3. B to A: “Your number of cats is the average of mine and C's.”
4. A to B: “My number of cats exceeds yours by at least 3.”
How many cats does B have? Prove that the positive-integer solution is unique.
### What a Strong Answer Covers
- Truth values derived from the direction of each comparison, rather than assumed independently.
- Elimination of the impossible ordering between A and B.
- Conversion of the 40% and average statements into exact equations.
- Integer and parity constraints that force B's value.
### Follow-up Questions
- Which statement first forces the complete ordering of the three owners?
- Would the solution remain unique if cat counts could be nonnegative rather than positive?
Overview: Deduce three distinct cat counts when each speaker's truthfulness depends on whether the listener owns more cats. The solution derives the ordering, converts the percentage and average claims into equations, applies parity and integrality, and proves that B uniquely owns 5 cats.
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