CLPFDを用いて解いた。こういうのがCLPFDの得意分野だと思う。
作成時間1時間弱？
変数の場所
:-use_module(library(clpfd)).
main:-
List = [A,B,C,D,E,F,G,H,I,J],
List ins 1..10,
all_different(List),
A #= 10 #\/ B #= 10 #\/ C #= 10 #\/ D #= 10 #\/ E #= 10,
maplist(#<(A),[B,C,D,E]),
maplist(
sum,
[[A,F,G],[B,G,H],[C,H,I],[D,I,J],[E,J,F]],
[#=,#=,#=,#=,#=],
[Sum,Sum,Sum,Sum,Sum]),
flatten([[A,F,G],[B,G,H],[C,H,I],[D,I,J],[E,J,F]],Flatten),
setof(Flatten,label(List),Num15List),
maplist(num_chr_recursive,Num15List,Num16List),
write(Num15List),nl,nl,
write(Num16List),nl,nl,
msort(Num16List,Sorted),
write(Sorted),nl,nl,
last(Sorted,Last),
write('answer:'),nl,
write(Last).
num_chr_recursive([],[]):-!.
num_chr_recursive([FirstNum|RestNums],Ret):-
!,
num_chr_recursive(RestNums,RestChrs),
atom_chars(FirstNum,Chrs),
append(Chrs,RestChrs,Ret).
%
%実行結果
%[10] 25 ?- main.
***********************(解答伏せます)**********************
%true.
%