Day 4

% The pair assignments
elf_pair(2,4,6,8).
elf_pair(2,3,4,5).
elf_pair(5,7,7,9).
elf_pair(2,8,3,7).
elf_pair(6,6,4,6).
elf_pair(2,6,4,8).

% If the start section of an elf is equal or higher than the start section of the other elf, and the end section of that elf is equal or lower than the end section of the other elf, then we have a complete overlap.
complete_overlap(A, B, C, D) :- A >= C, B =< D.
complete_overlap(A, B, C, D) :- C >= A, D =< B.

% Solve the puzzle
solve(Count) :- findall(A, (elf_pair(A, B, C, D), complete_overlap(A, B, C, D)), Overlaps), length(Overlaps, Count).