Hamming Distance, Bit message
The professor is asking you to find the lowest r such that the equation is true. At $r=1$, $2^1&lt;17+1$,
$r=2$, $2^2=4&lt;17+2=19$...
$r=4$, $2^4=16&lt;17+4=21$
 and finally $r=5$, $2^5=32\geq17+5=22$.