Question 49
A natural number $n$ is given. There are $n$ islands with $n-1$ bridges between them, such that you can get from every island to every other island. One afternoon a fire breaks out on one of the islands. Every morning the fire spreads to all neighbouring islands (the islands that are connected to it by a bridge). To control the fire, every night one bridge is blown up, as long as the fire still has room to spread. Let $X$ be the minimal number of bridges that have to be blown up for a given group of islands and a given origin of the fire. Find the maximum of $X$ over all possible groups of islands and fire origins.