The Jealous Neighbors

The answer to the “Jealous Neighbors” Puzzler on 3 March was wrong, wrong, wrongity, wrong.

Forget that A-B nonsense. Leave the squares numbered 1 to 25, and move every resident one square clockwise. That is, in the outer ring, 1 goes to 2, 2 goes to 3, 3 goes to 4, 4 goes to 5, 5 goes to 10, 10 goes to 15, and so forth in a circle. Do the same thing in the two inner rings. That leaves the square in the center, lucky #13, unmoved. He swaps with any of his neighbors.

26 moves. QED.

Any number of ways doing it as you describe. I thought their ‘it’s impossible’ answer bogus, too, because it implies a rule not stated in the question: that all moves must happen at the same time.

You’re surely correct. Their error.

From years ago.

It’s possible that I’m not the only one here that doesn’t have the foggiest idea what you are talking about. I haven’t heard the radio show since the last trip to Ohio months ago.

I wonder if JV919 knows there have not been any new shows for years and very few stations that are even broadcasting reruns.

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If you sign up for puzzler emails this one ‘s solution just came out today.

WAMU, the American University public radio station, broadcasts and streams Car Talk every Saturday morning at 10. Car Talk Plaza podcasts the same show. Yes they are old shows. So what?


a[quote=“JV919, post:1, topic:113562”]
That leaves the square in the center, lucky #13, unmoved. He swaps with any of his neighbors.

Sorry, but wouldn’t that mean that whoever ends up in your #13 will have moved into an apartment on a diagonal from his original location?

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Forget the process. Can you produce a final arrangement in which everyone ends up in an apartment adjacent to his original?

Now that I re-read the puzzler, the requirement that each neighbor end up only one square removed from their starting point means there isn’t a solution I can think of. The one I had ended up with a neighbor two squares removed.

So not so ‘bogus’, after all!

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(How about a check mark for me solving your problem?)


So what if it does? There’s no rule against that.

Have you actually read the puzzler?

Yes, but apparently you haven’t:

RAY: Right. Remember, each person is jealous of his adjacent neighbor. Not his diagonal neighbor, but the person up or down or left or right of him. Each aspires to move into the apartment of his adjacent neighbor.

Do you know what “adjacent” means??

I think the problem with your sol’n OP is that when the people in #13 move to an adjacent apartment at the end (which is indeed consistent with the puzzle for the people in #13), the people in that apartment have to move to #13. And those people lived on the diagonal to #13 prior to their rotation. In other words to become adjacent to #13 after the rotation, they had to be on the diagonal to #13 before the rotation. People moving to a diagonal apartment isn’t allowed. The same A,B,A,B … logic that applies to the 25 position square also applies to the inner 9 position square, maybe a little easier to see why it is impossible that way.

You can read the recent puzzlers, very easy to do. Click on CarTalk.Com at the top left of this page, then Our Show, then Puzzler. The one in question is the second week in March as I recall.

No thanks. Life is enough of a puzzler without adding math problems to it.

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I think the Jealous Neighbors puzzler has been resolved w/Ray being correct. But I heard another puzzler recently which I thought the hint was a little misleading. About a diy’er who replaced his front calipers and couldn’t get a hard pedal after that, no matter how much he bled the brakes. Finally after replacing several other parts and consulting several inde shops and the dealership somebody spotted the problem, & he figured it out. Ray asked 'So how did he fix the problem? And here’s a hint: It didn’t cost any money." … stop reading here if you don’t want to know the answer …

The solution was the diye’r had inadvertently switched the R and L calipers, which put the bleed screws pointing down rather than up. Switching them back to the correct R/L position solved the problem. But it isn’t really accurate to say that didn’t cost anything imo. It cost the time needed to switch the calipers. True, for a diy’er there isn’t a direct money charge for labor. But there’s still a lost opportunity cost, and the hint imo is maybe a little misleading. Given the hint I was initially thinking it was some kind of 5 minute fix involving installing a screw or something.

Of course, you’re right. They would probably put that in the “obfuscation” category of Puzzler formulation…