You are at the bottom of the elevator shaft of a 100 story building. You see 21 wires labelled 1...21. The wires go up to the 100th floor where the ends are labelled A...U, but you don't know how they correspond to the ends at the bottom.
You have a battery, a light bulb, and many small wires. How can you determine the pairing between the numbers and letters by only making one trip to the 100th floor and back down?
Remark: Light bulbs have no polarity.