Solving a puzzle in prolog - generating a solution with constraints?

Question

I'm using prolog to try to solve a kakuro puzzle. I have a list of rules like this, where R and C represent the row and starting point of each box, L represents the length and S is the sum of the numbers in the row,

 % across(R, C, L, S)
 across(2,4,2,4).
 across(2,10,2,4).  
 across(3,4,4,12).
 across(3,10,2,6).
 across(4,3,2,6).

As far as I can tell, to solve the puzzle across using constraints, for each element L, I would have to find distinct numbers between 1 and 9 which when added up are equal to S. I'm really struggling to work this out, the code I have so far is this:

solveAcross(Solution) :-
    findall([R,C,L,S], across(R,C,L,S), List), 
    Solution = length(List, L),
    Solution ins 1..9,
    all_distinct(Solution),
    labeling([], Solution).

But all this does is return false.

Any help would be appreciated.

Answer 1

So first you need to create your matrix, which will end up being the grid of your kakuro puzzle. That is definitely the first step - apologies if you've already made it.

Then you want to make a few rules for the across constraints:

acrossConstraints(Matrix) :- getAcross(List), applyAcross(Matrix,List).
%this is the overall thing to call, containing two predicates you need to make
getAcross :- findall([R,C,L,S],across(R,C,L,S),List).
%creates a list of the across facts
applyAcross(Matrix,[[R,C,L,S]|T]) :- acrossConstraints(R,C,L,S,M), applyAcross(Matrix,T). 
%call another rule and recurse over the list.

acrossConstraints is the tricky bit - here you want to grab the square you want and then make a list starting from that point. Hint: use append and hint.

Good luck!