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The question Is there a proof that a map of the United States requires 4 colors? was answered by showing that Nevada has five neighbors, each adjacent to the next (an "odd wheel"). "Adjacent" here means that they have a common border which is more than a single point.

Another possible proof would be to find a state with three neighbors, each adjacent to the next. That would constitute a "4-clique": four states which are mutually adjacent, in that each one is adjacent to each of the three others. (By our definition of "adjacent", Utah / Arizona / New Mexico / Colorado does not count.)

There actually is a 4-clique in the map of the United States. What are the four states?

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closed as off-topic by BmyGuest, Beastly Gerbil, JMP, GentlePurpleRain Aug 19 '16 at 17:46

  • This question does not appear to be about creation and solving of puzzles, within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Hm, I don t think that is a puzzle, just a quiz question (and an easy one)... $\endgroup$ – BmyGuest Aug 19 '16 at 16:04
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    $\begingroup$ I'm voting to close this question as off-topic because it is not a puzzle nor about a puzzle. It would make an interesting comment to the cited puzzle, though. $\endgroup$ – BmyGuest Aug 19 '16 at 16:05
  • $\begingroup$ @NateEldridge, is there any legal trickery here, e.g. Yellowstone jurisprudence? $\endgroup$ – John Aug 19 '16 at 16:07
  • $\begingroup$ I am referring to the physical state boundaries. But it's true that you may not see them at first glance. $\endgroup$ – Nate Eldredge Aug 19 '16 at 16:09
  • $\begingroup$ @BmyGuest I understand the puzzle of it now. It was just poorly worded. $\endgroup$ – dcfyj Aug 19 '16 at 16:26
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New York, bordered by Rhode Island, Connecticut, and Massachusets. The New York - Rhode Island border just happens to be under water, between Misquamicut Beach and Fisher's Island.

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  • $\begingroup$ Nice. Just a little bit slow on my part. I had to google Rhode Island and New York, it said they do border, but I couldn't see how. Good job and explanation. $\endgroup$ – John Aug 19 '16 at 16:13
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I believe it's

New York, Massachusetts, Connecticut, & Rhode Island.

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  • $\begingroup$ Yes, that's correct! $\endgroup$ – Nate Eldredge Aug 19 '16 at 16:14
  • $\begingroup$ @NateEldredge, that's an interesting fact "The state [R.I.] also shares a short maritime border with New York." $\endgroup$ – John Aug 19 '16 at 16:19
  • $\begingroup$ @John Michigan and Illinois also have a (submerged) border, which is what put me onto the solution. $\endgroup$ – RoadieRich Aug 19 '16 at 16:26
  • $\begingroup$ @RoadieRich, yeah that's kind of good cocktail party fact! Haha... $\endgroup$ – John Aug 19 '16 at 16:42

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