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Find the sum of the digits

Source: 1970 AHSME Problem 33

April 16, 2014
symmetryAMCAIMEUSA(J)MOUSAMOAIME II

Problem Statement

Find the sum of the digits of all numerals in the sequence 1,2,3,4,⋯ ,100001,2,3,4,\cdots ,10000.
<spanclass=′latex−bold′>(A)</span>180,001<spanclass=′latex−bold′>(B)</span>154,756<spanclass=′latex−bold′>(C)</span>45,001<spanclass=′latex−bold′>(D)</span>154,755<spanclass=′latex−bold′>(E)</span>270,001<span class='latex-bold'>(A) </span>180,001\qquad<span class='latex-bold'>(B) </span>154,756\qquad<span class='latex-bold'>(C) </span>45,001\qquad<span class='latex-bold'>(D) </span>154,755\qquad <span class='latex-bold'>(E) </span>270,001
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