Problem 14 · 2024 Math Kangaroo
Stretch
Logic & Word Problems
careful-counting
Simon has four cups with matching saucers (see picture). He places a randomly chosen cup on each saucer. Which statement is definitely true?
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Answer: D — It is impossible that exactly 3 cups are on the matching saucers.
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Hint 1 of 2
Test each statement: can you picture an arrangement where it fails? If yes, that statement is not certain.
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Hint 2 of 2
Think about what happens to the last cup if exactly three are already on their matching saucers.
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Approach: rule out the impossible count of correct matches
- If three cups sit on their matching saucers, then three cups and three saucers are correctly paired, leaving one cup and one saucer that must also match.
- So having exactly three matches forces a fourth match — you cannot have exactly three.
- The other options can each happen with some arrangement, so they are not certain.
- The statement that is definitely true is D: it is impossible that exactly 3 cups are on the matching saucers.
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