2018 AMC 10A Problems/Problem 25
Problem
For a positive integer and nonzero digits , , and , let be the -digit integer each of whose digits is equal to ; let be the -digit integer each of whose digits is equal to , and let be the -digit (not -digit) integer each of whose digits is equal to . What is the greatest possible value of for which there are at least two values of such that ?
Solution
Notice that and . Setting and , we see works for all possible values of . Similarly, if and , then works for all possible values of . The second solution yields a greater sum of .
See Also
2018 AMC 10A (Problems • Answer Key • Resources) | ||
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All AMC 10 Problems and Solutions |
2018 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 24 |
Followed by Last Problem |
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All AMC 12 Problems and Solutions |
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