The workings:
The problem with corruption is that it is very expensive. Few, if any, countries can afford levels of corruption beyond a certain limit. Beyond this limit, corruption destroys the institutions that should belong to everyone, generating a process of instability and mistrust. Corruption ends up enriching very few and driving many into misery.
Political corruption is possibly the tip of the iceberg, the bigger the greater the corruption in a society is. Given the resonance that these cases have, they also serve to sedate consciences: if the minister, the mayor or the king are corrupt, or consent to those who are, why shouldn’t I be corrupt? To prevent corruption from overflowing, it is essential, first of all, not to practise it, and then to demand that politicians clean up their act. Especially in the country that invented picaresque.
The fun:
Four corrupt politicians have arrived at a luxurious flat on the Spanish coast, having just received a thick envelope full of banknotes, the fruit of their latest dirty deed. Still exhausted after the lavish meal with which they have celebrated the operation, they take a siesta. After a while, one of them, suspicious (corrupt politicians tend to be), fearing that the others might wake up and keep some banknotes, gets up, makes four equal parts of the total number of banknotes, keeps his part and leaves the rest piled up, also throwing a remaining banknote into a money box they had for miscellaneous expenses. After an hour, a second politician wakes up and has the same idea: he makes four equal parts of the total number of banknotes he finds, keeps one part, piles up the rest and throws another exceeding banknote into the money box. After another hour, the third politician does exactly the same operation as the second, and finally, the fourth politician does the same operation an hour later, although in this case he has no remaining banknotes to put in the money box.
Hours later, when they wake up from their siesta, they decide to distribute the banknotes (the ones that were finally left in the envelope) among the four of them, each of them thinking that none of the other three had realised what he had done before.
Knowing that no banknotes were left over in this last distribution and that the politicians already knew that the envelope contained no more than 1000 banknotes, he wonders:
What is the total number of banknotes in the envelope?
How many banknotes did each politician keep?
(Cartoon: Antonio Fraguas – Forges)
Solution:
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
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