# What is the base for the following number system?

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!

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See this question: math.stackexchange.com/questions/47750/… :) – Sp3000 Feb 7 '12 at 13:43

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?

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Ok...I sort of understand where I am going with this.... but is there no algebraic formula to go about this....? – A_1_615 Feb 7 '12 at 13:50
What do you mean by "algebraic formula"? There are methods to go about this, but nothing to plug into your calculator. – Alex Becker Feb 7 '12 at 13:57
no I didn't mean plug and play, but what methods are there. i was looking at the link that someone posted....It seems to be the same sort of question...but Im still unsure – A_1_615 Feb 7 '12 at 13:59
Another observation you can make is that no matter what, # must be 1 as you are adding two 2-digit numbers to get a 3-digit number starting with #. – Alex Becker Feb 7 '12 at 14:00