% Francois Labelle & computer, February 26, 2012 % All 34 (out of 634 PG-4.5 SPG-3.0) that have the following property: % - 1 solution in 3.0 moves % - 1 solution in 3.5 moves % - 1 solution in 4.0 moves % - 1 solution in 4.5 moves. (Forsyth-Edwards Notation, followed by the same list in ascii diagrams) PG-4.5, SPG-3.0: rnbqkbn1/ppppppr1/8/8/3P4/8/PPP1PPPP/RN1QKBNR 1nbqkbnr/1rpppppp/8/8/4P3/8/PPPP1PPP/RNBQK1NR rnbqk1n1/ppppppbr/8/8/3P4/8/PPP1PPPP/RN1QKBNR rnbq1bnr/pppppkB1/5p1p/8/3P4/8/PPP1PPPP/RN1QKBNR rnbqk2r/ppppp1bp/5p2/8/3P4/8/PPP1PPPP/RN1QKBNR 1n1qkbnr/rbpppppp/8/8/4P3/8/PPPP1PPP/RNBQK1NR rnbqk1nr/ppppp1b1/5p2/8/3P4/8/PPP1PPPP/RN1QKBNR rnbqk1nr/1pppppb1/p7/8/3P4/8/PPP1PPPP/RN1QKBNR rnbq1b1r/pppppkBp/5p1n/8/3P4/8/PPP1PPPP/RN1QKBNR rnbqkb1r/ppppp1B1/5p1n/8/3P4/8/PPP1PPPP/RN1QKBNR rn1qkbnr/1bppp1pp/5p2/8/4P3/8/PPPP1PPP/RNBQK1NR r1bqk1nr/ppppppb1/n7/8/3P4/8/PPP1PPPP/RN1QKBNR rnbqk1nr/pp1pppb1/2p5/8/3P4/8/PPP1PPPP/RN1QKBNR rn1qkbnr/1bppppp1/7p/8/4P3/8/PPPP1PPP/RNBQK1NR r1bqk1nr/ppppppb1/2n5/8/3P4/8/PPP1PPPP/RN1QKBNR rn1qkb1r/1bpppppp/7n/8/4P3/8/PPPP1PPP/RNBQK1NR r2qkbnr/pb1ppppp/2p5/8/4P3/8/PPPP1PPP/RNBQK1NR rnbqk1nr/p1ppppb1/1p6/8/3P4/8/PPP1PPPP/RN1QKBNR rn1qkbnr/1b1ppppp/2p5/8/4P3/8/PPPP1PPP/RNBQK1NR rn1qkb1r/1bpppppp/5n2/8/4P3/8/PPPP1PPP/RNBQK1NR rnbqkb2/pppppprp/5n2/8/3P4/8/PPP1PPPP/RN1QKBNR r1bqkbnr/1B1ppppp/n1p5/8/4P3/8/PPPP1PPP/RNBQK1NR rn1qkbnr/1bpppp1p/6p1/8/4P3/8/PPPP1PPP/RNBQK1NR r2qkbnr/pbp1pppp/3p4/8/4P3/8/PPPP1PPP/RNBQK1NR 2bqkbnr/prpppppp/2n5/8/4P3/8/PPPP1PPP/RNBQK1NR rnbqkbr1/ppppppB1/5n1p/8/3P4/8/PPP1PPPP/RN1QKBNR 1rbqkbnr/1Bpppppp/p1n5/8/4P3/8/PPPP1PPP/RNBQK1NR 1rbqkbnr/p1pppppp/p7/8/2P5/8/PP1PPPPP/RNB1KBNR rnbqk1nr/ppp1ppb1/3p4/8/3P4/8/PPP1PPPP/RN1QKBNR rn1qkbnr/1bp1pppp/3p4/8/4P3/8/PPPP1PPP/RNBQK1NR rnbqk1nr/pppp1pb1/4p3/8/3P4/8/PPP1PPPP/RN1QKBNR r1bqkbnr/1Bp1pppp/n2p4/8/4P3/8/PPPP1PPP/RNBQK1NR rn1qkbnr/1bpp1ppp/4p3/8/4P3/8/PPPP1PPP/RNBQK1NR 1rbqkbnr/p1pppppp/p7/8/4P3/8/PPPP1PPP/RNB1KBNR _________________ _________________ _________________ _________________ | | | | | | r n b q k b n . | . n b q k b n r | r n b q k . n . | r n b q . b n r | | p p p p p p r . | . r p p p p p p | p p p p p p b r | p p p p p k B . | | . . . . . . . . | . . . . . . . . | . . . . . . . . | . . . . . 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 . P P P P | | R N . Q K B N R | R N B Q K . N R | R N . Q K B N R | R N . Q K B N R | |_________________|_________________|_________________|_________________| | | | | | | r n b q k . . r | . n . q k b n r | r n b q k . n r | r n b q k . n r | | p p p p p . b p | r b p p p p p p | p p p p p . b . | . 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 | P P P . P P P P | P P P . P P P P | | R N . Q K B N R | R N B Q K . N R | R N . Q K B N R | R N . Q K B N R | |_________________|_________________|_________________|_________________| | | | | | | r n b q . b . r | r n b q k b . r | r n . q k b n r | r . b q k . n r | | p p p p p k B p | p p p p p . B . | . b p p p . p p | p p p p p p b . | | . . . . . p . n | . . . . . p . n | . . . . . 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 P P . P P P P | | R N . Q K B N R | R N . Q K B N R | R N B Q K . N R | R N . Q K B N R | |_________________|_________________|_________________|_________________| | | | | | | r n b q k . n r | r n . q k b n r | r . b q k . n r | r n . q k b . r | | p p . p p p b . | . b p p p p p . | p p p p p p b . | . b 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 P | P P P . P P P P | P P P P . P P P | | R N . Q K B N R | R N B Q K . N R | R N . Q K B N R | R N B Q K . N R | |_________________|_________________|_________________|_________________| | | | | | | r . . q k b n r | r n b q k . n r | r n . q k b n r | r n . q k b . r | | p b . p p p p p | p . p p p p b . | . b . p p p p p | . b p p p 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 P P P . P P P | P P P P . P P P | | R N B Q K . N R | R N . Q K B N R | R N B Q K . N R | R N B Q K . N R | |_________________|_________________|_________________|_________________| | | | | | | r n b q k b . . | r . b q k b n r | r n . q k b n r | r . . q k b n r | | p p p p p p r p | . B . p p p p p | . b p p p p . p | p b 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 P | P P P P . P P P | | R N . Q K B N R | R N B Q K . N R | R N B Q K . N R | R N B Q K . N R | |_________________|_________________|_________________|_________________| | | | | | | . . b q k b n r | r n b q k b r . | . r b q k b n r | . r b q k b n r | | p r p p p p p p | p p p p p p B . | . B p p p p p p | p . p p p p p p | | . . n . . . . . | . . . . . n . 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 | P P . P P P P P | | R N B Q K . N R | R N . Q K B N R | R N B Q K . N R | R N B . K B N R | |_________________|_________________|_________________|_________________| | | | | | | r n b q k . n r | r n . q k b n r | r n b q k . n r | r . b q k b n r | | p p p . p p b . | . b p . p p p p | p p p p . p b . | . B p . p 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 | P P P . P P P P | P P P P . P P P | | R N . Q K B N R | R N B Q K . N R | R N . Q K B N R | R N B Q K . N R | |_________________|_________________|_________________|_________________| | | | | r n . q k b n r | . r b q k b n r | | . b 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 Q K . N R | R N B . K B N R | |_________________|_________________|