MathDB

One eastern country was ruled by an old Shah. The population of the country consisted of inhabitants and satraps. Each resident had his own place of residence (place of registration). Satraps moved around the country and carried out the decrees of the Shah. One day the Shah issued a decree containing the following points:
1) Some residents are bandits. 2) Every bandit must be destroyed. 3) Together with the bandit, all those residents who are located closer to the bandit than the Shah (in other words, than the location of the Shah’s palace) must be destroyed.
Finding out which of the residents was a bandit was entrusted to the Shah's adviser, known for his connections with one hostile state. Prove that:
a) if the country in question is on a plane, then the adviser has the opportunity to declare no more than six inhabitants bandits in such a way that all inhabitants of the country must be destroyed in accordance with the decrees;
b) if the country is located on a sphere, then you can get by with five bandits.

Problem Statement