Problem 22 · 2013 Math Kangaroo
Stretch
Number Theory
place-valuework-backward
The number 2013 is made up of the four consecutive digits 0, 1, 2, 3. How many years before the year 2013 was the date last made up of four consecutive digits?
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Answer: C — 581
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Hint 1 of 2
Search backward from 2013 for a year whose four digits are four consecutive values in some order.
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Hint 2 of 2
Try the digit-set {1,2,3,4} arranged to make the largest year below 2013.
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Approach: search backward for four-consecutive-digit years
- Just below 2013, the most recent year using four consecutive digits is 1432 (digits 1, 2, 3, 4).
- The gap is 2013 − 1432 = 581 years.
- So the answer is 581.
Mark:
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