Teacher asked the students to find the cube root of a natural number but she did not mention the base. Students assumed the base found the cube root. Each student got an integer. Find the sum of digits of that number.
Find the sum of digits of a natural number
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number-theory
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0@TonyK, it's that garbled version that I found in various places on the web. I didn't find an ungarbled version though I think you and I agree there must be one. Presumably it runs something like this: A teacher asked her students to find the cube root of a natural number. She did not mention what base the number was written in. Different students assumed different bases, and each student found an integer answer. Which of these could be the sum of the digits of the original number: 0, 1, 6, 7, 8. Well, you'd need something to rule out the trivial answers 0 and 1. – 2011-09-02
1 Answers
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This is not a well-formed question, as $1^3=1$ with digit sum $1$, $11^3=1331$ (in any base higher than $3$) with digit sum $2$, and $111^3=1367631$ (in any base higher than $7$) with digit sum $3$ appear to satisfy the requirement, among others.
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0@Michael Hardy: Right. Fixed. I saw the need for a digit $3$ and thought I got one in base $3$. – 2011-08-23