For the given circuit configuration, how many traveling wires are required excluding spares?

To determine the number of traveling wires required in a circuit configuration, we need to consider several factors, including the number of devices connected, their arrangement, and the signals or power they require.

In a typical circuit, the arrangement of elements such as switches, lights, motors, and power sources dictates how many separate paths (or "traveling wires") need to be run. Each device generally needs at least one wire for power and possibly one for control signals. Furthermore, if there are any parallel connections or if certain devices must share paths, this can affect the total count of traveling wires.

When arriving at the conclusion that 11 traveling wires are needed, it suggests that the configuration likely includes multiple devices, with a need for several wires dedicated to power and other functions. This number accounts for the total necessary connections to ensure that all devices operate correctly while minimizing wastage or redundancy (hence the exclusion of spare wires).

In summary, the determination of needing 11 traveling wires follows from a careful analysis of the circuit configuration, device requirements, and how those connections are made to maintain functionality without excess.