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2014 Math Kangaroo

Problem 15

Problem 15 · 2014 Math Kangaroo Medium
Arithmetic & Operations total-then-divide

Six weeks are \(n!\;(=n\cdot(n-1)\cdot\ldots\cdot2\cdot1)\) seconds. \(n={?}\)

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Answer: D — 10
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Hint 1 of 2
Turn six weeks into seconds, then recognise the number.
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Hint 2 of 2
The product 1·2·3·… that hits it is a factorial you may know.
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Approach: convert to seconds and match a factorial
  1. Six weeks = 6·7·24·3600 seconds = 3 628 800 seconds.
  2. That number is exactly 10! = 1·2·3·…·10.
  3. So n = 10.
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