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Author: LorenCobb Big gold star, 5000 posts Top Favorite Fools Top Recommended Fools Feste Award Nominee! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: of 5865  
Subject: Re: Jealous Neighbors Date: 8/16/2014 5:04 PM
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LF: Damn, I hate it when puzzles turn out to be "IMPOSSIBLE"; what a waste of time!

Oh, it's not so bad. I think one should always be aware of the possibility that a puzzle has no solution. It's just a part of life, and part of mathematics too.

I could not help thinking, "What if the grid were infinite?" Presumably then there would be a solution, with aleph-nought moves.

It reminds me strongly of the old chestnut involving a convention of mathematicians and only one hotel. The hotel has a countably infinite number of rooms, but they are all full. The last mathematician arrives, and is told the bad news (I've been there -- it's a sickening feeling).

Fortunately, the last mathematician has a plan. "Move every existing guest from Room #N to Room #N+1," he says, "and then put me in Room #1."

The clerk is dubious, but to his surprise everyone is eventually accommodated.

Then in walks a physicist...

Loren
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