Analysis of zz-www.sudokuoftheday.co.uk-20190315-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019
level: medium
position: ..1.9....6.2...8.......6....7.2..1....6.85.7..24..3.........354..51...6...7....8. initial
Autosolve
position: ..1.97.2.692..18.77...26.1..7.26.1....6.85.7..24713.9.....7.354..51..76...7....81 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B3: 3,8 => SOL * PRF # D3: 4 => SOL * PRF # C4: 9 => SOL * PRF # D2: 3,4 => SOL * PRF # A5: 1,3 => SOL * DIS # A5: 9 => CTR => A5: 1,3 * DIS # A4: 3,9 => CTR => A4: 5,8 * DIS # F8: 4,9 => CTR => F8: 2,8 * DIS # D9: 4,9 => CTR => D9: 3,5,6 * DIS # G1: 4 => CTR => G1: 5,6 * PRF # A7: 8,9 => SOL * DIS # F7: 8,9 => CTR => F7: 2 * DIS # C4: 3 => CTR => C4: 8,9 * DIS # D9: 6,9 => CTR => D9: 3,4,5 * PRF # D9: 3,4,5 => SOL * DIS # D9: 3,4 => CTR => D9: 5,6,9 * PRF # E9: 3,4 => SOL * DIS # A8: 3,4 => CTR => A8: 2,8,9 * PRF # E2: 5 => SOL * DIS # F8: 2,9 => CTR => F8: 4,8 * DIS # A9: 2,9 => CTR => A9: 3,4 * CNT 21 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B3: 3,8 => SOL * STA B3: 3,8 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..1.9....6.2...8.......6....7.2..1....6.85.7..24..3.........354..51...6...7....8. | initial |
| ..1.97.2.692..18.77...26.1..7.26.1....6.85.7..24713.9.....7.354..51..76...7....81 | autosolve |
| 451897623692351847783426915579264138136985472824713596918672354245138769367549281 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) C3: 3,8 H2: 3,4 B5: 1,3 A6: 5,8 F4: 4,9 D5: 4,9 H4: 3,4 G5: 2,4 I5: 2,3 G6: 5,6 C7: 8,9 D7: 6,9 E8: 3,4 I8: 2,9 G9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A5,B5: 1.. / A5 = 1 => 0 pairs (*) / B5 = 1 => 0 pairs (X) A7,B7: 1.. / A7 = 1 => 19 pairs (_) / B7 = 1 => 0 pairs (*) A5,A7: 1.. / A5 = 1 => 0 pairs (*) / A7 = 1 => 0 pairs (X) B5,B7: 1.. / B5 = 1 => 19 pairs (_) / B7 = 1 => 0 pairs (*) G5,I5: 2.. / G5 = 2 => 0 pairs (X) / I5 = 2 => 0 pairs (_) I8,G9: 2.. / I8 = 2 => 0 pairs (X) / G9 = 2 => 0 pairs (_) A7,F7: 2.. / A7 = 2 => 0 pairs (X) / F7 = 2 => 18 pairs (_) G5,G9: 2.. / G5 = 2 => 0 pairs (X) / G9 = 2 => 0 pairs (_) I5,I8: 2.. / I5 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) C3,C4: 3.. / C3 = 3 => 18 pairs (_) / C4 = 3 => 0 pairs (X) H2,H4: 3.. / H2 = 3 => 0 pairs (X) / H4 = 3 => 0 pairs (_) F4,D5: 4.. / F4 = 4 => 0 pairs (*) / D5 = 4 => 0 pairs (X) H4,G5: 4.. / H4 = 4 => 0 pairs (X) / G5 = 4 => 0 pairs (_) F4,H4: 4.. / F4 = 4 => 0 pairs (*) / H4 = 4 => 0 pairs (X) D5,G5: 4.. / D5 = 4 => 0 pairs (X) / G5 = 4 => 0 pairs (_) H2,H4: 4.. / H2 = 4 => 0 pairs (*) / H4 = 4 => 0 pairs (X) B1,B3: 5.. / B1 = 5 => 19 pairs (_) / B3 = 5 => 20 pairs (_) D2,E2: 5.. / D2 = 5 => 16 pairs (_) / E2 = 5 => 0 pairs (*) A4,A6: 5.. / A4 = 5 => 17 pairs (_) / A6 = 5 => 15 pairs (_) D9,E9: 5.. / D9 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) A4,I4: 5.. / A4 = 5 => 17 pairs (_) / I4 = 5 => 15 pairs (_) D2,D9: 5.. / D2 = 5 => 16 pairs (_) / D9 = 5 => 0 pairs (*) E2,E9: 5.. / E2 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) G1,I1: 6.. / G1 = 6 => 17 pairs (_) / I1 = 6 => 18 pairs (_) G6,I6: 6.. / G6 = 6 => 18 pairs (_) / I6 = 6 => 17 pairs (_) B7,B9: 6.. / B7 = 6 => 0 pairs (X) / B9 = 6 => 15 pairs (_) D7,D9: 6.. / D7 = 6 => 15 pairs (_) / D9 = 6 => 0 pairs (X) B7,D7: 6.. / B7 = 6 => 0 pairs (X) / D7 = 6 => 15 pairs (_) B9,D9: 6.. / B9 = 6 => 15 pairs (_) / D9 = 6 => 0 pairs (X) G1,G6: 6.. / G1 = 6 => 17 pairs (_) / G6 = 6 => 18 pairs (_) I1,I6: 6.. / I1 = 6 => 18 pairs (_) / I6 = 6 => 17 pairs (_) D1,D3: 8.. / D1 = 8 => 17 pairs (_) / D3 = 8 => 19 pairs (_) I4,I6: 8.. / I4 = 8 => 17 pairs (_) / I6 = 8 => 15 pairs (_) F7,F8: 8.. / F7 = 8 => 0 pairs (X) / F8 = 8 => 18 pairs (_) A6,I6: 8.. / A6 = 8 => 17 pairs (_) / I6 = 8 => 15 pairs (_) G3,I3: 9.. / G3 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) F4,D5: 9.. / F4 = 9 => 0 pairs (X) / D5 = 9 => 0 pairs (_) I8,G9: 9.. / I8 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) A5,D5: 9.. / A5 = 9 => 0 pairs (X) / D5 = 9 => 0 pairs (_) C4,C7: 9.. / C4 = 9 => 0 pairs (*) / C7 = 9 => 0 pairs (X) G3,G9: 9.. / G3 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) I3,I8: 9.. / I3 = 9 => 0 pairs (X) / I8 = 9 => 0 pairs (_) * DURATION: 0:00:49.235633 START: 04:32:29.901979 END: 04:33:19.137612 2019-05-01 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B5,C3,C7,D5,D7,E8,F4,G5,G6,G9,H2,H4,I5,I8) * ..1.97.2.692..18.77...26.1..7.26.1....6.85.7..24713.9.....7.354..51..76...7....81 * PAIR C3: 3,8 BLK 1 A1: 3,8,4 # reduction candidate for 3,8 A1: 3,8 # 21 pairs B1: 3,8,4,5 # reduction candidate for 3,8 B1: 3,8 # 21 pairs B3: 3,8,4,5 # reduction candidate for 3,8 B3: 3,8 => SOLVED * 451897623692351847783426915579264138136985472824713596918672354245138769367549281 B3: 4,5 # 16 pairs * PAIR C3: 3,8 ROW 3 D3: 3,8,4 # reduction candidate for 3,8 D3: 4 => SOLVED * 451897623692351847783426915579264138136985472824713596918672354245138769367549281 D3: 3,8 # 18 pairs * PAIR C3: 3,8 COL C C4: 3,8,9 # reduction candidate for 3,8 C4: 9 => SOLVED * 451897623692351847783426915579264138136985472824713596918672354245138769367549281 C4: 3,8 # 16 pairs * PAIR H2: 3,4 ROW 2 D2: 3,4,5 # reduction candidate for 3,4 D2: 3,4 => SOLVED * 451897623692351847783426915579264138136985472824713596918672354245138769367549281 D2: 5 # 16 pairs E2: 3,4,5 # reduction candidate for 3,4 E2: 3,4 # 16 pairs * PAIR B5: 1,3 BLK 4 A5: 1,3,9 # reduction candidate for 1,3 A5: 1,3 => SOLVED * 451897623692351847783426915579264138136985472824713596918672354245138769367549281 A5: 9 => CTR * ..1.97.2.692..18.77...26.1..7.26.1..916485273.24713.9.1.9672354..51.876...7....81 * PAIR A6: 5,8 BLK 4 A4: 5,8,3,9 # reduction candidate for 5,8 A4: 3,9 => CTR * ..1.97.26692..18.77.3.26.19.7826.1.5..6.85.73524713698..967.354.35149762467....81 A4: 5,8 # 19 pairs * PAIR A6: 5,8 ROW 6 I6: 5,8,6 # reduction candidate for 5,8 I6: 5,8 # 18 pairs I6: 6 # 17 pairs * PAIR F4: 4,9 COL F F8: 4,9,2,8 # reduction candidate for 4,9 F8: 4,9 => CTR * ..1.97.2.692..18.77...26.19.7.26.1....6.85273.24713.9.21..78354..51..76...7..2981 F8: 2,8 # 16 pairs F9: 4,9,2 # reduction candidate for 4,9 F9: 4,9 # 18 pairs * PAIR D5: 4,9 COL D D9: 4,9,3,5,6 # reduction candidate for 4,9 D9: 4,9 => CTR * ..1.97.2.6925418377...26.1..7.26.14...6485273.24713.9....67.354..513.76236795..81 D9: 3,5,6 # 15 pairs * PAIR G6: 5,6 BLK 6 I6: 5,6,8 # reduction candidate for 5,6 I6: 5,6 # 17 pairs I6: 8 # 15 pairs * PAIR G6: 5,6 COL G G1: 5,6,4 # reduction candidate for 5,6 G1: 4 => CTR * .51.9742669254183774..26519.7.26914.916485273.2471369.1.9672354..513.762..7...981 G1: 5,6 # 17 pairs * PAIR C7: 8,9 BLK 7 A7: 8,9,1,2 # reduction candidate for 8,9 A7: 8,9 => SOLVED * 451897623692351847783426915579264138136985472824713596918672354245138769367549281 A7: 1,2 # 16 pairs A8: 8,9,2,3,4 # reduction candidate for 8,9 A8: 8,9 # 27 pairs * PAIR C7: 8,9 ROW 7 F7: 8,9,2 # reduction candidate for 8,9 F7: 8,9 => CTR * ..1.97.2.692..18477.3.269155792641..136985472.24713.9.21.67.354..51.2769.67...281 F7: 2 # 18 pairs * PAIR C7: 8,9 COL C C4: 8,9,3 # reduction candidate for 8,9 C4: 3 => CTR * ..1.97.2.692..18.77...26.1..7326.14..16485273.24713.9.1.9672354..51.876...7....81 C4: 8,9 # 18 pairs * PAIR D7: 6,9 BLK 8 D9: 6,9,3,4,5 # reduction candidate for 6,9 D9: 6,9 => CTR * ..1.97.2.6925418377...26.19.7.26914.916485273.24713.9.1.967.354..513.762..7.5.981 D9: 3,4,5 => SOLVED * 451897623692351847783426915579264138136985472824713596918672354245138769367549281 * PAIR E8: 3,4 BLK 8 D9: 3,4,5,6,9 # reduction candidate for 3,4 D9: 3,4 => CTR * ..1.97.2.6925318477.3.26915579264138..6985472824713.9....67.354..514.769467359281 D9: 5,6,9 # 16 pairs E9: 3,4,5 # reduction candidate for 3,4 E9: 3,4 => SOLVED * 451897623692351847783426915579264138136985472824713596918672354245138769367549281 E9: 5 # 16 pairs * PAIR E8: 3,4 ROW 8 A8: 3,4,2,8,9 # reduction candidate for 3,4 A8: 3,4 => CTR * ..1.97.2.692..18477.3826915.7.26.1..136985472.24713.9.219678354.851.2769.67..9281 A8: 2,8,9 # 15 pairs B8: 3,4,8 # reduction candidate for 3,4 B8: 3,4 # 16 pairs * PAIR E8: 3,4 COL E E2: 3,4,5 # reduction candidate for 3,4 E2: 5 => SOLVED * 451897623692351847783426915579264138136985472824713596918672354245138769367549281 E2: 3,4 # 16 pairs * PAIR I8: 2,9 ROW 8 A8: 2,9,3,4,8 # reduction candidate for 2,9 A8: 2,9 # 17 pairs F8: 2,9,4,8 # reduction candidate for 2,9 F8: 2,9 => CTR * ..1.97.2.692..18477.3.26915.7.26.1..136985472.24713.9.219678354..51.2769.67..9281 F8: 4,8 # 17 pairs * PAIR G9: 2,9 ROW 9 A9: 2,9,3,4 # reduction candidate for 2,9 A9: 2,9 => CTR * ..1.97.2.692..18.77...26.1..7.26914.916485273.24713.9.....7.354..51..76...7....81 A9: 3,4 # 16 pairs F9: 2,9,4 # reduction candidate for 2,9 F9: 2,9 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190315-absurd-base-pr-000.dot * REASONING * PRF # B3: 3,8 => SOL * PRF # D3: 4 => SOL * PRF # C4: 9 => SOL * PRF # D2: 3,4 => SOL * PRF # A5: 1,3 => SOL * DIS # A5: 9 => CTR => A5: 1,3 * DIS # A4: 3,9 => CTR => A4: 5,8 * DIS # F8: 4,9 => CTR => F8: 2,8 * DIS # D9: 4,9 => CTR => D9: 3,5,6 * DIS # G1: 4 => CTR => G1: 5,6 * PRF # A7: 8,9 => SOL * DIS # F7: 8,9 => CTR => F7: 2 * DIS # C4: 3 => CTR => C4: 8,9 * DIS # D9: 6,9 => CTR => D9: 3,4,5 * PRF # D9: 3,4,5 => SOL * DIS # D9: 3,4 => CTR => D9: 5,6,9 * PRF # E9: 3,4 => SOL * DIS # A8: 3,4 => CTR => A8: 2,8,9 * PRF # E2: 5 => SOL * DIS # F8: 2,9 => CTR => F8: 4,8 * DIS # A9: 2,9 => CTR => A9: 3,4 * CNT 21 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B5,C3,C7,D5,D7,E8,F4,G5,G6,G9,H2,H4,I5,I8) * ..1.97.2.692..18.77...26.1..7.26.1....6.85.7..24713.9.....7.354..51..76...7....81 * PAIR C3: 3,8 BLK 1 A1: 3,8,4 # reduction candidate for 3,8 A1: 3,8 # 21 pairs B1: 3,8,4,5 # reduction candidate for 3,8 B1: 3,8 # 21 pairs B3: 3,8,4,5 # reduction candidate for 3,8 B3: 3,8 => SOLVED * 451897623692351847783426915579264138136985472824713596918672354245138769367549281 * DURATION: 0:00:02.825767 START: 04:33:50.532922 END: 04:33:53.358689 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190315-absurd-base-pr-001.dot * REASONING * PRF # B3: 3,8 => SOL * STA B3: 3,8 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190315, absurd
Solution
position: 451897623692351847783426915579264138136985472824713596918672354245138769367549281 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 # A1: 3,8 => UNS * INC # B1: 3,8 => UNS * PRF # B3: 3,8 => SOL * INC # B3: 4,5 => UNS * INC # D3: 3,8 => UNS * PRF # D3: 4 => SOL * INC # C4: 3,8 => UNS * PRF # C4: 9 => SOL * PRF # D2: 3,4 => SOL * INC # D2: 5 => UNS * INC # E2: 3,4 => UNS * PRF # A5: 1,3 => SOL * DIS # A5: 9 => CTR => A5: 1,3 * INC # A4: 5,8 => UNS * DIS # A4: 3,9 => CTR => A4: 5,8 * INC # I6: 5,8 => UNS * INC # I6: 6 => UNS * DIS # F8: 4,9 => CTR => F8: 2,8 * INC # F8: 2,8 => UNS * INC # F9: 4,9 => UNS * DIS # D9: 4,9 => CTR => D9: 3,5,6 * INC # D9: 3,5,6 => UNS * INC # I6: 5,6 => UNS * INC # I6: 8 => UNS * INC # G1: 5,6 => UNS * DIS # G1: 4 => CTR => G1: 5,6 * PRF # A7: 8,9 => SOL * INC # A7: 1,2 => UNS * INC # A8: 8,9 => UNS * DIS # F7: 8,9 => CTR => F7: 2 * INC # F7: 2 => UNS * INC # C4: 8,9 => UNS * DIS # C4: 3 => CTR => C4: 8,9 * DIS # D9: 6,9 => CTR => D9: 3,4,5 * PRF # D9: 3,4,5 => SOL * DIS # D9: 3,4 => CTR => D9: 5,6,9 * INC # D9: 5,6,9 => UNS * PRF # E9: 3,4 => SOL * INC # E9: 5 => UNS * DIS # A8: 3,4 => CTR => A8: 2,8,9 * INC # A8: 2,8,9 => UNS * INC # B8: 3,4 => UNS * INC # E2: 3,4 => UNS * PRF # E2: 5 => SOL * INC # A8: 2,9 => UNS * DIS # F8: 2,9 => CTR => F8: 4,8 * INC # F8: 4,8 => UNS * DIS # A9: 2,9 => CTR => A9: 3,4 * INC # A9: 3,4 => UNS * INC # F9: 2,9 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 3,8 => UNS * INC # B1: 3,8 => UNS * PRF # B3: 3,8 => SOL * STA B3: 3,8 * CNT 3 HDP CHAINS / 3 HYP OPENED