Problem 8 · 2014 Math Kangaroo
Easy
Logic & Word Problems
careful-counting
Grey and white pearls are threaded on a string (see picture). Monika wants 5 grey pearls, but she can only pull pearls off from an end of the string, so she has to pull off some white pearls too. What is the smallest number of white pearls she has to pull off to get 5 grey pearls?
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Answer: B — 3
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Hint 1 of 2
She can only take pearls from one of the two ends, so compare the two ends.
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Hint 2 of 2
Pick the end where the fifth grey pearl is reached after passing the fewest white pearls, and count just those whites.
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Approach: scan inward from the better end and count the white pearls passed
- Pearls come off only from an end, so check each end and stop once 5 grey pearls have come off.
- Reading in from the end that reaches the fifth grey pearl soonest, only a few white pearls sit among those first five greys.
- Counting just those white pearls gives a minimum of 3.
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