MathDB
Sum of Digits Equals 1000

Source: 2014 AMC 12A #16/10A #20

February 5, 2014
AMC

Problem Statement

The product (8)(8888)(8)(888\ldots 8), where the second factor has kk digits, is an integer whose digits have a sum of 10001000. What is kk?
<spanclass=latexbold>(A)</span>901<spanclass=latexbold>(B)</span>911<spanclass=latexbold>(C)</span>919<spanclass=latexbold>(D)</span>991<spanclass=latexbold>(E)</span>999<span class='latex-bold'>(A) </span>901\qquad <span class='latex-bold'>(B) </span>911\qquad <span class='latex-bold'>(C) </span>919\qquad <span class='latex-bold'>(D) </span>991\qquad <span class='latex-bold'>(E) </span>999\qquad