Brilliant Space Station
Brilliant Space Station has 99 rooms. Any two of the 99 rooms are connected by a tunnel directly; however, only 99 of the tunnels are two-way tunnels (the traffic is allowed to travel in both directions), and the rest of the tunnels are one-way tunnels (the traffic is only allowed to travel in one direction). If four of the rooms can be connected in a way that it is possible to travel from any one of the rooms to another one of the rooms, we call that a "four-room group". You being the designer of Brilliant Space Station, what is the maximum number of "four-room groups" that you can make?
Note: For 4 rooms to be a "four-room group", you cannot visit any room outside the group to get to another room in the group, i.e. you must be able to travel directly from one room to another.
The answer is 2052072.
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1 solution
C 9 9 4 − 9 9 C 4 8 3 = 2 0 5 2 0 7 2