Friday Puzzler -- Cable

Alex Y
You have a cable with 66 unmarked wires running from the basement to the penthouse of a building. You need to match the ends of the wires, and the only tools you have are pliers that you can use to twist wires together, a continuity tester to determine which wires are connected together, and tape to mark the ends.

For instance, you may twist three of the wires in the basement together, and label them A, B, and C. You could go to the penthouse and find which wires are connected, and label them "ABC" (since when you find two that are connected, you will not know if they are AB, AC, or BC) You can then twist any wires together in the penthouse and go to the basement and test wires there.

How many trips must you make to be able to correctly label both ends of each wire?

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