Problem 16 · 2013 Math Kangaroo
Medium
Logic & Word Problems
casework
Aron, Ben and Carl always lie. Each of them picks a red or a green stone.
Aron says: “My stone is the same colour as Ben's.”
Ben says: “My stone is the same colour as Carl's.”
Carl says: “Exactly two of us have red stones.”
Which of the following is correct?
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Answer: A — Aron's stone is green.
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Hint 1 of 2
Everything the three say is false — flip each statement to a true fact.
Still stuck? Show hint 2 →
Hint 2 of 2
From the flipped facts, pin down each stone's colour.
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Approach: negate every statement (all liars)
- Aron's claim is false: Aron ≠ Ben in colour.
- Ben's claim is false: Ben ≠ Carl, so Aron = Carl and Ben is the odd one.
- Carl's claim is false: it is NOT exactly two red, so the matching pair (Aron, Carl) cannot be the red pair — they are green, Ben is red.
- Thus Aron's stone is green, which is the correct statement.
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