An Out of this World Problem!

Number Theory Level 3

The first expedition to a distant planet found only the ruins of a civilization. The explorers were able to translate the "extraterrestrial" equation they found there as follows:

\[ 5x^2 -50x +125 = 0. \text{ Therefore, } x \text{ is equal to } 5 \text{ or } 8. \]

This was an extremely strange result. The value \(x=5\) seemed satisfactory, but \(x=8\) required some explanation. If their number system were similar to ours, how many fingers would you say the inhabitants in that planet had?

Make the assumption that if the inhabitants had \(n\) fingers, then they work in base \(n\).


Problem Loading...

Note Loading...

Set Loading...