Proof:

Suppose the red bottle was made by Menes. Then at most one of the bottles is made by Menes, so that necessarily it is the red bottle. Therefore, The yellow and blue bottles were both made by Nil, so that both yellow and blue bottles contain the cure. This is of course a contradiction to the fact that the cure is only in one of the bottles. Therefore, the red bottle must have been made by Nil. Then since at least two of the bottles were made by Menes, those bottles must have been the yellow and blue bottles. It follows that the yellow and blue bottles do not contain the cure and hence, the red bottle contains the cure.

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