Single-dose tablets

The workings

Who hasn’t recommended taking an ibuprofen tablet for a headache? In January this year, Stewart Adams, who is considered to be its inventor, died. The truth is that the discovery was the work of a group of four researchers from the Boots pharmaceutical company in the 1960s, led by Adams, including Antonio Ribera Blancafort, from Barcelona, as stated in the original patent (which lists the authors in alphabetical order). It seems that Ribera came up with the formula that would later be synthesised by another member of the team, John Nicholson. Although our protagonist became a professor at the University of Barcelona and rector of the University of the Balearic Islands, at that time he was only a lab technician and the merit was attributed, as is usually the case, strictly on the basis of rank. Although in cases such as this one the practice is not entirely unjustified, in other cases, unfortunately, it conceals serious situations of employment discrimination.

The fun

A bottle contains 50 single-dose tablets of a medicine and 50 double-dose tablets. On arrival, each patient randomly takes out a pill; if it is a single-dose pill, he takes it, and if not, he divides it with a pill cutter, takes half of it and returns the other half as a new single-dose pill to the bottle. When five patients have passed,

1. What possible compositions of single- or double-dose pills can the bottle have?
2. What is the probability that the bottle has 47 single-dose pills?

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Solutions

We encourage the readers to try to solve the divertimento for themselves. Whether you succeed or not, you can always consult the solution in this link.