Briefly

The problem of the pills

The problem of the pills

My uncle Joaquin has a disease that forces him to take one pill of each of the two different medicines that the doctor prescribed for 30 consecutive days. The pharmacist gave him a bottle of medicine "A" and a bottle of medicine "B" each of which contained exactly 30 pills. Since both pills have exactly the same appearance, he recommended that he be especially careful and not confuse them.

Last night he put on the table a pill from the bottle labeled "A" and a pill from the bottle labeled "B" but he got distracted for a moment and realized that there were three pills on the table. The pills are indistinguishable from each other but counting the ones left in the bottles my uncle realized that by mistake there were two pills from the “B” bottle instead of just one as prescribed by the doctor.

The doctor warned him that it was extremely dangerous to take more than one pill per day of each class and in addition the pills are too expensive to discard and take new ones from the bottles.

How did my uncle take that night and each of the following nights exactly one pill of each class?

Solution

There are several possible solutions to this problem although they all follow the same philosophy. One of them is to divide the pills we have on the table in half, so that we will leave one side of the table on one side of the table and the other half of each of the three tablets on the other side.

Since we know that we have two pills from the “B” bottle, we take another one from the “A” bottle, we split it and again we place one half on one side of the table and the other half on the other side. At this time we can ensure that we have two halves of “A” type pills and two halves of “B” type pills on each side of the table, that is, one tablet of each type in total.