2
$\begingroup$

enter image description here

For two different USA states the four possibilities happen considering their frontiers:

  • They don't share any frontier (e.g. Alaska and Utah or Florida and California)
  • They share a straight frontier (Montana and South Dakota)
  • They share a fractal frontier and a straight frontier (Texas and Oklahoma)
  • They share a fractal frontier (Tennesse and North Carolina)

The same occurs for African countries: enter image description here

  • They don't share any frontier (e.g. Madagascar and Egypt)
  • They share a straight frontier (Western Sahara and Morocco)
  • They share a fractal frontier and a straight frontier (Egypt and Lybia)
  • They share a fractal frontier (Ethiopia and Sudan)

Swap as many US states and African countries such that the number of neighbors don't change and the type of frontier also does not change! Once a state or a country has been swapped, it can not be swapped again.

As a trivial start, Alaska can be swapped with Madagascar as they don't share any frontier with any other state or country.

Then, Florida has two neighbors, Alabama and Georgia and Florida shares only fractal frontiers with both of them. The same occurs for Tunisia which has two neighbors, Algeria and Lybia and Tunisia shares only fractal frontiers with both of them. As a result, Florida and Tunisia could be swapped.

You can not swap Washington with Morocco even if they have the same number of neighbors (Idaho and Oregon for Washington) and (Western Sahara and Algeria for Morocco) because Washington shares fractal frontiers with Oregon and fractal and straight frontiers with Idaho while Morocco shares straight frontiers with Western Sahara!

How many pair State(USA)-Country(Africa) can be swapped at most?

Please consider the following two lists for this puzzle:

  1. Alabama
  2. Alaska
  3. Arizona
  4. Arkansas
  5. California
  6. Colorado
  7. Connecticut
  8. Delaware
  9. Florida
  10. Georgia
  11. Hawaii
  12. Idaho
  13. Illinois
  14. Indiana
  15. Iowa
  16. Kansas
  17. Kentucky
  18. Louisiana
  19. Maine
  20. Maryland
  21. Massachusetts
  22. Michigan
  23. Minnesota
  24. Mississippi
  25. Missouri
  26. Montana
  27. Nebraska
  28. Nevada
  29. New Hampshire
  30. New Jersey
  31. New Mexico
  32. New York
  33. North Carolina
  34. North Dakota
  35. Ohio
  36. Oklahoma
  37. Oregon
  38. Pennsylvania
  39. Rhode Island
  40. South Carolina
  41. South Dakota
  42. Tennessee
  43. Texas
  44. Utah
  45. Vermont
  46. Virginia
  47. Washington
  48. West Virginia
  49. Wisconsin
  50. Wyoming

And:

  1. Algeria
  2. Angola
  3. Benin
  4. Botswana
  5. Burkina Faso
  6. Burundi
  7. Cabo Verde (Cape Verde)
  8. Cameroon
  9. Central African Republic
  10. Chad
  11. Comoros
  12. Republic of the Congo
  13. Democratic Republic of the Congo
  14. Côte d'Ivoire (Ivory Coast)
  15. Djibouti
  16. Egypt
  17. Equatorial Guinea
  18. Eritrea
  19. Eswatini (formerly Swaziland)
  20. Ethiopia
  21. Gabon
  22. The Gambia
  23. Ghana
  24. Guinea
  25. Guinea-Bissau
  26. Kenya
  27. Lesotho
  28. Liberia
  29. Libya
  30. Madagascar
  31. Malawi
  32. Mali
  33. Mauritania
  34. Mauritius
  35. Morocco
  36. Mozambique
  37. Namibia
  38. Niger
  39. Nigeria
  40. Rwanda
  41. São Tomé and Príncipe
  42. Senegal
  43. Seychelles
  44. Sierra Leone
  45. Somalia
  46. South Africa
  47. South Sudan
  48. Sudan
  49. Tanzania
  50. Togo
  51. Tunisia
  52. Uganda
  53. Zambia
  54. Zimbabwe
Improve this question
$\endgroup$

1 Answer 1

Reset to default
4
$\begingroup$

The definitions aren't quite clear from the question, but I'm going to assume that a straight border is anything that looks like straight lines on a map, and a fractal border is any border other than that. We're not considering Morocco's border with Spain. The tiny border between Botswana and Zambia is assumed to be straight. The African map provided in the question is unusable here as it's missing Eritrea and South Sudan altogether. This answer is based on a map by the Nations Online Project.

With that out of the way, we can start by categorising each state and country by the number of each type of border. Note that each category can be considered separately as we're not allowed to swap between categories. I'll use the notation (a,b,c) for indicating a straight-only borders, b fractal-only borders and c mixed borders. For any category with x countries and y states, we can do min(x,y) swaps.

(0,0,0): 6 countries (Cabo Verde, Comoros, Madagascar, Mauritius, São Tomé and Príncipe, Seychelles), 2 states (Alaska, Hawaii). Swap 2.
(0,0,1): 1 country (The Gambia), 1 state (Maine). Swap 1.
(0,0,2): 1 country (Equatorial Guinea), 1 state (Florida). Swap 1.
(0,0,4): 1 country (Namibia), 0 states.
(0,1,0): 1 country (Lesotho), 0 states.
(0,1,1): 2 countries (Guinea-Bissau, Tunisia), 0 states.
(0,1,2): 1 country (Gabon), 1 state (New Hampshire). Swap 1.
(0,2,0): 2 countries (Eswatini, Sierra Leone), 1 state (South Carolina). Swap 1.
(0,2,1): 1 country (Ghana), 0 states.
(0,2,3): 1 country (Cameroon), 0 states.
(0,3,0): 4 countries (Burundi, Eritrea, Liberia, Malawi), 1 state (New Jersey). Swap 1.
(0,3,1): 2 countries (Benin, Zimbabwe), 0 states.
(0,3,2): 1 country (Senegal), 0 states.
(0,1,3): 1 country (Angola), 0 states.
(0,3,3): 1 country (Mozambique), 0 states.
(0,4,0): 1 country (Rwanda), 0 states.
(0,4,2): 2 countries (Ethiopia, South Africa), 0 states.
(0,4,3): 1 country (Mali), 0 states.
(0,5,0): 2 countries (Republic of the Congo, Côte d'Ivoire), 0 states.
(0,6,0): 2 countries (Central African Republic, Guinea), 0 states.
(0,7,2): 1 country (Democratic Republic of the Congo), 0 states.
(1,0,1): 1 country (Morocco), 1 state (Washington). Swap 1.
(1,0,2): 1 country (Egypt), 1 state (Louisiana). Swap 1.
(1,1,1): 1 country (Togo), 0 states.
(1,1,2): 1 country (Mauritania), 1 state (Texas). Swap 1.
(1,2,0): 1 country (Djibouti), 3 states (California, Delaware, Vermont). Swap 1.
(1,2,1): 1 country (Botswana), 1 state (Minnesota). Swap 1.
(1,2,2): 0 countries, 1 state (New York).
(1,3,0): 1 country (Nigeria), 1 state (Wisconsin). Swap 1.
(1,3,1): 1 country (Uganda), 2 state (Illinois, West Virginia). Swap 1.
(1,3,3): 0 countries, 1 state (Missouri).
(1,4,1): 2 countries (Burkina Faso, South Sudan), 1 state (Iowa). Swap 1.
(1,4,2): 1 country (Sudan), 0 states.
(1,4,3): 1 country (Zambia), 0 states.
(1,6,0): 0 countries, 1 state (Kentucky).
(1,6,1): 1 country (Tanzania), 0 states.
(2,0,0): 0 countries, 1 state (Rhode Island).
(2,0,1): 1 country (Somalia), 1 state (Connecticut). Swap 1.
(2,0,2): 0 countries, 2 states (Alabama, Oregon).
(2,1,0): 0 countries, 2 states (Michigan, North Dakota).
(2,1,1): 0 countries, 2 states (Indiana, Mississippi).
(2,1,2): 1 country (Kenya), 1 state (Georgia). Swap 1.
(2,2,0): 0 countries, 2 states (Maryland, North Carolina).
(2,2,1): 1 country (Libya), 0 states.
(2,2,2): 1 country (Chad), 1 state (Arkansas). Swap 1.
(2,3,0): 0 countries, 1 state (Virginia).
(2,3,2): 1 country (Niger), 0 states.
(3,0,1): 0 countries, 2 states (Kansas, Montana).
(3,0,4): 1 country (Algeria), 0 states.
(3,1,1): 0 countries, 2 states (Massachusetts, Pennsylvania).
(3,1,2): 0 countries, 1 state (South Dakota).
(3,2,0): 0 countries, 2 states (Arizona, Ohio).
(3,2,1): 0 countries, 1 state (Nebraska).
(4,0,0): 0 countries, 1 state (New Mexico).
(4,0,2): 0 countries, 1 state (Idaho).
(4,1,0): 0 countries, 1 state (Nevada).
(5,0,0): 0 countries, 1 state (Utah).
(5,0,1): 0 countries, 1 state (Oklahoma).
(6,0,0): 0 countries, 2 states (Colorado, Wyoming).
(6,2,0): 0 countries, 1 state (Tennessee).

Counting all the swaps together, we get a maximum of 18 swaps.

Improve this answer
$\endgroup$

You must log in to answer this question.

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.