199 corrupted ministers
Source: III Soros Olympiad 1996-97 R2 11.6 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics
May 31, 2024
combinatorics
Problem Statement
In one criminal kingdom, an underdeveloped state, the King decided to start a fight against corruption and, as an example, punish one of his ministers. The ministers were summoned to the palace and seated at a large round table. At first they wanted to find the one who had the most money in his bank account and declare him the main corrupt official. It takes minutes to determine the amount of money in the bank account of one minister. But the King ordered that the accused be found within four hours while he underwent medical procedures. According to the Noble Court Administrator, any minister can be accused, you just need to find a legal justification.The Chief Lawyer proposed that the first minister discovered, who has more money in his bank account than each of his two neighbors (one on the right and one on the left), be declared corrupt. How can one be sure to find a minister who meets this condition within the allotted hours? (During this time, it is possible to consistently determine the size of the bank accounts of no more than ministers. It is assumed that the amount of money in bank accounts is different.)