Question 52
Each of two people, $A$ and $B$, chose 3 positive one-digit integers (which need not be distinct). The sum of the 3 numbers $A$ chose is equal to the product of the 3 numbers $B$ chose, and the product of the 3 numbers $A$ chose is equal to the sum of the 3 numbers $B$ chose. How many possibilities are there for triplets of numbers chosen by $A$? Two triplets which are permutations of each other should be counted as the same triplet.