Analysis of zz-www.sudokuoftheday.co.uk-20060815-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: .8.6.49.5....1.......9.274..4.3...98...4....1..2.9....87.....54..4...8..9..8..17. initial
Autosolve
position: 2876349154.9.1..8....98274..4.3...98.984....1..2.984.787..69.54..4...8.99..84.17. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I2: 3,6 => CTR => I2: 2 * DIS # B9: 3,6 => CTR => B9: 2,5 * DIS # D8: 5,7 => CTR => D8: 1,2 * DIS # F4: 5,7 => CTR => F4: 1,6 * DIS # F5: 5,7 => CTR => F5: 6 * DIS # I2: 3,6 => CTR => I2: 2 * DIS # I9: 2 => CTR => I9: 3,6 * DIS # F4: 6,7 => CTR => F4: 1,5 * DIS # D8: 1,5 => CTR => D8: 2,7 * DIS # H5: 3,6 => CTR => H5: 2 * DIS # H8: 2 => CTR => H8: 3,6 * DIS # D8: 5,7 => CTR => D8: 1,2 * DIS # D8: 5,7 => CTR => D8: 1,2 * DIS # E4: 5,7 => CTR => E4: 2 * DIS # F8: 3,5 => CTR => F8: 1,7 * DIS # B9: 3,5 => CTR => B9: 2,6 * CNT 16 HDP CHAINS / 59 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I2: 3,6 => CTR => I2: 2 * DIS I2: 2 # D8: 5,7 => CTR => D8: 1,2 * PRF I2: 2 + D8: 1,2 => SOL * STA I2: 2 + D8: 1,2 * CNT 3 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8.6.49.5....1.......9.274..4.3...98...4....1..2.9....87.....54..4...8..9..8..17. | initial |
| 2876349154.9.1..8....98274..4.3...98.984....1..2.984.787..69.54..4...8.99..84.17. | autosolve |
| 287634915439715682651982743746321598598476321312598467873169254164257839925843176 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) B2: 3,6 D2: 5,7 F2: 5,7 I3: 3,6 D6: 1,5 H6: 3,6 C7: 1,3 D7: 1,2 E8: 5,7 F9: 3,5 G7: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F4,D6: 1.. / F4 = 1 => 15 pairs (_) / D6 = 1 => 0 pairs (X) C7,D7: 1.. / C7 = 1 => 12 pairs (_) / D7 = 1 => 0 pairs (*) F4,F8: 1.. / F4 = 1 => 15 pairs (_) / F8 = 1 => 0 pairs (X) G2,I2: 2.. / G2 = 2 => 0 pairs (X) / I2 = 2 => 13 pairs (_) E4,E5: 2.. / E4 = 2 => 13 pairs (_) / E5 = 2 => 0 pairs (X) B8,B9: 2.. / B8 = 2 => 0 pairs (X) / B9 = 2 => 13 pairs (_) D7,D8: 2.. / D7 = 2 => 12 pairs (_) / D8 = 2 => 0 pairs (*) E4,G4: 2.. / E4 = 2 => 13 pairs (_) / G4 = 2 => 0 pairs (X) D7,G7: 2.. / D7 = 2 => 12 pairs (_) / G7 = 2 => 0 pairs (*) B9,I9: 2.. / B9 = 2 => 13 pairs (_) / I9 = 2 => 0 pairs (X) H5,H8: 2.. / H5 = 2 => 14 pairs (_) / H8 = 2 => 0 pairs (X) I2,I9: 2.. / I2 = 2 => 13 pairs (_) / I9 = 2 => 0 pairs (X) F8,F9: 3.. / F8 = 3 => 0 pairs (X) / F9 = 3 => 13 pairs (_) C7,G7: 3.. / C7 = 3 => 0 pairs (*) / G7 = 3 => 0 pairs (X) D2,F2: 5.. / D2 = 5 => 0 pairs (X) / F2 = 5 => 13 pairs (_) G4,G5: 5.. / G4 = 5 => 13 pairs (_) / G5 = 5 => 15 pairs (_) F4,F5: 6.. / F4 = 6 => 0 pairs (X) / F5 = 6 => 12 pairs (_) H8,I9: 6.. / H8 = 6 => 17 pairs (_) / I9 = 6 => 12 pairs (_) D2,F2: 7.. / D2 = 7 => 13 pairs (_) / F2 = 7 => 0 pairs (X) A4,A5: 7.. / A4 = 7 => 12 pairs (_) / A5 = 7 => 14 pairs (_) D2,D8: 7.. / D2 = 7 => 13 pairs (_) / D8 = 7 => 0 pairs (X) * DURATION: 0:00:24.294173 START: 01:48:24.254686 END: 01:48:48.548859 2019-05-01 * CP COUNT: (21) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,C7,D2,D6,D7,E8,F2,F9,G7,H6,I3) * 2876349154.9.1..8....98274..4.3...98.984....1..2.984.787..69.54..4...8.99..84.17. * PAIR B2: 3,6 BLK 1 A3: 3,6,1,5 # reduction candidate for 3,6 A3: 3,6 # 14 pairs B3: 3,6,1,5 # reduction candidate for 3,6 B3: 3,6 # 17 pairs C3: 3,6,1,5 # reduction candidate for 3,6 C3: 3,6 # 14 pairs * PAIR B2: 3,6 ROW 2 G2: 3,6,2 # reduction candidate for 3,6 G2: 3,6 # 13 pairs I2: 3,6,2 # reduction candidate for 3,6 I2: 3,6 => CTR * 2876349154.9.1.28....98274..4.32..983984...21..2.98437871269354524.738699..845172 I2: 2 # 13 pairs * PAIR B2: 3,6 COL B B6: 3,6,1,5 # reduction candidate for 3,6 B6: 3,6 # 15 pairs B8: 3,6,1,2,5 # reduction candidate for 3,6 B8: 3,6 # 17 pairs B9: 3,6,2,5 # reduction candidate for 3,6 B9: 3,6 => CTR * 2876349154.9.1.28....98274..4.32..983984...21..2.98437871269354524.738699..845172 B9: 2,5 # 12 pairs * PAIR D2: 5,7 COL D D8: 5,7,1,2 # reduction candidate for 5,7 D8: 5,7 => CTR * 287634915469.1.283.1398274614.327.9879845...1..21984.7871269354..4..18699..843172 D8: 1,2 # 15 pairs * PAIR F2: 5,7 COL F F4: 5,7,1,6 # reduction candidate for 5,7 F4: 5,7 => CTR * 2876349154.9.1..8..1398274614.3..6987984.65.1..21984.7871269354..4..18.99..84317. F4: 1,6 # 12 pairs F5: 5,7,6 # reduction candidate for 5,7 F5: 5,7 => CTR * 2876349154.9.1..8..13982746145376298.984....1..21984.7871269354..4..18.99..84317. F5: 6 # 12 pairs F8: 5,7,1,3 # reduction candidate for 5,7 F8: 5,7 # 15 pairs * PAIR I3: 3,6 BLK 3 G2: 3,6,2 # reduction candidate for 3,6 G2: 3,6 # 13 pairs I2: 3,6,2 # reduction candidate for 3,6 I2: 3,6 => CTR * 2876349154.9.1.28....98274..4.32..983984...21..2.98437871269354524.738699..845172 I2: 2 # 13 pairs * PAIR I3: 3,6 ROW 3 A3: 3,6,1,5 # reduction candidate for 3,6 A3: 3,6 # 14 pairs B3: 3,6,1,5 # reduction candidate for 3,6 B3: 3,6 # 17 pairs C3: 3,6,1,5 # reduction candidate for 3,6 C3: 3,6 # 14 pairs * PAIR I3: 3,6 COL I I9: 3,6,2 # reduction candidate for 3,6 I9: 2 => CTR * 2876349154.9.1.28....98274..4.32..983984...21..2.98437871269354524.738699..845172 I9: 3,6 # 13 pairs * PAIR D6: 1,5 BLK 5 F4: 1,5,6,7 # reduction candidate for 1,5 F4: 6,7 => CTR * 2876349154.9.1..8..1398274614.3...987984...31..2198467871269354..4..18.99..84317. F4: 1,5 # 17 pairs * PAIR D6: 1,5 ROW 6 A6: 1,5,3,6 # reduction candidate for 1,5 A6: 1,5 # 15 pairs B6: 1,5,3,6 # reduction candidate for 1,5 B6: 1,5 # 13 pairs * PAIR D6: 1,5 COL D D8: 1,5,2,7 # reduction candidate for 1,5 D8: 1,5 => CTR * 287634915469715283..3982746.4.32..98.984...216.2.98437871269354..4...8699..843172 D8: 2,7 # 12 pairs * PAIR H6: 3,6 BLK 6 G5: 3,6,2,5 # reduction candidate for 3,6 G5: 3,6 # 15 pairs H5: 3,6,2 # reduction candidate for 3,6 H5: 3,6 => CTR * 287634915439517682...982743.4.3...98.984.6.313521984.787.269354..4...829923845176 H5: 2 # 14 pairs * PAIR H6: 3,6 ROW 6 A6: 3,6,1,5 # reduction candidate for 3,6 A6: 3,6 # 13 pairs B6: 3,6,1,5 # reduction candidate for 3,6 B6: 3,6 # 15 pairs * PAIR H6: 3,6 COL H H8: 3,6,2 # reduction candidate for 3,6 H8: 2 => CTR * 287634915439517682...982743.4.3...98.984.6.313521984.787.269354..4...829923845176 H8: 3,6 # 14 pairs * PAIR C7: 1,3 BLK 7 A8: 1,3,5,6 # reduction candidate for 1,3 A8: 1,3 # 13 pairs B8: 1,3,2,5,6 # reduction candidate for 1,3 B8: 1,3 # 16 pairs * PAIR C7: 1,3 COL C C3: 1,3,5,6 # reduction candidate for 1,3 C3: 1,3 # 14 pairs C3: 5,6 # 12 pairs * PAIR D7: 1,2 BLK 8 D8: 1,2,5,7 # reduction candidate for 1,2 D8: 5,7 => CTR * 287634915469.1.283.1398274614.327.9879845...1..21984.7871269354..4..18699..843172 D8: 1,2 # 15 pairs * PAIR E8: 5,7 BLK 8 D8: 5,7,1,2 # reduction candidate for 5,7 D8: 5,7 => CTR * 287634915469.1.283.1398274614.327.9879845...1..21984.7871269354..4..18699..843172 D8: 1,2 # 15 pairs F8: 5,7,1,3 # reduction candidate for 5,7 F8: 5,7 # 15 pairs * PAIR E8: 5,7 COL E E4: 5,7,2 # reduction candidate for 5,7 E4: 5,7 => CTR * 287634915439517682...982743.4.3..298.9842.5.1..2.984.7871269354..4...829923845176 E4: 2 # 13 pairs E5: 5,7,2 # reduction candidate for 5,7 E5: 5,7 # 13 pairs * PAIR F9: 3,5 BLK 8 F8: 3,5,1,7 # reduction candidate for 3,5 F8: 3,5 => CTR * 2876349154.9.1..8....98274..4.3.1.98.984.6..1..25984.787..69.54..4.538.99..84.17. F8: 1,7 # 14 pairs * PAIR F9: 3,5 ROW 9 B9: 3,5,2,6 # reduction candidate for 3,5 B9: 3,5 => CTR * 2876349154.9.1.28...3982746.4532.6983984.652161259843787126935452417.8699.684.172 B9: 2,6 # 12 pairs C9: 3,5,6 # reduction candidate for 3,5 C9: 3,5 # 15 pairs * PAIR G7: 2,3 BLK 9 H8: 2,3,6 # reduction candidate for 2,3 H8: 2,3 # 12 pairs I9: 2,3,6 # reduction candidate for 2,3 I9: 2,3 # 17 pairs * PAIR G7: 2,3 COL G G2: 2,3,6 # reduction candidate for 2,3 G2: 2,3 # 17 pairs G5: 2,3,5,6 # reduction candidate for 2,3 G5: 2,3 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060815-absurd-base-pr-000.dot * REASONING * DIS # I2: 3,6 => CTR => I2: 2 * DIS # B9: 3,6 => CTR => B9: 2,5 * DIS # D8: 5,7 => CTR => D8: 1,2 * DIS # F4: 5,7 => CTR => F4: 1,6 * DIS # F5: 5,7 => CTR => F5: 6 * DIS # I2: 3,6 => CTR => I2: 2 * DIS # I9: 2 => CTR => I9: 3,6 * DIS # F4: 6,7 => CTR => F4: 1,5 * DIS # D8: 1,5 => CTR => D8: 2,7 * DIS # H5: 3,6 => CTR => H5: 2 * DIS # H8: 2 => CTR => H8: 3,6 * DIS # D8: 5,7 => CTR => D8: 1,2 * DIS # D8: 5,7 => CTR => D8: 1,2 * DIS # E4: 5,7 => CTR => E4: 2 * DIS # F8: 3,5 => CTR => F8: 1,7 * DIS # B9: 3,5 => CTR => B9: 2,6 * CNT 16 HDP CHAINS / 59 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,C7,D2,D6,D7,E8,F2,F9,G7,H6,I3) * 2876349154.9.1..8....98274..4.3...98.984....1..2.984.787..69.54..4...8.99..84.17. * PAIR B2: 3,6 BLK 1 A3: 3,6,1,5 # reduction candidate for 3,6 A3: 3,6 # 14 pairs B3: 3,6,1,5 # reduction candidate for 3,6 B3: 3,6 # 17 pairs C3: 3,6,1,5 # reduction candidate for 3,6 C3: 3,6 # 14 pairs * PAIR B2: 3,6 ROW 2 G2: 3,6,2 # reduction candidate for 3,6 G2: 3,6 # 13 pairs I2: 3,6,2 # reduction candidate for 3,6 I2: 3,6 => CTR * 2876349154.9.1.28....98274..4.32..983984...21..2.98437871269354524.738699..845172 * RESTART * PAIR B2: 3,6 COL B B6: 3,6,1,5 # reduction candidate for 3,6 B6: 3,6 # 17 pairs B8: 3,6,1,5 # reduction candidate for 3,6 B8: 3,6 # 17 pairs * PAIR RESTART * PAIR B2: 3,6 BLK 1 A3: 3,6,1,5 # reduction candidate for 3,6 A3: 3,6 # 16 pairs B3: 3,6,1,5 # reduction candidate for 3,6 B3: 3,6 # 19 pairs C3: 3,6,1,5 # reduction candidate for 3,6 C3: 3,6 # 16 pairs * PAIR B2: 3,6 COL B B6: 3,6,1,5 # reduction candidate for 3,6 B6: 3,6 # 17 pairs B8: 3,6,1,5 # reduction candidate for 3,6 B8: 3,6 # 17 pairs * PAIR D2: 5,7 COL D D8: 5,7,1,2 # reduction candidate for 5,7 D8: 5,7 => CTR * 287634915439.1.682...982743.4.3...98.984....1..21984.7871269354364..1829925843176 D8: 1,2 => SOLVED * 287634915439715682651982743746321598598476321312598467873169254164257839925843176 * DURATION: 0:00:09.323019 START: 01:49:25.772482 END: 01:49:35.095501 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060815-absurd-base-pr-001.dot * REASONING * DIS # I2: 3,6 => CTR => I2: 2 * DIS I2: 2 # D8: 5,7 => CTR => D8: 1,2 * PRF I2: 2 + D8: 1,2 => SOL * STA I2: 2 + D8: 1,2 * CNT 3 HDP CHAINS / 13 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060815, absurd
Solution
position: 287634915439715682651982743746321598598476321312598467873169254164257839925843176 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 # A3: 3,6 => UNS * INC # B3: 3,6 => UNS * INC # C3: 3,6 => UNS * INC # G2: 3,6 => UNS * DIS # I2: 3,6 => CTR => I2: 2 * INC # I2: 2 => UNS * INC # B6: 3,6 => UNS * INC # B8: 3,6 => UNS * DIS # B9: 3,6 => CTR => B9: 2,5 * INC # B9: 2,5 => UNS * DIS # D8: 5,7 => CTR => D8: 1,2 * INC # D8: 1,2 => UNS * DIS # F4: 5,7 => CTR => F4: 1,6 * INC # F4: 1,6 => UNS * DIS # F5: 5,7 => CTR => F5: 6 * INC # F5: 6 => UNS * INC # F8: 5,7 => UNS * INC # G2: 3,6 => UNS * DIS # I2: 3,6 => CTR => I2: 2 * INC # I2: 2 => UNS * INC # A3: 3,6 => UNS * INC # B3: 3,6 => UNS * INC # C3: 3,6 => UNS * INC # I9: 3,6 => UNS * DIS # I9: 2 => CTR => I9: 3,6 * INC # F4: 1,5 => UNS * DIS # F4: 6,7 => CTR => F4: 1,5 * INC # A6: 1,5 => UNS * INC # B6: 1,5 => UNS * DIS # D8: 1,5 => CTR => D8: 2,7 * INC # D8: 2,7 => UNS * INC # G5: 3,6 => UNS * DIS # H5: 3,6 => CTR => H5: 2 * INC # H5: 2 => UNS * INC # A6: 3,6 => UNS * INC # B6: 3,6 => UNS * INC # H8: 3,6 => UNS * DIS # H8: 2 => CTR => H8: 3,6 * INC # A8: 1,3 => UNS * INC # B8: 1,3 => UNS * INC # C3: 1,3 => UNS * INC # C3: 5,6 => UNS * INC # D8: 1,2 => UNS * DIS # D8: 5,7 => CTR => D8: 1,2 * DIS # D8: 5,7 => CTR => D8: 1,2 * INC # D8: 1,2 => UNS * INC # F8: 5,7 => UNS * DIS # E4: 5,7 => CTR => E4: 2 * INC # E4: 2 => UNS * INC # E5: 5,7 => UNS * DIS # F8: 3,5 => CTR => F8: 1,7 * INC # F8: 1,7 => UNS * DIS # B9: 3,5 => CTR => B9: 2,6 * INC # B9: 2,6 => UNS * INC # C9: 3,5 => UNS * INC # H8: 2,3 => UNS * INC # I9: 2,3 => UNS * INC # G2: 2,3 => UNS * INC # G5: 2,3 => UNS * CNT 59 HDP CHAINS / 59 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 3,6 => UNS * INC # B3: 3,6 => UNS * INC # C3: 3,6 => UNS * INC # G2: 3,6 => UNS * DIS # I2: 3,6 => CTR => I2: 2 * INC I2: 2 # B6: 3,6 => UNS * INC I2: 2 # B8: 3,6 => UNS * INC I2: 2 # A3: 3,6 => UNS * INC I2: 2 # B3: 3,6 => UNS * INC I2: 2 # C3: 3,6 => UNS * INC I2: 2 # B6: 3,6 => UNS * INC I2: 2 # B8: 3,6 => UNS * DIS I2: 2 # D8: 5,7 => CTR => D8: 1,2 * PRF I2: 2 + D8: 1,2 => SOL * STA I2: 2 + D8: 1,2 * CNT 14 HDP CHAINS / 13 HYP OPENED