Problem 30 · 2020 Math Kangaroo
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Logic & Word Problems
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Adam and Bruna try to find out which is Carla's favourite figure, among the figures shown. Carla told Bruna the shape of the figure, and told Adam the colour of the figure. Then this conversation takes place. Adam: “I don't know what Carla's favourite figure is, and I know that Bruna doesn't know either.” Bruna: “At first I didn't know what Carla's favourite figure was, but now I know.” Adam: “Now I know too.” What is Carla's favourite figure?
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Answer: E
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Hint 1 of 2
Adam knows the colour, Bruna the shape; each statement eliminates possibilities.
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Hint 2 of 2
Adam knowing Bruna cannot know rules out any colour containing a one-of-a-kind shape.
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Approach: step through the knowledge statements
- Adam (knows colour) is sure Bruna cannot know yet, so the colour has no unique-shape figure — this rules out white (the lone hexagon), leaving green and pink.
- Bruna (knows shape) now can tell: among green/pink only square, star and triangle are unique, so the figure is green square, green star, or pink triangle.
- Adam now knows from the colour, which is unique only for pink, so it is the pink triangle (E).
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