Problem

Source: 2023 China Western Mathematical Olympiad Grade p2 CWMI

Tags: combinatorics



In a certain country there are $2023$ islands and $2022$ bridges, such that every bridge connects two different islands and any two islands have at most one bridge in common, and from any island, using bridges one can get to any other island. If in any three islands there is an island with bridges connected to each of the other two islands, call these three islands an "island group". We know that any two "island group"s have at least $1$ common island. What is the minimum number of islands with only $1$ bridge connected to it?