How to get a list of the Value of a number as the sum of 4 numbers in Prolog

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I'm having trouble making this predicate work. The idea is to use diabolic([A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P]) to obtain all the possible magic squares in that list.

At first I thought about using permutation/2 but it's hella slow for a list of 16 numbers.

Then I found an example here which uses an external library (clpfd) and has awesome performance, but I'm trying to solve it without any external library... so I tried something like this:

sum([X,Y,Z,W]) :-
  A = [1..16],
  member(X,A),
  member(Y,A),
  member(Z,A),
  member(W,A),
  X \== Y,
  X \== Z,
  X \== W,
  Y \== Z,
  Y \== W,
  Z \== W,
  34 is (X+Y+Z+W).

What I'm trying to do there is getting all the possible lists of different numbers which sum is 34 so I can then check which combination makes a magic square (in hopes of making it faster that using normal permutation.

Still, I'm getting an error about some Operator Expected in member(X,[1..16]), so maybe i'm doing something wrong. I'm pretty new to Prolog so I was hoping to get some help from you guys.

Thanks in advance.

asked 1 min ago

user3694499

1