e18.pl

getRow(R, Row) :-
nth0(R, [[75],
 [95,64],
 [17,47,82],
 [18,35,87,10],
 [20,4,82,47,65],
 [19,1,23,75,3,34],
 [88,2,77,73,7,63,67],
 [99,65,4,28,6,16,70,92],
 [41,41,26,56,83,40,80,70,33],
 [41,48,72,33,47,32,37,16,94,29],
 [53,71,44,65,25,43,91,52,97,51,14],
 [70,11,33,28,77,73,17,78,39,68,17,57],
 [91,71,52,38,17,14,91,43,58,50,27,29,48],
 [63,66,4,68,89,53,67,30,73,16,69,87,40,31],
 [4,62,98,27,23,9,70,98,73,93,38,53,60,4,23]], Row).

max(X, Y, Y) :- Y >= X.
max(X, Y, X) :- X >= Y.

prepend([], Z, [Z]).
prepend([X|Y], Z, [Z,X|Y]).

combineRows([X, Y], [Z], Row) :-
    XZ is X + Z,
    YZ is Y + Z,
    max(XZ, YZ, N),
    prepend([], N, Row).

combineRows([X,Y|T1], [Z|T2], Row) :-
    XZ is X + Z,
    YZ is Y + Z,
    max(XZ, YZ, N),
    combineRows([Y|T1], T2, Tail),
    prepend(Tail, N, Row).

ans(14, W) :- getRow(14, W).
ans(N, W)  :-
    N1 is N + 1,
    getRow(N, Top),
    ans(N1, Bottom),
    combineRows(Bottom, Top, W).

%% Command to Find the Answer:
e18(W) :- ans(0, List),
    nth0(0, List, W).