base

that's not a problem...

sorry. 

The following addition problem is not correct if the numbers are interpreted as base 10 numbers. in what number base is the problem correct?

66+87+85+48=132

Let the base be b. Off the bat, we know that $b>8$.

If we added everything, it would look something like this:

        66

        87 

+      85

        48 

$\overline{\color{white}{wwwwww}}$

       132

Adding up the ones digit gives us 26, so we have $26 \mod b = 2$

The only options for b are b = 12 or 24. 

If b = 12, the sum of the ones digit would be $22_{12}$, so we could carry the 2 to the tens column. Adding everything up would give us ${24}_{12}$, so our answer would be $242_{12}$.

This means that the base is $\color{brown}\boxed{24}$.

(Add it up to see for yourself.)

You could also look at it like this: