Setup/Scenario:
So let's suppose you have 4 types of apples: red, blue, yellow, and green
When present, each color apple will always be present in a proportionally consistent manner to other colored apples. Different apples will appear in different piles and you know which piles are limited to specific colors of apples.
R:B:Y:G being 4:2:0:1 for example
Pile 1: 8R, 4B, 0Y, 2G
Pile 2: 16R, 8B, 4G
Pile 3: 4R, 0Y, 1G
Pile 4: 16R, 8B
Pile 5: 8B, 2G
Pile 6: 8R, 0Y
Pile 7: 4R
Problem:
You are forced to wear glasses that make you see in greyscale, and can't discern the colors of the apples. The only information you have is:
Pile 1: 14 Total, pile contains RBYG
Pile 2: 28 Total, pile contains RBG
Pile 3: 5 Total, pile contains RYG
Pile 4: 24 Total, pile contains RB
Pile 5: 10 Total, pile contains BG
Pile 6: 8 Total, pile contains RY
Pile 7: 4 Total, pile contains R
Are there any ways to find the master ratio of 4:2:0:1 from the information you're given?
I'd also like to note that fractions of apples are fair play, they can exist in a pile.
Extra information on the question for the curious:
-If this isn't possible I would still find value in an answer that only solves for certain colors of apples, ie if only part of the master ratio can be solved I would still deem this information useful.
-General rules would be helpful if you happen to realize any. For example, if (# of piles) must be > (# of apple colors)
-If there's some sort of tweak necessary to the given information that doesn't simply add more piles of apples with individual colors, then I would also be interested.
-I would like to aim to limit the number of individual-colored-apple piles to 1 if possible, if switching pile 7's color gives a solution I would be interested.