From David: Let us suppose some companies have collaborated to place several satellites in orbit. Let us call the set of all satellites that a given company helped place in orbit a network. Finally let us assume the following 4 rules.

There are at least two distinct satellites.

For each pair of satellites there is exactly one network containing them.

Each network contains at least two distinct satellites.

For each network, there is a satellite not in it.

What is the least number of satellites.

what is the least number of networks?

Answered by Penny Nom.

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