Maximum number of connected groups among 99 space stations
Source: Chinese MO 1999
March 19, 2012
combinatorics proposedcombinatorics
Problem Statement
There are space stations. Each pair of space stations is connected by a tunnel. There are two-way main tunnels, and all the other tunnels are strictly one-way tunnels. A group of space stations is called connected if one can reach each station in the group from every other station in the group without using any tunnels other than the tunnels which connect them. Determine the maximum number of connected groups.