mathematics

# A Topological Problem

A country is singly landlocked, if there is at least one other country to be crossed in order to come to the sea shore. Austria and Andorra are singly landlocked.

A country is doubly landlocked if there are at least two countries to be crossed in order to come to the sea shore. Liechtenstein and Uzbekistan are doubly landlocked.

Nebraska is a triply landlocked US federal state.

An imaginary island has a 6 times landlocked country and the average number of neighbours of those island countries is at least 6. No country has an exclave like Russia with Kaliningrad or USA with Alaska. All countries are contiguous. A country may have an enclave country as Italy which surrounds Vatican and San Marino.

What is the minimal possible number of countries on this island or continent?

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## 5 thoughts on “A Topological Problem”

1. Well, 13 is the (maybe surprisingly small) number of states needed to land-lock one of them 6 times, having 6 neighbours on average.

Now, you may go and find the general solution for each pair of naturals. F(6,6)=13 (unless someone comes up with an image where F(6,6)=12 or even less) – but what is F(N,M)?

2. guest says:

I got two more for the list (in addition to the earth power cable & 10k BC thing), gotta keep you busy, keep those plates spinning!

– earth rotation speed / temperature, it deserves it’s own post
– disarming nuclear heads through earth with some waves