Question:

A man has to take two pills each day, at the exact same time or he will die. If he only takes one or he takes two of the same pill he will die. Both medications look the same and are the same weight. One day he drops both open pill bottles scattering the pills across the floor. There are two pills left in one bottle. How can he take his pills so he won’t die?

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Solution: First the man must take a scale and find the exact weight of two of the pills. Since the pills on the ground are randomly mixed, there is no possible way to separate them again. The solution is to go one step further in their mixing. Since the medications were of identical weight, and the man was taking one pill from each medication every day, half of the mixed pills will be from each medication.

The man should take the two pills remaining in the bottle and place them in the pile, then grind all of the mixed pills into a powder. The powder should be mixed so that both medications are equally distributed throughout the powder (in the manner a pharmacologist measures out pills; the actual medication only amounts to a small percentage of the actual pill).

With enough mixing, a sample of this powder will contain 50% of one medication and 50% of the other, a result of Probability. The man can now create new pills from this powder or simply ingest the powder, as long as the amount of the mixture he takes each day is equal in weight to the weight of two of the old pills. Ideally, he would now take one pill each day which is twice as large as either of the former pills. This way, he receives the same amount of each medication he would have as if he were to take two of the old pills.