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Ken's Puzzle of the Week

Wires and Rooms

- 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?
- 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)?
- 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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