I have 13 magnetic tapes on reels; one empty reel; and a machine that can unwind a tape from a full reel onto an empty one, reversing the tape’s direction. I need to reverse the direction of each tape while leaving it on its original reel. Can this be done?
|
SelectClick for Answer |
No. If each of the 13 reels must end with the tape it started with, then each of these reels must go through an even number of tape transfers. The empty reel, too, must go through an even number of transfers to remain empty. But each of the 13 tapes must be wound or rewound an odd number of times to end up reversed. These facts can’t be reconciled, so the task can’t be done.
From Dick Hess’ excellent All-Star Mathlete Puzzles, 2009.
|
