Analysis of zz-www.sudokuoftheday.co.uk-20060822-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: .95..............8.2.....61....9.3....7..4...9...21...8..269..41....39.2....4.6.. initial
Autosolve
position: .95.1......1....98.289...61..2.9.3....7..4..99...21...8.3269..41....39.22.914.6.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 4,6 => CTR => D1: 8 * PRF # D1: 8 => SOL * PRF # A2: 4,6 => SOL * PRF # F1: 2,6 => SOL * DIS # F1: 8 => CTR => F1: 2,6 * DIS # G3: 5,7 => CTR => G3: 4 * DIS # F4: 5,7 => CTR => F4: 6,8 * DIS # H1: 2,4 => CTR => H1: 3,7 * DIS # I9: 5 => CTR => I9: 3,7 * DIS # A4: 4,6 => CTR => A4: 5 * PRF # A4: 5 => SOL * PRF # B4: 4,6 => SOL * DIS # B6: 4,6 => CTR => B6: 3,8 * PRF # F4: 5,8 => SOL * DIS # D5: 5,8 => CTR => D5: 3,6 * DIS # D6: 5,8 => CTR => D6: 3,6,7 * DIS # E8: 7 => CTR => E8: 5,8 * DIS # H7: 1 => CTR => H7: 5,7 * PRF # B4: 4,6 => SOL * DIS # B6: 4,6 => CTR => B6: 3,8 * DIS # H9: 5,7 => CTR => H9: 3,8 * DIS # I9: 5,7 => CTR => I9: 3 * CNT 22 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 4,6 => CTR => D1: 8 * PRF D1: 8 => SOL * STA D1: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .95..............8.2.....61....9.3....7..4...9...21...8..269..41....39.2....4.6.. | initial |
| .95.1......1....98.289...61..2.9.3....7..4..99...21...8.3269..41....39.22.914.6.. | autosolve |
| 495816237631472598728935461542798316317654829986321745873269154164583972259147683 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) D2: 4,6 F2: 2,6 F3: 5,7 I1: 3,7 C6: 4,6 E5: 5,8 B7: 5,7 B8: 4,6 C8: 4,6 B9: 5,7 G7: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B4,B5: 1.. / B4 = 1 => 0 pairs (X) / B5 = 1 => 0 pairs (_) G7,H7: 1.. / G7 = 1 => 12 pairs (_) / H7 = 1 => 0 pairs (X) B4,H4: 1.. / B4 = 1 => 0 pairs (X) / H4 = 1 => 0 pairs (_) G5,G7: 1.. / G5 = 1 => 0 pairs (X) / G7 = 1 => 12 pairs (_) F1,F2: 2.. / F1 = 2 => 0 pairs (X) / F2 = 2 => 11 pairs (_) G5,H5: 2.. / G5 = 2 => 0 pairs (X) / H5 = 2 => 12 pairs (_) F2,G2: 2.. / F2 = 2 => 11 pairs (_) / G2 = 2 => 0 pairs (X) H1,H5: 2.. / H1 = 2 => 0 pairs (X) / H5 = 2 => 12 pairs (_) E2,E3: 3.. / E2 = 3 => 19 pairs (_) / E3 = 3 => 13 pairs (_) H1,I1: 3.. / H1 = 3 => 18 pairs (_) / I1 = 3 => 0 pairs (X) D5,D6: 3.. / D5 = 3 => 0 pairs (X) / D6 = 3 => 0 pairs (_) H9,I9: 3.. / H9 = 3 => 0 pairs (X) / I9 = 3 => 18 pairs (_) A3,E3: 3.. / A3 = 3 => 19 pairs (_) / E3 = 3 => 13 pairs (_) B6,D6: 3.. / B6 = 3 => 0 pairs (X) / D6 = 3 => 0 pairs (_) H1,H9: 3.. / H1 = 3 => 18 pairs (_) / H9 = 3 => 0 pairs (X) I1,I9: 3.. / I1 = 3 => 0 pairs (X) / I9 = 3 => 18 pairs (_) D1,D2: 4.. / D1 = 4 => 0 pairs (X) / D2 = 4 => 0 pairs (_) B8,C8: 4.. / B8 = 4 => 0 pairs (X) / C8 = 4 => 0 pairs (_) A3,G3: 4.. / A3 = 4 => 0 pairs (X) / G3 = 4 => 16 pairs (_) C6,C8: 4.. / C6 = 4 => 0 pairs (X) / C8 = 4 => 0 pairs (_) G2,G3: 5.. / G2 = 5 => 13 pairs (_) / G3 = 5 => 0 pairs (X) A4,A5: 5.. / A4 = 5 => 0 pairs (*) / A5 = 5 => 0 pairs (X) B7,B9: 5.. / B7 = 5 => 13 pairs (_) / B9 = 5 => 16 pairs (_) E2,G2: 5.. / E2 = 5 => 0 pairs (X) / G2 = 5 => 13 pairs (_) B7,H7: 5.. / B7 = 5 => 13 pairs (_) / H7 = 5 => 16 pairs (_) I4,I6: 6.. / I4 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) B8,C8: 6.. / B8 = 6 => 0 pairs (*) / C8 = 6 => 0 pairs (X) C6,C8: 6.. / C6 = 6 => 0 pairs (*) / C8 = 6 => 0 pairs (X) B7,B9: 7.. / B7 = 7 => 16 pairs (_) / B9 = 7 => 13 pairs (_) D1,F1: 8.. / D1 = 8 => 0 pairs (*) / F1 = 8 => 0 pairs (X) G5,G6: 8.. / G5 = 8 => 0 pairs (*) / G6 = 8 => 0 pairs (X) H8,H9: 8.. / H8 = 8 => 0 pairs (X) / H9 = 8 => 22 pairs (_) F9,H9: 8.. / F9 = 8 => 0 pairs (X) / H9 = 8 => 22 pairs (_) E5,E8: 8.. / E5 = 8 => 0 pairs (X) / E8 = 8 => 0 pairs (_) * DURATION: 0:00:45.561777 START: 01:59:08.008883 END: 01:59:53.570660 2019-05-01 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,B8,B9,C6,C8,D2,E5,F2,F3,G7,I1) * .95.1......1....98.289...61..2.9.3....7..4..99...21...8.3269..41....39.22.914.6.. * PAIR D2: 4,6 BLK 2 D1: 4,6,8 # reduction candidate for 4,6 D1: 4,6 => CTR * .95.18.37..1..2.98.289...61..2.963.5567384.2993..21..68.3269..41.6..39.22.914.683 D1: 8 => SOLVED * 495816237631472598728935461542798316317654829986321745873269154164583972259147683 * PAIR D2: 4,6 ROW 2 A2: 4,6,3,7 # reduction candidate for 4,6 A2: 4,6 => SOLVED * 495816237631472598728935461542798316317654829986321745873269154164583972259147683 A2: 3,7 # 12 pairs B2: 4,6,3 # reduction candidate for 4,6 B2: 4,6 # 17 pairs * PAIR F2: 2,6 BLK 2 F1: 2,6,8 # reduction candidate for 2,6 F1: 2,6 => SOLVED * 495816237631472598728935461542798316317654829986321745873269154164583972259147683 F1: 8 => CTR * .95.18.37..1..2.98.289...61..2.963.5567384.2993..21..68.3269..41.6..39.22.914.683 * PAIR F3: 5,7 BLK 2 E2: 5,7,3 # reduction candidate for 5,7 E2: 5,7 # 13 pairs E3: 5,7,3 # reduction candidate for 5,7 E3: 5,7 # 19 pairs * PAIR F3: 5,7 ROW 3 G3: 5,7,4 # reduction candidate for 5,7 G3: 5,7 => CTR * .95.1..377.1....9842893..61..2.9.3....7.54..99...21...8.3269..41..5839722.9147683 G3: 4 # 16 pairs * PAIR F3: 5,7 COL F F4: 5,7,6,8 # reduction candidate for 5,7 F4: 5,7 => CTR * .9581......14...98.289...61.82.9.31..17.842599..521847853269174146..39.22.914.6.. F4: 6,8 # 22 pairs F9: 5,7,8 # reduction candidate for 5,7 F9: 5,7 # 22 pairs * PAIR I1: 3,7 BLK 3 H1: 3,7,2,4 # reduction candidate for 3,7 H1: 2,4 => CTR * .9581...3..14...98.289...61.82.9.31..17.842599..521847853269174146..39822.914863. H1: 3,7 # 17 pairs * PAIR I1: 3,7 COL I I9: 3,7,5 # reduction candidate for 3,7 I9: 5 => CTR * .9581...3..14...98.289...61.82.9.31..17.842599..521847853269174146..3982279148635 I9: 3,7 # 16 pairs * PAIR C6: 4,6 BLK 4 A4: 4,6,5 # reduction candidate for 4,6 A4: 4,6 => CTR * .95.1......1....98.289...61.82.9.31.517.84..99...218..8.3269..41....39.22.914.6.. A4: 5 => SOLVED * 495816237631472598728935461542798316317654829986321745873269154164583972259147683 B4: 4,6,1,8 # reduction candidate for 4,6 B4: 4,6 => SOLVED * 495816237631472598728935461542798316317654829986321745873269154164583972259147683 B4: 1,8 # 12 pairs B6: 4,6,3,8 # reduction candidate for 4,6 B6: 4,6 => CTR * .9581.....314...98.2893..615.27983.6387654..99..3218..8.3269..41..5839722.9147683 B6: 3,8 # 12 pairs * PAIR E5: 5,8 BLK 5 D4: 5,8,6,7 # reduction candidate for 5,8 D4: 5,8 # 18 pairs F4: 5,8,6,7 # reduction candidate for 5,8 F4: 5,8 => SOLVED * 495816237631472598728935461542798316317654829986321745873269154164583972259147683 F4: 6,7 # 12 pairs D5: 5,8,3,6 # reduction candidate for 5,8 D5: 5,8 => CTR * .95.1......1....98.289...61..2.9.3....7..4..99..321...8.3269..41....39.22.914.6.. D5: 3,6 # 12 pairs D6: 5,8,3,6,7 # reduction candidate for 5,8 D6: 5,8 => CTR * .95.1......1....98.289...61..2.9.3.5567384..9934.21...8.3269..41....39.22.914.6.. D6: 3,6,7 # 13 pairs * PAIR E5: 5,8 COL E E8: 5,8,7 # reduction candidate for 5,8 E8: 7 => CTR * .95.1......1....98.289.7.61.82.9.31..17.842599..5218478532691741.48739.22.914.6.. E8: 5,8 # 16 pairs * PAIR B7: 5,7 ROW 7 H7: 5,7,1 # reduction candidate for 5,7 H7: 1 => CTR * .95.1......1....98.289...61.12.9.3...87.541299...218..8532697141..5.39.227914.6.. H7: 5,7 # 12 pairs * PAIR B8: 4,6 COL B B2: 4,6,3 # reduction candidate for 4,6 B2: 4,6 # 17 pairs B4: 4,6,1,8 # reduction candidate for 4,6 B4: 4,6 => SOLVED * 495816237631472598728935461542798316317654829986321745873269154164583972259147683 B4: 1,8 # 12 pairs B6: 4,6,3,8 # reduction candidate for 4,6 B6: 4,6 => CTR * .9581.....314...98.2893..615.27983.6387654..99..3218..8.3269..41..5839722.9147683 B6: 3,8 # 12 pairs * PAIR B9: 5,7 ROW 9 F9: 5,7,8 # reduction candidate for 5,7 F9: 5,7 # 22 pairs H9: 5,7,3,8 # reduction candidate for 5,7 H9: 5,7 => CTR * .9581..37..14...98.289...61.82.9.31..17.84.299...21...8.3269..41....39822.91486.3 H9: 3,8 # 12 pairs I9: 5,7,3 # reduction candidate for 5,7 I9: 5,7 => CTR * .9581...3..14...98.289...61.82.9.31..17.842599..521847853269174146..39822.914863. I9: 3 # 18 pairs * PAIR G7: 1,7 BLK 9 H7: 1,7,5 # reduction candidate for 1,7 H7: 5 # 16 pairs H7: 1,7 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060822-absurd-base-pr-000.dot * REASONING * DIS # D1: 4,6 => CTR => D1: 8 * PRF # D1: 8 => SOL * PRF # A2: 4,6 => SOL * PRF # F1: 2,6 => SOL * DIS # F1: 8 => CTR => F1: 2,6 * DIS # G3: 5,7 => CTR => G3: 4 * DIS # F4: 5,7 => CTR => F4: 6,8 * DIS # H1: 2,4 => CTR => H1: 3,7 * DIS # I9: 5 => CTR => I9: 3,7 * DIS # A4: 4,6 => CTR => A4: 5 * PRF # A4: 5 => SOL * PRF # B4: 4,6 => SOL * DIS # B6: 4,6 => CTR => B6: 3,8 * PRF # F4: 5,8 => SOL * DIS # D5: 5,8 => CTR => D5: 3,6 * DIS # D6: 5,8 => CTR => D6: 3,6,7 * DIS # E8: 7 => CTR => E8: 5,8 * DIS # H7: 1 => CTR => H7: 5,7 * PRF # B4: 4,6 => SOL * DIS # B6: 4,6 => CTR => B6: 3,8 * DIS # H9: 5,7 => CTR => H9: 3,8 * DIS # I9: 5,7 => CTR => I9: 3 * CNT 22 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,B8,B9,C6,C8,D2,E5,F2,F3,G7,I1) * .95.1......1....98.289...61..2.9.3....7..4..99...21...8.3269..41....39.22.914.6.. * PAIR D2: 4,6 BLK 2 D1: 4,6,8 # reduction candidate for 4,6 D1: 4,6 => CTR * .95.18.37..1..2.98.289...61..2.963.5567384.2993..21..68.3269..41.6..39.22.914.683 D1: 8 => SOLVED * 495816237631472598728935461542798316317654829986321745873269154164583972259147683 * DURATION: 0:00:02.550023 START: 02:00:28.280544 END: 02:00:30.830567 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060822-absurd-base-pr-001.dot * REASONING * DIS # D1: 4,6 => CTR => D1: 8 * PRF D1: 8 => SOL * STA D1: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060822, absurd
Solution
position: 495816237631472598728935461542798316317654829986321745873269154164583972259147683 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 # D1: 4,6 => CTR => D1: 8 * PRF # D1: 8 => SOL * PRF # A2: 4,6 => SOL * INC # A2: 3,7 => UNS * INC # B2: 4,6 => UNS * PRF # F1: 2,6 => SOL * DIS # F1: 8 => CTR => F1: 2,6 * INC # E2: 5,7 => UNS * INC # E3: 5,7 => UNS * DIS # G3: 5,7 => CTR => G3: 4 * INC # G3: 4 => UNS * DIS # F4: 5,7 => CTR => F4: 6,8 * INC # F4: 6,8 => UNS * INC # F9: 5,7 => UNS * INC # H1: 3,7 => UNS * DIS # H1: 2,4 => CTR => H1: 3,7 * INC # I9: 3,7 => UNS * DIS # I9: 5 => CTR => I9: 3,7 * DIS # A4: 4,6 => CTR => A4: 5 * PRF # A4: 5 => SOL * PRF # B4: 4,6 => SOL * INC # B4: 1,8 => UNS * DIS # B6: 4,6 => CTR => B6: 3,8 * INC # B6: 3,8 => UNS * INC # D4: 5,8 => UNS * PRF # F4: 5,8 => SOL * INC # F4: 6,7 => UNS * DIS # D5: 5,8 => CTR => D5: 3,6 * INC # D5: 3,6 => UNS * DIS # D6: 5,8 => CTR => D6: 3,6,7 * INC # D6: 3,6,7 => UNS * INC # E8: 5,8 => UNS * DIS # E8: 7 => CTR => E8: 5,8 * INC # H7: 5,7 => UNS * DIS # H7: 1 => CTR => H7: 5,7 * INC # B2: 4,6 => UNS * PRF # B4: 4,6 => SOL * INC # B4: 1,8 => UNS * DIS # B6: 4,6 => CTR => B6: 3,8 * INC # B6: 3,8 => UNS * INC # F9: 5,7 => UNS * DIS # H9: 5,7 => CTR => H9: 3,8 * INC # H9: 3,8 => UNS * DIS # I9: 5,7 => CTR => I9: 3 * INC # I9: 3 => UNS * INC # H7: 1,7 => UNS * INC # H7: 5 => UNS * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D1: 4,6 => CTR => D1: 8 * PRF D1: 8 => SOL * STA D1: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED