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2021 Math Kangaroo

Problem 4

Problem 4 · 2021 Math Kangaroo Easy
Counting & Probability careful-counting

How many four-digit numbers have the property that their digits, from left to right, are consecutive and in ascending order?

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Answer: B — 6
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Hint 1 of 2
A four-digit number with consecutive ascending digits is fixed once you pick its first digit.
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Hint 2 of 2
List the possible starting digits — the last digit cannot exceed 9.
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Approach: count valid starting digits
  1. Such a number looks like d, d+1, d+2, d+3 with d≥1 (no leading zero).
  2. The largest digit d+3 must be at most 9, so d can be 1, 2, 3, 4, 5, 6.
  3. That gives 1234, 2345, 3456, 4567, 5678, 6789 — six numbers.
  4. So the answer is B.
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