[EDIT]Highlited in red is incorrect!
I pick A, B, C, and D to be prices for the items being sold (in cents). The product will look like this:
A * B * C * D = 711
(A * B * C) * D = 711
>> 711 % (A * B * C) == 0
What I mean by above is that EACH of the items bust be an INTEGER FACTOR of 711, in order to divide 711 cents by either of the prices and get an integer value in cents again. This is based on the assumption that the prices are integer values in cents, can't have a dicimal of a cent in price.
Now, the integer factors of 711 are: 1, 3, 9, 79 and 237.
This is the same as:
$0.01, $0.03, $0.09, $0.79 or $2.37
Let's theorize that all items are priced below $2.37, that is either $0.01, $0.03, $0.09 or $0.79. This would mean that you must be able to get a sum of $7.11 out of 4 items that are $0.79 or below, which is impossible. If only 1 item is $2.37, then the other 3 must add to 7.11 = 2.37 = 4.74 >> impossible again with 3 items below $1. So, at least 2 items must be priced at $2.37 each, leaving other 2 to be: 7.11 - (2 * 2.37) = 2.37
As you can see, it's impossible to have 2 items priced $0.01, $0.03, $0.09, $0.79 or $2.37 to add to $2.37 without them being $0 and $2.37. Now, this again is impossible, because the product must be a non-zero value.
I see no solution for this probem.