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What is the sum of the digits of $(7^{10})(11^{10})(13^{10})$? The answer is $1024$.

Is there a simple way to approach this? Please help?

Danh Huynh
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    Hint: first compute $7\times 11 \times 13$ – Mark Bennet Jul 31 '17 at 15:57
  • And I can't see that the proposed answer will be correct, since there are $31$ digits at most $9$ - the hint does enable you to compute the answer efficiently, though. – Mark Bennet Jul 31 '17 at 16:02
  • That number isn't all that large...wolfram alpha can compute it (and the digit sum is much lower than $1024$). – lulu Jul 31 '17 at 16:06
  • Have you been asked to group the result into 3-digit numbers and add those? This would actually result in $1024$. – Reinhard Meier Jul 31 '17 at 16:37

1 Answers1

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Just an idea.

$7\times 11\times 13=1001$.

$7^{10}\times 11^{10}\times 13^{10}=1001^{10}=(10^3+1)^{10} $.

$1001^{10}=10^{30}+10\times10^{27}+45\times10^{24}+120\times10^{21}+210\times10^{18}+252\times10^{15}+210\times10^{12}+120\times10^{9}+45\times10^{6}+10\times10^3+1\times10^0.$

So $S=1+1+4+5+1+2+2+1+2+5+2+2+1+1+2+4+5+1+1=43$.

Janitha357
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