2019 AMC 10B Problems/Problem 12
Contents
Problem
What is the greatest possible sum of the digits in the base-seven representation of a positive integer less than ?
Solution 1
Observe that . To maximize the sum of the digits, we want as many s as possible (since is the highest value in base ), and this will occur with either of the numbers or . Thus, the answer is .
~IronicNinja
Solution 2
Note that all base numbers with or more digits are in fact greater than . Since the first answer that is possible using a digit number is , we start with the smallest base number that whose digits sum to , namely . But this is greater than , so we continue by trying , which is less than 2019. So the answer is .
LaTeX code fix by EthanYL
See Also
2019 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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All AMC 10 Problems and Solutions |
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