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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?

Community
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Nate Eldredge
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  • Hm, I don t think that is a puzzle, just a quiz question (and an easy one)... – BmyGuest Aug 19 '16 at 16:04
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    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. – BmyGuest Aug 19 '16 at 16:05
  • @NateEldridge, is there any legal trickery here, e.g. Yellowstone jurisprudence? – John Aug 19 '16 at 16:07
  • I am referring to the physical state boundaries. But it's true that you may not see them at first glance. – Nate Eldredge Aug 19 '16 at 16:09
  • @BmyGuest I understand the puzzle of it now. It was just poorly worded. – dcfyj Aug 19 '16 at 16:26
  • @dcfyj: Do you have any suggestions as to how to improve the wording? – Nate Eldredge Aug 19 '16 at 16:29
  • @dcfyj even with the answer I think it is a trivia question, not a puzzle.(Albeit slightly more challenging than 'totally easy'.) we should not encourage 'puzzles' which really are just questions with a minor hint, or there will soon bi zillions of it. – BmyGuest Aug 19 '16 at 16:29
  • I would clarify what you mean by the 4-clique. Like State 1 shares a border with states 2,3 and 4, State 2 shares a border with states 1,3 and 4, etc – dcfyj Aug 19 '16 at 16:30
  • @NateEldredge That is not meant to discourage you from this site (welcome, btw!), but if you stick around for a while (including meta) you will better understand what I mean. – BmyGuest Aug 19 '16 at 16:31
  • @dcfyj: Okay, I thought that was inherent in the word "mutually", but I tried spelling it out. – Nate Eldredge Aug 19 '16 at 16:31
  • Excuse my spelling. iPad is driving me mad with auto corrections! – BmyGuest Aug 19 '16 at 16:32
  • It is, but that escaped me when I first read it. It wasn't until I read the answer that I understood what you meant. – dcfyj Aug 19 '16 at 16:32
  • @BmyGuest: It seemed to me like an extension of the four-color map question (which was well received): in some sense, I'm asking for a solution of that problem with additional restrictions. But I see your point. – Nate Eldredge Aug 19 '16 at 16:33
  • I'm voting to close this question as off-topic because it is a trivia question, not a puzzle. – GentlePurpleRain Aug 19 '16 at 17:46
  • Ok, I have posted it as an answer on the four-color puzzle instead. Sorry for the noise. – Nate Eldredge Aug 19 '16 at 18:08

2 Answers2

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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.

RoadieRich
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  • 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. – John Aug 19 '16 at 16:13
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I believe it's

New York, Massachusetts, Connecticut, & Rhode Island.

John
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