Problem:
Hexadecimal (base-) numbers are written using the numeric digits through as well as the letters through to represent through . Among the first positive integers, there are whose hexadecimal representation contains only numeric digits. What is the sum of the digits of ?
Answer Choices:
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Solution:
Because , the largest number less than whose hexadecimal representation contains only numeric digits is . Thus the number of such positive integers is is excluded), and the sum of the digits of is .
The problems on this page are the property of the MAA's American Mathematics Competitions