Problem 6 · 2025 Math Kangaroo
Easy
Counting & Probability
careful-countingcasework
Lisa has four wooden digits. She can use them to make the number 2025. How many different numbers greater than 2025 can she make with these digits?
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Answer: C — 8
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Hint 1 of 2
You are rearranging the digits 2, 0, 2, 5 into four-digit numbers larger than 2025.
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Hint 2 of 2
Fix the leading digit and count valid arrangements, remembering 2025 itself does not count.
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Approach: count permutations greater than 2025
- The digits are 2, 0, 2, 5; distinct arrangements with a non-zero lead: leading 2 gives 202_/205_/220_/etc., leading 5 gives several.
- List those strictly above 2025: 2052, 2205, 2250, 2502, 2520, 5022, 5202, 5220.
- That is 8 numbers.
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