Problem 17 · 2013 Math Kangaroo
Medium
Number Theory
Counting & Probability
careful-countingplace-value
All four-digit positive numbers that use the same digits as 2013 were written on a blackboard in ascending order. Find the largest possible difference between two numbers that are next to each other on the blackboard.
Show answer
Answer: A — 702
Show hints
Hint 1 of 2
List the four-digit numbers using the digits 2, 0, 1, 3 each once (no leading 0), in order.
Still stuck? Show hint 2 →
Hint 2 of 2
The biggest jump happens where the leading digit changes.
Show solution
Approach: order the arrangements, find the largest jump
- Using digits 2,0,1,3 (no leading zero) gives numbers starting with 1, 2, or 3.
- The largest number starting with 2 is 2310; the smallest starting with 3 is 3012.
- Their difference 3012 − 2310 = 702 is the largest gap between consecutive numbers.
- So the answer is 702.
Mark:
· log in to save