Problem 25 · 2016 Math Kangaroo
Stretch
Number Theory
primes
In the Kangaroo Republic, every month has 40 days, which are numbered through from 1 to 40. Every day with a number that is divisible by 6 is a public holiday, and likewise every day with a prime number. How often per month does it occur that there is exactly one working day between two public holidays?
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Answer: A — 1
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Hint 1 of 2
Mark every day that is a multiple of 6 or a prime as a holiday.
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Hint 2 of 2
Look for a holiday, then a single working day, then another holiday.
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Approach: list and scan
- Holidays are the primes and the multiples of 6 up to 40.
- Scanning for the pattern holiday–working–holiday, only day 4 sits alone between holidays 3 and 5.
- So it happens 1 time.
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