Analysis of zz-www.sudokuoftheday.co.uk-20190101-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
level: medium
position: 9...5.2...3.2.9..674...6...1..58..3.2.84....7.5....6......7......7...85.51......4 initial
Autosolve
position: 961.5.2..8352.9..6742..6..5176582439298463517.5....6...8..75....27...85.51..28..4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E8: 1,4 => CTR => E8: 3,9 * PRF # E8: 3,9 => SOL * PRF # D3: 1,3 => SOL * PRF # G3: 9 => SOL * DIS # E8: 4,9 => CTR => E8: 1,3 * DIS # D1: 7 => CTR => D1: 3,8 * DIS # A7: 6 => CTR => A7: 3,4 * PRF # C7: 9 => SOL * DIS # D6: 1,9 => CTR => D6: 7 * DIS # E8: 1,9 => CTR => E8: 3,4 * DIS # D6: 9 => CTR => D6: 1,7 * DIS # D8: 3,6 => CTR => D8: 1,9 * DIS # G9: 3,9 => CTR => G9: 7 * DIS # E8: 1,4 => CTR => E8: 3,9 * PRF # E8: 3,9 => SOL * DIS # D7: 3,6 => CTR => D7: 1 * PRF # D7: 1 => SOL * DIS # D8: 3,6 => CTR => D8: 1,9 * DIS # G9: 3,9 => CTR => G9: 7 * DIS # G3: 1 => CTR => G3: 3,9 * DIS # I7: 1,3 => CTR => I7: 2 * PRF # I7: 2 => SOL * DIS # D8: 1,3 => CTR => D8: 6,9 * CNT 23 HDP CHAINS / 45 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E8: 1,4 => CTR => E8: 3,9 * PRF E8: 3,9 => SOL * STA E8: 3,9 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9...5.2...3.2.9..674...6...1..58..3.2.84....7.5....6......7......7...85.51......4 | initial |
| 961.5.2..8352.9..6742..6..5176582439298463517.5....6...8..75....27...85.51..28..4 | autosolve |
| 961857243835249176742316985176582439298463517354791628489175362627934851513628794 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) F1: 4,7 E2: 1,4 E3: 1,3 H1: 4,8 I1: 3,8 G2: 1,7 H2: 4,7 H3: 8,9 A6: 3,4 C6: 3,4 E6: 1,9 F6: 1,7 H6: 2,8 I6: 2,8 A8: 3,6 C9: 3,9 F8: 1,4 D9: 3,6 G7: 3,9 I8: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,G3: 1.. / G2 = 1 => 19 pairs (_) / G3 = 1 => 0 pairs (X) I7,I8: 1.. / I7 = 1 => 0 pairs (X) / I8 = 1 => 0 pairs (_) E2,G2: 1.. / E2 = 1 => 0 pairs (X) / G2 = 1 => 19 pairs (_) D7,I7: 1.. / D7 = 1 => 0 pairs (*) / I7 = 1 => 0 pairs (X) F6,F8: 1.. / F6 = 1 => 19 pairs (_) / F8 = 1 => 0 pairs (X) H6,I6: 2.. / H6 = 2 => 0 pairs (*) / I6 = 2 => 0 pairs (X) H7,I7: 2.. / H7 = 2 => 0 pairs (X) / I7 = 2 => 0 pairs (_) H6,H7: 2.. / H6 = 2 => 0 pairs (*) / H7 = 2 => 0 pairs (X) I6,I7: 2.. / I6 = 2 => 0 pairs (X) / I7 = 2 => 0 pairs (_) I1,G3: 3.. / I1 = 3 => 0 pairs (*) / G3 = 3 => 0 pairs (X) A6,C6: 3.. / A6 = 3 => 21 pairs (_) / C6 = 3 => 20 pairs (_) D1,I1: 3.. / D1 = 3 => 0 pairs (X) / I1 = 3 => 0 pairs (_) E3,E8: 3.. / E3 = 3 => 0 pairs (X) / E8 = 3 => 0 pairs (_) F1,E2: 4.. / F1 = 4 => 0 pairs (X) / E2 = 4 => 19 pairs (_) H1,H2: 4.. / H1 = 4 => 19 pairs (_) / H2 = 4 => 0 pairs (X) A6,C6: 4.. / A6 = 4 => 20 pairs (_) / C6 = 4 => 21 pairs (_) A7,C7: 4.. / A7 = 4 => 21 pairs (_) / C7 = 4 => 20 pairs (_) E8,F8: 4.. / E8 = 4 => 0 pairs (X) / F8 = 4 => 19 pairs (_) F1,H1: 4.. / F1 = 4 => 0 pairs (X) / H1 = 4 => 19 pairs (_) E2,H2: 4.. / E2 = 4 => 19 pairs (_) / H2 = 4 => 0 pairs (X) A6,A7: 4.. / A6 = 4 => 20 pairs (_) / A7 = 4 => 21 pairs (_) C6,C7: 4.. / C6 = 4 => 21 pairs (_) / C7 = 4 => 20 pairs (_) E2,E8: 4.. / E2 = 4 => 19 pairs (_) / E8 = 4 => 0 pairs (X) F1,F8: 4.. / F1 = 4 => 0 pairs (X) / F8 = 4 => 19 pairs (_) A7,A8: 6.. / A7 = 6 => 0 pairs (X) / A8 = 6 => 23 pairs (_) H7,H9: 6.. / H7 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) A8,D8: 6.. / A8 = 6 => 23 pairs (_) / D8 = 6 => 0 pairs (X) D9,H9: 6.. / D9 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) D1,F1: 7.. / D1 = 7 => 0 pairs (X) / F1 = 7 => 19 pairs (_) G2,H2: 7.. / G2 = 7 => 0 pairs (X) / H2 = 7 => 19 pairs (_) D6,F6: 7.. / D6 = 7 => 19 pairs (_) / F6 = 7 => 0 pairs (X) G9,H9: 7.. / G9 = 7 => 19 pairs (_) / H9 = 7 => 0 pairs (X) D1,D6: 7.. / D1 = 7 => 0 pairs (X) / D6 = 7 => 19 pairs (_) F1,F6: 7.. / F1 = 7 => 19 pairs (_) / F6 = 7 => 0 pairs (X) G2,G9: 7.. / G2 = 7 => 0 pairs (X) / G9 = 7 => 19 pairs (_) H2,H9: 7.. / H2 = 7 => 19 pairs (_) / H9 = 7 => 0 pairs (X) D1,D3: 8.. / D1 = 8 => 0 pairs (*) / D3 = 8 => 0 pairs (X) H6,I6: 8.. / H6 = 8 => 0 pairs (X) / I6 = 8 => 0 pairs (_) D3,H3: 8.. / D3 = 8 => 26 pairs (_) / H3 = 8 => 0 pairs (*) I1,I6: 8.. / I1 = 8 => 0 pairs (X) / I6 = 8 => 0 pairs (_) G3,H3: 9.. / G3 = 9 => 0 pairs (*) / H3 = 9 => 0 pairs (X) D6,E6: 9.. / D6 = 9 => 0 pairs (X) / E6 = 9 => 23 pairs (_) C7,C9: 9.. / C7 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) D8,E8: 9.. / D8 = 9 => 23 pairs (_) / E8 = 9 => 0 pairs (X) D6,D8: 9.. / D6 = 9 => 0 pairs (X) / D8 = 9 => 23 pairs (_) E6,E8: 9.. / E6 = 9 => 23 pairs (_) / E8 = 9 => 0 pairs (X) * DURATION: 0:00:55.405295 START: 02:37:44.191852 END: 02:38:39.597147 2019-05-01 * CP COUNT: (46) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A8,C6,C9,D9,E2,E3,E6,F1,F6,F8,G2,G7,H1,H2,H3,H6,I1,I6,I8) * 961.5.2..8352.9..6742..6..5176582439298463517.5....6...8..75....27...85.51..28..4 * PAIR E2: 1,4 COL E E8: 1,4,3,9 # reduction candidate for 1,4 E8: 1,4 => CTR * 961.5.2.38352.9..6742.36..5176582439298463517.5..9.6.8.8..75..2.279..85.51..28..4 E8: 3,9 => SOLVED * 961857243835249176742316985176582439298463517354791628489175362627934851513628794 * PAIR E3: 1,3 BLK 2 D3: 1,3,8 # reduction candidate for 1,3 D3: 1,3 => SOLVED * 961857243835249176742316985176582439298463517354791628489175362627934851513628794 D3: 8 # 26 pairs * PAIR E3: 1,3 ROW 3 G3: 1,3,9 # reduction candidate for 1,3 G3: 9 => SOLVED * 961857243835249176742316985176582439298463517354791628489175362627934851513628794 G3: 1,3 # 26 pairs * PAIR E3: 1,3 COL E E8: 1,3,4,9 # reduction candidate for 1,3 E8: 4,9 => CTR * 961.5.2.38352.9..6742.36..5176582439298463517.5...1628.8.175..2.27..485151..28..4 E8: 1,3 # 19 pairs * PAIR I1: 3,8 ROW 1 D1: 3,8,7 # reduction candidate for 3,8 D1: 7 => CTR * 961754283835219746742836195176582439298463517.5..97628.8..75.62627...85.51..28..4 D1: 3,8 # 19 pairs * PAIR A6: 3,4 COL A A7: 3,4,6 # reduction candidate for 3,4 A7: 6 => CTR * 961.57243835249176742.36985176582439298463517453...6..684.75...327694851519328764 A7: 3,4 # 23 pairs * PAIR C6: 3,4 COL C C7: 3,4,9 # reduction candidate for 3,4 C7: 9 => SOLVED * 961857243835249176742316985176582439298463517354791628489175362627934851513628794 C7: 3,4 # 22 pairs * PAIR E6: 1,9 BLK 5 D6: 1,9,7 # reduction candidate for 1,9 D6: 1,9 => CTR * 961754283835219746742836195176582439298463517.5..97628.8..75.62627...85.51..28..4 D6: 7 # 19 pairs * PAIR E6: 1,9 COL E E8: 1,9,3,4 # reduction candidate for 1,9 E8: 1,9 => CTR * 961857243835249176742136985176582439298463517.5.7..628.8..753.2.27..485151..287.4 E8: 3,4 # 25 pairs * PAIR F6: 1,7 BLK 5 D6: 1,7,9 # reduction candidate for 1,7 D6: 9 => CTR * 961754283835219746742836195176582439298463517.5.9..6...8..75....27...85.51..28..4 D6: 1,7 # 23 pairs * PAIR A8: 3,6 BLK 7 A7: 3,6,4 # reduction candidate for 3,6 A7: 4 # 21 pairs A7: 3,6 # 20 pairs * PAIR A8: 3,6 ROW 8 D8: 3,6,1,9 # reduction candidate for 3,6 D8: 3,6 => CTR * 961.5.2..8352.9..6742..6..5176582439298463517.5.9176...8..75....27.9.85.51..28..4 D8: 1,9 # 24 pairs * PAIR C9: 3,9 BLK 7 C7: 3,9,4 # reduction candidate for 3,9 C7: 3,9 # 21 pairs C7: 4 # 20 pairs * PAIR C9: 3,9 ROW 9 G9: 3,9,7 # reduction candidate for 3,9 G9: 3,9 => CTR * 961.5.2..8352.9746742..6195176582439298463517.5....6...8..75....27.4185351..289.4 G9: 7 # 19 pairs * PAIR F8: 1,4 BLK 8 E8: 1,4,3,9 # reduction candidate for 1,4 E8: 1,4 => CTR * 961.5.2.38352.9..6742.36..5176582439298463517.5..9.6.8.8..75..2.279..85.51..28..4 E8: 3,9 => SOLVED * 961857243835249176742316985176582439298463517354791628489175362627934851513628794 * PAIR D9: 3,6 BLK 8 D7: 3,6,1 # reduction candidate for 3,6 D7: 3,6 => CTR * 961357248835249176742816395176582439298463517.5.79.6...8..75..1.27...85351..28..4 D7: 1 => SOLVED * 961857243835249176742316985176582439298463517354791628489175362627934851513628794 D8: 3,6,1,9 # reduction candidate for 3,6 D8: 3,6 => CTR * 961.5.2..8352.9..6742..6..5176582439298463517.5.9176...8..75....27.9.85.51..28..4 D8: 1,9 # 24 pairs * PAIR G7: 3,9 BLK 9 G9: 3,9,7 # reduction candidate for 3,9 G9: 3,9 => CTR * 961.5.2..8352.9746742..6195176582439298463517.5....6...8..75....27.4185351..289.4 G9: 7 # 19 pairs * PAIR G7: 3,9 ROW 7 C7: 3,9,4 # reduction candidate for 3,9 C7: 3,9 # 21 pairs C7: 4 # 20 pairs * PAIR G7: 3,9 COL G G3: 3,9,1 # reduction candidate for 3,9 G3: 1 => CTR * 961.5.283835219746742836195176582439298463517.5..91628.8.175.62627...85151..28..4 G3: 3,9 # 19 pairs * PAIR I8: 1,3 BLK 9 I7: 1,3,2 # reduction candidate for 1,3 I7: 1,3 => CTR * 961.5.2.88352.9.767428.6395176582439298463517.5....682.8..7592..27.3.85.51..28.64 I7: 2 => SOLVED * 961857243835249176742316985176582439298463517354791628489175362627934851513628794 * PAIR I8: 1,3 ROW 8 D8: 1,3,6,9 # reduction candidate for 1,3 D8: 1,3 => CTR * 961.5.2..8352.9..6742..6..5176582439298463517.5.9176...8..75...627.9.85.51..28..4 D8: 6,9 # 21 pairs E8: 1,3,4,9 # reduction candidate for 1,3 E8: 1,3 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190101-absurd-base-pr-000.dot * REASONING * DIS # E8: 1,4 => CTR => E8: 3,9 * PRF # E8: 3,9 => SOL * PRF # D3: 1,3 => SOL * PRF # G3: 9 => SOL * DIS # E8: 4,9 => CTR => E8: 1,3 * DIS # D1: 7 => CTR => D1: 3,8 * DIS # A7: 6 => CTR => A7: 3,4 * PRF # C7: 9 => SOL * DIS # D6: 1,9 => CTR => D6: 7 * DIS # E8: 1,9 => CTR => E8: 3,4 * DIS # D6: 9 => CTR => D6: 1,7 * DIS # D8: 3,6 => CTR => D8: 1,9 * DIS # G9: 3,9 => CTR => G9: 7 * DIS # E8: 1,4 => CTR => E8: 3,9 * PRF # E8: 3,9 => SOL * DIS # D7: 3,6 => CTR => D7: 1 * PRF # D7: 1 => SOL * DIS # D8: 3,6 => CTR => D8: 1,9 * DIS # G9: 3,9 => CTR => G9: 7 * DIS # G3: 1 => CTR => G3: 3,9 * DIS # I7: 1,3 => CTR => I7: 2 * PRF # I7: 2 => SOL * DIS # D8: 1,3 => CTR => D8: 6,9 * CNT 23 HDP CHAINS / 45 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A8,C6,C9,D9,E2,E3,E6,F1,F6,F8,G2,G7,H1,H2,H3,H6,I1,I6,I8) * 961.5.2..8352.9..6742..6..5176582439298463517.5....6...8..75....27...85.51..28..4 * PAIR E2: 1,4 COL E E8: 1,4,3,9 # reduction candidate for 1,4 E8: 1,4 => CTR * 961.5.2.38352.9..6742.36..5176582439298463517.5..9.6.8.8..75..2.279..85.51..28..4 E8: 3,9 => SOLVED * 961857243835249176742316985176582439298463517354791628489175362627934851513628794 * DURATION: 0:00:02.178823 START: 02:39:10.732831 END: 02:39:12.911654 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190101-absurd-base-pr-001.dot * REASONING * DIS # E8: 1,4 => CTR => E8: 3,9 * PRF E8: 3,9 => SOL * STA E8: 3,9 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190101, absurd
Solution
position: 961857243835249176742316985176582439298463517354791628489175362627934851513628794 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 # E8: 1,4 => CTR => E8: 3,9 * PRF # E8: 3,9 => SOL * PRF # D3: 1,3 => SOL * INC # D3: 8 => UNS * INC # G3: 1,3 => UNS * PRF # G3: 9 => SOL * INC # E8: 1,3 => UNS * DIS # E8: 4,9 => CTR => E8: 1,3 * INC # D1: 3,8 => UNS * DIS # D1: 7 => CTR => D1: 3,8 * INC # A7: 3,4 => UNS * DIS # A7: 6 => CTR => A7: 3,4 * INC # C7: 3,4 => UNS * PRF # C7: 9 => SOL * DIS # D6: 1,9 => CTR => D6: 7 * INC # D6: 7 => UNS * DIS # E8: 1,9 => CTR => E8: 3,4 * INC # E8: 3,4 => UNS * INC # D6: 1,7 => UNS * DIS # D6: 9 => CTR => D6: 1,7 * INC # A7: 3,6 => UNS * INC # A7: 4 => UNS * DIS # D8: 3,6 => CTR => D8: 1,9 * INC # D8: 1,9 => UNS * INC # C7: 3,9 => UNS * INC # C7: 4 => UNS * DIS # G9: 3,9 => CTR => G9: 7 * INC # G9: 7 => UNS * DIS # E8: 1,4 => CTR => E8: 3,9 * PRF # E8: 3,9 => SOL * DIS # D7: 3,6 => CTR => D7: 1 * PRF # D7: 1 => SOL * DIS # D8: 3,6 => CTR => D8: 1,9 * INC # D8: 1,9 => UNS * DIS # G9: 3,9 => CTR => G9: 7 * INC # G9: 7 => UNS * INC # C7: 3,9 => UNS * INC # C7: 4 => UNS * INC # G3: 3,9 => UNS * DIS # G3: 1 => CTR => G3: 3,9 * DIS # I7: 1,3 => CTR => I7: 2 * PRF # I7: 2 => SOL * DIS # D8: 1,3 => CTR => D8: 6,9 * INC # D8: 6,9 => UNS * INC # E8: 1,3 => UNS * CNT 45 HDP CHAINS / 45 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E8: 1,4 => CTR => E8: 3,9 * PRF E8: 3,9 => SOL * STA E8: 3,9 * CNT 2 HDP CHAINS / 1 HYP OPENED