Puzzle 10 | (A Man with Medical Condition and 2 Pills)
Puzzle: A man has a medical condition that requires him to take two kinds of pills, call them A and B. The man must take exactly one A pill and exactly one B pill each day, or he will die. The pills are taken by first dissolving them in water.
The man has a jar of A pills and a jar of B pills. One day, as he is about to take his pills, he takes out one A pill from the A jar and puts it in a glass of water. Then he accidentally takes out two B pills from the B jar and puts them in the water. Now, he is in the situation of having a glass of water with three dissolved pills, one A pill and two B pills. Unfortunately, the pills are very expensive, so the thought of throwing out the water with the 3 pills and starting over is out of the question. How should the man proceed in order to get the right quantity of A and B while not wasting any pills?
Solution: Follow this step-wise approach to help the man take his medicine in the correct way.
- Step 1: Add one more A pill to the glass and let it dissolve.
- Step 2: Take half of the water today and half tomorrow.
It works under the following assumptions.
- The dissolved Pills can be used the next day.
- The man has to take pills at least for one more day.
- The pills are uniformly dissolved in water
- The person should add pill A to the glass of water.
- Now, the person can boil the solution in a jar and the water will get evaporated. Thus, the residue of the medicine will be left.
- Now he can take half of the residue, which will be equivalent to a single day dosage (1 Pill A + 1 Pill B) and take the rest tomorrow.
It works under the following assumptions:
- The medicine does not evaporate with the water.
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