Problem 13 · 2022 Math Kangaroo
Hard
Number Theory
place-valuecareful-counting
We check the water meter and see that all digits on the display are different. What is the minimum amount of water that has to be used before this happens again?
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Answer: D — 0.137 m³
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Hint 1 of 2
The meter shows 91.876; you want the next reading whose five digits are all different.
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Hint 2 of 2
Step up the reading until no digit repeats, then subtract.
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Approach: find next all-distinct reading
- Current reading 91.876 (digits 9,1,8,7,6 all different).
- Stepping up, the next reading with five different digits is 92.013.
- Water used = 92.013 − 91.876 = 0.137 m³.
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