Question

In prolog we can get a solution for a map coloring problem as follows:

different(red, green). different(red, blue). 
different(green, red). different(green, blue). 
different(blue, red). different(blue, green). 

coloring(Alabama, Mississippi, Georgia, Tennessee, Florida) :-
  different(Mississippi, Tennessee), 
  different(Mississippi, Alabama), 
  different(Alabama, Tennessee), 
  different(Alabama, Mississippi), 
  different(Alabama, Georgia), 
  different(Alabama, Florida), 
  different(Georgia, Florida), 
  different(Georgia, Tennessee). 

?- coloring(Alabama, Mississippi, Georgia, Tennessee, Florida).
Alabama = blue
Florida = green
Georgia = red
Mississippi = red
Tennessee = green

Is it possible to count the total number of possible map colorings?

Answer 1

With Anders solution, please note that the word ‘colouring’ should be in lower case, which will give the correct answer – 6 solutions.

aggregate_all(count, coloring(Alabama, Mississippi, Georgia, Tennessee, Florida), Count).
Count = 6.