MathDB
Hexadecimal Numbers

Source: 2015 10A #18

February 4, 2015
AMC

Problem Statement

Hexadecimal (base-16) numbers are written using numeric digits 00 through 99 as well as the letters AA through FF to represent 1010 through 1515. Among the first 10001000 positive integers, there are nn whose hexadecimal representation contains only numeric digits. What is the sum of the digits of nn?
<spanclass=latexbold>(A)</span>17<spanclass=latexbold>(B)</span>18<spanclass=latexbold>(C)</span>19<spanclass=latexbold>(D)</span>20<spanclass=latexbold>(E)</span>21 <span class='latex-bold'>(A) </span>17\qquad<span class='latex-bold'>(B) </span>18\qquad<span class='latex-bold'>(C) </span>19\qquad<span class='latex-bold'>(D) </span>20\qquad<span class='latex-bold'>(E) </span>21