Much like the original problem, you need to identify 12 wires running between the attic and the basement. There is no way to visually distinguish the wires. The only electrical tool you have is a continuity tester. You may travel between the attic and basement as often as you need.
But this time one of the wires is broken and will never conduct a current. The continuity tester cannot tell the difference between testing a closed circuit with this wire versus testing an open circuit.
Identify the ends of all 12 wires making the minimum number of trips.