Problem 17 · 2018 Math Kangaroo
Medium
Logic & Word Problems
careful-counting
A hotel in the Caribbean correctly advertises with the slogan “350 days of sun in the year!” How many days does Mr. Happy have to spend in the hotel in a 365-day year to be guaranteed two consecutive days of sunshine to enjoy?
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Answer: D — 32
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Hint 1 of 2
There are 365 − 350 = 15 cloudy days to break up the sunny ones.
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Hint 2 of 2
Worst case, each cloudy day separates single sunny days; find the longest stay that could still avoid two sunny days in a row.
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Approach: worst-case spacing (pigeonhole)
- With 15 cloudy days you can separate sunny days into at most 16 single sunny days, giving 15 + 16 = 31 days with no two sunny days adjacent.
- So 31 days might not be enough, but on the very next day two sunny days must touch.
- He must stay 32 days to be guaranteed two consecutive sunny days.
Mark:
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