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2011 Math Kangaroo

Problem 5

Problem 5 · 2011 Math Kangaroo Easy
Counting & Probability careful-counting

All four-digit numbers whose digits add up to 4 are written down in descending order. In which position does the number 2011 appear?

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Answer: D — 9.
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Hint 1 of 2
List the four-digit numbers with digit sum 4 from the largest downward.
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Hint 2 of 2
Count how many come before 2011 in that descending list.
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Approach: enumerate in descending order until reaching 2011
  1. Descending: 4000; then 3100, 3010, 3001; then 2200, 2110, 2101, 2020, 2011.
  2. Counting them, 2011 is the 9th number.
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