What is the base for the following number system?

Question

So there was a spaceship sent back with the following picture that assumed to constitute an addition. What is the base of the number system?

   # *
   # *
_________
 # ^ #

How would I find this out...? I have no clue how to approach this!

Answer 1

Have you considered the possibility that this is base 3? This would have the following implications:

1. * is either 1 or 2, because * + * $\neq$ *.
2. # is either 1 or 2 as well for the same reasons.
3. This means ^ must be 0.

What happens when you assume * = 1 and # = 2? Does the result make sense? What about when you assume * = 2 and # = 1?