Problem 24 · 2022 Math Kangaroo
Stretch
Logic & Word Problems
casework
In a certain city the inhabitants only communicate by asking questions. There are two kinds of inhabitants: the ‘positive’ that only ask questions that are answered with ‘yes’ and the ‘negative’ that only ask questions that are answered with ‘no’. We meet the inhabitants Albert and Berta, and Berta asks us: “Are Albert and I both negative?” What kind of inhabitants are they?
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Answer: C — Albert is positive and Berta is negative
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Hint 1 of 2
A positive only asks questions whose true answer is 'yes'; a negative only 'no'.
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Hint 2 of 2
Test the four type-combinations against Berta's question 'Are Albert and I both negative?'
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Approach: test each type assignment for consistency with Berta asking the question
- Berta can only ask her question if its true answer matches her type (yes for positive, no for negative).
- Check each combination of Albert and Berta being positive or negative for consistency.
- Only 'Albert positive, Berta negative' is consistent, giving answer C.
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