Help devising recursive function

[Panphobia]

So I had a contest last friday, I did get to the next round finishing 1,2,3, and 5 in less than an hour, but I could not finish this question, I know you can just brute force through all possible arrangements of prices to coupons to taxes to bogo, but I am not sure how, I was thinking that you could do this recursively, but I am stuck on finding a certain base case for it, and also I would like to find out how to through every recursive call figure out a different ordering of the coupons to prices