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In this puzzle, we only consider independent countries and we do not count overseas territories as actual part of a country. We say that three countries form a well-connected triple, if each pair shares a piece of common border with strictly positive length. Most of these well-connected triples furthermore meet at a point (at least theoretically).

Q: What are the twelve well-connected triples that do not have any common point that is shared by all three countries?

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  • $\begingroup$ I have corrected my question from ten to twelve triples. I had overlooked the two triples with Turkey. The "correct answer" sign goes to Christopher Fish who found the last two (and hence hardest) answers. $\endgroup$
    – Alexis
    Commented Feb 12, 2015 at 13:28

3 Answers 3

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Two more as yet unmentioned:

  • Armenia, Iran, Turkey
  • Croatia, Montenegro, Serbia

By my count this makes 12, not counting the dubious borders-in-lakes ones.

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There are a number of possible triples with Russia, thanks to Kaliningrad Oblast. You may wish to exclude this, even though it is not an overseas territory, and it is an oblast (roughly, a state or province) of Russia.

  • Russia, Poland, Belarus
  • Russia, Poland, Ukraine
  • Russia, Lithuania, Belarus
  • Russia, Lithuania, Latvia

Another, possibly more "legitimate" answer not yet given is

  • Tanzania, Malawi, Mozambique
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  • $\begingroup$ I find it really odd that you want to discount ones involving the Kaliningrad Oblast, yet count one where the only sense in which there isn't a common point is that it's in the middle of a lake. $\endgroup$
    – Christopher
    Commented Feb 11, 2015 at 16:27
  • $\begingroup$ @ChristopherFish I don't want to discount them, I just didn't know if the OP intended to allow them. $\endgroup$
    – KSmarts
    Commented Feb 12, 2015 at 14:40
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Some quick and easy answers:

  1. France, Germany, Belgium
  2. Brazil, Argentina, Bolivia
  3. Congo, Tanzania, Uganda
  4. Congo, Tanzania, Rwanda
  5. Tanzania, Mozambique, Zambia
  6. Turkey, Georgia, Azerbaijan
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  • $\begingroup$ Kenya, Uganda, Tanzania $\endgroup$
    – dmg
    Commented Feb 11, 2015 at 13:56
  • $\begingroup$ @dmg: But Kenya, Uganda, Tanzania share a common point somewhere in the middle of Lake Victoria... $\endgroup$
    – Gamow
    Commented Feb 11, 2015 at 14:08
  • $\begingroup$ I guess it depends on the interpretation of borders. Lakes are often considered the end of the territory of a country, rather than some line going through the lake. $\endgroup$
    – dmg
    Commented Feb 11, 2015 at 14:15
  • $\begingroup$ But this is not the case with Lake Victoria. $\endgroup$
    – Gamow
    Commented Feb 11, 2015 at 14:17

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