A small island nation has just installed its first telephone network. The six towns on the island are connected to the network, but the network is not yet complete.
Alfatown, which is the capital is connected to all the other towns. Bravotown is connected to only four other towns, as is Charlietown. Deltatown, Echotown and Foxtrotown are connected to only three other towns.
The telephone exchanges are running old software, and so they cannot pass through calls. So, unless two towns are connected directly, calls cannot be made between the towns.
It is possible to call from Deltatown to Foxtrotown. Which town can receive calls from Echotown?
Alfatown, Bravotown and Charlietown can receive calls from Echotown.
A is connected to all five others and thus to E.
If the link B-C does not exist B and C must be connected to A, D, E and F, which uses up all the connections for D, E and F. Leaving no connections for the link D-F that we know exists.
So B-C does exist and E is connected to both, leaving no connections for the other towns.