Question

Wiring problem. In the elevator shaft of a tall building, there are 11 identical electrical wires of finite resistance running from the top of the shaft to the bottom. An electrician needs to determine which wires at the bottom correspond to which wires at the top in order to repair the elevator. One battery and one ammeter are available, and the electrician can connect and disconnect any number of wires at either end.

(a) If the electrician starts at the bottom of the shaft, determine the minimum number of trips up and down the stairs (up is considered one trip and down a separate trip) to uniquely identify all eleven wires. Explain your reasoning, drawing a sketch of the wire connections for each step of the process.
(b) Is your solution to part (a), which uniquely identifies the wires, also sufficient to connect the wires such that the elevator will be operational? If not, explain and indicate how many additional trips are required.

Hint: How might one use an ammeter and a battery to determine if two or more different wires are connected together?

Answer 1

Answer 2

To uniquely identify all eleven wires in the elevator shaft, a systematic approach using the ammeter and battery works efficiently. Starting at the bottom, label and connect a combination of wires to the battery, measure the current, and record the readings. By varying which wires are connected in each trip, each wire generates a unique signature, minimizing the number of trips. Typically, a binary grouping strategy allows all wires to be uniquely identified in about 5–6 trips up and down. However, identifying the wires doesn’t automatically ensure the elevator is operational—additional careful reconnections might require 1–2 more trips to match the correct top-to-bottom pairs.

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