AMC 10 Step by Step
2020 AMC 10BProblem 15P11-15~6 minPrint

Steve wrote the digits 11 , 22 , 33 , 44 , and 55 in order repeatedly from left to right, forming a list of 10,00010,000 digits, beginning 123451234512.123451234512\ldots. He then erased every third digit from his list (that is, the 33 rd, 66 th, 99 th, \ldots digits from the left), then erased every fourth digit from the resulting list (that is, the 44 th, 88 th, 1212 th, \ldots digits from the left in what remained), and then erased every fifth digit from what remained at that point. What is the sum of the three digits that were then in the positions 2019,2020,20212019, 2020, 2021 ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.