Problem 5 · 2013 Math Kangaroo
Easy
Number Theory
place-valuework-backward
The year 2013 is made up of four consecutive digits 0, 1, 2, 3 (in some order). How many years before 2013 was the most recent year also made up of four consecutive digits?
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Answer: C — 581
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Hint 1 of 2
You need the most recent earlier year whose four digits are four consecutive integers in some order.
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Hint 2 of 2
Try the digit sets {1,2,3,4} and {0,1,2,3} and find the largest valid year below 2013.
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Approach: search digit-consecutive years just below 2013
- A year of four consecutive digits uses a set like {0,1,2,3}, {1,2,3,4}, etc.
- Below 2013, the largest such year comes from {1,2,3,4}: arranging them as 1432.
- 2013 − 1432 = 581, so C.
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