Question: We have one kind of drink in cup A and another kind in cup B. The cups are all same sizes and no cup can hold 100% of both drinks. (If we pour everything into one cup, it will overflow) How do we mix, only using these two cups, such that cup A contains 50% of drink A and 50% of drink B and cup B contains 50% of drink A and 50% of drink B?
The easiest solution occurs if you can actually put both drinks into a cup – then you mix and pour half into the other cup. However, this is not the case.
I did end up proving that this is impossible in finite number of steps. Now suppose we want to mix different drinks (so that cup A contains one mixture and cup B contains another mixture, proportion of those specified) for each cup such that cup A and cup B’s drinks are different. Is this possible?
My intuition, as soon as I typed the question, is that it should be possible as long as it’s not 50/50 (and also under the assumption that cup A and cup B are identical) – but it would be an interesting result if there exists a similar question such that the answer of such question is actually a smaller interval.
Now this is not really mathematically fascinating – but it did challenge my intuition to some degree today thinking about different variations. Think about this: if there are three cups with three different drinks – does it get more complicated?
