Analysis of zz-menneske-no-05925446-base.sdk
Contents
Sudoku from http://www.menneske.no/sudoku/utskrift.html?number=5925446
level: medium
position: .1......47...5.......3.8.......3....9...6.8....3..7.2.46.....7.......2..57..2.31. initial
Autosolve
position: .1......47...5.......3.8.......3....9...6.8....3..7.2.462..3.7.......24.57..2.31. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 2,6 => CTR => A1: 3,8 * PRF # I5: 1,7 => SOL * DIS # C8: 8,9 => CTR => C8: 1 * DIS # G3: 5,9 => CTR => G3: 1,6,7 * DIS # G4: 5,9 => CTR => G4: 1,4,6,7 * DIS # G6: 5,9 => CTR => G6: 1,4,6 * CNT 6 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 2,6 => CTR => A1: 3,8 * PRF A1: 3,8 # I5: 1,7 => SOL * STA A1: 3,8 + I5: 1,7 * CNT 2 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1......47...5.......3.8.......3....9...6.8....3..7.2.46.....7.......2..57..2.31. | initial |
| .1......47...5.......3.8.......3....9...6.8....3..7.2.462..3.7.......24.57..2.31. | autosolve |
| 315276984728459163694318752256831497947562831183947625462183579831795246579624318 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) A3: 2,6 E1: 7,9 H5: 3,5 C9: 8,9 G7: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A8,C8: 1.. / A8 = 1 => 0 pairs (X) / C8 = 1 => 6 pairs (_) D7,E7: 1.. / D7 = 1 => 8 pairs (_) / E7 = 1 => 6 pairs (_) I2,I3: 2.. / I2 = 2 => 10 pairs (_) / I3 = 2 => 0 pairs (*) A1,B2: 3.. / A1 = 3 => 6 pairs (_) / B2 = 3 => 9 pairs (_) H5,I5: 3.. / H5 = 3 => 0 pairs (*) / I5 = 3 => 0 pairs (X) A8,B8: 3.. / A8 = 3 => 9 pairs (_) / B8 = 3 => 6 pairs (_) A1,H1: 3.. / A1 = 3 => 6 pairs (_) / H1 = 3 => 9 pairs (_) A1,A8: 3.. / A1 = 3 => 6 pairs (_) / A8 = 3 => 9 pairs (_) B2,B8: 3.. / B2 = 3 => 9 pairs (_) / B8 = 3 => 6 pairs (_) I2,I5: 3.. / I2 = 3 => 0 pairs (*) / I5 = 3 => 0 pairs (X) G4,G6: 4.. / G4 = 4 => 5 pairs (_) / G6 = 4 => 0 pairs (X) D9,F9: 4.. / D9 = 4 => 6 pairs (_) / F9 = 4 => 5 pairs (_) E3,E6: 4.. / E3 = 4 => 0 pairs (X) / E6 = 4 => 6 pairs (_) I8,I9: 6.. / I8 = 6 => 9 pairs (_) / I9 = 6 => 6 pairs (_) A6,G6: 6.. / A6 = 6 => 12 pairs (_) / G6 = 6 => 11 pairs (_) C4,C5: 7.. / C4 = 7 => 0 pairs (X) / C5 = 7 => 5 pairs (_) D8,E8: 7.. / D8 = 7 => 8 pairs (_) / E8 = 7 => 8 pairs (_) C5,I5: 7.. / C5 = 7 => 5 pairs (_) / I5 = 7 => 0 pairs (X) D1,D8: 7.. / D1 = 7 => 8 pairs (_) / D8 = 7 => 8 pairs (_) H1,H2: 8.. / H1 = 8 => 7 pairs (_) / H2 = 8 => 5 pairs (_) * DURATION: 0:00:17.869254 START: 01:26:06.845532 END: 01:26:24.714786 2019-05-01 * CP COUNT: (20) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C9,E1,G7,H5) * .1......47...5.......3.8.......3....9...6.8....3..7.2.462..3.7.......24.57..2.31. * PAIR A3: 2,6 BLK 1 A1: 2,6,3,8 # reduction candidate for 2,6 A1: 2,6 => CTR * .18...534734.5.18929534876.....3..9.9.7.6.853..3..7.21462.1397.381...24.579.2.31. A1: 3,8 # 6 pairs * PAIR A3: 2,6 COL A A4: 2,6,1,8 # reduction candidate for 2,6 A4: 2,6 # 13 pairs A4: 1,8 # 6 pairs * PAIR E1: 7,9 BLK 2 D1: 7,9,2,6 # reduction candidate for 7,9 D1: 7,9 # 9 pairs E3: 7,9,1,4 # reduction candidate for 7,9 E3: 7,9 # 32 pairs * PAIR E1: 7,9 ROW 1 G1: 7,9,5,6 # reduction candidate for 7,9 G1: 7,9 # 13 pairs G1: 5,6 # 6 pairs * PAIR E1: 7,9 COL E E8: 7,9,8 # reduction candidate for 7,9 E8: 8 # 19 pairs E8: 7,9 # 8 pairs * PAIR H5: 3,5 BLK 6 I5: 3,5,1,7 # reduction candidate for 3,5 I5: 1,7 => SOLVED * 315276984728459163694318752256831497947562831183947625462183579831795246579624318 I5: 3,5 # 9 pairs * PAIR H5: 3,5 COL H H1: 3,5,6,8,9 # reduction candidate for 3,5 H1: 3,5 # 8 pairs H1: 6,8,9 # 6 pairs * PAIR C9: 8,9 BLK 7 B8: 8,9,3 # reduction candidate for 8,9 B8: 8,9 # 9 pairs C8: 8,9,1 # reduction candidate for 8,9 C8: 8,9 => CTR * 31579..84786.5..322943.8.656.183.497947.6.8538539476214621.357.13.57.24.57..2.31. C8: 1 # 6 pairs * PAIR C9: 8,9 ROW 9 D9: 8,9,4,6 # reduction candidate for 8,9 D9: 8,9 # 6 pairs I9: 8,9,6 # reduction candidate for 8,9 I9: 8,9 # 9 pairs * PAIR C9: 8,9 COL C C1: 8,9,5,6 # reduction candidate for 8,9 C1: 8,9 # 9 pairs C2: 8,9,4,6 # reduction candidate for 8,9 C2: 8,9 # 12 pairs * PAIR G7: 5,9 BLK 9 I7: 5,9,8 # reduction candidate for 5,9 I7: 5,9 # 12 pairs I8: 5,9,6,8 # reduction candidate for 5,9 I8: 5,9 # 8 pairs * PAIR G7: 5,9 ROW 7 D7: 5,9,1,8 # reduction candidate for 5,9 D7: 5,9 # 8 pairs D7: 1,8 # 6 pairs * PAIR G7: 5,9 COL G G1: 5,9,6,7 # reduction candidate for 5,9 G1: 5,9 # 7 pairs G3: 5,9,1,6,7 # reduction candidate for 5,9 G3: 5,9 => CTR * .15.9.7.47...5.6.2..4378591..6.3.4.7947.6.853..3.47129462.1397....78.24.578.2.316 G3: 1,6,7 # 5 pairs G4: 5,9,1,4,6,7 # reduction candidate for 5,9 G4: 5,9 => CTR * .1......47...5...22..348.......3..679.7.6.8536.3..7421462.13.7.......24.57..2.31. G4: 1,4,6,7 # 5 pairs G6: 5,9,1,4,6 # reduction candidate for 5,9 G6: 5,9 => CTR * .15.....47...5...22463.8.95....3.467927.6.8536.3.47921462..357.......24.57..2.31. G6: 1,4,6 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-05925446-base-pr-000.dot * REASONING * DIS # A1: 2,6 => CTR => A1: 3,8 * PRF # I5: 1,7 => SOL * DIS # C8: 8,9 => CTR => C8: 1 * DIS # G3: 5,9 => CTR => G3: 1,6,7 * DIS # G4: 5,9 => CTR => G4: 1,4,6,7 * DIS # G6: 5,9 => CTR => G6: 1,4,6 * CNT 6 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C9,E1,G7,H5) * .1......47...5.......3.8.......3....9...6.8....3..7.2.462..3.7.......24.57..2.31. * PAIR A3: 2,6 BLK 1 A1: 2,6,3,8 # reduction candidate for 2,6 A1: 2,6 => CTR * .18...534734.5.18929534876.....3..9.9.7.6.853..3..7.21462.1397.381...24.579.2.31. * PAIR A3: 2,6 COL A A4: 2,6,1,8 # reduction candidate for 2,6 A4: 2,6 # 13 pairs A4: 1,8 # 12 pairs * PAIR E1: 7,9 BLK 2 D1: 7,9,2,6 # reduction candidate for 7,9 D1: 7,9 # 10 pairs E3: 7,9,1,4 # reduction candidate for 7,9 E3: 7,9 # 32 pairs * PAIR E1: 7,9 ROW 1 G1: 7,9,5,6 # reduction candidate for 7,9 G1: 7,9 # 13 pairs G1: 5,6 # 7 pairs * PAIR E1: 7,9 COL E E8: 7,9,8 # reduction candidate for 7,9 E8: 8 # 19 pairs E8: 7,9 # 9 pairs * PAIR H5: 3,5 BLK 6 I5: 3,5,1,7 # reduction candidate for 3,5 I5: 1,7 => SOLVED * 315276984728459163694318752256831497947562831183947625462183579831795246579624318 * DURATION: 0:00:07.477717 START: 01:26:40.633630 END: 01:26:48.111347 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-05925446-base-pr-001.dot * REASONING * DIS # A1: 2,6 => CTR => A1: 3,8 * PRF A1: 3,8 # I5: 1,7 => SOL * STA A1: 3,8 + I5: 1,7 * CNT 2 HDP CHAINS / 11 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=5925446 umulig
Solution
position: 315276984728459163694318752256831497947562831183947625462183579831795246579624318 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: 2,6 => CTR => A1: 3,8 * INC # A1: 3,8 => UNS * INC # A4: 2,6 => UNS * INC # A4: 1,8 => UNS * INC # D1: 7,9 => UNS * INC # E3: 7,9 => UNS * INC # G1: 7,9 => UNS * INC # G1: 5,6 => UNS * INC # E8: 7,9 => UNS * INC # E8: 8 => UNS * INC # I5: 3,5 => UNS * PRF # I5: 1,7 => SOL * INC # H1: 3,5 => UNS * INC # H1: 6,8,9 => UNS * INC # B8: 8,9 => UNS * DIS # C8: 8,9 => CTR => C8: 1 * INC # C8: 1 => UNS * INC # D9: 8,9 => UNS * INC # I9: 8,9 => UNS * INC # C1: 8,9 => UNS * INC # C2: 8,9 => UNS * INC # I7: 5,9 => UNS * INC # I8: 5,9 => UNS * INC # D7: 5,9 => UNS * INC # D7: 1,8 => UNS * INC # G1: 5,9 => UNS * DIS # G3: 5,9 => CTR => G3: 1,6,7 * INC # G3: 1,6,7 => UNS * DIS # G4: 5,9 => CTR => G4: 1,4,6,7 * INC # G4: 1,4,6,7 => UNS * DIS # G6: 5,9 => CTR => G6: 1,4,6 * INC # G6: 1,4,6 => UNS * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 2,6 => CTR => A1: 3,8 * INC A1: 3,8 # A4: 2,6 => UNS * INC A1: 3,8 # A4: 1,8 => UNS * INC A1: 3,8 # D1: 7,9 => UNS * INC A1: 3,8 # E3: 7,9 => UNS * INC A1: 3,8 # G1: 7,9 => UNS * INC A1: 3,8 # G1: 5,6 => UNS * INC A1: 3,8 # E8: 7,9 => UNS * INC A1: 3,8 # E8: 8 => UNS * INC A1: 3,8 # I5: 3,5 => UNS * PRF A1: 3,8 # I5: 1,7 => SOL * STA A1: 3,8 + I5: 1,7 * CNT 11 HDP CHAINS / 11 HYP OPENED