Problem 12 · 2011 Math Kangaroo
Medium
Number Theory
careful-counting
All the four-digit numbers with the same digits as 2011 (i.e. 0, 1, 1, 2) are written in a row in ascending order. What is the difference between the two numbers that are next to 2011 in this list?
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Answer: B — 891
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Hint 1 of 2
List all four-digit numbers using the digits 0, 1, 1, 2 in increasing order.
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Hint 2 of 2
Find 2011 in the list and look at its immediate neighbours.
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Approach: order the arrangements and subtract the neighbours
- Using digits 0,1,1,2 (no leading zero), the ordered list is 1012, 1021, 1102, 1120, 1201, 1210, 2011, 2101, 2110.
- The numbers just before and after 2011 are 1210 and 2101.
- Their difference is 2101 − 1210 = 891.
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