Problem 15 · 2010 Math Kangaroo
Stretch
Logic & Word Problems
casework
In a bag are blue, green and red balls (at least one ball of each colour). If we randomly take five balls out of the bag, we know: at least two balls are red and at least three are of the same colour. How many blue balls are in the bag?
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Answer: A — 1
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Hint 1 of 2
'We always know' means it must hold no matter which five balls come out.
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Hint 2 of 2
Work out the smallest set of balls that forces both guarantees.
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Approach: use the guarantees to pin down the counts
- For any 5 balls to surely include at least two red, at most 3 balls can be non-red.
- For any 5 to surely include three of one colour as well, the counts are forced to red = 3, plus one each of the others.
- That makes exactly 1 blue ball.
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