Problem 16 · 2013 Math Kangaroo
Hard
Number Theory
factorizationages
Today is Hans' and his son's birthday. Hans multiplies his age by the age of his son and obtains 2013. In which year was Hans born?
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Answer: A — 1952
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Hint 1 of 2
Factor 2013 and look for a pair of ages that could realistically be a father and son sharing a birthday.
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Hint 2 of 2
2013 = 3 × 11 × 61.
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Approach: factor 2013 into a sensible father-son age pair
- 2013 = 3 × 11 × 61.
- The only realistic father–son pair is 61 and 33 (61 × 33 = 2013).
- So Hans is 61 in 2013, meaning he was born in 2013 − 61 = 1952.
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