Problem 7 · 2011 Math Kangaroo
Medium
Counting & Probability
careful-counting
All four-digit numbers whose digit sum is 4 are written down in order of size, starting with the biggest. In which position is the number 2011?
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Answer: D — 9.
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Hint 1 of 2
List four-digit numbers with digit sum 4 from biggest to smallest.
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Hint 2 of 2
Stop when you reach 2011 and read off its position.
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Approach: enumerate in decreasing order
- Biggest first: 4000, 3100, 3010, 3001, 2200, 2110, 2101, 2020, 2011, ...
- Count the positions: 2011 is the 9th number in the list.
- So 2011 sits in position 9.
- The answer is 9, choice (D).
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