There is an interesting Sporcle quiz here that asks one to list the countries of the world, where by listing each country all its neighbouring countries also appear. In that way there is no need to list all 197 countries. For example typing Russia or China alone leads to 14 more countries appearing since that is how many countries each of those countries borders. It led me to think of what is a minimal list of countries I could type in order to have all the countries listed. Mathematically speaking, if each country were represented as a node and I connect two nodes with an edge if they share a land border, then I am looking for a minimum vertex cover for the resulting graph.
After some trial and error I came up with the list below that may or not be minimal. Listed first are the continental countries and secondly the island nations.
The only island nations to share borders with other nations are:
- UK with Ireland and Cyprus (at Akrotiri and Dhekelia)
- Indonesia with East Timor
- Indonesia with Papua New Guinea
- Haiti with the Dominican Republic
Not counted are artificial bridge or tunnel borders such as between:
Other curious borders are:
As the following list shows, 149 continental countries can be covered by 9 + 10 + 8 + 3 + 2 = 32 countries which border the other 117.
continental Africa (9):
- South Africa
- Democratic Republic of Congo
- Burkina Faso
- any country that borders or is Malawi
- one of Guinea, Liberia, Sierra Leone
continental Europe (including Russia) (10):
- France or Monaco
- one of Liechtenstein, Austria, Switzerland
- Montenegro (borders all former Yugoslavia countries except Slovenia and Macedonia)
- Norway or Sweden
continental Asia (excluding Russia) (8):
- Saudi Arabia
- one of North/South Korea
continental North America (3):
- Costa Rica
- Canada or USA
continental South America (2):
- Brazil (borders all except Chile and Ecuador)
For completeness we give a minimal list (42 entries) of the island sovereign states too.
Island sovereign states
Africa (6): Cape Verde, Comoros, Madagascar, Mauritius, São Tomé and Príncipe, Seychelles
Europe (3): Iceland, Malta, United Kingdom
(Ireland borders the United Kingdom)
Asia (8): Bahrain, Indonesia, Japan, Maldives, Philippines, Singapore, Sri Lanka, Taiwan
(East Timor borders Indonesia, Cyprus borders the United Kingdom, Brunei borders Malaysia)
North America (12): Antigua and Barbuda, Bahamas, Barbados, Cuba, Dominica, Dominican Republic or Haiti, Grenada, Jamaica, St Kitts and Nevis, St Lucia, St Vincent and the Grenadines, Trinidad and Tobago
Oceania (13): Australia, Fiji, Kiribati, Marshall Islands, Federated States of Micronesia, Nauru, New Zealand, Samoa, Solomon Islands, Palau, Tonga, Tuvalu, Vanuatu
(all except Papua New Guinea which borders Indonesia)
Below is a map of the world showing in black the countries listed above. It should be possible to reach a non-black labelled sovereign country from a black-labelled country via one land border crossing. Recall that Morocco is accessed via its small land border with Spain.