Problem 19 · 2024 Math Kangaroo
Stretch
Counting & Probability
careful-counting
60 children stand in a row. Each child wears a high-visibility vest and a backpack. The vest colours always alternate: yellow, green, yellow, green, … The backpack colours follow the pattern red, brown, purple, red, brown, purple, … How many children have both a yellow vest and a purple backpack?
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Answer: E — 10
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Hint 1 of 2
Yellow vests are on odd positions; purple backpacks repeat every third child.
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Hint 2 of 2
Find positions that are both odd and a multiple of 3 — that's every 6th child starting at 3.
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Approach: combine the two repeating patterns
- Vests go yellow, green, ..., so yellow is on positions 1, 3, 5, ... (odd).
- Backpacks go red, brown, purple, ..., so purple is on positions 3, 6, 9, ...
- Both happen at positions 3, 9, 15, ..., i.e. every 6th child starting at 3.
- From 3 to 57 that is 10 children — 10 (E).
Mark:
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