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