CZ-SK-MO 1991 Problem 5
In a group of mathematicians everybody has at least one friend (friendship is a symmetric relation). Show that there is a mathematician all of whose friends have average number of friends not smaller than the average number of friends in the whole group.
Dataset text AI-MO AoPS. Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.
Similar problems
These problems have the most words in common with this statement.