## Repeating Digits In Different Bases

931 (in base 10) is an interesting number since in two other bases, it’s a repeating 3-digit number, namely, in base 11 and base 30.

$931=777_{11}$ and $931=111_{30}$

Can you find the other three-digit numbers with this property?

## Solution

$273=333_{9}$; $273=111_{16}$

$546=666_{9}$; $546=222_{16}$