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min multiple of 81 that only contains the digit 1

Source: 2019 Dürer Math Competition Finals Day2 E6 E+2 https://artofproblemsolving.com/community/c1621835_2019_

January 5, 2022
number theorymultipledividesdivisibleDigits

Problem Statement

Find the smallest multiple of 8181 that only contains the digit 11. How many 1 1’s does it contain?
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