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?


closed as off-topic by BmyGuest, Beastly Gerbil, JonMark Perry, 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.
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  • $\begingroup$ 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
  • 2
    $\begingroup$ 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

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.

  • $\begingroup$ 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

I believe it's

New York, Massachusetts, Connecticut, & Rhode Island.

  • $\begingroup$ 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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