Problem 9 · 2023 Math Kangaroo
Stretch
Counting & Probability
caseworksum-constraint
23 animals are sitting in the first row of a cinema. Each animal is either a beaver or a kangaroo. Each animal has at least one kangaroo next to it. What is the maximum amount of beavers in the row?
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Answer: D — 11
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Hint 1 of 2
Every animal — including each kangaroo — needs a kangaroo as a neighbour.
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Hint 2 of 2
So kangaroos can't sit alone; they must come in adjacent pairs, and at most two beavers can sit between groups.
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Approach: kangaroos must be paired; pack beavers between pairs
- A lone kangaroo would have no kangaroo neighbour, so kangaroos occur in adjacent pairs.
- Between two such pairs at most two beavers fit (a third would be too far from any kangaroo).
- The tightest packing of 23 seats uses 12 kangaroos, leaving a maximum of 11 beavers.
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