Please help ASAP!
Zip codes consist of five digits. How many zip codes read the same upside down as right side up?
The answer is $75$, but why? Shouldn't it be $3^5$ because $0$, $1$, and $8$ can be read the same upside down, and right side up?
Thanks.
Hints:
Normal strings are read left-to-right, but upside down strings are read right-to-left (w.r.t. the original orientation). Thus, any zip codes containing only $0, 1$, and $8$ that are the same upside-down and right-side-up need to be palindromic, and from this notice that the first $3$ digits determine such a string.
Moreover, don't forget that a $6$ becomes a $9$ upside-down. This means that the string $06890$, for instance, is read the same upside-down and right-side-up.