% Francois Labelle & computer, January 30, 2004 % All 53 mirror-symmetric PG-4.5 with exactly 1 solution. % 51 SPG-4.5 % 2 PG-4.5, SPG-4.0 (Forsyth-Edwards Notation, followed by the same list in ascii diagrams) SPG-4.5: 1nbqkb1r/1ppppppp/5n2/p7/P7/5N2/1PPPPPPP/1NBQKB1R 1nbqkb1r/1ppppppp/7n/p7/P7/7N/1PPPPPPP/1NBQKB1R Qnb1kbnr/p2ppppp/2p5/8/8/2P5/P2PPPPP/qNB1KBNR Qnb1kbnr/1p1ppppp/8/2p5/2P5/8/1P1PPPPP/qNB1KBNR r1bqkbn1/ppppppp1/2n5/7p/7P/2N5/PPPPPPP1/R1BQKBN1 r1bqkbn1/ppppppp1/n7/7p/7P/N7/PPPPPPP1/R1BQKBN1 r1bqk1nr/pppn1ppp/8/4p3/4P3/8/PPPN1PPP/R1BQK1NR rn2kbnr/pp1bpppp/8/2p5/2P5/8/PP1BPPPP/RN2KBNR rn2kbnr/pp1bpppp/2pp4/8/8/2PP4/PP1BPPPP/RN2KBNR rn2kbnr/pp1bpppp/2p5/3p4/3P4/2P5/PP1BPPPP/RN2KBNR rn2kbnr/pppb1ppp/3pp3/8/8/3PP3/PPPB1PPP/RN2KBNR rn2kbnr/pppb1ppp/4p3/3p4/3P4/4P3/PPPB1PPP/RN2KBNR rn2kbnr/pppb1ppp/8/4p3/4P3/8/PPPB1PPP/RN2KBNR 2bqkbnr/1ppppppp/2n5/p7/P7/2N5/1PPPPPPP/2BQKBNR rQb1kbnr/p2ppppp/2p5/8/8/2P5/P2PPPPP/RqB1KBNR rQb1kbnr/1p1ppppp/8/2p5/2P5/8/1P1PPPPP/RqB1KBNR 1nb1kbnr/rp1ppppp/8/2p5/2P5/8/RP1PPPPP/1NB1KBNR r1b1kbnr/pp1ppppp/8/q1p5/Q1P5/8/PP1PPPPP/R1B1KBNR r1b1kbnr/ppp1pppp/2np4/8/8/2NP4/PPP1PPPP/R1B1KBNR r1b1kbnr/pppn1ppp/3pp3/8/8/3PP3/PPPN1PPP/R1B1KBNR r1b1kbnr/pppn1ppp/4p3/3p4/3P4/4P3/PPPN1PPP/R1B1KBNR r1b1kbnr/pppn1ppp/8/4p3/4P3/8/PPPN1PPP/R1B1KBNR r1b1kbnr/pp1npppp/8/2p5/2P5/8/PP1NPPPP/R1B1KBNR r1b1kbnr/pp1npppp/2pp4/8/8/2PP4/PP1NPPPP/R1B1KBNR r1b1kbnr/pp1npppp/2p5/3p4/3P4/2P5/PP1NPPPP/R1B1KBNR rnbqkb2/ppppppp1/5n2/7p/7P/5N2/PPPPPPP1/RNBQKB2 rnb2bnr/pppp1ppp/5k2/4p3/4P3/5K2/PPPP1PPP/RNB2BNR rnb2bnr/pppp1ppp/4pk2/8/8/4PK2/PPPP1PPP/RNB2BNR rnb2bnr/pppk1ppp/3pp3/8/8/3PP3/PPPK1PPP/RNB2BNR rnb2bnr/pppk1ppp/4p3/3p4/3P4/4P3/PPPK1PPP/RNB2BNR rnb2bnr/pp1kpppp/2pp4/8/8/2PP4/PP1KPPPP/RNB2BNR rnb2bnr/pp1kpppp/2p5/3p4/3P4/2P5/PP1KPPPP/RNB2BNR rnb1kb1r/pppp1ppp/4p3/4N3/4n3/4P3/PPPP1PPP/RNB1KB1R rnb1kb1r/pppp1ppp/8/4N3/4n3/8/PPPP1PPP/RNB1KB1R rnb1kbnr/pp1pppp1/2p5/7q/7Q/2P5/PP1PPPP1/RNB1KBNR rnb1kbnr/pp1ppppp/8/3P4/3p4/8/PP1PPPPP/RNB1KBNR rnb1kbnr/pp1pppp1/8/2p4q/2P4Q/8/PP1PPPP1/RNB1KBNR rnb1kbnr/Q2ppppp/1p6/2p5/2P5/1P6/q2PPPPP/RNB1KBNR rnb1kbnr/1p1ppppp/8/2Q5/2q5/8/1P1PPPPP/RNB1KBNR rnb1kbnr/1p1ppppp/1Q6/2p5/2P5/1q6/1P1PPPPP/RNB1KBNR rnb1kbnr/p1pp1ppp/4p3/1q6/1Q6/4P3/P1PP1PPP/RNB1KBNR rnb1kbnr/p1pp1ppp/1q2p3/8/8/1Q2P3/P1PP1PPP/RNB1KBNR rnb1kbnr/p1Qppppp/2p5/8/8/2P5/P1qPPPPP/RNB1KBNR rnb1kbnr/p2ppppp/Q1p5/8/8/q1P5/P2PPPPP/RNB1KBNR rnb1kbnr/pppp2pp/4p3/4p3/4P3/4P3/PPPP2PP/RNB1KBNR rnb1kbnr/pppp1ppp/8/3P4/3p4/8/PPPP1PPP/RNB1KBNR rnb1kbnr/ppp1ppp1/8/3p3q/3P3Q/8/PPP1PPP1/RNB1KBNR rnb1kbr1/pppp1ppp/4pn2/8/8/4PN2/PPPP1PPP/RNB1KBR1 rnb1kbr1/pppp1ppp/5n2/4p3/4P3/5N2/PPPP1PPP/RNB1KBR1 rnb1k1nr/pppq1ppp/4p3/8/8/4P3/PPPQ1PPP/RNB1K1NR rn1qk1nr/pppb1ppp/8/4p3/4P3/8/PPPB1PPP/RN1QK1NR _________________ _________________ _________________ _________________ | | | | | | . n b q k b . r | . n b q k b . r | Q n b . k b n r | Q n b . k b n r | | . p p p p p p p | . p p p p p p p | p . . p p p p p | . p . p p p p p | | . . . . . n . . | . . . . . . . n | . . p . . . . . | . . . . . . . . | | p . . . . . . . | p . . . . . . . | . . . . . . . . | . . p . . . . . | | P . . . . . . . | P . . . . . . . | . . . . . . . . | . . P . . . . . | | . . . . . N . . | . . . . . . . N | . . P . . . . . | . . . . . . . . | | . P P P P P P P | . P P P P P P P | P . . P P P P P | . P . P P P P P | | . N B Q K B . R | . N B Q K B . R | q N B . K B N R | q N B . K B N R | |_________________|_________________|_________________|_________________| | | | | | | r . b q k b n . | r . b q k b n . | r . b q k . n r | r n . . k b n r | | p p p p p p p . | p p p p p p p . | p p p n . p p p | p p . b p p p p | | . . n . . . . . | n . . . . . . . | . . . . . . . . | . . . . . . . . | | . . . . . . . p | . . . . . . . p | . . . . p . . . | . . p . . . . . | | . . . . . . . P | . . . . . . . P | . . . . P . . . | . . P . . . . . | | . . N . . . . . | N . . . . . . . | . . . . . . . . | . . . . . . . . | | P P P P P P P . | P P P P P P P . | P P P N . P P P | P P . B P P P P | | R . B Q K B N . | R . B Q K B N . | R . B Q K . N R | R N . . K B N R | |_________________|_________________|_________________|_________________| | | | | | | r n . . k b n r | r n . . k b n r | r n . . k b n r | r n . . k b n r | | p p . b p p p p | p p . b p p p p | p p p b . p p p | p p p b . p p p | | . . p p . . . . | . . p . . . . . | . . . p p . . . | . . . . p . . . | | . . . . . . . . | . . . p . . . . | . . . . . . . . | . . . p . . . . | | . . . . . . . . | . . . P . . . . | . . . . . . . . | . . . P . . . . | | . . P P . . . . | . . P . . . . . | . . . P P . . . | . . . . P . . . | | P P . B P P P P | P P . B P P P P | P P P B . P P P | P P P B . P P P | | R N . . K B N R | R N . . K B N R | R N . . K B N R | R N . . K B N R | |_________________|_________________|_________________|_________________| | | | | | | r n . . k b n r | . . b q k b n r | r Q b . k b n r | r Q b . k b n r | | p p p b . p p p | . p p p p p p p | p . . p p p p p | . p . p p p p p | | . . . . . . . . | . . n . . . . . | . . p . . . . . | . . . . . . . . | | . . . . p . . . | p . . . . . . . | . . . . . . . . | . . p . . . . . | | . . . . P . . . | P . . . . . . . | . . . . . . . . | . . P . . . . . | | . . . . . . . . | . . N . . . . . | . . P . . . . . | . . . . . . . . | | P P P B . P P P | . P P P P P P P | P . . P P P P P | . P . P P P P P | | R N . . K B N R | . . B Q K B N R | R q B . K B N R | R q B . K B N R | |_________________|_________________|_________________|_________________| | | | | | | . n b . k b n r | r . b . k b n r | r . b . k b n r | r . b . k b n r | | r p . p p p p p | p p . p p p p p | p p p . p p p p | p p p n . p p p | | . . . . . . . . | . . . . . . . . | . . n p . . . . | . . . p p . . . | | . . p . . . . . | q . p . . . . . | . . . . . . . . | . . . . . . . . | | . . P . . . . . | Q . P . . . . . | . . . . . . . . | . . . . . . . . | | . . . . . . . . | . . . . . . . . | . . N P . . . . | . . . P P . . . | | R P . P P P P P | P P . P P P P P | P P P . P P P P | P P P N . P P P | | . N B . K B N R | R . B . K B N R | R . B . K B N R | R . B . K B N R | |_________________|_________________|_________________|_________________| | | | | | | r . b . k b n r | r . b . k b n r | r . b . k b n r | r . b . k b n r | | p p p n . p p p | p p p n . p p p | p p . n p p p p | p p . n p p p p | | . . . . p . . . | . . . . . . . . | . . . . . . . . | . . p p . . . . | | . . . p . . . . | . . . . p . . . | . . p . . . . . | . . . . . . . . | | . . . P . . . . | . . . . P . . . | . . P . . . . . | . . . . . . . . | | . . . . P . . . | . . . . . . . . | . . . . . . . . | . . P P . . . . | | P P P N . P P P | P P P N . P P P | P P . N P P P P | P P . N P P P P | | R . B . K B N R | R . B . K B N R | R . B . K B N R | R . B . K B N R | |_________________|_________________|_________________|_________________| | | | | | | r . b . k b n r | r n b q k b . . | r n b . . b n r | r n b . . b n r | | p p . n p p p p | p p p p p p p . | p p p p . p p p | p p p p . p p p | | . . p . . . . . | . . . . . n . . | . . . . . k . . | . . . . p k . . | | . . . p . . . . | . . . . . . . p | . . . . p . . . | . . . . . . . . | | . . . P . . . . | . . . . . . . P | . . . . P . . . | . . . . . . . . | | . . P . . . . . | . . . . . N . . | . . . . . K . . | . . . . P K . . | | P P . N P P P P | P P P P P P P . | P P P P . P P P | P P P P . P P P | | R . B . K B N R | R N B Q K B . . | R N B . . B N R | R N B . . B N R | |_________________|_________________|_________________|_________________| | | | | | | r n b . . b n r | r n b . . b n r | r n b . . b n r | r n b . . b n r | | p p p k . p p p | p p p k . p p p | p p . k p p p p | p p . k p p p p | | . . . p p . . . | . . . . p . . . | . . p p . . . . | . . p . . . . . | | . . . . . . . . | . . . p . . . . | . . . . . . . . | . . . p . . . . | | . . . . . . . . | . . . P . . . . | . . . . . . . . | . . . P . . . . | | . . . P P . . . | . . . . P . . . | . . P P . . . . | . . P . . . . . | | P P P K . P P P | P P P K . P P P | P P . K P P P P | P P . K P P P P | | R N B . . B N R | R N B . . B N R | R N B . . B N R | R N B . . B N R | |_________________|_________________|_________________|_________________| | | | | | | r n b . k b . r | r n b . k b . r | r n b . k b n r | r n b . k b n r | | p p p p . p p p | p p p p . p p p | p p . p p p p . | p p . p p p p p | | . . . . p . . . | . . . . . . . . | . . p . . . . . | . . . . . . . . | | . . . . N . . . | . . . . N . . . | . . . . . . . q | . . . P . . . . | | . . . . n . . . | . . . . n . . . | . . . . . . . Q | . . . p . . . . | | . . . . P . . . | . . . . . . . . | . . P . . . . . | . . . . . . . . | | P P P P . P P P | P P P P . P P P | P P . P P P P . | P P . P P P P P | | R N B . K B . R | R N B . K B . R | R N B . K B N R | R N B . K B N R | |_________________|_________________|_________________|_________________| | | | | | | r n b . k b n r | r n b . k b n r | r n b . k b n r | r n b . k b n r | | p p . p p p p . | Q . . p p p p p | . p . p p p p p | . p . p p p p p | | . . . . . . . . | . p . . . . . . | . . . . . . . . | . Q . . . . . . | | . . p . . . . q | . . p . . . . . | . . Q . . . . . | . . p . . . . . | | . . P . . . . Q | . . P . . . . . | . . q . . . . . | . . P . . . . . | | . . . . . . . . | . P . . . . . . | . . . . . . . . | . q . . . . . . | | P P . P P P P . | q . . P P P P P | . P . P P P P P | . P . P P P P P | | R N B . K B N R | R N B . K B N R | R N B . K B N R | R N B . K B N R | |_________________|_________________|_________________|_________________| | | | | | | r n b . k b n r | r n b . k b n r | r n b . k b n r | r n b . k b n r | | p . p p . p p p | p . p p . p p p | p . Q p p p p p | p . . p p p p p | | . . . . p . . . | . q . . p . . . | . . p . . . . . | Q . p . . . . . | | . q . . . . . . | . . . . . . . . | . . . . . . . . | . . . . . . . . | | . Q . . . . . . | . . . . . . . . | . . . . . . . . | . . . . . . . . | | . . . . P . . . | . Q . . P . . . | . . P . . . . . | q . P . . . . . | | P . P P . P P P | P . P P . P P P | P . q P P P P P | P . . P P P P P | | R N B . K B N R | R N B . K B N R | R N B . K B N R | R N B . K B N R | |_________________|_________________|_________________|_________________| | | | | | | r n b . k b n r | r n b . k b n r | r n b . k b n r | r n b . k b r . | | p p p p . . p p | p p p p . p p p | p p p . p p p . | p p p p . p p p | | . . . . p . . . | . . . . . . . . | . . . . . . . . | . . . . p n . . | | . . . . p . . . | . . . P . . . . | . . . p . . . q | . . . . . . . . | | . . . . P . . . | . . . p . . . . | . . . P . . . Q | . . . . . . . . | | . . . . P . . . | . . . . . . . . | . . . . . . . . | . . . . P N . . | | P P P P . . P P | P P P P . P P P | P P P . P P P . | P P P P . P P P | | R N B . K B N R | R N B . K B N R | R N B . K B N R | R N B . K B R . | |_________________|_________________|_________________|_________________| | | | | | r n b . k b r . | r n b . k . n r | r n . q k . n r | | p p p p . p p p | p p p q . p p p | p p p b . p p p | | . . . . . n . . | . . . . p . . . | . . . . . . . . | | . . . . p . . . | . . . . . . . . | . . . . p . . . | | . . . . P . . . | . . . . . . . . | . . . . P . . . | | . . . . . N . . | . . . . P . . . | . . . . . . . . | | P P P P . P P P | P P P Q . P P P | P P P B . P P P | | R N B . K B R . | R N B . K . N R | R N . Q K . N R | |_________________|_________________|_________________| PG-4.5, SPG-4.0: r1b1kbnr/pp1ppppp/1qp5/n7/N7/1QP5/PP1PPPPP/R1B1KBNR r1b1kbnr/ppqppppp/2p5/n7/N7/2P5/PPQPPPPP/R1B1KBNR _________________ _________________ | | | | r . b . k b n r | r . b . k b n r | | p p . p p p p p | p p q p p p p p | | . q p . . . . . | . . p . . . . . | | n . . . . . . . | n . . . . . . . | | N . . . . . . . | N . . . . . . . | | . Q P . . . . . | . . P . . . . . | | P P . P P P P P | P P Q P P P P P | | R . B . K B N R | R . B . K B N R | |_________________|_________________|