Problem 14 · 2023 Math Kangaroo
Hard
Logic & Word Problems
casework
6 beavers and 2 kangaroos are standing on the fields 1 to 8 in a row. Of any three animals in a row there is always exactly one kangaroo. On which of these numbers stands a kangaroo?
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Answer: C — 3
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Hint 1 of 2
Split the eight fields into the blocks 1-2-3, 4-5-6 and note each must hold one kangaroo.
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Hint 2 of 2
Test where the two kangaroos can sit so every three-in-a-row has exactly one.
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Approach: place the two kangaroos so each consecutive triple has exactly one
- Fields 1-2-3 must contain one kangaroo and fields 4-5-6 another, using both kangaroos.
- Checking every window of three forces the kangaroos onto fields 3 and 6.
- Among the offered choices, a kangaroo stands on field 3.
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