Analysis of zz-www.sudokuoftheday.co.uk-20060320-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006
level: medium
position: .......5.8...6...96....2..1.....37...6..84....716............3..8...1..52..549.6. initial
Autosolve
position: .....865.8...67..96...52..1..8..37.6.6.78451..716.5......8.6.3..86..1..52..549.6. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # I1: 2,4 => SOL * DIS # H6: 2,4 => CTR => H6: 8,9 * PRF # H8: 2,4 => SOL * DIS # B4: 2 => CTR => B4: 4,5 * DIS # A7: 4,5 => CTR => A7: 1,7,9 * DIS # C5: 3,9 => CTR => C5: 2 * DIS # A1: 3,9 => CTR => A1: 1,4,7 * PRF # I6: 3,4 => SOL * DIS # A1: 3,4 => CTR => A1: 1,7,9 * DIS # E4: 2,9 => CTR => E4: 1 * DIS # H6: 2,9 => CTR => H6: 4,8 * DIS # I6: 2,3 => CTR => I6: 4,8 * DIS # C5: 9 => CTR => C5: 2,3 * PRF # I1: 2,3 => SOL * DIS # C1: 3,7 => CTR => C1: 2,4,9 * PRF # E8: 7 => SOL * CNT 16 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:
* PRF # I1: 2,4 => SOL * STA I1: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......5.8...6...96....2..1.....37...6..84....716............3..8...1..52..549.6. | initial |
| .....865.8...67..96...52..1..8..37.6.6.78451..716.5......8.6.3..86..1..52..549.6. | autosolve |
| 714938652825167349693452871548213796962784513371695284159826437486371925237549168 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) H2: 2,4 A4: 4,5 A5: 3,9 A6: 3,4 E6: 2,9 I5: 2,3 B9: 1,3 C9: 3,7 E7: 2,7 D8: 2,3 G9: 1,8 I9: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D4,E4: 1.. / D4 = 1 => 0 pairs (X) / E4 = 1 => 14 pairs (_) G7,G9: 1.. / G7 = 1 => 0 pairs (X) / G9 = 1 => 0 pairs (_) B2,D2: 1.. / B2 = 1 => 0 pairs (X) / D2 = 1 => 14 pairs (_) B9,G9: 1.. / B9 = 1 => 0 pairs (X) / G9 = 1 => 0 pairs (_) A1,A7: 1.. / A1 = 1 => 0 pairs (X) / A7 = 1 => 0 pairs (_) E1,E4: 1.. / E1 = 1 => 0 pairs (X) / E4 = 1 => 14 pairs (_) B4,C5: 2.. / B4 = 2 => 0 pairs (X) / C5 = 2 => 12 pairs (_) C5,I5: 2.. / C5 = 2 => 12 pairs (_) / I5 = 2 => 0 pairs (X) D4,D8: 2.. / D4 = 2 => 12 pairs (_) / D8 = 2 => 14 pairs (_) B9,C9: 3.. / B9 = 3 => 0 pairs (*) / C9 = 3 => 0 pairs (X) D8,E8: 3.. / D8 = 3 => 12 pairs (_) / E8 = 3 => 14 pairs (_) E1,E8: 3.. / E1 = 3 => 12 pairs (_) / E8 = 3 => 14 pairs (_) B2,C2: 5.. / B2 = 5 => 15 pairs (_) / C2 = 5 => 12 pairs (_) A4,B4: 5.. / A4 = 5 => 12 pairs (_) / B4 = 5 => 0 pairs (X) A4,A7: 5.. / A4 = 5 => 12 pairs (_) / A7 = 5 => 0 pairs (X) C2,C7: 5.. / C2 = 5 => 12 pairs (_) / C7 = 5 => 15 pairs (_) I1,H3: 7.. / I1 = 7 => 0 pairs (X) / H3 = 7 => 0 pairs (_) E7,E8: 7.. / E7 = 7 => 14 pairs (_) / E8 = 7 => 0 pairs (*) C3,H3: 7.. / C3 = 7 => 0 pairs (X) / H3 = 7 => 0 pairs (_) C9,I9: 7.. / C9 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) H3,H8: 7.. / H3 = 7 => 0 pairs (*) / H8 = 7 => 0 pairs (X) G3,H3: 8.. / G3 = 8 => 0 pairs (*) / H3 = 8 => 0 pairs (X) G9,I9: 8.. / G9 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) H3,H6: 8.. / H3 = 8 => 0 pairs (X) / H6 = 8 => 0 pairs (_) I6,I9: 8.. / I6 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) A5,C5: 9.. / A5 = 9 => 13 pairs (_) / C5 = 9 => 0 pairs (X) * DURATION: 0:00:28.696205 START: 20:01:33.006126 END: 20:02:01.702331 2019-04-30 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,A6,B9,C9,D8,E6,E7,G9,H2,I5,I9) * .....865.8...67..96...52..1..8..37.6.6.78451..716.5......8.6.3..86..1..52..549.6. * PAIR H2: 2,4 BLK 3 I1: 2,4,3,7 # reduction candidate for 2,4 I1: 2,4 => SOLVED * 714938652825167349693452871548213796962784513371695284159826437486371925237549168 I1: 3,7 # 13 pairs G2: 2,4,3 # reduction candidate for 2,4 G2: 2,4 # 18 pairs * PAIR H2: 2,4 ROW 2 B2: 2,4,1,3,5 # reduction candidate for 2,4 B2: 2,4 # 16 pairs C2: 2,4,3,5 # reduction candidate for 2,4 C2: 2,4 # 17 pairs * PAIR H2: 2,4 COL H H4: 2,4,9 # reduction candidate for 2,4 H4: 2,4 # 18 pairs H6: 2,4,8,9 # reduction candidate for 2,4 H6: 2,4 => CTR * .....865.8...67..96...52.81..8..37.6.6.78451..716.5......8.6.3..86..1.752.7549.68 H6: 8,9 # 13 pairs H8: 2,4,7,9 # reduction candidate for 2,4 H8: 2,4 => SOLVED * 714938652825167349693452871548213796962784513371695284159826437486371925237549168 H8: 7,9 # 13 pairs * PAIR A4: 4,5 BLK 4 B4: 4,5,2 # reduction candidate for 4,5 B4: 2 => CTR * .....865.8...67..96...52..1528..3746.6.784512471625......876234.862319752..549.6. B4: 4,5 # 12 pairs * PAIR A4: 4,5 COL A A7: 4,5,1,7,9 # reduction candidate for 4,5 A7: 4,5 => CTR * 1.7..865.8..167..96...52.71..8.137.69627845133716.5.8....876.3.786..1..5213549867 A7: 1,7,9 # 12 pairs * PAIR A5: 3,9 BLK 4 C5: 3,9,2 # reduction candidate for 3,9 C5: 3,9 => CTR * .....865.8...67..96...52..1.28..37.6.6.784512.71625......8762344862319752.7549168 C5: 2 # 12 pairs * PAIR A5: 3,9 COL A A1: 3,9,1,4,7 # reduction candidate for 3,9 A1: 3,9 => CTR * .....865.8...67..96...52..1..8..37.6.6.78451..716.5...1..8.6.3.786..1..523.549.6. A1: 1,4,7 # 13 pairs * PAIR A6: 3,4 ROW 6 G6: 3,4,2,8,9 # reduction candidate for 3,4 G6: 3,4 # 14 pairs I6: 3,4,2,8 # reduction candidate for 3,4 I6: 3,4 => SOLVED * 714938652825167349693452871548213796962784513371695284159826437486371925237549168 I6: 2,8 # 13 pairs * PAIR A6: 3,4 COL A A1: 3,4,1,7,9 # reduction candidate for 3,4 A1: 3,4 => CTR * .....865.8...67..96...52..1..8..37.6.6.78451..716.5...1..8.6.3.786..1..523.549.6. A1: 1,7,9 # 13 pairs * PAIR E6: 2,9 BLK 5 D4: 2,9,1 # reduction candidate for 2,9 D4: 2,9 # 14 pairs E4: 2,9,1 # reduction candidate for 2,9 E4: 2,9 => CTR * 7...1865.815.67..96...52.715.81.37.6.6.78451..716.5.8.15.876.3..86231..5237549168 E4: 1 # 14 pairs * PAIR E6: 2,9 ROW 6 G6: 2,9,3,4,8 # reduction candidate for 2,9 G6: 2,9 # 14 pairs H6: 2,9,4,8 # reduction candidate for 2,9 H6: 2,9 => CTR * .....865.8...67..96...52.81..8..37.6.6.78451..716.5......8.6.3..86..1.752.7549.68 H6: 4,8 # 13 pairs * PAIR I5: 2,3 BLK 6 G6: 2,3,4,8,9 # reduction candidate for 2,3 G6: 2,3 # 15 pairs I6: 2,3,4,8 # reduction candidate for 2,3 I6: 2,3 => CTR * 7...386548...673296.3.528715.8213796.627845133716954821..826937.863712.5237549168 I6: 4,8 # 13 pairs * PAIR I5: 2,3 ROW 5 C5: 2,3,9 # reduction candidate for 2,3 C5: 9 => CTR * .....865.8...67..96...52..1.28..37.6.69784512.71625......8762344862319752.7549168 C5: 2,3 # 13 pairs * PAIR I5: 2,3 COL I I1: 2,3,4,7 # reduction candidate for 2,3 I1: 2,3 => SOLVED * 714938652825167349693452871548213796962784513371695284159826437486371925237549168 I1: 4,7 # 13 pairs * PAIR B9: 1,3 COL B B1: 1,3,2,4,9 # reduction candidate for 1,3 B1: 1,3 # 16 pairs B2: 1,3,2,4,5 # reduction candidate for 1,3 B2: 1,3 # 14 pairs * PAIR C9: 3,7 COL C C1: 3,7,2,4,9 # reduction candidate for 3,7 C1: 3,7 => CTR * 7.3..865.8...673.96..352871..8..37.6.6.78451..716.5.8.1..826.37.86.71..52.7549168 C1: 2,4,9 # 12 pairs C3: 3,7,4,9 # reduction candidate for 3,7 C3: 3,7 # 14 pairs * PAIR E7: 2,7 BLK 8 E8: 2,7,3 # reduction candidate for 2,7 E8: 3 # 14 pairs E8: 2,7 # 12 pairs * PAIR E7: 2,7 ROW 7 I7: 2,7,4 # reduction candidate for 2,7 I7: 4 # 18 pairs I7: 2,7 # 13 pairs * PAIR D8: 2,3 BLK 8 E8: 2,3,7 # reduction candidate for 2,3 E8: 7 => SOLVED * 714938652825167349693452871548213796962784513371695284159826437486371925237549168 E8: 2,3 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060320-absurd-base-pr-000.dot * REASONING * PRF # I1: 2,4 => SOL * DIS # H6: 2,4 => CTR => H6: 8,9 * PRF # H8: 2,4 => SOL * DIS # B4: 2 => CTR => B4: 4,5 * DIS # A7: 4,5 => CTR => A7: 1,7,9 * DIS # C5: 3,9 => CTR => C5: 2 * DIS # A1: 3,9 => CTR => A1: 1,4,7 * PRF # I6: 3,4 => SOL * DIS # A1: 3,4 => CTR => A1: 1,7,9 * DIS # E4: 2,9 => CTR => E4: 1 * DIS # H6: 2,9 => CTR => H6: 4,8 * DIS # I6: 2,3 => CTR => I6: 4,8 * DIS # C5: 9 => CTR => C5: 2,3 * PRF # I1: 2,3 => SOL * DIS # C1: 3,7 => CTR => C1: 2,4,9 * PRF # E8: 7 => SOL * CNT 16 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,A6,B9,C9,D8,E6,E7,G9,H2,I5,I9) * .....865.8...67..96...52..1..8..37.6.6.78451..716.5......8.6.3..86..1..52..549.6. * PAIR H2: 2,4 BLK 3 I1: 2,4,3,7 # reduction candidate for 2,4 I1: 2,4 => SOLVED * 714938652825167349693452871548213796962784513371695284159826437486371925237549168 * DURATION: 0:00:01.778152 START: 20:02:28.200583 END: 20:02:29.978735 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060320-absurd-base-pr-001.dot * REASONING * PRF # I1: 2,4 => SOL * STA I1: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060320, absurd
Solution
position: 714938652825167349693452871548213796962784513371695284159826437486371925237549168 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:
* PRF # I1: 2,4 => SOL * INC # I1: 3,7 => UNS * INC # G2: 2,4 => UNS * INC # B2: 2,4 => UNS * INC # C2: 2,4 => UNS * INC # H4: 2,4 => UNS * DIS # H6: 2,4 => CTR => H6: 8,9 * INC # H6: 8,9 => UNS * PRF # H8: 2,4 => SOL * INC # H8: 7,9 => UNS * INC # B4: 4,5 => UNS * DIS # B4: 2 => CTR => B4: 4,5 * DIS # A7: 4,5 => CTR => A7: 1,7,9 * INC # A7: 1,7,9 => UNS * DIS # C5: 3,9 => CTR => C5: 2 * INC # C5: 2 => UNS * DIS # A1: 3,9 => CTR => A1: 1,4,7 * INC # A1: 1,4,7 => UNS * INC # G6: 3,4 => UNS * PRF # I6: 3,4 => SOL * INC # I6: 2,8 => UNS * DIS # A1: 3,4 => CTR => A1: 1,7,9 * INC # A1: 1,7,9 => UNS * INC # D4: 2,9 => UNS * DIS # E4: 2,9 => CTR => E4: 1 * INC # E4: 1 => UNS * INC # G6: 2,9 => UNS * DIS # H6: 2,9 => CTR => H6: 4,8 * INC # H6: 4,8 => UNS * INC # G6: 2,3 => UNS * DIS # I6: 2,3 => CTR => I6: 4,8 * INC # I6: 4,8 => UNS * INC # C5: 2,3 => UNS * DIS # C5: 9 => CTR => C5: 2,3 * PRF # I1: 2,3 => SOL * INC # I1: 4,7 => UNS * INC # B1: 1,3 => UNS * INC # B2: 1,3 => UNS * DIS # C1: 3,7 => CTR => C1: 2,4,9 * INC # C1: 2,4,9 => UNS * INC # C3: 3,7 => UNS * INC # E8: 2,7 => UNS * INC # E8: 3 => UNS * INC # I7: 2,7 => UNS * INC # I7: 4 => UNS * INC # E8: 2,3 => UNS * PRF # E8: 7 => SOL * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # I1: 2,4 => SOL * STA I1: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED