[sqlite] help with simple query, please

[Brannon King]

Suppose I have two tables, A and B. A has two columns: score, location. 
B has two columns leftLocation, rightLocation.

I need the maximum score located outside all entries in table B. B is a 
small table, say less than 100 entries.

I tried this:

SELECT max(score),location FROM A, B GROUP BY score HAVING location < 
min(leftLocation) && location > max(rightLocation)

It doesn't work the way I think it should, not to mention it's the wrong 
algorithm because left/rightLocation are made to be used in pairs.

So, how is it done?

Thanks,
Brannon