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sum of digits of 99x9999x...x99..99

Source: Switzerland - 2006 Swiss MO Final Round p3

December 26, 2022
number theorysum of digitsDigits

Problem Statement

Calculate the sum of digit of the number 9×99×9999×...×99...99⏟2n9 \times 99 \times 9999 \times ... \times \underbrace{ 99...99}_{2^n} where the number of nines doubles in each factor.
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