## Ken's Puzzle of the WeekWires and Rooms

1. The original problem of wires and rooms is this: You are in one room and have nine identical wires going into the wall.  In another room, the other ends of these same wires are accessible.  You may twist together the ends of any wires in one room, and you have a tester that will identify any closed loop.  How can you correctly label both ends of all wires in the smallest number of trips between rooms?  How would you do this with eight wires?
2. Now there are three rooms, with eight wires in each room (24 wire ends means 12 wires in the walls.)  The wires in one room could go to either of the other two rooms.  How can you correctly label both ends of all wires with the smallest number of trips among rooms? How would you do this with one additional wire (nine ends in two rooms and eight ends in one)?
3. Four rooms with eight wires in each room?  Nine wires in each room?
Source: Extended from rec.puzzles's Wire Labels, most recently seen as Problem #268 at Dan's Math (#1a copied from there.)
Solution
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