A solution of the programming problem (Japanese) http://nabetani.sakura.ne.jp/hena/orde09_penwa/

penta.pl

link(0, 0, 2,  0,  0, 2).  link(0, 1, 3,  0,  0, 3).  link(0, 2, 1, -1, -1, 4).  link(0, 3, 3,  0, -1, 0).  link(0, 4, 1,  0,  0, 1).
link(1, 0, 2,  0,  0, 3).  link(1, 1, 0,  0,  0, 4).  link(1, 2, 2,  0, -1, 0).  link(1, 3, 3,  1,  0, 1).  link(1, 4, 0,  1,  1, 2).
link(2, 0, 1,  0,  1, 2).  link(2, 1, 3,  0,  0, 4).  link(2, 2, 0,  0,  0, 0).  link(2, 3, 1,  0,  0, 0).  link(2, 4, 3,  1,  1, 2).
link(3, 0, 0,  0,  1, 3).  link(3, 1, 1, -1,  0, 3).  link(3, 2, 2, -1, -1, 4).  link(3, 3, 0,  0,  0, 1).  link(3, 4, 2,  0,  0, 1).

move((C1, X1, Y1, D1), [], (C2, X2, Y2, D2)) :- link(C1, D1, C2, DX, DY, D2), X2 is X1 + DX, Y2 is Y1 + DY.
move((C, X, Y, D1), [cw|Cs], S) :- D2 is (D1 + 4) mod 5, move((C, X, Y, D2), Cs, S).
move((C, X, Y, D1), [ccw|Cs], S) :- D2 is (D1 + 1) mod 5, move((C, X, Y, D2), Cs, S).

next_command([fw|Cs], [], Cs).
next_command([cw|Cs1], [cw|Cs3], Cs2) :- next_command(Cs1, Cs3, Cs2).
next_command([ccw|Cs1], [ccw|Cs3], Cs2) :- next_command(Cs1, Cs3, Cs2).

same_node((C, X, Y, _), (C, X, Y, _)).

is_answer_2(S1, N, S2, _, N) :- same_node(S1, S2).
is_answer_2(S1, N2, S2, Cs2, N4) :- next_command(Cs2, A, Cs3), move(S2, A, S3), N3 is N2 + 1, is_answer_2(S1, N3, S3, Cs3, N4).

is_answer_1(S1, Cs1, N1, N1, N3) :- next_command(Cs1, A, Cs2), move(S1, A, S2), N2 is N1 + 1, is_answer_2(S1, N2, S2, Cs2, N3).
is_answer_1(S1, Cs1, N1, N3, N4) :- next_command(Cs1, A, Cs2), move(S1, A, S2), N2 is N1 + 1, is_answer_1(S2, Cs2, N2, N3, N4).

is_answer(Cs, M, N) :- is_answer_1((0, 0, 0, 0), Cs, 0, M, N).