Which box holds the prize — Aptitude Question
Which box holds the prize: Three boxes are labelled A, B and C, and exactly one holds a prize. Answer and worked solution on CodeKairo.
- Topic: Mathematical Reasoning
- Section: Logical Reasoning
- Difficulty: Hard
- Time target: 135 seconds
Question
Three boxes are labelled A, B and C, and exactly one holds a prize. Box A says 'the prize is not here', Box B says 'the prize is here', and Box C says 'the prize is not in B'. If exactly one statement is true, where is the prize?
Options
- Box A
- Box B
- Box C
- Cannot be determined
Show the answer and the worked solution
Correct answer: A. Box A
Worked solution
- Prize in A: A false, B false, C true → 1 true. ✓
- Prize in B: A true, B true, C false → 2 true. ✗
- Prize in C: A true, B false, C true → 2 true. ✗
- Only the first case gives exactly one true statement, so the prize is in Box A.
Answer: Box A.
The idea
Test each case exhaustively against the constraint. Counting the true statements per case is faster than reasoning about the statements directly.
Shortcut. B ('here') and C ('not in B') contradict each other, so exactly one of them is true — that uses up the single truth. A's statement must be false, so the prize is in A.
Common trap. "Box C" — taking A's statement as the lone truth, ruling out A and B, and not noticing that C's 'not in B' is then true as well.