# Country triples without common point

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?

• 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. Feb 12, 2015 at 13:28

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.

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
• 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. Feb 11, 2015 at 16:27
• @ChristopherFish I don't want to discount them, I just didn't know if the OP intended to allow them. Feb 12, 2015 at 14:40

1. France, Germany, Belgium
2. Brazil, Argentina, Bolivia
3. Congo, Tanzania, Uganda
4. Congo, Tanzania, Rwanda
5. Tanzania, Mozambique, Zambia
6. Turkey, Georgia, Azerbaijan
• Kenya, Uganda, Tanzania
– dmg
Feb 11, 2015 at 13:56
• @dmg: But Kenya, Uganda, Tanzania share a common point somewhere in the middle of Lake Victoria... Feb 11, 2015 at 14:08
• 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.
– dmg
Feb 11, 2015 at 14:15
• But this is not the case with Lake Victoria. Feb 11, 2015 at 14:17