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    1. COThanks Ralu, someone on the math site said something simlair so I updated the question to add a new condition(without changing the process for the user). What if the value of the fruit changes randomly everyday(I would have no control over it, since I could easily put extreme values to isolate possibilities)? If fruits prices are changing, wouldn't certain possibilities be less likely and over time the possibilities actually decrease to something more accurate?
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    2. COThere is no such thing as less an more probable. It is just about possible/impossible. And yes you can probably throw out some solutions if you know that they are integer solutions, but that is all. Think about that user begin whit 1000000, 1000000 and 1000000 and then it can change each value by +/- 50000 each time. So it does not matter if you limit difference for each step.
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    3. COI agree with you and thank you for explaining. I'm just thinking there's two things I need to solve to get to the answer. One is to limit the possibilities. If the total value is 5 and the price of apples jumped to $100 then clearly the user has no apples so I can eliminate that and so on..until maybe I have a range. Once I have that range then I think a simple guessing game structure can occur, the point of this question though is not to get the most accurate answer(which would be nice) but realistic how to get the most narrow range.
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