A network is points joined by links. A message reaches its destination by following one complete path. Two paths may share endpoints while using different links between. Trace either route from start to finish.
A broken link removes one step. If another complete path still joins start to destination, the message can detour. Otherwise it stops at the break.
This cut still leaves a complete path.
A spare wire helps only when it makes a complete route around the planned cut. Try the cut without it, then add the crossing and try again.
Choose whether to add the spare, then make the planned cut.
A new town has three groups. Add one wire. Break any one wire, repair it, then try another.
Guess before the message tests all three maps.
Which spare wire keeps all three groups connected after ANY one wire breaks?
Cut one wire. Trace from A. Repair. Repeat.
Move to test each wire; the end replays all tests.
