What are letters doing with my numbers?

Number Theory Level 4

Consider a three digit number where:

A 3 + B 3 + C 3 + A B C = A B C ‾ { A }^{ 3 }+{ B }^{ 3 }+{ C }^{ 3 }+ABC\quad =\quad \overline { ABC }

A + 2 B + 4 C 3 = A \frac { A+2B+4C }{ 3 } =A

What is A B C ‾ \overline {ABC} ?

Details and Assumptions: A B C ‾ \overline {ABC} is a three digit number, whereas ABC indicates multiplication. A B C ‾ \overline {ABC} is positive.
NOTE: A, B, and C are the digits of the number A B C ‾ \overline {ABC} . By that definition, A, B, and C are integers from 0 to 9.


The answer is 952.

Seth Lovelace by Seth Lovelace , 23, USA

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1 solution

Seth Lovelace
Aug 22, 2014

Hey @Calvin Lin ! Sorry, did not realize that a 3 that I typed was supposed to be a 4. I changed the wording of the problem to be correct and prettier, but I feel bad that people got points off for my typing error. Is there any way to give users back points and attempts for this problem? Thank you very much! - Seth

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Thanks. I've updated things accordingly.

Calvin Lin Staff - 6 years, 9 months ago

And to whoever reported this question, THANK YOU! I appreciate having someone find my error and tell me, because if no one ever did, this problem would forever be unsolved. :(

Seth Lovelace - 6 years, 9 months ago

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