Analysis of zz-www.sudokuoftheday.co.uk-20060524-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006
level: medium
position: 2.1...5..9..6.2.4.3....4.9.57..6.............12.48..534.2..61.....1..9...1.9....8 initial
Autosolve
position: 241.985..9..6.2.4.3....4.9.57..6.............12.48..534928.61.....1..9...1.9....8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B3: 5,8 => SOL * PRF # E2: 1,5 => SOL * DIS # H1: 6 => CTR => H1: 3,7 * DIS # D5: 3,7 => CTR => D5: 2,5 * PRF # E2: 5,7 => SOL * DIS # E3: 5,7 => CTR => E3: 1 * PRF # D5: 5,7 => SOL * DIS # D5: 2,3 => CTR => D5: 5,7 * PRF # H1: 6,7 => SOL * DIS # H1: 3 => CTR => H1: 6,7 * DIS # I8: 6,7 => CTR => I8: 4,5 * DIS # I3: 1,7 => CTR => I3: 2 * DIS # E2: 1,7 => CTR => E2: 3,5 * PRF # B5: 6,8 => SOL * DIS # C5: 6,8 => CTR => C5: 3,4,9 * DIS # C5: 6,9 => CTR => C5: 3,4,8 * DIS # D5: 2,3 => CTR => D5: 5,7 * PRF # D5: 5,7 => SOL * PRF # F5: 7,9 => SOL * DIS # I4: 2,4 => CTR => I4: 9 * PRF # G9: 6,7 => SOL * DIS # A8: 8 => CTR => A8: 6,7 * PRF # G9: 6,7 => SOL * DIS # H9: 6,7 => CTR => H9: 2,3 * DIS # H8: 3,7 => CTR => H8: 2,6 * DIS # H9: 3,7 => CTR => H9: 2,6 * DIS # E7: 5 => CTR => E7: 3,7 * DIS # H1: 6 => CTR => H1: 3,7 * DIS # I8: 5,7 => CTR => I8: 4,6 * PRF # E7: 5,7 => SOL * DIS # E7: 3 => CTR => E7: 5,7 * CNT 31 HDP CHAINS / 68 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B3: 5,8 => SOL * STA B3: 5,8 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2.1...5..9..6.2.4.3....4.9.57..6.............12.48..534.2..61.....1..9...1.9....8 | initial |
| 241.985..9..6.2.4.3....4.9.57..6.............12.48..534928.61.....1..9...1.9....8 | autosolve |
| 241398576987652341356714892573261489864539217129487653492876135738125964615943728 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) B2: 5,8 D1: 3,7 D3: 5,7 I1: 6,7 I2: 1,7 A5: 6,8 C6: 6,9 D4: 2,3 F6: 7,9 G4: 2,4 H4: 1,8 H5: 1,8 G6: 6,7 A9: 6,7 E8: 2,4 E9: 2,4 H7: 3,7 I7: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,E3: 1.. / E2 = 1 => 0 pairs (X) / E3 = 1 => 18 pairs (_) I2,I3: 1.. / I2 = 1 => 18 pairs (_) / I3 = 1 => 0 pairs (X) F4,F5: 1.. / F4 = 1 => 16 pairs (_) / F5 = 1 => 0 pairs (X) H4,H5: 1.. / H4 = 1 => 0 pairs (X) / H5 = 1 => 16 pairs (_) E2,I2: 1.. / E2 = 1 => 0 pairs (X) / I2 = 1 => 18 pairs (_) E3,I3: 1.. / E3 = 1 => 18 pairs (_) / I3 = 1 => 0 pairs (X) F4,H4: 1.. / F4 = 1 => 16 pairs (_) / H4 = 1 => 0 pairs (X) F5,H5: 1.. / F5 = 1 => 0 pairs (X) / H5 = 1 => 16 pairs (_) G3,I3: 2.. / G3 = 2 => 0 pairs (X) / I3 = 2 => 19 pairs (_) D4,D5: 2.. / D4 = 2 => 0 pairs (*) / D5 = 2 => 0 pairs (X) E8,E9: 2.. / E8 = 2 => 17 pairs (_) / E9 = 2 => 0 pairs (X) H8,H9: 2.. / H8 = 2 => 0 pairs (X) / H9 = 2 => 17 pairs (_) E8,H8: 2.. / E8 = 2 => 17 pairs (_) / H8 = 2 => 0 pairs (X) E9,H9: 2.. / E9 = 2 => 0 pairs (X) / H9 = 2 => 17 pairs (_) D1,E2: 3.. / D1 = 3 => 0 pairs (*) / E2 = 3 => 0 pairs (X) H1,G2: 3.. / H1 = 3 => 0 pairs (X) / G2 = 3 => 0 pairs (_) D1,H1: 3.. / D1 = 3 => 0 pairs (*) / H1 = 3 => 0 pairs (X) E2,G2: 3.. / E2 = 3 => 0 pairs (X) / G2 = 3 => 0 pairs (_) E7,H7: 3.. / E7 = 3 => 0 pairs (X) / H7 = 3 => 0 pairs (_) B5,B8: 3.. / B5 = 3 => 19 pairs (_) / B8 = 3 => 0 pairs (*) G2,G9: 3.. / G2 = 3 => 0 pairs (*) / G9 = 3 => 0 pairs (X) C4,C5: 4.. / C4 = 4 => 0 pairs (X) / C5 = 4 => 18 pairs (_) E8,E9: 4.. / E8 = 4 => 0 pairs (X) / E9 = 4 => 17 pairs (_) I8,G9: 4.. / I8 = 4 => 17 pairs (_) / G9 = 4 => 0 pairs (X) E8,I8: 4.. / E8 = 4 => 0 pairs (X) / I8 = 4 => 17 pairs (_) E9,G9: 4.. / E9 = 4 => 17 pairs (_) / G9 = 4 => 0 pairs (X) I7,I8: 5.. / I7 = 5 => 18 pairs (_) / I8 = 5 => 0 pairs (X) E7,I7: 5.. / E7 = 5 => 0 pairs (X) / I7 = 5 => 18 pairs (_) C9,F9: 5.. / C9 = 5 => 21 pairs (_) / F9 = 5 => 20 pairs (_) D3,D5: 5.. / D3 = 5 => 19 pairs (_) / D5 = 5 => 0 pairs (*) B3,C3: 6.. / B3 = 6 => 19 pairs (_) / C3 = 6 => 0 pairs (*) H1,I1: 6.. / H1 = 6 => 0 pairs (X) / I1 = 6 => 20 pairs (_) C6,G6: 6.. / C6 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) C2,C3: 7.. / C2 = 7 => 20 pairs (_) / C3 = 7 => 21 pairs (_) A8,A9: 7.. / A8 = 7 => 19 pairs (_) / A9 = 7 => 19 pairs (_) F6,G6: 7.. / F6 = 7 => 0 pairs (*) / G6 = 7 => 0 pairs (X) G2,G3: 8.. / G2 = 8 => 0 pairs (X) / G3 = 8 => 20 pairs (_) H4,H5: 8.. / H4 = 8 => 16 pairs (_) / H5 = 8 => 0 pairs (X) C4,H4: 8.. / C4 = 8 => 0 pairs (X) / H4 = 8 => 16 pairs (_) A5,A8: 8.. / A5 = 8 => 18 pairs (_) / A8 = 8 => 0 pairs (X) I4,I5: 9.. / I4 = 9 => 19 pairs (_) / I5 = 9 => 0 pairs (X) C6,F6: 9.. / C6 = 9 => 0 pairs (*) / F6 = 9 => 0 pairs (X) * DURATION: 0:00:50.150404 START: 23:22:31.433307 END: 23:23:21.583711 2019-04-30 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,B2,C6,D1,D3,D4,E8,E9,F6,G4,G6,H4,H5,H7,I1,I2,I7) * 241.985..9..6.2.4.3....4.9.57..6.............12.48..534928.61.....1..9...1.9....8 * PAIR B2: 5,8 BLK 1 C2: 5,8,7 # reduction candidate for 5,8 C2: 5,8 # 21 pairs B3: 5,8,6 # reduction candidate for 5,8 B3: 5,8 => SOLVED * 241398576987652341356714892573261489864539217129487653492876135738125964615943728 B3: 6 # 19 pairs C3: 5,8,6,7 # reduction candidate for 5,8 C3: 5,8 # 22 pairs * PAIR B2: 5,8 COL B B8: 5,8,3,6 # reduction candidate for 5,8 B8: 5,8 # 20 pairs B8: 3,6 # 20 pairs * PAIR D1: 3,7 BLK 2 E2: 3,7,1,5 # reduction candidate for 3,7 E2: 1,5 => SOLVED * 241398576987652341356714892573261489864539217129487653492876135738125964615943728 E2: 3,7 # 19 pairs * PAIR D1: 3,7 ROW 1 H1: 3,7,6 # reduction candidate for 3,7 H1: 6 => CTR * 2413985679..6.23413...1489257.26.4.9..4..921612.48..534928.61.....1..9...1.9....8 H1: 3,7 # 20 pairs * PAIR D1: 3,7 COL D D5: 3,7,2,5 # reduction candidate for 3,7 D5: 3,7 => CTR * 241.985..9..6.2.4.3..5.4.9.57.26.4.9..4..9.1.129487653492876135...1..9.4.1.94.728 D5: 2,5 # 20 pairs * PAIR D3: 5,7 BLK 2 E2: 5,7,1,3 # reduction candidate for 5,7 E2: 5,7 => SOLVED * 241398576987652341356714892573261489864539217129487653492876135738125964615943728 E2: 1,3 # 20 pairs E3: 5,7,1 # reduction candidate for 5,7 E3: 5,7 => CTR * 241.985..9..6123473.75.4.9.57..6.............12.48..534928.61.....1..9...1.9....8 E3: 1 # 18 pairs * PAIR D3: 5,7 ROW 3 C3: 5,7,6,8 # reduction candidate for 5,7 C3: 6,8 # 21 pairs C3: 5,7 # 21 pairs * PAIR D3: 5,7 COL D D5: 5,7,2,3 # reduction candidate for 5,7 D5: 5,7 => SOLVED * 241398576987652341356714892573261489864539217129487653492876135738125964615943728 D5: 2,3 => CTR * 2417985369..632.413..514.9.57..6.............12.48..534928.6175...1..9...1.9....8 * PAIR I1: 6,7 BLK 3 H1: 6,7,3 # reduction candidate for 6,7 H1: 6,7 => SOLVED * 241398576987652341356714892573261489864539217129487653492876135738125964615943728 H1: 3 => CTR * 241.985369..632.413...14.9.57..6.............12.48..534928.6175...1..9...1.9....8 * PAIR I1: 6,7 COL I I5: 6,7,2,4,9 # reduction candidate for 6,7 I5: 6,7 # 19 pairs I8: 6,7,4,5 # reduction candidate for 6,7 I8: 6,7 => CTR * 2413985..9..6.234.3....489257..6.2.....2.....12.48..534928.61.5...14.92..1.92.4.8 I8: 4,5 # 19 pairs * PAIR I2: 1,7 BLK 3 I3: 1,7,2 # reduction candidate for 1,7 I3: 1,7 => CTR * 241.985369576328413...1429757..6.4....4.5....12.48..534928761.5...12.9.4.1.94.328 I3: 2 # 19 pairs * PAIR I2: 1,7 ROW 2 E2: 1,7,3,5 # reduction candidate for 1,7 E2: 1,7 => CTR * 2413985769.761234.3....489257.26.4.9..4..921.129487653492876135...1..9.4.1.94.728 E2: 3,5 # 19 pairs * PAIR A5: 6,8 BLK 4 B5: 6,8,3 # reduction candidate for 6,8 B5: 6,8 => SOLVED * 241398576987652341356714892573261489864539217129487653492876135738125964615943728 B5: 3 # 19 pairs C5: 6,8,3,4,9 # reduction candidate for 6,8 C5: 6,8 => CTR * 2413985..9..6.2.4.3....4.9.574.6.289.3.2.9.1.129487653492876135...1..9...1.9....8 C5: 3,4,9 # 18 pairs * PAIR A5: 6,8 COL A A8: 6,8,7 # reduction candidate for 6,8 A8: 7 # 19 pairs A8: 6,8 # 19 pairs * PAIR C6: 6,9 BLK 4 C5: 6,9,3,4,8 # reduction candidate for 6,9 C5: 6,9 => CTR * 2417985369..632.413..514.9257436128983.2...1.12.48..534928.6175...1..9...1.9....8 C5: 3,4,8 # 18 pairs * PAIR D4: 2,3 BLK 5 D5: 2,3,5,7 # reduction candidate for 2,3 D5: 2,3 => CTR * 2417985369..632.413..514.9.57..6.............12.48..534928.6175...1..9...1.9....8 D5: 5,7 => SOLVED * 241398576987652341356714892573261489864539217129487653492876135738125964615943728 * PAIR F6: 7,9 BLK 5 F5: 7,9,1,3,5 # reduction candidate for 7,9 F5: 7,9 => SOLVED * 241398576987652341356714892573261489864539217129487653492876135738125964615943728 F5: 1,3,5 # 18 pairs * PAIR G4: 2,4 BLK 6 I4: 2,4,9 # reduction candidate for 2,4 I4: 2,4 => CTR * 2417985369..6328413..51429757.36.4.2.342....912.48..534928.6175...1..9...1.9....8 I4: 9 # 19 pairs G5: 2,4,6,7 # reduction candidate for 2,4 G5: 2,4 # 19 pairs I5: 2,4,6,7,9 # reduction candidate for 2,4 I5: 2,4 # 24 pairs * PAIR G6: 6,7 BLK 6 G5: 6,7,2,4 # reduction candidate for 6,7 G5: 6,7 # 22 pairs I5: 6,7,2,4,9 # reduction candidate for 6,7 I5: 6,7 # 19 pairs * PAIR G6: 6,7 COL G G9: 6,7,3,4 # reduction candidate for 6,7 G9: 6,7 => SOLVED * 241398576987652341356714892573261489864539217129487653492876135738125964615943728 G9: 3,4 # 19 pairs * PAIR A9: 6,7 BLK 7 A8: 6,7,8 # reduction candidate for 6,7 A8: 8 => CTR * 2413985..9..6.234.3..7.489257.26....6........1294876534928761358..1..9..71.9..4.8 A8: 6,7 # 18 pairs * PAIR A9: 6,7 ROW 9 G9: 6,7,3,4 # reduction candidate for 6,7 G9: 6,7 => SOLVED * 241398576987652341356714892573261489864539217129487653492876135738125964615943728 G9: 3,4 # 19 pairs H9: 6,7,2,3 # reduction candidate for 6,7 H9: 6,7 => CTR * 2413985..9..6.234.3....489257..6.2.....2.....12.48..534928.613....14.92..1.92.4.8 H9: 2,3 # 19 pairs * PAIR H7: 3,7 BLK 9 H8: 3,7,2,6 # reduction candidate for 3,7 H8: 3,7 => CTR * 2413985679..6.234136..1489257.26.4.98.......61264897534928.61.5...12.9.4.1.94.628 H8: 2,6 # 19 pairs G9: 3,7,4,6 # reduction candidate for 3,7 G9: 3,7 # 19 pairs H9: 3,7,2,6 # reduction candidate for 3,7 H9: 3,7 => CTR * 241.985679..6.23413...1489257..6.2.....2.....12.48..534928.61.5...14.926.1.92.4.8 H9: 2,6 # 19 pairs * PAIR H7: 3,7 ROW 7 E7: 3,7,5 # reduction candidate for 3,7 E7: 5 => CTR * 24139857695.6.23413..51489257326.............12.48..53492856137...1..9.5.159.34.8 E7: 3,7 # 18 pairs * PAIR H7: 3,7 COL H H1: 3,7,6 # reduction candidate for 3,7 H1: 6 => CTR * 2413985679..6.23413...1489257.26.4.9..4..921612.48..534928.61.....1..9...1.9....8 H1: 3,7 # 20 pairs * PAIR I7: 5,7 BLK 9 I8: 5,7,4,6 # reduction candidate for 5,7 I8: 5,7 => CTR * 2413985.69..6.234.3....489257..6.2.....2.....12.48..534928.613....14.92.71.92.468 I8: 4,6 # 19 pairs * PAIR I7: 5,7 ROW 7 E7: 5,7,3 # reduction candidate for 5,7 E7: 5,7 => SOLVED * 241398576987652341356714892573261489864539217129487653492876135738125964615943728 E7: 3 => CTR * 2413985679..6.23413...1489257.26.4.9..4..921612.48..53492836175...1..9...1.9....8 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060524-absurd-base-pr-000.dot * REASONING * PRF # B3: 5,8 => SOL * PRF # E2: 1,5 => SOL * DIS # H1: 6 => CTR => H1: 3,7 * DIS # D5: 3,7 => CTR => D5: 2,5 * PRF # E2: 5,7 => SOL * DIS # E3: 5,7 => CTR => E3: 1 * PRF # D5: 5,7 => SOL * DIS # D5: 2,3 => CTR => D5: 5,7 * PRF # H1: 6,7 => SOL * DIS # H1: 3 => CTR => H1: 6,7 * DIS # I8: 6,7 => CTR => I8: 4,5 * DIS # I3: 1,7 => CTR => I3: 2 * DIS # E2: 1,7 => CTR => E2: 3,5 * PRF # B5: 6,8 => SOL * DIS # C5: 6,8 => CTR => C5: 3,4,9 * DIS # C5: 6,9 => CTR => C5: 3,4,8 * DIS # D5: 2,3 => CTR => D5: 5,7 * PRF # D5: 5,7 => SOL * PRF # F5: 7,9 => SOL * DIS # I4: 2,4 => CTR => I4: 9 * PRF # G9: 6,7 => SOL * DIS # A8: 8 => CTR => A8: 6,7 * PRF # G9: 6,7 => SOL * DIS # H9: 6,7 => CTR => H9: 2,3 * DIS # H8: 3,7 => CTR => H8: 2,6 * DIS # H9: 3,7 => CTR => H9: 2,6 * DIS # E7: 5 => CTR => E7: 3,7 * DIS # H1: 6 => CTR => H1: 3,7 * DIS # I8: 5,7 => CTR => I8: 4,6 * PRF # E7: 5,7 => SOL * DIS # E7: 3 => CTR => E7: 5,7 * CNT 31 HDP CHAINS / 68 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,B2,C6,D1,D3,D4,E8,E9,F6,G4,G6,H4,H5,H7,I1,I2,I7) * 241.985..9..6.2.4.3....4.9.57..6.............12.48..534928.61.....1..9...1.9....8 * PAIR B2: 5,8 BLK 1 C2: 5,8,7 # reduction candidate for 5,8 C2: 5,8 # 21 pairs B3: 5,8,6 # reduction candidate for 5,8 B3: 5,8 => SOLVED * 241398576987652341356714892573261489864539217129487653492876135738125964615943728 * DURATION: 0:00:02.328279 START: 23:24:07.990342 END: 23:24:10.318621 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060524-absurd-base-pr-001.dot * REASONING * PRF # B3: 5,8 => SOL * STA B3: 5,8 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060524, absurd
Solution
position: 241398576987652341356714892573261489864539217129487653492876135738125964615943728 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 # C2: 5,8 => UNS * PRF # B3: 5,8 => SOL * INC # B3: 6 => UNS * INC # C3: 5,8 => UNS * INC # B8: 5,8 => UNS * INC # B8: 3,6 => UNS * INC # E2: 3,7 => UNS * PRF # E2: 1,5 => SOL * INC # H1: 3,7 => UNS * DIS # H1: 6 => CTR => H1: 3,7 * DIS # D5: 3,7 => CTR => D5: 2,5 * INC # D5: 2,5 => UNS * PRF # E2: 5,7 => SOL * INC # E2: 1,3 => UNS * DIS # E3: 5,7 => CTR => E3: 1 * INC # E3: 1 => UNS * INC # C3: 5,7 => UNS * INC # C3: 6,8 => UNS * PRF # D5: 5,7 => SOL * DIS # D5: 2,3 => CTR => D5: 5,7 * PRF # H1: 6,7 => SOL * DIS # H1: 3 => CTR => H1: 6,7 * INC # I5: 6,7 => UNS * DIS # I8: 6,7 => CTR => I8: 4,5 * INC # I8: 4,5 => UNS * DIS # I3: 1,7 => CTR => I3: 2 * INC # I3: 2 => UNS * DIS # E2: 1,7 => CTR => E2: 3,5 * INC # E2: 3,5 => UNS * PRF # B5: 6,8 => SOL * INC # B5: 3 => UNS * DIS # C5: 6,8 => CTR => C5: 3,4,9 * INC # C5: 3,4,9 => UNS * INC # A8: 6,8 => UNS * INC # A8: 7 => UNS * DIS # C5: 6,9 => CTR => C5: 3,4,8 * INC # C5: 3,4,8 => UNS * DIS # D5: 2,3 => CTR => D5: 5,7 * PRF # D5: 5,7 => SOL * PRF # F5: 7,9 => SOL * INC # F5: 1,3,5 => UNS * DIS # I4: 2,4 => CTR => I4: 9 * INC # I4: 9 => UNS * INC # G5: 2,4 => UNS * INC # I5: 2,4 => UNS * INC # G5: 6,7 => UNS * INC # I5: 6,7 => UNS * PRF # G9: 6,7 => SOL * INC # G9: 3,4 => UNS * INC # A8: 6,7 => UNS * DIS # A8: 8 => CTR => A8: 6,7 * PRF # G9: 6,7 => SOL * INC # G9: 3,4 => UNS * DIS # H9: 6,7 => CTR => H9: 2,3 * INC # H9: 2,3 => UNS * DIS # H8: 3,7 => CTR => H8: 2,6 * INC # H8: 2,6 => UNS * INC # G9: 3,7 => UNS * DIS # H9: 3,7 => CTR => H9: 2,6 * INC # H9: 2,6 => UNS * INC # E7: 3,7 => UNS * DIS # E7: 5 => CTR => E7: 3,7 * INC # H1: 3,7 => UNS * DIS # H1: 6 => CTR => H1: 3,7 * DIS # I8: 5,7 => CTR => I8: 4,6 * INC # I8: 4,6 => UNS * PRF # E7: 5,7 => SOL * DIS # E7: 3 => CTR => E7: 5,7 * CNT 68 HDP CHAINS / 68 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 5,8 => UNS * PRF # B3: 5,8 => SOL * STA B3: 5,8 * CNT 2 HDP CHAINS / 2 HYP OPENED