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?
I agree that the way you have put things makes no sense.
Here is a usual type problem in this category.
Suppose there are ten bins each containing a different ingredient.
In order to make seven different pies each containing exactly two different ingredients, what is the least number of bins we can choose?
This is what I thought you meant.
But now, I have no idea what you mean to ask.
Hmm, your interpretation is close, except each bin contains specific ingredients (plural) which can be used for different pies.
It's not supposed to be realistic (although I can think of a real situation for it) though.
What is the category called?Here is a usual type problem in this category.
As for duplicate baskets -- it's simply the way it is presented. If it makes no mathematical difference whether there are two baskets or one, I will go ahead and make it 7 baskets. I'm very inexperienced with this so I wanted to present the information as I have it.
Thanks for your patience.
Now I notice 2 more duplicates:
4 - A1, B, C2
6 - A1, B, C2
Like, if A1 + A1 does not make up A (A1 + A2 being required)
then these duplicates make no sense; so there's only 6 baskets.
Like Plato, I give up...
Make it 6 baskets if you like. It's a simple matter or organizing the question so that it makes sense to you.
The data is not negotiable. How you interpret it is a matter of mathematical reason, and it is up to you to do that if you want to solve the question.
Well, not to leave you empty-handed (no pun intended!),
we have 6 baskets; and you [PICK] comme suit (maximum of 2 per basket):
1: A2, B2 [NONE]
2: A1, B, C2 [C2]
3: A1, C1, F1 [C1]
4: C, D, E, F [D, E]
5: A, B, C2, E1 [A, B]
6: A2, B1, C, D1, E, F, G [F, G]
So now we can cook 7 pies, from an Apple pie to a Gooseberry pie