Contents
level: medium
The following important HDP chains were detected:
* DIS # C1: 5 => CTR => C1: 1,3 * DIS # C2: 8,9 => CTR => C2: 5,7 * DIS # B3: 8,9 => CTR => B3: 1,2,7 * DIS # C3: 8,9 => CTR => C3: 1,2,7 * DIS # G3: 8,9 => CTR => G3: 1 * DIS # C2: 7,9 => CTR => C2: 5,8 * DIS # I3: 8 => CTR => I3: 7,9 * DIS # H5: 7,9 => CTR => H5: 8 * PRF # H5: 8 => SOL * DIS # B3: 8,9 => CTR => B3: 1,2,7 * DIS # B8: 8,9 => CTR => B8: 2,6,7 * DIS # C2: 8,9 => CTR => C2: 5,7 * DIS # C3: 8,9 => CTR => C3: 1,2,7 * PRF # C8: 8,9 => SOL * DIS # C9: 8,9 => CTR => C9: 6 * PRF # C9: 6 => SOL * DIS # I5: 8,9 => CTR => I5: 7 * DIS # G3: 8,9 => CTR => G3: 1 * DIS # B8: 8,9 => CTR => B8: 2,6,7 * PRF # C8: 8,9 => SOL * DIS # C9: 8,9 => CTR => C9: 6 * PRF # C9: 6 => SOL * DIS # H8: 8,9 => CTR => H8: 2 * PRF # H8: 2 => SOL * DIS # B8: 6,9 => CTR => B8: 2,7,8 * DIS # C8: 6,9 => CTR => C8: 2,7,8 * PRF # C9: 6,9 => SOL * DIS # C9: 8 => CTR => C9: 6,9 * PRF # H8: 2,9 => SOL * DIS # H8: 8 => CTR => H8: 2,9 * DIS # H8: 8,9 => CTR => H8: 2 * PRF # H8: 2 => SOL * DIS # C9: 8,9 => CTR => C9: 6 * PRF # C9: 6 => SOL * DIS # I5: 8,9 => CTR => I5: 7 * CNT 35 HDP CHAINS / 65 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
The following important HDP chains were detected:
* DIS # C1: 5 => CTR => C1: 1,3 * DIS C1: 1,3 # B3: 8,9 => CTR => B3: 2,7 * DIS C1: 1,3 + B3: 2,7 # C3: 8,9 => CTR => C3: 2,7 * PRF C1: 1,3 + B3: 2,7 + C3: 2,7 # C8: 8,9 => SOL * STA C1: 1,3 + B3: 2,7 + C3: 2,7 + C8: 8,9 * CNT 4 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
6..8........2....3.......4....7..61..54............2......4.7.6....35...1........ | initial |
6..8.4..24..2.1.63...563.4.3..752614254316...7..4892355..1487.6....354.114..2735. | autosolve |
613894572495271863827563149389752614254316987761489235532148796978635421146927358 | solved |
level: medium
-------------------------------------------------- * PAIRS (16) B1: 1,3 A3: 8,9 E1: 7,9 E2: 7,9 G1: 1,5 H1: 7,9 B4: 8,9 C4: 8,9 B6: 1,6 C6: 1,6 G5: 8,9 A8: 8,9 D8: 6,9 D9: 6,9 H7: 2,9 I9: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,G3: 1.. / G1 = 1 => 0 pairs (X) / G3 = 1 => 17 pairs (_) B6,C6: 1.. / B6 = 1 => 0 pairs (X) / C6 = 1 => 15 pairs (_) B3,C3: 2.. / B3 = 2 => 17 pairs (_) / C3 = 2 => 17 pairs (_) H7,H8: 2.. / H7 = 2 => 0 pairs (X) / H8 = 2 => 0 pairs (_) B1,C1: 3.. / B1 = 3 => 17 pairs (_) / C1 = 3 => 14 pairs (_) B7,C7: 3.. / B7 = 3 => 14 pairs (_) / C7 = 3 => 17 pairs (_) B1,B7: 3.. / B1 = 3 => 17 pairs (_) / B7 = 3 => 14 pairs (_) C1,C7: 3.. / C1 = 3 => 14 pairs (_) / C7 = 3 => 17 pairs (_) C1,C2: 5.. / C1 = 5 => 0 pairs (X) / C2 = 5 => 17 pairs (_) G1,G2: 5.. / G1 = 5 => 17 pairs (_) / G2 = 5 => 0 pairs (X) C1,G1: 5.. / C1 = 5 => 0 pairs (X) / G1 = 5 => 17 pairs (_) C2,G2: 5.. / C2 = 5 => 17 pairs (_) / G2 = 5 => 0 pairs (X) B6,C6: 6.. / B6 = 6 => 15 pairs (_) / C6 = 6 => 0 pairs (X) D8,D9: 6.. / D8 = 6 => 0 pairs (*) / D9 = 6 => 0 pairs (X) C9,D9: 6.. / C9 = 6 => 0 pairs (*) / D9 = 6 => 0 pairs (X) B6,B8: 6.. / B6 = 6 => 15 pairs (_) / B8 = 6 => 0 pairs (X) E1,E2: 7.. / E1 = 7 => 0 pairs (X) / E2 = 7 => 20 pairs (_) H1,I3: 7.. / H1 = 7 => 20 pairs (_) / I3 = 7 => 0 pairs (X) H5,I5: 7.. / H5 = 7 => 0 pairs (X) / I5 = 7 => 20 pairs (_) B8,C8: 7.. / B8 = 7 => 20 pairs (_) / C8 = 7 => 16 pairs (_) E1,H1: 7.. / E1 = 7 => 0 pairs (X) / H1 = 7 => 20 pairs (_) H1,H5: 7.. / H1 = 7 => 20 pairs (_) / H5 = 7 => 0 pairs (X) I3,I5: 7.. / I3 = 7 => 0 pairs (X) / I5 = 7 => 20 pairs (_) B4,C4: 8.. / B4 = 8 => 19 pairs (_) / C4 = 8 => 0 pairs (X) H8,I9: 8.. / H8 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) C9,I9: 8.. / C9 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) A3,A8: 8.. / A3 = 8 => 0 pairs (*) / A8 = 8 => 0 pairs (X) H5,H8: 8.. / H5 = 8 => 0 pairs (*) / H8 = 8 => 0 pairs (X) E1,E2: 9.. / E1 = 9 => 20 pairs (_) / E2 = 9 => 0 pairs (X) B4,C4: 9.. / B4 = 9 => 0 pairs (X) / C4 = 9 => 19 pairs (_) D8,D9: 9.. / D8 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) E1,H1: 9.. / E1 = 9 => 20 pairs (_) / H1 = 9 => 0 pairs (X) A3,A8: 9.. / A3 = 9 => 0 pairs (X) / A8 = 9 => 0 pairs (_) * DURATION: 0:00:57.696674 START: 11:36:58.902007 END: 11:37:56.598681 2017-05-04 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B1,B4,B6,C4,C6,D8,D9,E1,E2,G1,G5,H1,H7,I9) * 6..8.4..24..2.1.63...563.4.3..752614254316...7..4892355..1487.6....354.114..2735. * PAIR B1: 1,3 BLK 1 C1: 1,3,5 # reduction candidate for 1,3 C1: 5 => CTR * 6358.41.24..2.15639..5638473..7526142543169787..4892355.31487.6....354.114..2735. C1: 1,3 # 17 pairs * PAIR A3: 8,9 BLK 1 B2: 8,9,7 # reduction candidate for 8,9 B2: 8,9 # 19 pairs C2: 8,9,5,7 # reduction candidate for 8,9 C2: 8,9 => CTR * 6358.41.24..2.15639..5638473..7526142543169787..4892355.31487.6....354.114..2735. C2: 5,7 # 17 pairs B3: 8,9,1,2,7 # reduction candidate for 8,9 B3: 8,9 => CTR * 6..8.4..24..2.1.63..25631473..752614254316.7.7..4892355..1487.6....35481148627359 B3: 1,2,7 # 16 pairs C3: 8,9,1,2,7 # reduction candidate for 8,9 C3: 8,9 => CTR * 6..8.4..24..2.1.63.2.5631473..752614254316.7.7..4892355..1487.6....35481148627359 C3: 1,2,7 # 16 pairs * PAIR A3: 8,9 ROW 3 G3: 8,9,1 # reduction candidate for 8,9 G3: 8,9 => CTR * 6358.41.24..2.15639..5638473..7526142543169787..4892355.31487.6....354.114..2735. G3: 1 # 17 pairs I3: 8,9,7 # reduction candidate for 8,9 I3: 8,9 # 20 pairs * PAIR E2: 7,9 ROW 2 B2: 7,9,8 # reduction candidate for 7,9 B2: 7,9 # 19 pairs C2: 7,9,5,8 # reduction candidate for 7,9 C2: 7,9 => CTR * 6358.41.248.2.15639..5638473987526142543169787..4892355.31487.6....354.114..2735. C2: 5,8 # 17 pairs * PAIR G1: 1,5 ROW 1 C1: 1,5,3 # reduction candidate for 1,5 C1: 1,5 # 17 pairs C1: 3 # 14 pairs * PAIR H1: 7,9 BLK 3 I3: 7,9,8 # reduction candidate for 7,9 I3: 8 => CTR * 6..8.4.724..271.63...563.483..7526142543168977..4892355..1487268...354.114..2735. I3: 7,9 # 20 pairs * PAIR H1: 7,9 COL H H5: 7,9,8 # reduction candidate for 7,9 H5: 7,9 => CTR * 6..8.4..24..2.1.63...563.4.3..752614254316...7..4892355..1487.6....35481148627359 H5: 8 => SOLVED * 613894572495271863827563149389752614254316987761489235532148796978635421146927358 * PAIR B4: 8,9 COL B B2: 8,9,7 # reduction candidate for 8,9 B2: 8,9 # 19 pairs B3: 8,9,1,2,7 # reduction candidate for 8,9 B3: 8,9 => CTR * 6..8.4..24..2.1.63..25631473..752614254316.7.7..4892355..1487.6....35481148627359 B3: 1,2,7 # 16 pairs B8: 8,9,2,6,7 # reduction candidate for 8,9 B8: 8,9 => CTR * 6..894.724..271.63.725631493..752614254316987761489235523148796987635421146927358 B8: 2,6,7 # 16 pairs * PAIR C4: 8,9 COL C C2: 8,9,5,7 # reduction candidate for 8,9 C2: 8,9 => CTR * 6358.41.24..2.15639..5638473..7526142543169787..4892355.31487.6....354.114..2735. C2: 5,7 # 17 pairs C3: 8,9,1,2,7 # reduction candidate for 8,9 C3: 8,9 => CTR * 6..8.4..24..2.1.63.2.5631473..752614254316.7.7..4892355..1487.6....35481148627359 C3: 1,2,7 # 16 pairs C8: 8,9,2,6,7 # reduction candidate for 8,9 C8: 8,9 => SOLVED * 613894572495271863827563149389752614254316987761489235532148796978635421146927358 C8: 2,6,7 # 16 pairs C9: 8,9,6 # reduction candidate for 8,9 C9: 8,9 => CTR * 6..8.4..24..2.1.639..563.47398752614254316...7..4892355..1487.68..935421149627358 C9: 6 => SOLVED * 613894572495271863827563149389752614254316987761489235532148796978635421146927358 * PAIR G5: 8,9 BLK 6 H5: 8,9,7 # reduction candidate for 8,9 H5: 8,9 # 20 pairs I5: 8,9,7 # reduction candidate for 8,9 I5: 8,9 => CTR * 6..8.4..24..2.1.63...563.473..752614254316.7.7..4892355..1487.6....35481148627359 I5: 7 # 20 pairs * PAIR G5: 8,9 COL G G2: 8,9,5 # reduction candidate for 8,9 G2: 8,9 # 17 pairs G3: 8,9,1 # reduction candidate for 8,9 G3: 8,9 => CTR * 6358.41.24..2.15639..5638473..7526142543169787..4892355.31487.6....354.114..2735. G3: 1 # 17 pairs * PAIR A8: 8,9 BLK 7 B8: 8,9,2,6,7 # reduction candidate for 8,9 B8: 8,9 => CTR * 6..894.724..271.63.725631493..752614254316987761489235523148796987635421146927358 B8: 2,6,7 # 16 pairs C8: 8,9,2,6,7 # reduction candidate for 8,9 C8: 8,9 => SOLVED * 613894572495271863827563149389752614254316987761489235532148796978635421146927358 C8: 2,6,7 # 16 pairs C9: 8,9,6 # reduction candidate for 8,9 C9: 8,9 => CTR * 6..8.4..24..2.1.639..563.47398752614254316...7..4892355..1487.68..935421149627358 C9: 6 => SOLVED * 613894572495271863827563149389752614254316987761489235532148796978635421146927358 * PAIR A8: 8,9 ROW 8 H8: 8,9,2 # reduction candidate for 8,9 H8: 8,9 => CTR * 6..8.4..24..2.1.639..563.4.3..752614254316...7..4892355..1487268...35491146927358 H8: 2 => SOLVED * 613894572495271863827563149389752614254316987761489235532148796978635421146927358 * PAIR D8: 6,9 ROW 8 B8: 6,9,2,7,8 # reduction candidate for 6,9 B8: 6,9 => CTR * 6..8.4..24..2.1.63...563.4.3..752614254316.877..4892355..1487968.7.3542114..27358 B8: 2,7,8 # 15 pairs C8: 6,9,2,7,8 # reduction candidate for 6,9 C8: 6,9 => CTR * 6..8.4..24..2.1.63...563.4.3..752614254316.877614892355..14879687..3542114..27358 C8: 2,7,8 # 16 pairs * PAIR D9: 6,9 ROW 9 C9: 6,9,8 # reduction candidate for 6,9 C9: 6,9 => SOLVED * 613894572495271863827563149389752614254316987761489235532148796978635421146927358 C9: 8 => CTR * 6..8.4..24..2.1.63...563.4.3..752614254316...7..4892355..1487.6....354.1148627359 * PAIR H7: 2,9 BLK 9 H8: 2,9,8 # reduction candidate for 2,9 H8: 2,9 => SOLVED * 613894572495271863827563149389752614254316987761489235532148796978635421146927358 H8: 8 => CTR * 6..8.4..24..2.1.63...563.4.3..752614254316...7..4892355..148726....35481148627359 * PAIR H7: 2,9 ROW 7 B7: 2,9,3 # reduction candidate for 2,9 B7: 2,9 # 17 pairs C7: 2,9,3 # reduction candidate for 2,9 C7: 2,9 # 14 pairs * PAIR I9: 8,9 BLK 9 H8: 8,9,2 # reduction candidate for 8,9 H8: 8,9 => CTR * 6..8.4..24..2.1.639..563.4.3..752614254316...7..4892355..1487268...35491146927358 H8: 2 => SOLVED * 613894572495271863827563149389752614254316987761489235532148796978635421146927358 * PAIR I9: 8,9 ROW 9 C9: 8,9,6 # reduction candidate for 8,9 C9: 8,9 => CTR * 6..8.4..24..2.1.639..563.47398752614254316...7..4892355..1487.68..935421149627358 C9: 6 => SOLVED * 613894572495271863827563149389752614254316987761489235532148796978635421146927358 * PAIR I9: 8,9 COL I I3: 8,9,7 # reduction candidate for 8,9 I3: 8,9 # 20 pairs I5: 8,9,7 # reduction candidate for 8,9 I5: 8,9 => CTR * 6..8.4..24..2.1.63...563.473..752614254316.7.7..4892355..1487.6....35481148627359 I5: 7 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-258-base-pr-000.dot * REASONING * DIS # C1: 5 => CTR => C1: 1,3 * DIS # C2: 8,9 => CTR => C2: 5,7 * DIS # B3: 8,9 => CTR => B3: 1,2,7 * DIS # C3: 8,9 => CTR => C3: 1,2,7 * DIS # G3: 8,9 => CTR => G3: 1 * DIS # C2: 7,9 => CTR => C2: 5,8 * DIS # I3: 8 => CTR => I3: 7,9 * DIS # H5: 7,9 => CTR => H5: 8 * PRF # H5: 8 => SOL * DIS # B3: 8,9 => CTR => B3: 1,2,7 * DIS # B8: 8,9 => CTR => B8: 2,6,7 * DIS # C2: 8,9 => CTR => C2: 5,7 * DIS # C3: 8,9 => CTR => C3: 1,2,7 * PRF # C8: 8,9 => SOL * DIS # C9: 8,9 => CTR => C9: 6 * PRF # C9: 6 => SOL * DIS # I5: 8,9 => CTR => I5: 7 * DIS # G3: 8,9 => CTR => G3: 1 * DIS # B8: 8,9 => CTR => B8: 2,6,7 * PRF # C8: 8,9 => SOL * DIS # C9: 8,9 => CTR => C9: 6 * PRF # C9: 6 => SOL * DIS # H8: 8,9 => CTR => H8: 2 * PRF # H8: 2 => SOL * DIS # B8: 6,9 => CTR => B8: 2,7,8 * DIS # C8: 6,9 => CTR => C8: 2,7,8 * PRF # C9: 6,9 => SOL * DIS # C9: 8 => CTR => C9: 6,9 * PRF # H8: 2,9 => SOL * DIS # H8: 8 => CTR => H8: 2,9 * DIS # H8: 8,9 => CTR => H8: 2 * PRF # H8: 2 => SOL * DIS # C9: 8,9 => CTR => C9: 6 * PRF # C9: 6 => SOL * DIS # I5: 8,9 => CTR => I5: 7 * CNT 35 HDP CHAINS / 65 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B1,B4,B6,C4,C6,D8,D9,E1,E2,G1,G5,H1,H7,I9) * 6..8.4..24..2.1.63...563.4.3..752614254316...7..4892355..1487.6....354.114..2735. * PAIR B1: 1,3 BLK 1 C1: 1,3,5 # reduction candidate for 1,3 C1: 5 => CTR * 6358.41.24..2.15639..5638473..7526142543169787..4892355.31487.6....354.114..2735. * PAIR A3: 8,9 BLK 1 B2: 8,9,7 # reduction candidate for 8,9 B2: 8,9 # 20 pairs B3: 8,9,2,7 # reduction candidate for 8,9 B3: 8,9 => CTR * 6..8.45.24.52.1.63..25631473..752614254316.7.7..4892355..1487.6..7.35481148627359 C3: 8,9,2,7 # reduction candidate for 8,9 C3: 8,9 => CTR * 6..8.45.24.52.1.63.2.5631473..752614254316.7.7..4892355..1487.6..7.354.114..2735. * RESTART * PAIR C4: 8,9 COL C C8: 8,9,2,6,7 # reduction candidate for 8,9 C8: 8,9 => SOLVED * 613894572495271863827563149389752614254316987761489235532148796978635421146927358 * DURATION: 0:00:07.638494 START: 11:39:01.362695 END: 11:39:09.001189 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-258-base-pr-001.dot * REASONING * DIS # C1: 5 => CTR => C1: 1,3 * DIS C1: 1,3 # B3: 8,9 => CTR => B3: 2,7 * DIS C1: 1,3 + B3: 2,7 # C3: 8,9 => CTR => C3: 2,7 * PRF C1: 1,3 + B3: 2,7 + C3: 2,7 # C8: 8,9 => SOL * STA C1: 1,3 + B3: 2,7 + C3: 2,7 + C8: 8,9 * CNT 4 HDP CHAINS / 6 HYP OPENED
Top 500 Minimum 17 258 solution: 613894572495271863827563149389752614254316987761489235532148796978635421146927358 info: 2080 FNBTWXY S8.f 35253 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
See section Pair Reduction for the HDP chains leading to this result.
Full list of HDP chains traversed:
* INC # C1: 1,3 => UNS * DIS # C1: 5 => CTR => C1: 1,3 * INC # B2: 8,9 => UNS * DIS # C2: 8,9 => CTR => C2: 5,7 * INC # C2: 5,7 => UNS * DIS # B3: 8,9 => CTR => B3: 1,2,7 * INC # B3: 1,2,7 => UNS * DIS # C3: 8,9 => CTR => C3: 1,2,7 * INC # C3: 1,2,7 => UNS * DIS # G3: 8,9 => CTR => G3: 1 * INC # G3: 1 => UNS * INC # I3: 8,9 => UNS * INC # B2: 7,9 => UNS * DIS # C2: 7,9 => CTR => C2: 5,8 * INC # C2: 5,8 => UNS * INC # C1: 1,5 => UNS * INC # C1: 3 => UNS * INC # I3: 7,9 => UNS * DIS # I3: 8 => CTR => I3: 7,9 * DIS # H5: 7,9 => CTR => H5: 8 * PRF # H5: 8 => SOL * INC # B2: 8,9 => UNS * DIS # B3: 8,9 => CTR => B3: 1,2,7 * INC # B3: 1,2,7 => UNS * DIS # B8: 8,9 => CTR => B8: 2,6,7 * INC # B8: 2,6,7 => UNS * DIS # C2: 8,9 => CTR => C2: 5,7 * INC # C2: 5,7 => UNS * DIS # C3: 8,9 => CTR => C3: 1,2,7 * INC # C3: 1,2,7 => UNS * PRF # C8: 8,9 => SOL * INC # C8: 2,6,7 => UNS * DIS # C9: 8,9 => CTR => C9: 6 * PRF # C9: 6 => SOL * INC # H5: 8,9 => UNS * DIS # I5: 8,9 => CTR => I5: 7 * INC # I5: 7 => UNS * INC # G2: 8,9 => UNS * DIS # G3: 8,9 => CTR => G3: 1 * INC # G3: 1 => UNS * DIS # B8: 8,9 => CTR => B8: 2,6,7 * INC # B8: 2,6,7 => UNS * PRF # C8: 8,9 => SOL * INC # C8: 2,6,7 => UNS * DIS # C9: 8,9 => CTR => C9: 6 * PRF # C9: 6 => SOL * DIS # H8: 8,9 => CTR => H8: 2 * PRF # H8: 2 => SOL * DIS # B8: 6,9 => CTR => B8: 2,7,8 * INC # B8: 2,7,8 => UNS * DIS # C8: 6,9 => CTR => C8: 2,7,8 * INC # C8: 2,7,8 => UNS * PRF # C9: 6,9 => SOL * DIS # C9: 8 => CTR => C9: 6,9 * PRF # H8: 2,9 => SOL * DIS # H8: 8 => CTR => H8: 2,9 * INC # B7: 2,9 => UNS * INC # C7: 2,9 => UNS * DIS # H8: 8,9 => CTR => H8: 2 * PRF # H8: 2 => SOL * DIS # C9: 8,9 => CTR => C9: 6 * PRF # C9: 6 => SOL * INC # I3: 8,9 => UNS * DIS # I5: 8,9 => CTR => I5: 7 * INC # I5: 7 => UNS * CNT 65 HDP CHAINS / 65 HYP OPENED
Full list of HDP chains traversed:
* INC # C1: 1,3 => UNS * DIS # C1: 5 => CTR => C1: 1,3 * INC C1: 1,3 # B2: 8,9 => UNS * DIS C1: 1,3 # B3: 8,9 => CTR => B3: 2,7 * DIS C1: 1,3 + B3: 2,7 # C3: 8,9 => CTR => C3: 2,7 * PRF C1: 1,3 + B3: 2,7 + C3: 2,7 # C8: 8,9 => SOL * STA C1: 1,3 + B3: 2,7 + C3: 2,7 + C8: 8,9 * CNT 6 HDP CHAINS / 6 HYP OPENED