Analysis of zz-www.sudokuwiki.org-0123-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=123
level: medium
position: .....6.5.7.4.8.9...6..4............5..14382..3......1.....5..7...9.2.5.8.1.7..... initial
Autosolve
position: .....6.5.7.4.8.9...6..4............5..14382.73......1....85..7..79.2.5.8.1.7..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H4: 6,9 => CTR => H4: 3,4,8 * DIS # I7: 1,6 => CTR => I7: 4,9 * DIS # I9: 6,9 => CTR => I9: 2,3,4 * PRF # E4: 6,9 => SOL * CNT 4 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H4: 6,9 => CTR => H4: 3,4,8 * DIS H4: 3,4,8 # I6: 4 => CTR => I6: 6,9 * DIS H4: 3,4,8 + I6: 6,9 # A5: 5 => CTR => A5: 6,9 * DIS H4: 3,4,8 + I6: 6,9 + A5: 6,9 # A7: 4,6 => CTR => A7: 2 * DIS H4: 3,4,8 + I6: 6,9 + A5: 6,9 + A7: 2 # A4: 4,6 => CTR => A4: 8,9 * PRF H4: 3,4,8 + I6: 6,9 + A5: 6,9 + A7: 2 + A4: 8,9 => SOL * STA H4: 3,4,8 + I6: 6,9 + A5: 6,9 + A7: 2 + A4: 8,9 * CNT 6 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....6.5.7.4.8.9...6..4............5..14382..3......1.....5..7...9.2.5.8.1.7..... | initial |
| .....6.5.7.4.8.9...6..4............5..14382.73......1....85..7..79.2.5.8.1.7..... | autosolve |
| 893216754724385961165947823947162385651438297382579416236854179479621538518793642 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) B5: 5,9 H5: 6,9 A8: 4,6 A9: 5,8 C9: 5,8 F7: 4,9 E9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 1.. / A1 = 1 => 8 pairs (_) / A3 = 1 => 9 pairs (_) D8,F8: 1.. / D8 = 1 => 9 pairs (_) / F8 = 1 => 8 pairs (_) G7,I7: 1.. / G7 = 1 => 7 pairs (_) / I7 = 1 => 0 pairs (X) E1,E4: 1.. / E1 = 1 => 0 pairs (*) / E4 = 1 => 0 pairs (X) H9,I9: 2.. / H9 = 2 => 10 pairs (_) / I9 = 2 => 10 pairs (_) G4,H4: 3.. / G4 = 3 => 8 pairs (_) / H4 = 3 => 15 pairs (_) B7,C7: 3.. / B7 = 3 => 9 pairs (_) / C7 = 3 => 19 pairs (_) G1,I1: 4.. / G1 = 4 => 10 pairs (_) / I1 = 4 => 11 pairs (_) A5,B5: 5.. / A5 = 5 => 10 pairs (_) / B5 = 5 => 8 pairs (_) D6,F6: 5.. / D6 = 5 => 7 pairs (_) / F6 = 5 => 7 pairs (_) A9,C9: 5.. / A9 = 5 => 8 pairs (_) / C9 = 5 => 5 pairs (_) B2,B5: 5.. / B2 = 5 => 10 pairs (_) / B5 = 5 => 8 pairs (_) C3,C9: 5.. / C3 = 5 => 8 pairs (_) / C9 = 5 => 5 pairs (_) H2,I2: 6.. / H2 = 6 => 0 pairs (*) / I2 = 6 => 0 pairs (X) D8,E9: 6.. / D8 = 6 => 14 pairs (_) / E9 = 6 => 9 pairs (_) A5,H5: 6.. / A5 = 6 => 20 pairs (_) / H5 = 6 => 12 pairs (_) E1,F3: 7.. / E1 = 7 => 8 pairs (_) / F3 = 7 => 12 pairs (_) G1,G3: 7.. / G1 = 7 => 12 pairs (_) / G3 = 7 => 8 pairs (_) C4,C6: 7.. / C4 = 7 => 7 pairs (_) / C6 = 7 => 10 pairs (_) E1,G1: 7.. / E1 = 7 => 8 pairs (_) / G1 = 7 => 12 pairs (_) F3,G3: 7.. / F3 = 7 => 12 pairs (_) / G3 = 7 => 8 pairs (_) A9,C9: 8.. / A9 = 8 => 5 pairs (_) / C9 = 8 => 8 pairs (_) H3,H4: 8.. / H3 = 8 => 7 pairs (_) / H4 = 8 => 0 pairs (*) F7,I7: 9.. / F7 = 9 => 0 pairs (X) / I7 = 9 => 11 pairs (_) * DURATION: 0:00:31.027314 START: 05:46:07.750550 END: 05:46:38.777864 2017-05-01 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,B5,C9,E9,F7,H5) * .....6.5.7.4.8.9...6..4............5..14382.73......1....85..7..79.2.5.8.1.7..... * PAIR B5: 5,9 BLK 4 A5: 5,9,6 # reduction candidate for 5,9 A5: 6 # 20 pairs A5: 5,9 # 12 pairs * PAIR H5: 6,9 BLK 6 H4: 6,9,3,4,8 # reduction candidate for 6,9 H4: 6,9 => CTR * .82.7645.734185926.65.4.78.24..1.3.5.514382.73..56.814.23854179479621538.1.793642 H4: 3,4,8 # 7 pairs I6: 6,9,4 # reduction candidate for 6,9 I6: 6,9 # 10 pairs * PAIR H5: 6,9 ROW 5 A5: 6,9,5 # reduction candidate for 6,9 A5: 5 # 10 pairs A5: 6,9 # 8 pairs * PAIR H5: 6,9 COL H H9: 6,9,2,3,4 # reduction candidate for 6,9 H9: 6,9 # 19 pairs H9: 2,3,4 # 8 pairs * PAIR A8: 4,6 BLK 7 A7: 4,6,2 # reduction candidate for 4,6 A7: 4,6 # 18 pairs A7: 2 # 9 pairs * PAIR A8: 4,6 ROW 8 H8: 4,6,3 # reduction candidate for 4,6 H8: 3 # 13 pairs H8: 4,6 # 12 pairs * PAIR A8: 4,6 COL A A4: 4,6,2,8,9 # reduction candidate for 4,6 A4: 4,6 # 15 pairs A4: 2,8,9 # 8 pairs * PAIR A9: 5,8 COL A A3: 5,8,1,2,9 # reduction candidate for 5,8 A3: 5,8 # 11 pairs A3: 1,2,9 # 7 pairs * PAIR C9: 5,8 COL C C3: 5,8,2,3 # reduction candidate for 5,8 C3: 5,8 # 9 pairs C3: 2,3 # 6 pairs * PAIR F7: 4,9 BLK 8 F9: 4,9,3 # reduction candidate for 4,9 F9: 3 # 13 pairs F9: 4,9 # 12 pairs * PAIR F7: 4,9 ROW 7 I7: 4,9,1,6 # reduction candidate for 4,9 I7: 1,6 => CTR * .....67547.4.8.926.6..47183..7691..5..14382673.6.72.19...85967167912.5.8.1.76..92 I7: 4,9 # 11 pairs * PAIR E9: 6,9 ROW 9 H9: 6,9,2,3,4 # reduction candidate for 6,9 H9: 6,9 # 19 pairs I9: 6,9,2,3,4 # reduction candidate for 6,9 I9: 6,9 => CTR * .....6.5.7.4.8.96..6..4..8.........56514382973......1...685..7.479621538.1.793426 I9: 2,3,4 # 7 pairs * PAIR E9: 6,9 COL E E4: 6,9,1,7 # reduction candidate for 6,9 E4: 6,9 => SOLVED * 893216754724385961165947823947162385651438297382579416236854179479621538518793642 E4: 1,7 # 8 pairs E6: 6,9,7 # reduction candidate for 6,9 E6: 6,9 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0123-base-pr-000.dot * REASONING * DIS # H4: 6,9 => CTR => H4: 3,4,8 * DIS # I7: 1,6 => CTR => I7: 4,9 * DIS # I9: 6,9 => CTR => I9: 2,3,4 * PRF # E4: 6,9 => SOL * CNT 4 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,B5,C9,E9,F7,H5) * .....6.5.7.4.8.9...6..4............5..14382.73......1....85..7..79.2.5.8.1.7..... * PAIR B5: 5,9 BLK 4 A5: 5,9,6 # reduction candidate for 5,9 A5: 6 # 20 pairs A5: 5,9 # 12 pairs * PAIR H5: 6,9 BLK 6 H4: 6,9,3,4,8 # reduction candidate for 6,9 H4: 6,9 => CTR * .82.7645.734185926.65.4.78.24..1.3.5.514382.73..56.814.23854179479621538.1.793642 I6: 6,9,4 # reduction candidate for 6,9 I6: 6,9 # 10 pairs * RESTART * PAIR H5: 6,9 BLK 6 I6: 6,9,4 # reduction candidate for 6,9 I6: 4 => CTR * ....7645.7.4.8.926.6..4.78..4..1..356514382973...9..1423685.179479.2.568.1.769342 * PAIR H5: 6,9 ROW 5 A5: 6,9,5 # reduction candidate for 6,9 A5: 5 => CTR * .....6754754.8.9.6.6..47183..7691..55914382673.6.75.19...85967167912.5.881576..92 * PAIR RESTART * PAIR A8: 4,6 BLK 7 A7: 4,6,2 # reduction candidate for 4,6 A7: 4,6 => CTR * .9..167547.4.8.9.6165947.232...9...59514382673...7..19...859671679.2.5.8.1.76..92 * PAIR A8: 4,6 COL A A4: 4,6,8,9 # reduction candidate for 4,6 A4: 4,6 => CTR * .9..167547.4.8.9.6165947.23....9...59514382673...7..192..859671679.2.5.8.1.76..92 A4: 8,9 => SOLVED * 893216754724385961165947823947162385651438297382579416236854179479621538518793642 * DURATION: 0:00:12.256741 START: 05:47:00.238427 END: 05:47:12.495168 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0123-base-pr-001.dot * REASONING * DIS # H4: 6,9 => CTR => H4: 3,4,8 * DIS H4: 3,4,8 # I6: 4 => CTR => I6: 6,9 * DIS H4: 3,4,8 + I6: 6,9 # A5: 5 => CTR => A5: 6,9 * DIS H4: 3,4,8 + I6: 6,9 + A5: 6,9 # A7: 4,6 => CTR => A7: 2 * DIS H4: 3,4,8 + I6: 6,9 + A5: 6,9 + A7: 2 # A4: 4,6 => CTR => A4: 8,9 * PRF H4: 3,4,8 + I6: 6,9 + A5: 6,9 + A7: 2 + A4: 8,9 => SOL * STA H4: 3,4,8 + I6: 6,9 + A5: 6,9 + A7: 2 + A4: 8,9 * CNT 6 HDP CHAINS / 10 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=123
Solution
position: 893216754724385961165947823947162385651438297382579416236854179479621538518793642 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:
* INC # A5: 5,9 => UNS * INC # A5: 6 => UNS * DIS # H4: 6,9 => CTR => H4: 3,4,8 * INC # H4: 3,4,8 => UNS * INC # I6: 6,9 => UNS * INC # A5: 6,9 => UNS * INC # A5: 5 => UNS * INC # H9: 6,9 => UNS * INC # H9: 2,3,4 => UNS * INC # A7: 4,6 => UNS * INC # A7: 2 => UNS * INC # H8: 4,6 => UNS * INC # H8: 3 => UNS * INC # A4: 4,6 => UNS * INC # A4: 2,8,9 => UNS * INC # A3: 5,8 => UNS * INC # A3: 1,2,9 => UNS * INC # C3: 5,8 => UNS * INC # C3: 2,3 => UNS * INC # F9: 4,9 => UNS * INC # F9: 3 => UNS * INC # I7: 4,9 => UNS * DIS # I7: 1,6 => CTR => I7: 4,9 * INC # H9: 6,9 => UNS * DIS # I9: 6,9 => CTR => I9: 2,3,4 * INC # I9: 2,3,4 => UNS * PRF # E4: 6,9 => SOL * INC # E4: 1,7 => UNS * INC # E6: 6,9 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A5: 5,9 => UNS * INC # A5: 6 => UNS * DIS # H4: 6,9 => CTR => H4: 3,4,8 * INC H4: 3,4,8 # I6: 6,9 => UNS * INC H4: 3,4,8 # I6: 6,9 => UNS * DIS H4: 3,4,8 # I6: 4 => CTR => I6: 6,9 * INC H4: 3,4,8 + I6: 6,9 # A5: 6,9 => UNS * DIS H4: 3,4,8 + I6: 6,9 # A5: 5 => CTR => A5: 6,9 * DIS H4: 3,4,8 + I6: 6,9 + A5: 6,9 # A7: 4,6 => CTR => A7: 2 * DIS H4: 3,4,8 + I6: 6,9 + A5: 6,9 + A7: 2 # A4: 4,6 => CTR => A4: 8,9 * PRF H4: 3,4,8 + I6: 6,9 + A5: 6,9 + A7: 2 + A4: 8,9 => SOL * STA H4: 3,4,8 + I6: 6,9 + A5: 6,9 + A7: 2 + A4: 8,9 * CNT 11 HDP CHAINS / 10 HYP OPENED