Contents
level: medium
The following important HDP chains were detected:
* DIS # B1: 3,6 => CTR => B1: 5 * DIS # D2: 2 => CTR => D2: 5,6 * DIS # H2: 9 => CTR => H2: 2,6 * DIS # H2: 6,9 => CTR => H2: 2 * PRF # C8: 1,4 => SOL * DIS # C8: 2,8 => CTR => C8: 1,4 * DIS # B6: 3,7 => CTR => B6: 4,5 * DIS # B6: 3,7 => CTR => B6: 4,5 * DIS # H2: 6,9 => CTR => H2: 2 * PRF # B7: 6,7 => SOL * DIS # B7: 4 => CTR => B7: 6,7 * DIS # D9: 1,5 => CTR => D9: 6,7 * PRF # F7: 4,6 => SOL * PRF # B7: 7 => SOL * DIS # E4: 5 => CTR => E4: 4,6 * DIS # A8: 1,7 => CTR => A8: 2,8 * CNT 16 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
The following important HDP chains were detected:
* DIS # B1: 3,6 => CTR => B1: 5 * DIS B1: 5 # D2: 2 => CTR => D2: 5,6 * DIS B1: 5 + D2: 5,6 # B6: 3,7 => CTR => B6: 4 * PRF B1: 5 + D2: 5,6 + B6: 4 => SOL * STA B1: 5 + D2: 5,6 + B6: 4 * CNT 4 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
9..4......17.8..........45..2.......689..7......91..8.5.3...2.9....3...6....92..4 | initial |
9..4.....417.8...3.....945..2.......689..7.4....91..825.3...2.9.9..3...6....92.34 | autosolve |
952473168417685923836129457721348695689257341345916782573864219294531876168792534 | solved |
level: medium
-------------------------------------------------- * PAIRS (22) B3: 3,6 F1: 1,3 F2: 5,6 D3: 1,3 G1: 1,7 H1: 2,6 G2: 6,9 C4: 1,4 A6: 3,7 C6: 4,5 D5: 2,3 E5: 2,5 H4: 6,9 I4: 5,7 G5: 1,3 I5: 1,5 B9: 6,7 E7: 4,6 H7: 1,7 G8: 5,8 H8: 1,7 G9: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,D3: 1.. / F1 = 1 => 0 pairs (X) / D3 = 1 => 24 pairs (_) A4,C4: 1.. / A4 = 1 => 0 pairs (X) / C4 = 1 => 27 pairs (_) G5,I5: 1.. / G5 = 1 => 0 pairs (X) / I5 = 1 => 22 pairs (_) H7,H8: 1.. / H7 = 1 => 21 pairs (_) / H8 = 1 => 25 pairs (_) D3,I3: 1.. / D3 = 1 => 24 pairs (_) / I3 = 1 => 0 pairs (X) G1,G5: 1.. / G1 = 1 => 22 pairs (_) / G5 = 1 => 0 pairs (X) H1,H2: 2.. / H1 = 2 => 0 pairs (X) / H2 = 2 => 22 pairs (_) D5,E5: 2.. / D5 = 2 => 22 pairs (_) / E5 = 2 => 0 pairs (X) A8,C8: 2.. / A8 = 2 => 23 pairs (_) / C8 = 2 => 0 pairs (X) D2,H2: 2.. / D2 = 2 => 0 pairs (X) / H2 = 2 => 22 pairs (_) A3,A8: 2.. / A3 = 2 => 0 pairs (X) / A8 = 2 => 23 pairs (_) D2,D5: 2.. / D2 = 2 => 0 pairs (X) / D5 = 2 => 22 pairs (_) F1,D3: 3.. / F1 = 3 => 24 pairs (_) / D3 = 3 => 0 pairs (X) B1,F1: 3.. / B1 = 3 => 0 pairs (X) / F1 = 3 => 24 pairs (_) D5,G5: 3.. / D5 = 3 => 0 pairs (X) / G5 = 3 => 22 pairs (_) B7,C8: 4.. / B7 = 4 => 0 pairs (X) / C8 = 4 => 0 pairs (_) C8,F8: 4.. / C8 = 4 => 0 pairs (*) / F8 = 4 => 0 pairs (X) B6,B7: 4.. / B6 = 4 => 0 pairs (*) / B7 = 4 => 0 pairs (X) E4,E7: 4.. / E4 = 4 => 0 pairs (*) / E7 = 4 => 0 pairs (X) B1,C1: 5.. / B1 = 5 => 22 pairs (_) / C1 = 5 => 0 pairs (X) D2,F2: 5.. / D2 = 5 => 0 pairs (X) / F2 = 5 => 23 pairs (_) B6,C6: 5.. / B6 = 5 => 0 pairs (X) / C6 = 5 => 22 pairs (_) E4,E5: 5.. / E4 = 5 => 0 pairs (X) / E5 = 5 => 22 pairs (_) I4,I5: 5.. / I4 = 5 => 22 pairs (_) / I5 = 5 => 0 pairs (X) G8,G9: 5.. / G8 = 5 => 0 pairs (X) / G9 = 5 => 20 pairs (_) E4,I4: 5.. / E4 = 5 => 0 pairs (X) / I4 = 5 => 22 pairs (_) E5,I5: 5.. / E5 = 5 => 22 pairs (_) / I5 = 5 => 0 pairs (X) D9,G9: 5.. / D9 = 5 => 0 pairs (X) / G9 = 5 => 20 pairs (_) B1,B6: 5.. / B1 = 5 => 22 pairs (_) / B6 = 5 => 0 pairs (X) C1,C6: 5.. / C1 = 5 => 0 pairs (X) / C6 = 5 => 22 pairs (_) F2,F8: 5.. / F2 = 5 => 23 pairs (_) / F8 = 5 => 0 pairs (X) F6,G6: 6.. / F6 = 6 => 31 pairs (_) / G6 = 6 => 24 pairs (_) E1,E3: 7.. / E1 = 7 => 20 pairs (_) / E3 = 7 => 26 pairs (_) H7,H8: 7.. / H7 = 7 => 25 pairs (_) / H8 = 7 => 21 pairs (_) E3,I3: 7.. / E3 = 7 => 26 pairs (_) / I3 = 7 => 20 pairs (_) I1,I3: 8.. / I1 = 8 => 23 pairs (_) / I3 = 8 => 27 pairs (_) D4,F4: 8.. / D4 = 8 => 22 pairs (_) / F4 = 8 => 23 pairs (_) D7,F7: 8.. / D7 = 8 => 23 pairs (_) / F7 = 8 => 22 pairs (_) G8,G9: 8.. / G8 = 8 => 20 pairs (_) / G9 = 8 => 0 pairs (X) C1,I1: 8.. / C1 = 8 => 27 pairs (_) / I1 = 8 => 23 pairs (_) D4,D7: 8.. / D4 = 8 => 22 pairs (_) / D7 = 8 => 23 pairs (_) F4,F7: 8.. / F4 = 8 => 23 pairs (_) / F7 = 8 => 22 pairs (_) G2,H2: 9.. / G2 = 9 => 21 pairs (_) / H2 = 9 => 0 pairs (X) G4,H4: 9.. / G4 = 9 => 0 pairs (X) / H4 = 9 => 21 pairs (_) G2,G4: 9.. / G2 = 9 => 21 pairs (_) / G4 = 9 => 0 pairs (X) H2,H4: 9.. / H2 = 9 => 0 pairs (X) / H4 = 9 => 21 pairs (_) * DURATION: 0:01:02.844572 START: 22:02:20.133605 END: 22:03:22.978177 2019-04-30 * CP COUNT: (46) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B3,B9,C4,C6,D3,D5,E5,E7,F1,F2,G1,G2,G5,G8,G9,H1,H4,H7,H8,I4,I5) * 9..4.....417.8...3.....945..2.......689..7.4....91..825.3...2.9.9..3...6....92.34 * PAIR B3: 3,6 BLK 1 B1: 3,6,5 # reduction candidate for 3,6 B1: 3,6 => CTR * 9354.1..8417.85..3.6...945..21.4...5689.57.41.5491..82543.6.2.9.9..34..6.76.92.34 B1: 5 # 22 pairs * PAIR F2: 5,6 BLK 2 D2: 5,6,2 # reduction candidate for 5,6 D2: 2 => CTR * 9.8463721417285..3..2179458.21.54..7689327145.459163825.3.48219294531876....92.34 D2: 5,6 # 22 pairs * PAIR G1: 1,7 BLK 3 I1: 1,7,8 # reduction candidate for 1,7 I1: 1,7 # 27 pairs I3: 1,7,8 # reduction candidate for 1,7 I3: 1,7 # 23 pairs * PAIR H1: 2,6 BLK 3 H2: 2,6,9 # reduction candidate for 2,6 H2: 9 => CTR * 9..4.3721417285693.3.1794583218549676893271457..9163825.3.48219.94.31.761...92.34 H2: 2,6 # 21 pairs * PAIR H1: 2,6 ROW 1 C1: 2,6,5,8 # reduction candidate for 2,6 C1: 2,6 # 20 pairs E1: 2,6,7 # reduction candidate for 2,6 E1: 2,6 # 26 pairs * PAIR G2: 6,9 BLK 3 H2: 6,9,2 # reduction candidate for 6,9 H2: 6,9 => CTR * 9.8463721417285..3..2179458.21.54..7689327145.459163825.3.48219294531876....92.34 H2: 2 # 22 pairs * PAIR G2: 6,9 COL G G4: 6,9,3,7 # reduction candidate for 6,9 G4: 6,9 # 31 pairs G4: 3,7 # 24 pairs * PAIR C4: 1,4 COL C C8: 1,4,2,8 # reduction candidate for 1,4 C8: 1,4 => SOLVED * 952473168417685923836129457721348695689257341345916782573864219294531876168792534 C8: 2,8 => CTR * 9.54..1.8417685923...1.945..2..4...5689.57.41..491..82543.6.2.9.9..34..6....92.34 * PAIR A6: 3,7 BLK 4 A4: 3,7,1 # reduction candidate for 3,7 A4: 3,7 # 27 pairs B6: 3,7,4,5 # reduction candidate for 3,7 B6: 3,7 => CTR * 95.4.3...417.8...3...1.945..2.......689..7.4...5914682543.6.2.9.9..3...6....92.34 B6: 4,5 # 27 pairs * PAIR A6: 3,7 ROW 6 G6: 3,7,6 # reduction candidate for 3,7 G6: 3,7 # 31 pairs G6: 6 # 24 pairs * PAIR C6: 4,5 BLK 4 B6: 4,5,3,7 # reduction candidate for 4,5 B6: 3,7 => CTR * 95.4.3...417.8...3...1.945..2.......689..7.4...5914682543.6.2.9.9..3...6....92.34 B6: 4,5 # 27 pairs * PAIR H4: 6,9 BLK 6 G4: 6,9,3,7 # reduction candidate for 6,9 G4: 6,9 # 31 pairs G4: 3,7 # 24 pairs * PAIR H4: 6,9 COL H H2: 6,9,2 # reduction candidate for 6,9 H2: 6,9 => CTR * 9.8463721417285..3..2179458.21.54..7689327145.459163825.3.48219294531876....92.34 H2: 2 # 22 pairs * PAIR B9: 6,7 BLK 7 B7: 6,7,4 # reduction candidate for 6,7 B7: 6,7 => SOLVED * 952473168417685923836129457721348695689257341345916782573864219294531876168792534 B7: 4 => CTR * 9.54..1.8417685923...1.945..2..4...5689.57.41..491..82543.6.2.9.9..34..6....92.34 * PAIR B9: 6,7 ROW 9 D9: 6,7,1,5 # reduction candidate for 6,7 D9: 1,5 => CTR * 9.54..1.8417685923...1.945..2..4...5689.57.41..491..82543.6.2.9.9..34..6....92.34 D9: 6,7 # 26 pairs * PAIR E7: 4,6 BLK 8 F7: 4,6,1,8 # reduction candidate for 4,6 F7: 4,6 => SOLVED * 952473168417685923836129457721348695689257341345916782573864219294531876168792534 F7: 1,8 # 23 pairs * PAIR E7: 4,6 ROW 7 B7: 4,6,7 # reduction candidate for 4,6 B7: 7 => SOLVED * 952473168417685923836129457721348695689257341345916782573864219294531876168792534 B7: 4,6 # 24 pairs * PAIR E7: 4,6 COL E E4: 4,6,5 # reduction candidate for 4,6 E4: 5 => CTR * 9..4..7..417285..3....7945..21.54..7689327145.459163825.3.482.9294.318761.8.92534 E4: 4,6 # 22 pairs * PAIR H7: 1,7 ROW 7 D7: 1,7,6,8 # reduction candidate for 1,7 D7: 1,7 # 24 pairs D7: 6,8 # 23 pairs * PAIR H8: 1,7 ROW 8 A8: 1,7,2,8 # reduction candidate for 1,7 A8: 1,7 => CTR * 9.542.16.417.85..32....945..2..4...5689.57.41..491..82543.6.2.9.925348.68...92534 A8: 2,8 # 23 pairs D8: 1,7,5 # reduction candidate for 1,7 D8: 1,7 # 25 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060331-absurd-base-pr-000.dot * REASONING * DIS # B1: 3,6 => CTR => B1: 5 * DIS # D2: 2 => CTR => D2: 5,6 * DIS # H2: 9 => CTR => H2: 2,6 * DIS # H2: 6,9 => CTR => H2: 2 * PRF # C8: 1,4 => SOL * DIS # C8: 2,8 => CTR => C8: 1,4 * DIS # B6: 3,7 => CTR => B6: 4,5 * DIS # B6: 3,7 => CTR => B6: 4,5 * DIS # H2: 6,9 => CTR => H2: 2 * PRF # B7: 6,7 => SOL * DIS # B7: 4 => CTR => B7: 6,7 * DIS # D9: 1,5 => CTR => D9: 6,7 * PRF # F7: 4,6 => SOL * PRF # B7: 7 => SOL * DIS # E4: 5 => CTR => E4: 4,6 * DIS # A8: 1,7 => CTR => A8: 2,8 * CNT 16 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B3,B9,C4,C6,D3,D5,E5,E7,F1,F2,G1,G2,G5,G8,G9,H1,H4,H7,H8,I4,I5) * 9..4.....417.8...3.....945..2.......689..7.4....91..825.3...2.9.9..3...6....92.34 * PAIR B3: 3,6 BLK 1 B1: 3,6,5 # reduction candidate for 3,6 B1: 3,6 => CTR * 9354.1..8417.85..3.6...945..21.4...5689.57.41.5491..82543.6.2.9.9..34..6.76.92.34 * PAIR F2: 5,6 BLK 2 D2: 5,6,2 # reduction candidate for 5,6 D2: 2 => CTR * 958463721417285..3..2179458.21.54..7689327145.459163825.3.48219294531876....92.34 * PAIR A6: 3,7 BLK 4 B6: 3,7,4 # reduction candidate for 3,7 B6: 3,7 => CTR * 95.4.316.417.8.923...1.945..24368795689257341..59146825438..2.9.9..3...6....92.34 B6: 4 => SOLVED * 952473168417685923836129457721348695689257341345916782573864219294531876168792534 * DURATION: 0:00:06.277176 START: 22:03:55.725003 END: 22:04:02.002179 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060331-absurd-base-pr-001.dot * REASONING * DIS # B1: 3,6 => CTR => B1: 5 * DIS B1: 5 # D2: 2 => CTR => D2: 5,6 * DIS B1: 5 + D2: 5,6 # B6: 3,7 => CTR => B6: 4 * PRF B1: 5 + D2: 5,6 + B6: 4 => SOL * STA B1: 5 + D2: 5,6 + B6: 4 * CNT 4 HDP CHAINS / 4 HYP OPENED
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060331, absurd
See section Pair Reduction for the HDP chains leading to this result.
Full list of HDP chains traversed:
* DIS # B1: 3,6 => CTR => B1: 5 * INC # B1: 5 => UNS * INC # D2: 5,6 => UNS * DIS # D2: 2 => CTR => D2: 5,6 * INC # I1: 1,7 => UNS * INC # I3: 1,7 => UNS * INC # H2: 2,6 => UNS * DIS # H2: 9 => CTR => H2: 2,6 * INC # C1: 2,6 => UNS * INC # E1: 2,6 => UNS * DIS # H2: 6,9 => CTR => H2: 2 * INC # H2: 2 => UNS * INC # G4: 6,9 => UNS * INC # G4: 3,7 => UNS * PRF # C8: 1,4 => SOL * DIS # C8: 2,8 => CTR => C8: 1,4 * INC # A4: 3,7 => UNS * DIS # B6: 3,7 => CTR => B6: 4,5 * INC # B6: 4,5 => UNS * INC # G6: 3,7 => UNS * INC # G6: 6 => UNS * INC # B6: 4,5 => UNS * DIS # B6: 3,7 => CTR => B6: 4,5 * INC # G4: 6,9 => UNS * INC # G4: 3,7 => UNS * DIS # H2: 6,9 => CTR => H2: 2 * INC # H2: 2 => UNS * PRF # B7: 6,7 => SOL * DIS # B7: 4 => CTR => B7: 6,7 * INC # D9: 6,7 => UNS * DIS # D9: 1,5 => CTR => D9: 6,7 * PRF # F7: 4,6 => SOL * INC # F7: 1,8 => UNS * INC # B7: 4,6 => UNS * PRF # B7: 7 => SOL * INC # E4: 4,6 => UNS * DIS # E4: 5 => CTR => E4: 4,6 * INC # D7: 1,7 => UNS * INC # D7: 6,8 => UNS * DIS # A8: 1,7 => CTR => A8: 2,8 * INC # A8: 2,8 => UNS * INC # D8: 1,7 => UNS * CNT 42 HDP CHAINS / 42 HYP OPENED
Full list of HDP chains traversed:
* DIS # B1: 3,6 => CTR => B1: 5 * INC B1: 5 # D2: 5,6 => UNS * DIS B1: 5 # D2: 2 => CTR => D2: 5,6 * DIS B1: 5 + D2: 5,6 # B6: 3,7 => CTR => B6: 4 * PRF B1: 5 + D2: 5,6 + B6: 4 => SOL * STA B1: 5 + D2: 5,6 + B6: 4 * CNT 5 HDP CHAINS / 4 HYP OPENED