Solve the following “Liars” puzzle from The Sphinx Problem Book by Phillips Hubert in 1934.

liars-puzzle.pl

/* What in fact was the order in which the five girls were placed?
 *
 * Five schoolgirls sat for an examination. Their parents--so they thought--showed an undue degree of interest
 * in the result. They therefore agreed that, in writing home about the examination, each girl should make one
 * true statement and one untrue one. The following are the relevant passages from their letters:
 *
 * 1. Betty: "Kitty was second in the examination. I was only third."
 * 2. Ethel: "You'll be glad to hear that I was on top. Joan was 2nd."
 * 3. Joan: "I was third, and poor old Ethel was bottom."
 * 4. Kitty: I came out second. Mary was only fourth."
 * 5. Mary: "I was fourth. Top place was taken by Betty."
 */
xor(A, B) :-
    A, not(B);
    B, not(A).

liars(Ls) :-
    length(Ls, 5),
    member(betty, Ls), member(ethel, Ls), member(joan, Ls), member(kitty, Ls), member(mary, Ls),
    xor(nth1(2, Ls, kitty), nth1(3, Ls, betty)),
    xor(nth1(1, Ls, ethel), nth1(2, Ls, joan)),
    xor(nth1(3, Ls, joan),  nth1(5, Ls, ethel)),
    xor(nth1(2, Ls, kitty), nth1(4, Ls, mary)),
    xor(nth1(4, Ls, mary),  nth1(1, Ls, betty)).

Answer

$ swipl liars-puzzle.pl

?- liars(Ls).
Ls = [kitty, joan, betty, mary, ethel] ;
false.