Problem 7 · 2011 Math Kangaroo
Medium
Number Theory
careful-counting
The date 01-03-05 (1st March 2005) has three consecutive odd numbers. This is the first day in the 21st Century with this property. How many days with this property are there in total in the 21st Century?
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Answer: A — 5
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Hint 1 of 2
The date reads day-month-year as three numbers that are consecutive odd numbers.
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Hint 2 of 2
List consecutive-odd triples and check that the day and month stay valid.
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Approach: list consecutive odd triples that form a valid date
- We need day, month, year to be three consecutive odd numbers, with day ≤ 31 and month ≤ 12.
- The triples that work: (1,3,5), (3,5,7), (5,7,9), (7,9,11), (9,11,13).
- (11,13,15) fails because month 13 does not exist.
- That gives 5 such dates in the 21st century.
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