Analysis of zz-www.sudokuoftheday.co.uk-20190210-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019
level: medium
position: 2..8..7..6...2.1...95........3.......8...6437..6..7.29.....2.....917.6..31.6.4..8 initial
Autosolve
position: 2..8..7..6...2.1...95........3.......8...6437..6..7.29.6...2.....917.6..31.6.4..8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 3,4 => CTR => B2: 7 * DIS # E1: 3,4 => CTR => E1: 5,6,9 * DIS # F1: 1,3 => CTR => F1: 5,9 * DIS # I3: 4,6 => CTR => I3: 2,3 * DIS # A4: 4,5 => CTR => A4: 7,9 * PRF # B4: 4,5 => SOL * PRF # D6: 4,5 => SOL * DIS # E6: 4,5 => CTR => E6: 1,3,8 * DIS # B8: 4,5 => CTR => B8: 2 * PRF # E4: 5,8 => SOL * DIS # E6: 5,8 => CTR => E6: 1,3,4 * PRF # E7: 5,9 => SOL * DIS # E1: 5,9 => CTR => E1: 3,4,6 * DIS # E4: 5,9 => CTR => E4: 4,8 * DIS # E7: 3,9 => CTR => E7: 5,8 * DIS # H7: 4,5 => CTR => H7: 1,7 * DIS # I7: 4,5 => CTR => I7: 1,3 * DIS # I8: 4,5 => CTR => I8: 2,3 * PRF # A8: 4,5 => SOL * DIS # B8: 4,5 => CTR => B8: 2 * DIS # H1: 4,5 => CTR => H1: 6,9 * DIS # H2: 4,5 => CTR => H2: 8,9 * DIS # H7: 1,4 => CTR => H7: 5,7 * CNT 23 HDP CHAINS / 54 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 3,4 => CTR => B2: 7 * PRF B2: 7 # A3: 8 => SOL * STA B2: 7 + A3: 8 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2..8..7..6...2.1...95........3.......8...6437..6..7.29.....2.....917.6..31.6.4..8 | initial |
| 2..8..7..6...2.1...95........3.......8...6437..6..7.29.6...2.....917.6..31.6.4..8 | autosolve |
| 231865794674923185895741362743289516982516437156437829468352971529178643317694258 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) B1: 3,4 C1: 1,4 F3: 1,3 G3: 2,3 C5: 1,2 B6: 4,5 G4: 5,8 H4: 1,6 I4: 1,6 G6: 5,8 C9: 2,7 E9: 5,9 G7: 3,9 H8: 4,5 G9: 2,9 H9: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,A3: 1.. / C1 = 1 => 23 pairs (_) / A3 = 1 => 0 pairs (X) F1,F3: 1.. / F1 = 1 => 0 pairs (X) / F3 = 1 => 23 pairs (_) E5,E6: 1.. / E5 = 1 => 0 pairs (*) / E6 = 1 => 0 pairs (X) H4,I4: 1.. / H4 = 1 => 18 pairs (_) / I4 = 1 => 0 pairs (X) H7,I7: 1.. / H7 = 1 => 0 pairs (X) / I7 = 1 => 18 pairs (_) C1,F1: 1.. / C1 = 1 => 23 pairs (_) / F1 = 1 => 0 pairs (X) A3,F3: 1.. / A3 = 1 => 0 pairs (X) / F3 = 1 => 23 pairs (_) A6,E6: 1.. / A6 = 1 => 0 pairs (*) / E6 = 1 => 0 pairs (X) C1,C5: 1.. / C1 = 1 => 23 pairs (_) / C5 = 1 => 0 pairs (X) H4,H7: 1.. / H4 = 1 => 18 pairs (_) / H7 = 1 => 0 pairs (X) I4,I7: 1.. / I4 = 1 => 0 pairs (X) / I7 = 1 => 18 pairs (_) G3,I3: 2.. / G3 = 2 => 0 pairs (X) / I3 = 2 => 23 pairs (_) B4,C5: 2.. / B4 = 2 => 0 pairs (X) / C5 = 2 => 23 pairs (_) D4,D5: 2.. / D4 = 2 => 23 pairs (_) / D5 = 2 => 0 pairs (X) B8,C9: 2.. / B8 = 2 => 23 pairs (_) / C9 = 2 => 0 pairs (X) I8,G9: 2.. / I8 = 2 => 0 pairs (X) / G9 = 2 => 23 pairs (_) B4,D4: 2.. / B4 = 2 => 0 pairs (X) / D4 = 2 => 23 pairs (_) C5,D5: 2.. / C5 = 2 => 23 pairs (_) / D5 = 2 => 0 pairs (X) B8,I8: 2.. / B8 = 2 => 23 pairs (_) / I8 = 2 => 0 pairs (X) C9,G9: 2.. / C9 = 2 => 0 pairs (X) / G9 = 2 => 23 pairs (_) B4,B8: 2.. / B4 = 2 => 0 pairs (X) / B8 = 2 => 23 pairs (_) C5,C9: 2.. / C5 = 2 => 23 pairs (_) / C9 = 2 => 0 pairs (X) G3,G9: 2.. / G3 = 2 => 0 pairs (X) / G9 = 2 => 23 pairs (_) I3,I8: 2.. / I3 = 2 => 23 pairs (_) / I8 = 2 => 0 pairs (X) B1,B2: 3.. / B1 = 3 => 16 pairs (_) / B2 = 3 => 0 pairs (X) D6,E6: 3.. / D6 = 3 => 20 pairs (_) / E6 = 3 => 0 pairs (*) F8,I8: 3.. / F8 = 3 => 0 pairs (X) / I8 = 3 => 23 pairs (_) G3,G7: 3.. / G3 = 3 => 23 pairs (_) / G7 = 3 => 0 pairs (X) G4,G6: 5.. / G4 = 5 => 15 pairs (_) / G6 = 5 => 0 pairs (X) E9,H9: 5.. / E9 = 5 => 0 pairs (X) / H9 = 5 => 23 pairs (_) E1,E3: 6.. / E1 = 6 => 17 pairs (_) / E3 = 6 => 17 pairs (_) H4,I4: 6.. / H4 = 6 => 0 pairs (X) / I4 = 6 => 18 pairs (_) D2,D3: 7.. / D2 = 7 => 0 pairs (X) / D3 = 7 => 16 pairs (_) A4,B4: 7.. / A4 = 7 => 20 pairs (_) / B4 = 7 => 0 pairs (X) H7,H9: 7.. / H7 = 7 => 23 pairs (_) / H9 = 7 => 0 pairs (X) A3,D3: 7.. / A3 = 7 => 0 pairs (X) / D3 = 7 => 16 pairs (_) C9,H9: 7.. / C9 = 7 => 23 pairs (_) / H9 = 7 => 0 pairs (X) B2,B4: 7.. / B2 = 7 => 20 pairs (_) / B4 = 7 => 0 pairs (X) C2,A3: 8.. / C2 = 8 => 17 pairs (_) / A3 = 8 => 0 pairs (*) H2,H3: 8.. / H2 = 8 => 0 pairs (*) / H3 = 8 => 0 pairs (X) G4,G6: 8.. / G4 = 8 => 0 pairs (X) / G6 = 8 => 15 pairs (_) E7,F8: 8.. / E7 = 8 => 18 pairs (_) / F8 = 8 => 0 pairs (*) C2,H2: 8.. / C2 = 8 => 17 pairs (_) / H2 = 8 => 0 pairs (*) A3,H3: 8.. / A3 = 8 => 0 pairs (*) / H3 = 8 => 0 pairs (X) E6,G6: 8.. / E6 = 8 => 0 pairs (X) / G6 = 8 => 15 pairs (_) A8,F8: 8.. / A8 = 8 => 18 pairs (_) / F8 = 8 => 0 pairs (*) C2,C7: 8.. / C2 = 8 => 17 pairs (_) / C7 = 8 => 0 pairs (*) F4,F8: 8.. / F4 = 8 => 18 pairs (_) / F8 = 8 => 0 pairs (*) H1,H2: 9.. / H1 = 9 => 16 pairs (_) / H2 = 9 => 18 pairs (_) A4,A5: 9.. / A4 = 9 => 0 pairs (X) / A5 = 9 => 20 pairs (_) G7,G9: 9.. / G7 = 9 => 23 pairs (_) / G9 = 9 => 0 pairs (X) E9,G9: 9.. / E9 = 9 => 23 pairs (_) / G9 = 9 => 0 pairs (X) * DURATION: 0:00:58.531135 START: 03:37:33.352500 END: 03:38:31.883635 2019-05-01 * CP COUNT: (52) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B6,C1,C5,C9,E9,F3,G3,G4,G6,G7,G9,H4,H8,H9,I4) * 2..8..7..6...2.1...95........3.......8...6437..6..7.29.6...2.....917.6..31.6.4..8 * PAIR B1: 3,4 BLK 1 B2: 3,4,7 # reduction candidate for 3,4 B2: 3,4 => CTR * 2.18..7..6.872.19.795461382.732..516.82956437.56317829.64532971.2917.643317694258 B2: 7 # 20 pairs * PAIR B1: 3,4 ROW 1 E1: 3,4,5,6,9 # reduction candidate for 3,4 E1: 3,4 => CTR * 23184.7656785231944957613827432.9.16.82..6437..6..7.29.64..2971.2917.643317694258 E1: 5,6,9 # 16 pairs I1: 3,4,5,6 # reduction candidate for 3,4 I1: 3,4 # 23 pairs * PAIR C1: 1,4 BLK 1 A3: 1,4,7,8 # reduction candidate for 1,4 A3: 7,8 # 25 pairs A3: 1,4 # 21 pairs * PAIR F3: 1,3 BLK 2 F1: 1,3,5,9 # reduction candidate for 1,3 F1: 1,3 => CTR * 2418.379.63872914..95...3.2.732......82..6437..6..7.29.6...29...2917.6.3317694258 F1: 5,9 # 24 pairs * PAIR G3: 2,3 BLK 3 I3: 2,3,4,6 # reduction candidate for 2,3 I3: 4,6 => CTR * 2..8..7..6...2.1...95..12...23..85...812.6437..6.17829.6..823..8.91736.2312654978 I3: 2,3 # 23 pairs * PAIR B6: 4,5 BLK 4 A4: 4,5,7,9 # reduction candidate for 4,5 A4: 4,5 => CTR * 2.18..7..6..72.1..795..1382.732.....982516437156..7829.6.9.2....2917.6..3176.4258 A4: 7,9 # 17 pairs B4: 4,5,2,7 # reduction candidate for 4,5 B4: 4,5 => SOLVED * 231865794674923185895741362743289516982516437156437829468352971529178643317694258 B4: 2,7 # 17 pairs A6: 4,5,1 # reduction candidate for 4,5 A6: 4,5 # 25 pairs * PAIR B6: 4,5 ROW 6 D6: 4,5,3 # reduction candidate for 4,5 D6: 4,5 => SOLVED * 231865794674923185895741362743289516982516437156437829468352971529178643317694258 D6: 3 # 20 pairs E6: 4,5,1,3,8 # reduction candidate for 4,5 E6: 4,5 => CTR * 2.18..7..6...2.1...95.61382..3289516982516437156347829.6...2971.2917.643317694258 E6: 1,3,8 # 16 pairs * PAIR B6: 4,5 COL B B8: 4,5,2 # reduction candidate for 4,5 B8: 4,5 => CTR * 2.48.17..678.2.1..1957.328.723...5..981256437..6.17829.6...2.....917.6.23126.4978 B8: 2 # 23 pairs * PAIR G4: 5,8 ROW 4 E4: 5,8,4,9 # reduction candidate for 5,8 E4: 5,8 => SOLVED * 231865794674923185895741362743289516982516437156437829468352971529178643317694258 E4: 4,9 # 17 pairs F4: 5,8,9 # reduction candidate for 5,8 F4: 5,8 # 18 pairs * PAIR G6: 5,8 ROW 6 E6: 5,8,1,3,4 # reduction candidate for 5,8 E6: 5,8 => CTR * 2318..7..67..2.1...957.13.27532498..982516437146387529.6.9.2....2917.6..3176.4258 E6: 1,3,4 # 15 pairs * PAIR E9: 5,9 BLK 8 D7: 5,9,3 # reduction candidate for 5,9 D7: 5,9 # 19 pairs E7: 5,9,3,8 # reduction candidate for 5,9 E7: 5,9 => SOLVED * 231865794674923185895741362743289516982516437156437829468352971529178643317694258 E7: 3,8 # 17 pairs * PAIR E9: 5,9 COL E E1: 5,9,3,4,6 # reduction candidate for 5,9 E1: 5,9 => CTR * 2318597646.8.23195.95.6138297324..165829164371.6..7.29.6...2971.2917.643317694258 E1: 3,4,6 # 16 pairs E4: 5,9,4,8 # reduction candidate for 5,9 E4: 5,9 => CTR * 2..8..7..6...2.1...95........3......98.516437156..7829.6..82...8.917.6..31.654978 E4: 4,8 # 17 pairs E5: 5,9,1 # reduction candidate for 5,9 E5: 5,9 # 25 pairs * PAIR G7: 3,9 ROW 7 D7: 3,9,5 # reduction candidate for 3,9 D7: 3,9 # 19 pairs E7: 3,9,5,8 # reduction candidate for 3,9 E7: 3,9 => CTR * 2.18..7..6...2.1...95..13.2..32...16.82956437..6..7.29.6.532971529178643317694258 E7: 5,8 # 17 pairs * PAIR H8: 4,5 BLK 9 H7: 4,5,1,7 # reduction candidate for 4,5 H7: 4,5 => CTR * 2..8..7..6...2.1...95...2...23....16.81296437..6.17829.6.9.23.1..91736.2312654978 H7: 1,7 # 17 pairs I7: 4,5,1,3 # reduction candidate for 4,5 I7: 4,5 => CTR * 2..8..7..6...2.1...95...2...23....61.81296437..6.17829.6.9.231...91736.2312654978 I7: 1,3 # 17 pairs I8: 4,5,2,3 # reduction candidate for 4,5 I8: 4,5 => CTR * 2..8..7..6...2.1...95.....2..3.......8...6437..6..7.29.6...2....291736..3176.4258 I8: 2,3 # 17 pairs * PAIR H8: 4,5 ROW 8 A8: 4,5,8 # reduction candidate for 4,5 A8: 4,5 => SOLVED * 231865794674923185895741362743289516982516437156437829468352971529178643317694258 A8: 8 # 18 pairs B8: 4,5,2 # reduction candidate for 4,5 B8: 4,5 => CTR * 2.48.17..678.2.1..1957.328.723...5..981256437..6.17829.6...2.....917.6.23126.4978 B8: 2 # 23 pairs * PAIR H8: 4,5 COL H H1: 4,5,6,9 # reduction candidate for 4,5 H1: 4,5 => CTR * 2.48.175.6.8.2.19.1957.328.723..9.61981..6437..6..7.29.67..2.1...917.6..312654978 H1: 6,9 # 17 pairs H2: 4,5,8,9 # reduction candidate for 4,5 H2: 4,5 => CTR * 2.48.17956.8.2.1431957432867234...61981..6437..6..7.29.67..2.1...917.6..312654978 H2: 8,9 # 17 pairs * PAIR H9: 5,7 BLK 9 H7: 5,7,1,4 # reduction candidate for 5,7 H7: 1,4 => CTR * 2..8..7..6...2.1...95...2...23.......81296437..6.17829.6.9.23....91736.2312654978 H7: 5,7 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190210-absurd-base-pr-000.dot * REASONING * DIS # B2: 3,4 => CTR => B2: 7 * DIS # E1: 3,4 => CTR => E1: 5,6,9 * DIS # F1: 1,3 => CTR => F1: 5,9 * DIS # I3: 4,6 => CTR => I3: 2,3 * DIS # A4: 4,5 => CTR => A4: 7,9 * PRF # B4: 4,5 => SOL * PRF # D6: 4,5 => SOL * DIS # E6: 4,5 => CTR => E6: 1,3,8 * DIS # B8: 4,5 => CTR => B8: 2 * PRF # E4: 5,8 => SOL * DIS # E6: 5,8 => CTR => E6: 1,3,4 * PRF # E7: 5,9 => SOL * DIS # E1: 5,9 => CTR => E1: 3,4,6 * DIS # E4: 5,9 => CTR => E4: 4,8 * DIS # E7: 3,9 => CTR => E7: 5,8 * DIS # H7: 4,5 => CTR => H7: 1,7 * DIS # I7: 4,5 => CTR => I7: 1,3 * DIS # I8: 4,5 => CTR => I8: 2,3 * PRF # A8: 4,5 => SOL * DIS # B8: 4,5 => CTR => B8: 2 * DIS # H1: 4,5 => CTR => H1: 6,9 * DIS # H2: 4,5 => CTR => H2: 8,9 * DIS # H7: 1,4 => CTR => H7: 5,7 * CNT 23 HDP CHAINS / 54 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B6,C1,C5,C9,E9,F3,G3,G4,G6,G7,G9,H4,H8,H9,I4) * 2..8..7..6...2.1...95........3.......8...6437..6..7.29.6...2.....917.6..31.6.4..8 * PAIR B1: 3,4 BLK 1 B2: 3,4,7 # reduction candidate for 3,4 B2: 3,4 => CTR * 2.18..7..6.872.19.795461382.732..516.82956437.56317829.64532971.2917.643317694258 * PAIR C1: 1,4 BLK 1 A3: 1,4,8 # reduction candidate for 1,4 A3: 8 => SOLVED * 231865794674923185895741362743289516982516437156437829468352971529178643317694258 * DURATION: 0:00:03.632591 START: 03:39:04.481046 END: 03:39:08.113637 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190210-absurd-base-pr-001.dot * REASONING * DIS # B2: 3,4 => CTR => B2: 7 * PRF B2: 7 # A3: 8 => SOL * STA B2: 7 + A3: 8 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190210, absurd
Solution
position: 231865794674923185895741362743289516982516437156437829468352971529178643317694258 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 # B2: 3,4 => CTR => B2: 7 * INC # B2: 7 => UNS * DIS # E1: 3,4 => CTR => E1: 5,6,9 * INC # E1: 5,6,9 => UNS * INC # I1: 3,4 => UNS * INC # A3: 1,4 => UNS * INC # A3: 7,8 => UNS * DIS # F1: 1,3 => CTR => F1: 5,9 * INC # F1: 5,9 => UNS * INC # I3: 2,3 => UNS * DIS # I3: 4,6 => CTR => I3: 2,3 * DIS # A4: 4,5 => CTR => A4: 7,9 * INC # A4: 7,9 => UNS * PRF # B4: 4,5 => SOL * INC # B4: 2,7 => UNS * INC # A6: 4,5 => UNS * PRF # D6: 4,5 => SOL * INC # D6: 3 => UNS * DIS # E6: 4,5 => CTR => E6: 1,3,8 * INC # E6: 1,3,8 => UNS * DIS # B8: 4,5 => CTR => B8: 2 * INC # B8: 2 => UNS * PRF # E4: 5,8 => SOL * INC # E4: 4,9 => UNS * INC # F4: 5,8 => UNS * DIS # E6: 5,8 => CTR => E6: 1,3,4 * INC # E6: 1,3,4 => UNS * INC # D7: 5,9 => UNS * PRF # E7: 5,9 => SOL * INC # E7: 3,8 => UNS * DIS # E1: 5,9 => CTR => E1: 3,4,6 * INC # E1: 3,4,6 => UNS * DIS # E4: 5,9 => CTR => E4: 4,8 * INC # E4: 4,8 => UNS * INC # E5: 5,9 => UNS * INC # D7: 3,9 => UNS * DIS # E7: 3,9 => CTR => E7: 5,8 * INC # E7: 5,8 => UNS * DIS # H7: 4,5 => CTR => H7: 1,7 * INC # H7: 1,7 => UNS * DIS # I7: 4,5 => CTR => I7: 1,3 * INC # I7: 1,3 => UNS * DIS # I8: 4,5 => CTR => I8: 2,3 * INC # I8: 2,3 => UNS * PRF # A8: 4,5 => SOL * INC # A8: 8 => UNS * DIS # B8: 4,5 => CTR => B8: 2 * INC # B8: 2 => UNS * DIS # H1: 4,5 => CTR => H1: 6,9 * INC # H1: 6,9 => UNS * DIS # H2: 4,5 => CTR => H2: 8,9 * INC # H2: 8,9 => UNS * INC # H7: 5,7 => UNS * DIS # H7: 1,4 => CTR => H7: 5,7 * CNT 54 HDP CHAINS / 54 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B2: 3,4 => CTR => B2: 7 * INC B2: 7 # A3: 1,4 => UNS * PRF B2: 7 # A3: 8 => SOL * STA B2: 7 + A3: 8 * CNT 3 HDP CHAINS / 3 HYP OPENED