Sum of digits?

Algebra Level 3

The digit sum of a number is the sum of its decimal digits. For example, the digit sum of 3406 3406 is 3 + 4 + 0 + 6 = 13 3+4+0+6=13 .

Determine the digit sum of the number ( 1 0 2018 + 1 ) 4 \left(10^{2018}+1\right)^4


The answer is 16.

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Chew-Seong Cheong
Oct 30, 2018

( 1 0 2018 + 1 ) 4 = 1 0 8072 + 4 × 1 0 6054 + 6 × 1 0 4036 + 4 × 1 0 2018 + 1 = 10000 ⋯ 00400 ⋯ 00600 ⋯ 00400 ⋯ 00001 \begin{aligned} \left(10^{2018} + 1\right)^4 & = 10^{8072} + 4\times 10^{6054} + 6 \times 10^{4036} + 4 \times 10^{2018} + 1 \\ & = 10000 \cdots 00400 \cdots 00600 \cdots 00400 \cdots 00001 \end{aligned}

Therefore, the digit sum of the given number is 1 + 4 + 6 + 4 + 1 = 16 1+4+6+4+1 = \boxed{16} .

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