Fun Mathy Type Riddles

[brewer]

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If each glass only contained one spoonful each, then it does not matter how many cycles. Remember this comes from a math tard cheater.

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Sorry I've spent the day outside choking on the smokey air.

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It is a special case but the answer is the same in every other case too.  Interestingly, even if you began with exactly one spoonful in each glass the answer will be the same, namely "the same amount of each contaminant in each glass".  In this case there would be 50% of each liquid in each glass, but that doesn't affect the answer.  As F&F said, the quantity of liquid in each glass is the same in each glass at the end of each cycle.  So however much is missing from the grape juice is not in the milk glass, and exactly that much milk can only then go into the grape juice glass.

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Nobody responded.

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Is the answer that it will be unequal until at least half the volume is exchanged, and then equal after that?

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So long as complete cycles are completed in the manner specified it will be equal after each and every cycle .. no matter the size of the glass, the spoon or the number of cycles.

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Sorry, that makes no sense to me. After you transfer one spoonful of juice to the milk, stir, then transfer back one spoonful of juice/milk to the juice you're replacing a minute amount of juice back to the juice and transferring a lesser minute amount of milk. The concentrations will not be exactly the same, only the volume will. 

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Please ignore my crankiness.

Edit: NVM, fog lifted.