Here is an interesting problem. I'm not sure how to approach it yet.
You have eight baskets. 1,2,3 etc.
Each basket is filled with different ingredients to different pies. Each pie takes exactly two ingredients.
You want to make seven types of pies. A,B,C etc.
But you can only pick 5 of the baskets to take home, or less.
You're only allowed to take two ingredients (e.g., A1, B2, or A) from any one basket for a pie.
Here are the ingredient contents for each basket. A1 or A2 would be one or the other half of the ingredients to make pie A. "A" means both the ingredients to make pie A -- a combination of the both the two ingredients A1 and A2.
1 - A2, B2
2 - C,D,E,F
3 - A2, B2
4 - A1, B, C2
5 - A2, B1, C, D1, E, F, G
6 - A1, B, C2
7 - A1, C1, F1
8 - A, B, C2, E1
Assuming I'm some kind of efficiency nut , how do I figure out which five baskets to take home, to make *all seven pies*.
i) Do I need to take five baskets or can I get away with less?
ii) Assume there is an arbitrary advantage to taking baskets that have both ingredients to any one pie, does this change your answer?