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2014 Math Kangaroo

Problem 5

Problem 5 · 2014 Math Kangaroo Easy
Number Theory digit-sumplace-value

In the year 2014, the last digit is bigger than the sum of the other three digits. How many years ago did this last happen?

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Answer: C — 5
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Hint 1 of 2
You need the most recent earlier year where the last digit beats the sum of the first three.
Still stuck? Show hint 2 →
Hint 2 of 2
Step back year by year and check the digit condition.
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Approach: check the digit condition on recent years
  1. In 2014 the last digit 4 beats 2+0+1 = 3.
  2. Going back, years like 2013, 2012, ... fail (last digit not big enough), until 2009: 9 > 2+0+0 = 2.
  3. 2009 is 2014 − 2009 = 5 years ago.
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