A spoon of milk into the water, a spoon back

Question

Two jars hold equal amounts of liquid: one is milk, the other is water. You take one spoonful of milk and stir it into the water jar. Then you take one spoonful of the mixture from the water jar and put it back into the milk jar. The spoon is the same size both times, and there is no spillage.

Afterwards, is there more milk in the water jar, or more water in the milk jar? Does it matter how well you stirred?

Accepted Answer

They are exactly equal, and stirring makes no difference. The counting argument. Each jar starts with, say, a full cup of liquid. One spoonful leaves the milk jar, then one spoonful comes back, so at the end the milk jar holds exactly one cup of liquid again. That cup is made of some milk and some water. Whatever amount of water is now in the milk jar, that water displaced an equal amount of milk, and that displaced milk can only be in one place: the water jar. So the volume of water in the milk jar equals the volume of milk in the water jar. An analogy. Two boxes each hold 100 marbles, one b…

A spoon of milk into the water, a spoon back

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