Analysis of zz-www.sudokuwiki.org-0111-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=111
level: medium
position: .2.....9...1.8...47.....6....3..6..8...2.1...6..5..3....9.....23...5.4.6.5.....8. initial
Autosolve
position: .2....89...1.8...47.....6....3..6..8...231.6.6..5.83....9.....23...5.4.6.5.....8. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A5: 4,5 => CTR => A5: 8,9 * DIS # A5: 5,9 => CTR => A5: 4,8 * DIS # H6: 2,7 => CTR => H6: 1,4 * PRF # C9: 2,7 => SOL * DIS # H7: 1,7 => CTR => H7: 3,5 * DIS # I9: 1,7 => CTR => I9: 3,9 * DIS # D8: 1,7 => CTR => D8: 8,9 * DIS # H4: 1,7 => CTR => H4: 2,4,5 * DIS # H6: 1,7 => CTR => H6: 2,4 * CNT 9 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 # A5: 4,5 => CTR => A5: 8,9 * DIS A5: 8,9 # H6: 2,7 => CTR => H6: 1,4 * DIS A5: 8,9 + H6: 1,4 # H7: 1,7 => CTR => H7: 3,5 * DIS A5: 8,9 + H6: 1,4 + H7: 3,5 # I9: 1,7 => CTR => I9: 3,9 * DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 # B8: 8 => CTR => B8: 1,7 * DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 # H4: 1,7 => CTR => H4: 2,4,5 * DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 # G7: 1,7 => CTR => G7: 5 * DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 # F1: 5,7 => CTR => F1: 3,4 * PRF A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 + F1: 3,4 # I3: 1,5 => SOL * STA A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 + F1: 3,4 + I3: 1,5 * CNT 9 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2.....9...1.8...47.....6....3..6..8...2.1...6..5..3....9.....23...5.4.6.5.....8. | initial |
| .2....89...1.8...47.....6....3..6..8...231.6.6..5.83....9.....23...5.4.6.5.....8. | autosolve |
| 526174893931685724784329615193746258845231967672598341469817532318952476257463189 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) A1: 4,5 A2: 5,9 C6: 2,7 H8: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A4,C6: 2.. / A4 = 2 => 0 pairs (X) / C6 = 2 => 6 pairs (_) C6,H6: 2.. / C6 = 2 => 6 pairs (_) / H6 = 2 => 0 pairs (X) C8,F8: 2.. / C8 = 2 => 0 pairs (X) / F8 = 2 => 7 pairs (_) A4,A9: 2.. / A4 = 2 => 0 pairs (X) / A9 = 2 => 6 pairs (_) E3,E9: 2.. / E3 = 2 => 5 pairs (_) / E9 = 2 => 0 pairs (X) G2,G4: 2.. / G2 = 2 => 6 pairs (_) / G4 = 2 => 0 pairs (*) B2,B3: 3.. / B2 = 3 => 5 pairs (_) / B3 = 3 => 9 pairs (_) H7,I9: 3.. / H7 = 3 => 7 pairs (_) / I9 = 3 => 6 pairs (_) H4,H6: 4.. / H4 = 4 => 0 pairs (X) / H6 = 4 => 7 pairs (_) E6,H6: 4.. / E6 = 4 => 0 pairs (X) / H6 = 4 => 7 pairs (_) G7,H7: 5.. / G7 = 5 => 6 pairs (_) / H7 = 5 => 7 pairs (_) C1,B2: 6.. / C1 = 6 => 6 pairs (_) / B2 = 6 => 14 pairs (_) B7,C9: 6.. / B7 = 6 => 6 pairs (_) / C9 = 6 => 14 pairs (_) B2,D2: 6.. / B2 = 6 => 14 pairs (_) / D2 = 6 => 6 pairs (_) B2,B7: 6.. / B2 = 6 => 14 pairs (_) / B7 = 6 => 6 pairs (_) C1,C9: 6.. / C1 = 6 => 6 pairs (_) / C9 = 6 => 14 pairs (_) B3,C3: 8.. / B3 = 8 => 12 pairs (_) / C3 = 8 => 7 pairs (_) D7,D8: 8.. / D7 = 8 => 5 pairs (_) / D8 = 8 => 0 pairs (X) A5,A7: 8.. / A5 = 8 => 5 pairs (_) / A7 = 8 => 0 pairs (X) D8,F8: 9.. / D8 = 9 => 7 pairs (_) / F8 = 9 => 0 pairs (X) G9,I9: 9.. / G9 = 9 => 5 pairs (_) / I9 = 9 => 10 pairs (_) * DURATION: 0:00:29.316827 START: 05:29:59.836891 END: 05:30:29.153718 2017-05-01 * CP COUNT: (21) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,C6,H8) * .2....89...1.8...47.....6....3..6..8...231.6.6..5.83....9.....23...5.4.6.5.....8. * PAIR A1: 4,5 BLK 1 C1: 4,5,6 # reduction candidate for 4,5 C1: 4,5 # 14 pairs C3: 4,5,8 # reduction candidate for 4,5 C3: 4,5 # 12 pairs * PAIR A1: 4,5 ROW 1 F1: 4,5,3,7 # reduction candidate for 4,5 F1: 4,5 # 8 pairs F1: 3,7 # 5 pairs * PAIR A1: 4,5 COL A A5: 4,5,8,9 # reduction candidate for 4,5 A5: 4,5 => CTR * .2....89.9.1.8.2.47.....6..2.3..6.48...231.6.6.754832.8.9.....237285941615.....8. A5: 8,9 # 5 pairs * PAIR A2: 5,9 ROW 2 F2: 5,9,2,3,7 # reduction candidate for 5,9 F2: 5,9 # 7 pairs F2: 2,3,7 # 4 pairs * PAIR A2: 5,9 COL A A4: 5,9,1,2 # reduction candidate for 5,9 A4: 5,9 # 21 pairs A5: 5,9,4,8 # reduction candidate for 5,9 A5: 5,9 => CTR * 42....89...1.8.2.47.....6..2.3..6.48...231.6.6.754832.8.9.....237285941615.....8. A5: 4,8 # 5 pairs * PAIR C6: 2,7 ROW 6 H6: 2,7,1,4 # reduction candidate for 2,7 H6: 2,7 => CTR * 524613897961785234738...61521397654884523176969754832147986.152382159476156...983 H6: 1,4 # 7 pairs * PAIR C6: 2,7 COL C C8: 2,7,8 # reduction candidate for 2,7 C8: 2,7 # 6 pairs C9: 2,7,4,6 # reduction candidate for 2,7 C9: 2,7 => SOLVED * 526174893931685724784329615193746258845231967672598341469817532318952476257463189 C9: 4,6 # 5 pairs * PAIR H8: 1,7 BLK 9 G7: 1,7,5 # reduction candidate for 1,7 G7: 1,7 # 7 pairs H7: 1,7,3,5 # reduction candidate for 1,7 H7: 1,7 => CTR * 42....8979.1.8.2.47...296.1573.96128894231765612578349149863572387952416256.47983 H7: 3,5 # 5 pairs G9: 1,7,9 # reduction candidate for 1,7 G9: 1,7 # 10 pairs I9: 1,7,3,9 # reduction candidate for 1,7 I9: 1,7 => CTR * 42....89.9.1.8.2.47...296..573.96128894231765612578349149867532387952416256.43987 I9: 3,9 # 5 pairs * PAIR H8: 1,7 ROW 8 B8: 1,7,8 # reduction candidate for 1,7 B8: 1,7 # 10 pairs D8: 1,7,8,9 # reduction candidate for 1,7 D8: 1,7 => CTR * 524613897961785234738...61521397654884523176969754832147986.152382159476156...983 D8: 8,9 # 5 pairs * PAIR H8: 1,7 COL H H4: 1,7,2,4,5 # reduction candidate for 1,7 H4: 1,7 => CTR * .2....89...1.8..247...2.6..5.3..62.8...231.6.6.25.834.1.9.....23..95241625.....8. H4: 2,4,5 # 4 pairs H6: 1,7,2,4 # reduction candidate for 1,7 H6: 1,7 => CTR * .2....89...1.8..247...2.6..513796248...231.6.6.25483..1.98....23..95241625.....8. H6: 2,4 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0111-base-pr-000.dot * REASONING * DIS # A5: 4,5 => CTR => A5: 8,9 * DIS # A5: 5,9 => CTR => A5: 4,8 * DIS # H6: 2,7 => CTR => H6: 1,4 * PRF # C9: 2,7 => SOL * DIS # H7: 1,7 => CTR => H7: 3,5 * DIS # I9: 1,7 => CTR => I9: 3,9 * DIS # D8: 1,7 => CTR => D8: 8,9 * DIS # H4: 1,7 => CTR => H4: 2,4,5 * DIS # H6: 1,7 => CTR => H6: 2,4 * CNT 9 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,C6,H8) * .2....89...1.8...47.....6....3..6..8...231.6.6..5.83....9.....23...5.4.6.5.....8. * PAIR A1: 4,5 BLK 1 C1: 4,5,6 # reduction candidate for 4,5 C1: 4,5 # 14 pairs C3: 4,5,8 # reduction candidate for 4,5 C3: 4,5 # 12 pairs * PAIR A1: 4,5 ROW 1 F1: 4,5,3,7 # reduction candidate for 4,5 F1: 4,5 # 8 pairs F1: 3,7 # 5 pairs * PAIR A1: 4,5 COL A A5: 4,5,8,9 # reduction candidate for 4,5 A5: 4,5 => CTR * .2....89.9.1.8.2.47.....6..2.3..6.48...231.6.6.754832.8.9.....237285941615.....8. * PAIR RESTART * PAIR A1: 4,5 BLK 1 C1: 4,5,6 # reduction candidate for 4,5 C1: 4,5 # 15 pairs C3: 4,5,8 # reduction candidate for 4,5 C3: 4,5 # 10 pairs * PAIR A1: 4,5 ROW 1 F1: 4,5,3,7 # reduction candidate for 4,5 F1: 4,5 # 9 pairs F1: 3,7 # 6 pairs * PAIR A2: 5,9 ROW 2 F2: 5,9,2,3,7 # reduction candidate for 5,9 F2: 5,9 # 8 pairs F2: 2,3,7 # 5 pairs * PAIR A2: 5,9 COL A A4: 5,9,1,2 # reduction candidate for 5,9 A4: 1,2 # 25 pairs A4: 5,9 # 21 pairs * PAIR C6: 2,7 ROW 6 H6: 2,7,1,4 # reduction candidate for 2,7 H6: 2,7 => CTR * 524613897961785234738...61521397654884523176969754832147986.152382159476156...983 * PAIR RESTART * PAIR H8: 1,7 BLK 9 G7: 1,7,5 # reduction candidate for 1,7 G7: 1,7 # 14 pairs H7: 1,7,3,5 # reduction candidate for 1,7 H7: 1,7 => CTR * 42.3..897..1.8.2.47...2.6.15734.61288..2317656125783491.98.35723..95241625....983 G9: 1,7,9 # reduction candidate for 1,7 G9: 1,7 # 14 pairs I9: 1,7,3,9 # reduction candidate for 1,7 I9: 1,7 => CTR * 42....89...1.8.2747...2.65.5734961288942317656125783491498675323..95241625....987 * PAIR H8: 1,7 ROW 8 B8: 1,7,8 # reduction candidate for 1,7 B8: 8 => CTR * 4256..89.961385274738.296515.3..61288.4231.656125.834714986.5323879524162561...8. * PAIR H8: 1,7 COL H H4: 1,7,2,4,5 # reduction candidate for 1,7 H4: 1,7 => CTR * .26...89.93168..2478..296..5.3..62.8847231.6.6.25.834.1698....237895241625416..8. * PAIR RESTART * PAIR H8: 1,7 BLK 9 G7: 1,7,5 # reduction candidate for 1,7 G7: 1,7 => CTR * .2631.89.93168...478.429631..37.6..884.231.696.25.83.7.698731523.89524.625.16.983 * RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,A4,A7,B8,C3,C5,C9,D4,F2,F7,F9,G2,G9,H3,H6,H8,I5,I6) * .26...89.93168...478..296....3..6..884.23196.6.25.83...698..5323.89524.625..6..89 * PAIR A1: 4,5 ROW 1 F1: 4,5,3,7 # reduction candidate for 4,5 F1: 3,7 # 22 pairs F1: 4,5 # 20 pairs * PAIR F2: 5,7 BLK 2 F1: 5,7,3,4 # reduction candidate for 5,7 F1: 5,7 => CTR * 426.1.89.93168.27478542961...3..6..884.23196.6.25.83...698.45323.89524.6254163789 * PAIR H3: 1,5 BLK 3 I1: 1,5,3 # reduction candidate for 1,5 I1: 1,5 # 22 pairs I3: 1,5,3 # reduction candidate for 1,5 I3: 1,5 => SOLVED * 526174893931685724784329615193746258845231967672598341469817532318952476257463189 * DURATION: 0:00:28.661996 START: 05:30:50.299137 END: 05:31:18.961133 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0111-base-pr-001.dot * REASONING * DIS # A5: 4,5 => CTR => A5: 8,9 * DIS A5: 8,9 # H6: 2,7 => CTR => H6: 1,4 * DIS A5: 8,9 + H6: 1,4 # H7: 1,7 => CTR => H7: 3,5 * DIS A5: 8,9 + H6: 1,4 + H7: 3,5 # I9: 1,7 => CTR => I9: 3,9 * DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 # B8: 8 => CTR => B8: 1,7 * DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 # H4: 1,7 => CTR => H4: 2,4,5 * DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 # G7: 1,7 => CTR => G7: 5 * DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 # F1: 5,7 => CTR => F1: 3,4 * PRF A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 + F1: 3,4 # I3: 1,5 => SOL * STA A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 + F1: 3,4 + I3: 1,5 * CNT 9 HDP CHAINS / 27 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=111
Solution
position: 526174893931685724784329615193746258845231967672598341469817532318952476257463189 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 # C1: 4,5 => UNS * INC # C3: 4,5 => UNS * INC # F1: 4,5 => UNS * INC # F1: 3,7 => UNS * DIS # A5: 4,5 => CTR => A5: 8,9 * INC # A5: 8,9 => UNS * INC # F2: 5,9 => UNS * INC # F2: 2,3,7 => UNS * INC # A4: 5,9 => UNS * DIS # A5: 5,9 => CTR => A5: 4,8 * INC # A5: 4,8 => UNS * DIS # H6: 2,7 => CTR => H6: 1,4 * INC # H6: 1,4 => UNS * INC # C8: 2,7 => UNS * PRF # C9: 2,7 => SOL * INC # C9: 4,6 => UNS * INC # G7: 1,7 => UNS * DIS # H7: 1,7 => CTR => H7: 3,5 * INC # H7: 3,5 => UNS * INC # G9: 1,7 => UNS * DIS # I9: 1,7 => CTR => I9: 3,9 * INC # I9: 3,9 => UNS * INC # B8: 1,7 => UNS * DIS # D8: 1,7 => CTR => D8: 8,9 * INC # D8: 8,9 => UNS * DIS # H4: 1,7 => CTR => H4: 2,4,5 * INC # H4: 2,4,5 => UNS * DIS # H6: 1,7 => CTR => H6: 2,4 * INC # H6: 2,4 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 4,5 => UNS * INC # C3: 4,5 => UNS * INC # F1: 4,5 => UNS * INC # F1: 3,7 => UNS * DIS # A5: 4,5 => CTR => A5: 8,9 * INC A5: 8,9 # C1: 4,5 => UNS * INC A5: 8,9 # C3: 4,5 => UNS * INC A5: 8,9 # F1: 4,5 => UNS * INC A5: 8,9 # F1: 3,7 => UNS * INC A5: 8,9 # F2: 5,9 => UNS * INC A5: 8,9 # F2: 2,3,7 => UNS * INC A5: 8,9 # A4: 5,9 => UNS * INC A5: 8,9 # A4: 1,2 => UNS * DIS A5: 8,9 # H6: 2,7 => CTR => H6: 1,4 * INC A5: 8,9 + H6: 1,4 # G7: 1,7 => UNS * DIS A5: 8,9 + H6: 1,4 # H7: 1,7 => CTR => H7: 3,5 * INC A5: 8,9 + H6: 1,4 + H7: 3,5 # G9: 1,7 => UNS * DIS A5: 8,9 + H6: 1,4 + H7: 3,5 # I9: 1,7 => CTR => I9: 3,9 * INC A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 # B8: 1,7 => UNS * DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 # B8: 8 => CTR => B8: 1,7 * DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 # H4: 1,7 => CTR => H4: 2,4,5 * DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 # G7: 1,7 => CTR => G7: 5 * INC A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 # F1: 4,5 => UNS * INC A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 # F1: 3,7 => UNS * DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 # F1: 5,7 => CTR => F1: 3,4 * INC A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 + F1: 3,4 # I1: 1,5 => UNS * PRF A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 + F1: 3,4 # I3: 1,5 => SOL * STA A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 + F1: 3,4 + I3: 1,5 * CNT 27 HDP CHAINS / 27 HYP OPENED