Whoa, it’s been a long time!
I found this puzzle recently and thought it was fantastic, so I decided to share it with you guys. It isn’t too difficult compared to the others I uploaded onto this topic, but it should still keep you busy for a while.
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You are a construction worker, and you have just finished building a power cable underneath a major city. This cable connects two neighbourhoods 10km away from each other (assume the cable is 10km long too). This power cable consists of 120 wires. Each of these wires ends in a bendable metal tip, which can be wrapped around a power source (or another wire) to form a connection.
However, a few hours after the cable was fitted, your boss noticed something very wrong: none of the wires were labelled! You are given the thoroughly tedious job of labelling the ends of each wire. All you have to accomplish this task is a pencil, a power source, and a lightbulb. The only way you can find out where each wire ends is by connecting the end of one (or more) wires to your power source, walking 10km to the other neighbourhood, and connecting your lightbulb to every possible output until you discover the one with power.
You may label the wires however you wish. However, you must finish with 120 “pairs” of labels – each pair designating the ends of a single wire.
Any time you spend experimenting with wires may be ignored. The only time you need to worry about is the 10km journey between the cable’s ends. (For example, a method in which you walk 20km but only check one wire is
worse than a method in which you walk 10km but check a million wires.)
Assume that you do not need a loop for current to flow. For example, if you join your power source up to one wire and the lightbulb up to the other end, the lightbulb will switch on. However, the current will only flow if the distance of wire between the power source and the lightbulb is less than or equal to 20km.
1: First, try and find the best solution for this 120 wire-problem.
2: Can you find a general solution, enabling you to answer this question for ANY number of wires?
3: Now try the problem again, but with slightly different rules: remove the 20km restriction on how far current can travel, but enforce a rule which states you can only tie two wires together at each "connection". Can you find a new method which allows you to solve the puzzle for any number of wires?