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.
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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
- In 2014 the last digit 4 beats 2+0+1 = 3.
- Going back, years like 2013, 2012, ... fail (last digit not big enough), until 2009: 9 > 2+0+0 = 2.
- 2009 is 2014 − 2009 = 5 years ago.
Mark:
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