Before the magician knows that one is lower than all the others, he knows what his debt is. So, we want to look at sets that add to 12 where the lowest number is repeated at least once. Those are as follows, with the products in paranthesis after the set:
Those are the possibilities so far. Then the magician is told that the lion tamer's is the lowest. So, we know that the lowest number does not repeat. What are the possiblities without the lowest number repeating?
Now, you know that before and after the magician knew his debt, which means that there should be one set from each where the products are equal. The only ones that have an equal product are 48 (2,2,2,6 and 1,3,4,4)
So the debts are: Lion tamer owes $3, magician owes $48, and the other three owe $3, $4 and $4. Course if I were the magician I would go with the 1,2,3,6 set just cause it means that he owes less. Brett was wrong; never trust magicians, not clowns.