Analysis of xx-top500-204-base.sdk
Contents
Original Sudoku
level: medium
position: ..7....5..1..8........4.3...4.2....13...5...........7.4..6..5.....7.1............ initial
Autosolve
position: .3791..5451438.7.....54731..45279.3137.154...1..8634754.16385.7.5.7.1.4.7..4.51.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 6,8 => CTR => A1: 2 * PRF # A1: 2 => SOL * DIS # A3: 6,8 => CTR => A3: 2,9 * PRF # C3: 6,8 => SOL * DIS # C3: 2,9 => CTR => C3: 6,8 * DIS # I3: 6,8 => CTR => I3: 2 * PRF # I3: 2 => SOL * PRF # A1: 2,6 => SOL * DIS # A1: 8 => CTR => A1: 2,6 * DIS # G1: 2,6 => CTR => G1: 8 * PRF # G1: 8 => SOL * DIS # A1: 6,8 => CTR => A1: 2 * PRF # A1: 2 => SOL * DIS # A3: 6,8 => CTR => A3: 2,9 * PRF # A8: 6,8 => SOL * DIS # A8: 2,9 => CTR => A8: 6,8 * DIS # G5: 6,8 => CTR => G5: 2,9 * DIS # I5: 6,8 => CTR => I5: 2,9 * PRF # C3: 6,8 => SOL * DIS # C3: 2,9 => CTR => C3: 6,8 * DIS # C8: 6,8 => CTR => C8: 2,3,9 * DIS # C9: 6,8 => CTR => C9: 2,3,9 * DIS # C3: 2,9 => CTR => C3: 6,8 * PRF # C3: 6,8 => SOL * DIS # C8: 2,9 => CTR => C8: 3,6,8 * PRF # C9: 2,9 => SOL * DIS # G5: 6,8 => CTR => G5: 2,9 * DIS # I5: 6,8 => CTR => I5: 2,9 * PRF # G1: 6,8 => SOL * DIS # G1: 2 => CTR => G1: 6,8 * DIS # G8: 6,8 => CTR => G8: 2,9 * PRF # G8: 2,9 => SOL * DIS # A8: 2,9 => CTR => A8: 6,8 * PRF # A8: 6,8 => SOL * DIS # C8: 2,9 => CTR => C8: 3,6,8 * PRF # C9: 2,9 => SOL * PRF # A8: 6,8 => SOL * DIS # A8: 2,9 => CTR => A8: 6,8 * DIS # C8: 6,8 => CTR => C8: 2,3,9 * DIS # C9: 6,8 => CTR => C9: 2,3,9 * DIS # I9: 6,8 => CTR => I9: 2,3,9 * DIS # A8: 2,9 => CTR => A8: 6,8 * PRF # A8: 6,8 => SOL * DIS # C8: 2,9 => CTR => C8: 3,6,8 * PRF # G8: 2,9 => SOL * DIS # G8: 6,8 => CTR => G8: 2,9 * DIS # I8: 2,9 => CTR => I8: 3,6,8 * PRF # C9: 2,9 => SOL * DIS # H9: 2,9 => CTR => H9: 6,8 * DIS # I9: 2,9 => CTR => I9: 3,6,8 * PRF # G8: 2,9 => SOL * DIS # G8: 6,8 => CTR => G8: 2,9 * DIS # I8: 2,9 => CTR => I8: 3,6,8 * DIS # H9: 2,9 => CTR => H9: 6,8 * DIS # I9: 2,9 => CTR => I9: 3,6,8 * DIS # H5: 2,9 => CTR => H5: 6,8 * CNT 56 HDP CHAINS / 86 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 6,8 => CTR => A1: 2 * PRF A1: 2 => SOL * STA A1: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..7....5..1..8........4.3...4.2....13...5...........7.4..6..5.....7.1............ | initial |
| .3791..5451438.7.....54731..45279.3137.154...1..8634754.16385.7.5.7.1.4.7..4.51.. | autosolve |
| 237916854514382796968547312845279631376154289129863475491638527653721948782495163 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) B3: 6,8 F1: 2,6 F2: 2,6 A4: 6,8 C5: 6,8 B6: 2,9 C6: 2,9 G4: 6,8 B7: 2,9 B9: 6,8 E8: 2,9 E9: 2,9 H7: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,F2: 2.. / F1 = 2 => 0 pairs (X) / F2 = 2 => 16 pairs (_) B6,C6: 2.. / B6 = 2 => 10 pairs (_) / C6 = 2 => 10 pairs (_) E8,E9: 2.. / E8 = 2 => 11 pairs (_) / E9 = 2 => 11 pairs (_) B7,H7: 2.. / B7 = 2 => 10 pairs (_) / H7 = 2 => 10 pairs (_) B6,B7: 2.. / B6 = 2 => 10 pairs (_) / B7 = 2 => 10 pairs (_) C8,C9: 3.. / C8 = 3 => 13 pairs (_) / C9 = 3 => 13 pairs (_) I8,I9: 3.. / I8 = 3 => 13 pairs (_) / I9 = 3 => 13 pairs (_) C8,I8: 3.. / C8 = 3 => 13 pairs (_) / I8 = 3 => 13 pairs (_) C9,I9: 3.. / C9 = 3 => 13 pairs (_) / I9 = 3 => 13 pairs (_) F1,F2: 6.. / F1 = 6 => 16 pairs (_) / F2 = 6 => 0 pairs (X) A4,C5: 6.. / A4 = 6 => 0 pairs (X) / C5 = 6 => 0 pairs (_) A4,G4: 6.. / A4 = 6 => 0 pairs (X) / G4 = 6 => 0 pairs (_) B3,B9: 6.. / B3 = 6 => 0 pairs (*) / B9 = 6 => 0 pairs (X) G1,I3: 8.. / G1 = 8 => 0 pairs (*) / I3 = 8 => 0 pairs (X) A4,C5: 8.. / A4 = 8 => 0 pairs (*) / C5 = 8 => 0 pairs (X) A1,G1: 8.. / A1 = 8 => 0 pairs (X) / G1 = 8 => 0 pairs (_) A4,G4: 8.. / A4 = 8 => 0 pairs (*) / G4 = 8 => 0 pairs (X) B3,B9: 8.. / B3 = 8 => 0 pairs (X) / B9 = 8 => 0 pairs (_) H5,H9: 8.. / H5 = 8 => 0 pairs (*) / H9 = 8 => 0 pairs (X) A3,C3: 9.. / A3 = 9 => 13 pairs (_) / C3 = 9 => 0 pairs (X) H2,I2: 9.. / H2 = 9 => 16 pairs (_) / I2 = 9 => 14 pairs (_) B6,C6: 9.. / B6 = 9 => 10 pairs (_) / C6 = 9 => 10 pairs (_) E8,E9: 9.. / E8 = 9 => 11 pairs (_) / E9 = 9 => 11 pairs (_) B7,H7: 9.. / B7 = 9 => 10 pairs (_) / H7 = 9 => 10 pairs (_) A3,A8: 9.. / A3 = 9 => 13 pairs (_) / A8 = 9 => 0 pairs (X) B6,B7: 9.. / B6 = 9 => 10 pairs (_) / B7 = 9 => 10 pairs (_) G5,G8: 9.. / G5 = 9 => 13 pairs (_) / G8 = 9 => 0 pairs (*) * DURATION: 0:00:46.019564 START: 09:46:16.736375 END: 09:47:02.755939 2017-05-04 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B3,B6,B7,B9,C5,C6,E8,E9,F1,F2,G4,H7) * .3791..5451438.7.....54731..45279.3137.154...1..8634754.16385.7.5.7.1.4.7..4.51.. * PAIR B3: 6,8 BLK 1 A1: 6,8,2 # reduction candidate for 6,8 A1: 6,8 => CTR * 8379162545143827...6.5473186452798313781549..1..8634754.16385.7.5.7.16437..4.51.. A1: 2 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 A3: 6,8,2,9 # reduction candidate for 6,8 A3: 6,8 => CTR * .3791..5451438.7....9547312.45279.3137.154...19286347542163859795.721.4.7..49512. A3: 2,9 # 14 pairs C3: 6,8,2,9 # reduction candidate for 6,8 C3: 6,8 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 C3: 2,9 => CTR * 8379162545143827...6.5473186452798313781549..1..8634754.16385.7.5.7.16437..4.51.. * PAIR B3: 6,8 ROW 3 I3: 6,8,2 # reduction candidate for 6,8 I3: 6,8 => CTR * 8379162545143827...6.5473186452798313781549..1..8634754.16385.7.5.7.16437..4.51.. I3: 2 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 * PAIR F1: 2,6 ROW 1 A1: 2,6,8 # reduction candidate for 2,6 A1: 2,6 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 A1: 8 => CTR * 83791..5451438.7...6.547318645279831378154...1..8634754.16385.7.5.7.1.4.78.4.51.. G1: 2,6,8 # reduction candidate for 2,6 G1: 2,6 => CTR * 83791..5451438.7...6.547318645279831378154...1..8634754.16385.7.5.7.1.4.78.4.51.. G1: 8 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 * PAIR F2: 2,6 ROW 2 H2: 2,6,9 # reduction candidate for 2,6 H2: 2,6 # 14 pairs I2: 2,6,9 # reduction candidate for 2,6 I2: 2,6 # 16 pairs * PAIR A4: 6,8 COL A A1: 6,8,2 # reduction candidate for 6,8 A1: 6,8 => CTR * 8379162545143827...6.5473186452798313781549..1..8634754.16385.7.5.7.16437..4.51.. A1: 2 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 A3: 6,8,2,9 # reduction candidate for 6,8 A3: 6,8 => CTR * .3791..5451438.7....9547312.45279.3137.154...19286347542163859795.721.4.7..49512. A3: 2,9 # 14 pairs A8: 6,8,2,9 # reduction candidate for 6,8 A8: 6,8 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 A8: 2,9 => CTR * 8379162545143827...6.5473186452798313781549..1..8634754.16385.7.5.7.16437..4.51.. * PAIR C5: 6,8 ROW 5 G5: 6,8,2,9 # reduction candidate for 6,8 G5: 6,8 => CTR * .3791.2545143827..9.2547318.45279.3137.154...12986347549163852725.7.194.7..4951.. G5: 2,9 # 14 pairs H5: 6,8,2,9 # reduction candidate for 6,8 H5: 6,8 # 16 pairs I5: 6,8,2,9 # reduction candidate for 6,8 I5: 6,8 => CTR * .37916.54514382769.8.547312.45279.3137.154..81..8634754.16385.7.587.1.4376.4.518. I5: 2,9 # 14 pairs * PAIR C5: 6,8 COL C C3: 6,8,2,9 # reduction candidate for 6,8 C3: 6,8 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 C3: 2,9 => CTR * 8379162545143827...6.5473186452798313781549..1..8634754.16385.7.5.7.16437..4.51.. C8: 6,8,2,3,9 # reduction candidate for 6,8 C8: 6,8 => CTR * 8379162545143827...6.547318645279831378154...1..8634754.16385.7.5.7.1.437.34.51.. C8: 2,3,9 # 13 pairs C9: 6,8,2,3,9 # reduction candidate for 6,8 C9: 6,8 => CTR * 837916254514382769.6.54731864527983137.154...1..8634754.16385.7.537.1.4.7..4.51.3 C9: 2,3,9 # 13 pairs * PAIR C6: 2,9 COL C C3: 2,9,6,8 # reduction candidate for 2,9 C3: 2,9 => CTR * 8379162545143827...6.5473186452798313781549..1..8634754.16385.7.5.7.16437..4.51.. C3: 6,8 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 C8: 2,9,3,6,8 # reduction candidate for 2,9 C8: 2,9 => CTR * .3791..5451438.7.....54731..45279.3137.154...1..8634754.16385.7.5.7.1.437.34.51.. C8: 3,6,8 # 13 pairs C9: 2,9,3,6,8 # reduction candidate for 2,9 C9: 2,9 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 C9: 3,6,8 # 13 pairs * PAIR G4: 6,8 BLK 6 G5: 6,8,2,9 # reduction candidate for 6,8 G5: 6,8 => CTR * .3791.2545143827..9.2547318.45279.3137.154...12986347549163852725.7.194.7..4951.. G5: 2,9 # 14 pairs H5: 6,8,2,9 # reduction candidate for 6,8 H5: 6,8 # 16 pairs I5: 6,8,2,9 # reduction candidate for 6,8 I5: 6,8 => CTR * .37916.54514382769.8.547312.45279.3137.154..81..8634754.16385.7.587.1.4376.4.518. I5: 2,9 # 14 pairs * PAIR G4: 6,8 COL G G1: 6,8,2 # reduction candidate for 6,8 G1: 6,8 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 G1: 2 => CTR * 8379162545143827...6.547318645279831378154...1..8634754.16385.7.5.7.1.4.78.4.51.. G8: 6,8,2,9 # reduction candidate for 6,8 G8: 6,8 => CTR * 8379162545143827...6.54731864527983137.1549..1..8634754.16385.7.5.7.1.4.78.4.51.. G8: 2,9 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 * PAIR B7: 2,9 BLK 7 A8: 2,9,6,8 # reduction candidate for 2,9 A8: 2,9 => CTR * 8379162545143827...6.5473186452798313781549..1..8634754.16385.7.5.7.16437..4.51.. A8: 6,8 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 C8: 2,9,3,6,8 # reduction candidate for 2,9 C8: 2,9 => CTR * .3791..5451438.7.....54731..45279.3137.154...1..8634754.16385.7.5.7.1.437.34.51.. C8: 3,6,8 # 13 pairs C9: 2,9,3,6,8 # reduction candidate for 2,9 C9: 2,9 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 C9: 3,6,8 # 13 pairs * PAIR B9: 6,8 BLK 7 A8: 6,8,2,9 # reduction candidate for 6,8 A8: 6,8 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 A8: 2,9 => CTR * 8379162545143827...6.5473186452798313781549..1..8634754.16385.7.5.7.16437..4.51.. C8: 6,8,2,3,9 # reduction candidate for 6,8 C8: 6,8 => CTR * 8379162545143827...6.547318645279831378154...1..8634754.16385.7.5.7.1.437.34.51.. C8: 2,3,9 # 13 pairs C9: 6,8,2,3,9 # reduction candidate for 6,8 C9: 6,8 => CTR * 837916254514382769.6.54731864527983137.154...1..8634754.16385.7.537.1.4.7..4.51.3 C9: 2,3,9 # 13 pairs * PAIR B9: 6,8 ROW 9 H9: 6,8,2,9 # reduction candidate for 6,8 H9: 6,8 # 14 pairs I9: 6,8,2,3,9 # reduction candidate for 6,8 I9: 6,8 => CTR * .37916254514382769.6.547318845279.3137.1549821..8634754.16385.7.5.7.1.437.34.51.6 I9: 2,3,9 # 13 pairs * PAIR E8: 2,9 ROW 8 A8: 2,9,6,8 # reduction candidate for 2,9 A8: 2,9 => CTR * 8379162545143827...6.5473186452798313781549..1..8634754.16385.7.5.7.16437..4.51.. A8: 6,8 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 C8: 2,9,3,6,8 # reduction candidate for 2,9 C8: 2,9 => CTR * .3791..5451438.7.....54731..45279.3137.154...1..8634754.16385.7.5.7.1.437.34.51.. C8: 3,6,8 # 13 pairs G8: 2,9,6,8 # reduction candidate for 2,9 G8: 2,9 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 G8: 6,8 => CTR * 8379162545143827...6.54731864527983137.1549..1..8634754.16385.7.5.7.1.4.78.4.51.. I8: 2,9,3,6,8 # reduction candidate for 2,9 I8: 2,9 => CTR * .3791..5451438.7.....54731..45279.3137.154...1..8634754.16385.7.537.1.4.7..4.51.3 I8: 3,6,8 # 13 pairs * PAIR E9: 2,9 ROW 9 C9: 2,9,3,6,8 # reduction candidate for 2,9 C9: 2,9 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 C9: 3,6,8 # 13 pairs H9: 2,9,6,8 # reduction candidate for 2,9 H9: 2,9 => CTR * .3791..5451438.769...54731.8452796313761549821..8634754.16385.7.5.7.1.4.7..4.51.. H9: 6,8 # 14 pairs I9: 2,9,3,6,8 # reduction candidate for 2,9 I9: 2,9 => CTR * 8379162545143827...6.547318645279831378154...1..8634754.16385.7.5.7.1.437.34.51.. I9: 3,6,8 # 13 pairs * PAIR H7: 2,9 BLK 9 G8: 2,9,6,8 # reduction candidate for 2,9 G8: 2,9 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 G8: 6,8 => CTR * 8379162545143827...6.54731864527983137.1549..1..8634754.16385.7.5.7.1.4.78.4.51.. I8: 2,9,3,6,8 # reduction candidate for 2,9 I8: 2,9 => CTR * .3791..5451438.7.....54731..45279.3137.154...1..8634754.16385.7.537.1.4.7..4.51.3 I8: 3,6,8 # 13 pairs H9: 2,9,6,8 # reduction candidate for 2,9 H9: 2,9 => CTR * .3791..5451438.769...54731.8452796313761549821..8634754.16385.7.5.7.1.4.7..4.51.. H9: 6,8 # 14 pairs I9: 2,9,3,6,8 # reduction candidate for 2,9 I9: 2,9 => CTR * 8379162545143827...6.547318645279831378154...1..8634754.16385.7.5.7.1.437.34.51.. I9: 3,6,8 # 13 pairs * PAIR H7: 2,9 COL H H2: 2,9,6 # reduction candidate for 2,9 H2: 2,9 # 18 pairs H5: 2,9,6,8 # reduction candidate for 2,9 H5: 2,9 => CTR * .3791..5451438.769.8.547312.45279.3137.154..81..8634754.16385.7.587.1.4376.4.518. H5: 6,8 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-204-base-pr-000.dot * REASONING * DIS # A1: 6,8 => CTR => A1: 2 * PRF # A1: 2 => SOL * DIS # A3: 6,8 => CTR => A3: 2,9 * PRF # C3: 6,8 => SOL * DIS # C3: 2,9 => CTR => C3: 6,8 * DIS # I3: 6,8 => CTR => I3: 2 * PRF # I3: 2 => SOL * PRF # A1: 2,6 => SOL * DIS # A1: 8 => CTR => A1: 2,6 * DIS # G1: 2,6 => CTR => G1: 8 * PRF # G1: 8 => SOL * DIS # A1: 6,8 => CTR => A1: 2 * PRF # A1: 2 => SOL * DIS # A3: 6,8 => CTR => A3: 2,9 * PRF # A8: 6,8 => SOL * DIS # A8: 2,9 => CTR => A8: 6,8 * DIS # G5: 6,8 => CTR => G5: 2,9 * DIS # I5: 6,8 => CTR => I5: 2,9 * PRF # C3: 6,8 => SOL * DIS # C3: 2,9 => CTR => C3: 6,8 * DIS # C8: 6,8 => CTR => C8: 2,3,9 * DIS # C9: 6,8 => CTR => C9: 2,3,9 * DIS # C3: 2,9 => CTR => C3: 6,8 * PRF # C3: 6,8 => SOL * DIS # C8: 2,9 => CTR => C8: 3,6,8 * PRF # C9: 2,9 => SOL * DIS # G5: 6,8 => CTR => G5: 2,9 * DIS # I5: 6,8 => CTR => I5: 2,9 * PRF # G1: 6,8 => SOL * DIS # G1: 2 => CTR => G1: 6,8 * DIS # G8: 6,8 => CTR => G8: 2,9 * PRF # G8: 2,9 => SOL * DIS # A8: 2,9 => CTR => A8: 6,8 * PRF # A8: 6,8 => SOL * DIS # C8: 2,9 => CTR => C8: 3,6,8 * PRF # C9: 2,9 => SOL * PRF # A8: 6,8 => SOL * DIS # A8: 2,9 => CTR => A8: 6,8 * DIS # C8: 6,8 => CTR => C8: 2,3,9 * DIS # C9: 6,8 => CTR => C9: 2,3,9 * DIS # I9: 6,8 => CTR => I9: 2,3,9 * DIS # A8: 2,9 => CTR => A8: 6,8 * PRF # A8: 6,8 => SOL * DIS # C8: 2,9 => CTR => C8: 3,6,8 * PRF # G8: 2,9 => SOL * DIS # G8: 6,8 => CTR => G8: 2,9 * DIS # I8: 2,9 => CTR => I8: 3,6,8 * PRF # C9: 2,9 => SOL * DIS # H9: 2,9 => CTR => H9: 6,8 * DIS # I9: 2,9 => CTR => I9: 3,6,8 * PRF # G8: 2,9 => SOL * DIS # G8: 6,8 => CTR => G8: 2,9 * DIS # I8: 2,9 => CTR => I8: 3,6,8 * DIS # H9: 2,9 => CTR => H9: 6,8 * DIS # I9: 2,9 => CTR => I9: 3,6,8 * DIS # H5: 2,9 => CTR => H5: 6,8 * CNT 56 HDP CHAINS / 86 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B3,B6,B7,B9,C5,C6,E8,E9,F1,F2,G4,H7) * .3791..5451438.7.....54731..45279.3137.154...1..8634754.16385.7.5.7.1.4.7..4.51.. * PAIR B3: 6,8 BLK 1 A1: 6,8,2 # reduction candidate for 6,8 A1: 6,8 => CTR * 8379162545143827...6.5473186452798313781549..1..8634754.16385.7.5.7.16437..4.51.. A1: 2 => SOLVED * 237916854514382796968547312845279631376154289129863475491638527653721948782495163 * DURATION: 0:00:01.784586 START: 09:48:27.841811 END: 09:48:29.626397 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-204-base-pr-001.dot * REASONING * DIS # A1: 6,8 => CTR => A1: 2 * PRF A1: 2 => SOL * STA A1: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 204 solution: 237916854514382796968547312845279631376154289129863475491638527653721948782495163 info: 1893 FNBTHWX S8.f 42690 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 237916854514382796968547312845279631376154289129863475491638527653721948782495163 solved
See section Pair Reduction for the HDP chains leading to this result.
Appendix: Full HDP Chains
A1. Pair Reduction Analysis
Full list of HDP chains traversed:
* DIS # A1: 6,8 => CTR => A1: 2 * PRF # A1: 2 => SOL * DIS # A3: 6,8 => CTR => A3: 2,9 * INC # A3: 2,9 => UNS * PRF # C3: 6,8 => SOL * DIS # C3: 2,9 => CTR => C3: 6,8 * DIS # I3: 6,8 => CTR => I3: 2 * PRF # I3: 2 => SOL * PRF # A1: 2,6 => SOL * DIS # A1: 8 => CTR => A1: 2,6 * DIS # G1: 2,6 => CTR => G1: 8 * PRF # G1: 8 => SOL * INC # H2: 2,6 => UNS * INC # I2: 2,6 => UNS * DIS # A1: 6,8 => CTR => A1: 2 * PRF # A1: 2 => SOL * DIS # A3: 6,8 => CTR => A3: 2,9 * INC # A3: 2,9 => UNS * PRF # A8: 6,8 => SOL * DIS # A8: 2,9 => CTR => A8: 6,8 * DIS # G5: 6,8 => CTR => G5: 2,9 * INC # G5: 2,9 => UNS * INC # H5: 6,8 => UNS * DIS # I5: 6,8 => CTR => I5: 2,9 * INC # I5: 2,9 => UNS * PRF # C3: 6,8 => SOL * DIS # C3: 2,9 => CTR => C3: 6,8 * DIS # C8: 6,8 => CTR => C8: 2,3,9 * INC # C8: 2,3,9 => UNS * DIS # C9: 6,8 => CTR => C9: 2,3,9 * INC # C9: 2,3,9 => UNS * DIS # C3: 2,9 => CTR => C3: 6,8 * PRF # C3: 6,8 => SOL * DIS # C8: 2,9 => CTR => C8: 3,6,8 * INC # C8: 3,6,8 => UNS * PRF # C9: 2,9 => SOL * INC # C9: 3,6,8 => UNS * DIS # G5: 6,8 => CTR => G5: 2,9 * INC # G5: 2,9 => UNS * INC # H5: 6,8 => UNS * DIS # I5: 6,8 => CTR => I5: 2,9 * INC # I5: 2,9 => UNS * PRF # G1: 6,8 => SOL * DIS # G1: 2 => CTR => G1: 6,8 * DIS # G8: 6,8 => CTR => G8: 2,9 * PRF # G8: 2,9 => SOL * DIS # A8: 2,9 => CTR => A8: 6,8 * PRF # A8: 6,8 => SOL * DIS # C8: 2,9 => CTR => C8: 3,6,8 * INC # C8: 3,6,8 => UNS * PRF # C9: 2,9 => SOL * INC # C9: 3,6,8 => UNS * PRF # A8: 6,8 => SOL * DIS # A8: 2,9 => CTR => A8: 6,8 * DIS # C8: 6,8 => CTR => C8: 2,3,9 * INC # C8: 2,3,9 => UNS * DIS # C9: 6,8 => CTR => C9: 2,3,9 * INC # C9: 2,3,9 => UNS * INC # H9: 6,8 => UNS * DIS # I9: 6,8 => CTR => I9: 2,3,9 * INC # I9: 2,3,9 => UNS * DIS # A8: 2,9 => CTR => A8: 6,8 * PRF # A8: 6,8 => SOL * DIS # C8: 2,9 => CTR => C8: 3,6,8 * INC # C8: 3,6,8 => UNS * PRF # G8: 2,9 => SOL * DIS # G8: 6,8 => CTR => G8: 2,9 * DIS # I8: 2,9 => CTR => I8: 3,6,8 * INC # I8: 3,6,8 => UNS * PRF # C9: 2,9 => SOL * INC # C9: 3,6,8 => UNS * DIS # H9: 2,9 => CTR => H9: 6,8 * INC # H9: 6,8 => UNS * DIS # I9: 2,9 => CTR => I9: 3,6,8 * INC # I9: 3,6,8 => UNS * PRF # G8: 2,9 => SOL * DIS # G8: 6,8 => CTR => G8: 2,9 * DIS # I8: 2,9 => CTR => I8: 3,6,8 * INC # I8: 3,6,8 => UNS * DIS # H9: 2,9 => CTR => H9: 6,8 * INC # H9: 6,8 => UNS * DIS # I9: 2,9 => CTR => I9: 3,6,8 * INC # I9: 3,6,8 => UNS * INC # H2: 2,9 => UNS * DIS # H5: 2,9 => CTR => H5: 6,8 * INC # H5: 6,8 => UNS * CNT 86 HDP CHAINS / 86 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 6,8 => CTR => A1: 2 * PRF A1: 2 => SOL * STA A1: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED