Fun Mathy Type Riddles

[FatAndFaithless]

This can be approached as a mathy puzzle or one can work like a dog with some pretty ugly fractions.  (Don't be that guy.)

There are two glasses containing an equal volume, one of milk and one of grape juice.  A spoonful of grape juice is taken from its glass and stirred into milk glass.  Then a spoonful of what had started as pure milk is returned to the grape juice glass and stirred in.  At the end of each such cycle the two glasses again contain exactly the same volume of liquid.  The process is repeated some number of times.  When finished will there be more grape juice in the milk glass or more milk in the grape juice glass or ..?

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Wouldn't there be equal amounts of grape juice in the milk as milk in the grape juice?  if the glasses always return to the original, equal volume, then any crossover between the two glasses must be equivalent or the volumes would be different.  If the volume of each glass is V1 = Gr1 + M1 and V2 = Gr2 + M2, and V1 = V2, then there must either be 100% Gr or M in one cup (impossible as they are being mixed), or Gr1 must = M2, and M1 must = Gr2, meaning that there is as much milk in the wine as there is wine in the milk.

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