Problem 14 · 2022 Math Kangaroo
Hard
Number Theory
digit-sum
The year 2022 has three equal digits. This is the third time that Tortoise Eva has experienced a year where the same digit appears three times. What is the minimum age that Tortoise Eva can be this year?
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Answer: C — 23
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Hint 1 of 2
List recent years whose four digits include the same digit three times.
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Hint 2 of 2
She has lived through three such years; to make her as young as possible, pick the latest possible earlier two.
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Approach: find the three latest triple-digit years up to 2022
- 2022 has three 2s. The two latest earlier such years are 2000 (three 0s) and 1999 (three 9s).
- If 2022 is her third, she was alive in 1999, so she was born by 1999.
- The smallest age is 2022 minus 1999 = 23.
- So the answer is C.
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