Analysis of zz-www.sudokuoftheday.co.uk-20190312-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: .4.2.......8...3....918...2..3..1......745.3..5.9....7.92...7..6....9.1448......3 initial
Autosolve
position: .4.2.......8...3....918...2..3..1......745.3..549....7.92...7..6....9.1448......3 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 1,6 => CTR => C1: 5,7 * DIS # F6: 6,8 => CTR => F6: 2,3 * PRF # F6: 2,3 => SOL * DIS # G4: 6,8 => CTR => G4: 2,4,5,9 * DIS # H4: 6,8 => CTR => H4: 2,4,5,9 * DIS # I4: 6,8 => CTR => I4: 5,9 * DIS # E6: 2,6 => CTR => E6: 3 * PRF # F6: 2,6 => SOL * DIS # F6: 3,8 => CTR => F6: 2,6 * PRF # B4: 2,6 => SOL * DIS # B4: 7 => CTR => B4: 2,6 * DIS # G4: 2,6 => CTR => G4: 4,5,8,9 * DIS # H4: 2,6 => CTR => H4: 4,5,8,9 * DIS # E9: 2,6 => CTR => E9: 1,5,7 * PRF # B3: 3,7 => SOL * DIS # B3: 6 => CTR => B3: 3,7 * DIS # C9: 5,7 => CTR => C9: 1 * DIS # E8: 5,7 => CTR => E8: 2 * PRF # E8: 2 => SOL * DIS # C1: 1,6 => CTR => C1: 5,7 * PRF # D7: 4,8 => SOL * DIS # D7: 3 => CTR => D7: 4,8 * DIS # D7: 3,8 => CTR => D7: 4 * PRF # D7: 4 => SOL * DIS # E7: 5,6 => CTR => E7: 1 * PRF # E9: 5,6 => SOL * DIS # G9: 5,6 => CTR => G9: 2,9 * DIS # H9: 5,6 => CTR => H9: 2,9 * PRF # D2: 5,6 => SOL * DIS # D2: 4 => CTR => D2: 5,6 * CNT 30 HDP CHAINS / 48 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 1,6 => CTR => C1: 5,7 * DIS C1: 5,7 # F6: 6,8 => CTR => F6: 2,3 * PRF C1: 5,7 + F6: 2,3 => SOL * STA C1: 5,7 + F6: 2,3 * CNT 3 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .4.2.......8...3....918...2..3..1......745.3..5.9....7.92...7..6....9.1448......3 | initial |
| .4.2.......8...3....918...2..3..1......745.3..549....7.92...7..6....9.1448......3 | autosolve |
| 147293685268574391539186472723861549916745238854932167392418756675329814481657923 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) C5: 1,6 D4: 6,8 E4: 2,6 B8: 3,7 C8: 5,7 F7: 4,8 D8: 3,8 D9: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A7,C9: 1.. / A7 = 1 => 0 pairs (X) / C9 = 1 => 12 pairs (_) E7,E9: 1.. / E7 = 1 => 12 pairs (_) / E9 = 1 => 0 pairs (X) A6,G6: 1.. / A6 = 1 => 0 pairs (X) / G6 = 1 => 9 pairs (_) A7,E7: 1.. / A7 = 1 => 0 pairs (X) / E7 = 1 => 12 pairs (_) C9,E9: 1.. / C9 = 1 => 12 pairs (_) / E9 = 1 => 0 pairs (X) B2,B5: 1.. / B2 = 1 => 10 pairs (_) / B5 = 1 => 10 pairs (_) A2,B2: 2.. / A2 = 2 => 9 pairs (_) / B2 = 2 => 0 pairs (X) E8,G8: 2.. / E8 = 2 => 0 pairs (*) / G8 = 2 => 0 pairs (X) F6,F9: 2.. / F6 = 2 => 0 pairs (*) / F9 = 2 => 0 pairs (X) E6,F6: 3.. / E6 = 3 => 8 pairs (_) / F6 = 3 => 0 pairs (X) A7,B8: 3.. / A7 = 3 => 0 pairs (*) / B8 = 3 => 0 pairs (X) D7,D8: 3.. / D7 = 3 => 0 pairs (X) / D8 = 3 => 0 pairs (_) A7,D7: 3.. / A7 = 3 => 0 pairs (*) / D7 = 3 => 0 pairs (X) B8,D8: 3.. / B8 = 3 => 0 pairs (X) / D8 = 3 => 0 pairs (_) B3,B8: 3.. / B3 = 3 => 0 pairs (*) / B8 = 3 => 0 pairs (X) E1,E6: 3.. / E1 = 3 => 0 pairs (X) / E6 = 3 => 8 pairs (_) G4,H4: 4.. / G4 = 4 => 9 pairs (_) / H4 = 4 => 8 pairs (_) D7,F7: 4.. / D7 = 4 => 0 pairs (*) / F7 = 4 => 0 pairs (X) D2,D7: 4.. / D2 = 4 => 0 pairs (X) / D7 = 4 => 0 pairs (_) G3,G4: 4.. / G3 = 4 => 8 pairs (_) / G4 = 4 => 9 pairs (_) D2,D9: 5.. / D2 = 5 => 0 pairs (*) / D9 = 5 => 0 pairs (X) C1,C5: 6.. / C1 = 6 => 0 pairs (X) / C5 = 6 => 9 pairs (_) A4,B4: 7.. / A4 = 7 => 0 pairs (*) / B4 = 7 => 0 pairs (X) D4,F6: 8.. / D4 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) D8,G8: 8.. / D8 = 8 => 0 pairs (X) / G8 = 8 => 0 pairs (_) F6,F7: 8.. / F6 = 8 => 0 pairs (X) / F7 = 8 => 0 pairs (_) E1,E2: 9.. / E1 = 9 => 8 pairs (_) / E2 = 9 => 8 pairs (_) A4,A5: 9.. / A4 = 9 => 0 pairs (X) / A5 = 9 => 10 pairs (_) G9,H9: 9.. / G9 = 9 => 8 pairs (_) / H9 = 9 => 12 pairs (_) * DURATION: 0:00:34.187588 START: 04:27:22.270340 END: 04:27:56.457928 2019-05-01 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,C5,C8,D4,D8,D9,E4,F7) * .4.2.......8...3....918...2..3..1......745.3..549....7.92...7..6....9.1448......3 * PAIR C5: 1,6 BLK 4 B5: 1,6,2 # reduction candidate for 1,6 B5: 1,6 # 12 pairs B5: 2 # 10 pairs * PAIR C5: 1,6 ROW 5 G5: 1,6,2,8,9 # reduction candidate for 1,6 G5: 1,6 # 13 pairs I5: 1,6,8,9 # reduction candidate for 1,6 I5: 1,6 # 13 pairs * PAIR C5: 1,6 COL C C1: 1,6,5,7 # reduction candidate for 1,6 C1: 1,6 => CTR * .4.2.......84..3....918...2.73621......745.3.2549381671923647..635879214487512693 C1: 5,7 # 12 pairs * PAIR D4: 6,8 BLK 5 F6: 6,8,2,3 # reduction candidate for 6,8 F6: 6,8 => CTR * .4.2.......84..3....918...2.73621......745.3.1549386275923.47..63.8.921448.5.2963 F6: 2,3 => SOLVED * 147293685268574391539186472723861549916745238854932167392418756675329814481657923 * PAIR D4: 6,8 ROW 4 G4: 6,8,2,4,5,9 # reduction candidate for 6,8 G4: 6,8 => CTR * .4.2.......8...3...6918.4.2973621845826745.3.1549386275923147..63785921448...2..3 G4: 2,4,5,9 # 8 pairs H4: 6,8,2,4,5,9 # reduction candidate for 6,8 H4: 6,8 => CTR * .4.2.......8...3...6918.5.2973621485826745.3.15493862759231476863785921448...2..3 H4: 2,4,5,9 # 8 pairs I4: 6,8,5,9 # reduction candidate for 6,8 I4: 6,8 => CTR * .4.2.......8...3...6918...2973621..8826745.3.15493862759231478663785921448...2..3 I4: 5,9 # 9 pairs * PAIR E4: 2,6 BLK 5 E6: 2,6,3 # reduction candidate for 2,6 E6: 2,6 => CTR * .4.23......8.9.3....918...2..3..1......745.3..549.3..7.92..87..6..3.981448...2..3 E6: 3 # 8 pairs F6: 2,6,3,8 # reduction candidate for 2,6 F6: 2,6 => SOLVED * 147293685268574391539186472723861549916745238854932167392418756675329814481657923 F6: 3,8 => CTR * .4.2.......84..3....918...2.73621......745.3.1549386275923147..6378.921448.5.2..3 * PAIR E4: 2,6 ROW 4 B4: 2,6,7 # reduction candidate for 2,6 B4: 2,6 => SOLVED * 147293685268574391539186472723861549916745238854932167392418756675329814481657923 B4: 7 => CTR * .4.2.......84..3...6918...2.73621.....6745.3..54938.27.923.47..635879214487512..3 G4: 2,6,4,5,8,9 # reduction candidate for 2,6 G4: 2,6 => CTR * .4.2.......8...3....918.4.29738.1.45...745.3..549....7.92..87.663...9.1448......3 G4: 4,5,8,9 # 8 pairs H4: 2,6,4,5,8,9 # reduction candidate for 2,6 H4: 2,6 => CTR * .4.2.......8...3....918...29738.14.5...745.3..549....7.92..87.663...9.1448......3 H4: 4,5,8,9 # 8 pairs * PAIR E4: 2,6 COL E E9: 2,6,1,5,7 # reduction candidate for 2,6 E9: 2,6 => CTR * .4.2.......8...3...3918...2..3861.....6745.3..54932..73924187..675329814481..7..3 E9: 1,5,7 # 8 pairs * PAIR B8: 3,7 COL B B3: 3,7,6 # reduction candidate for 3,7 B3: 3,7 => SOLVED * 147293685268574391539186472723861549916745238854932167392418756675329814481657923 B3: 6 => CTR * .4.2.......84..3...6918...2.73621.....6745.3..54938.27.923.47..635879214487512..3 * PAIR C8: 5,7 BLK 7 C9: 5,7,1 # reduction candidate for 5,7 C9: 5,7 => CTR * .4.2.......84..3....918...2..3621......745.3..549381671923.47..63.8.921448.512693 C9: 1 # 12 pairs * PAIR C8: 5,7 ROW 8 E8: 5,7,2 # reduction candidate for 5,7 E8: 5,7 => CTR * .4.2.......84..3....918...2.73621......745.3.1549386275923147..6378.921448.5.2..3 E8: 2 => SOLVED * 147293685268574391539186472723861549916745238854932167392418756675329814481657923 * PAIR C8: 5,7 COL C C1: 5,7,1,6 # reduction candidate for 5,7 C1: 1,6 => CTR * .4.2.......84..3....918...2.73621......745.3.2549381671923647..635879214487512693 C1: 5,7 # 12 pairs * PAIR F7: 4,8 BLK 8 D7: 4,8,3 # reduction candidate for 4,8 D7: 4,8 => SOLVED * 147293685268574391539186472723861549916745238854932167392418756675329814481657923 D7: 3 => CTR * .4.2.......84..3....918...2.73621......745.3..54938.271923.47..63.879214487512..3 * PAIR D8: 3,8 BLK 8 D7: 3,8,4 # reduction candidate for 3,8 D7: 3,8 => CTR * .4.2.......84..3....918...2.73621......745.3..54938.27192..47..6...79214487512..3 D7: 4 => SOLVED * 147293685268574391539186472723861549916745238854932167392418756675329814481657923 * PAIR D9: 5,6 BLK 8 E7: 5,6,1 # reduction candidate for 5,6 E7: 5,6 => CTR * .4.2.......84..3....918...2..3621......745.3..549381671923.47..63.8.921448.512693 E7: 1 # 12 pairs E9: 5,6,1,2,7 # reduction candidate for 5,6 E9: 5,6 => SOLVED * 147293685268574391539186472723861549916745238854932167392418756675329814481657923 E9: 1,2,7 # 8 pairs * PAIR D9: 5,6 ROW 9 G9: 5,6,2,9 # reduction candidate for 5,6 G9: 5,6 => CTR * .4.2.......8...3....918...2..3621......745.3..54938.27.923.47..63.8.921448.5.2693 G9: 2,9 # 9 pairs H9: 5,6,2,9 # reduction candidate for 5,6 H9: 5,6 => CTR * .4.2.......84..3....918...2.73621......745.3.1549386275923.47..63.8.921448.5.2963 H9: 2,9 # 9 pairs * PAIR D9: 5,6 COL D D2: 5,6,4 # reduction candidate for 5,6 D2: 5,6 => SOLVED * 147293685268574391539186472723861549916745238854932167392418756675329814481657923 D2: 4 => CTR * .4.2.......84..3....918...2.73621......745.3..54938.27192..47..6...79214487512..3 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190312-absurd-base-pr-000.dot * REASONING * DIS # C1: 1,6 => CTR => C1: 5,7 * DIS # F6: 6,8 => CTR => F6: 2,3 * PRF # F6: 2,3 => SOL * DIS # G4: 6,8 => CTR => G4: 2,4,5,9 * DIS # H4: 6,8 => CTR => H4: 2,4,5,9 * DIS # I4: 6,8 => CTR => I4: 5,9 * DIS # E6: 2,6 => CTR => E6: 3 * PRF # F6: 2,6 => SOL * DIS # F6: 3,8 => CTR => F6: 2,6 * PRF # B4: 2,6 => SOL * DIS # B4: 7 => CTR => B4: 2,6 * DIS # G4: 2,6 => CTR => G4: 4,5,8,9 * DIS # H4: 2,6 => CTR => H4: 4,5,8,9 * DIS # E9: 2,6 => CTR => E9: 1,5,7 * PRF # B3: 3,7 => SOL * DIS # B3: 6 => CTR => B3: 3,7 * DIS # C9: 5,7 => CTR => C9: 1 * DIS # E8: 5,7 => CTR => E8: 2 * PRF # E8: 2 => SOL * DIS # C1: 1,6 => CTR => C1: 5,7 * PRF # D7: 4,8 => SOL * DIS # D7: 3 => CTR => D7: 4,8 * DIS # D7: 3,8 => CTR => D7: 4 * PRF # D7: 4 => SOL * DIS # E7: 5,6 => CTR => E7: 1 * PRF # E9: 5,6 => SOL * DIS # G9: 5,6 => CTR => G9: 2,9 * DIS # H9: 5,6 => CTR => H9: 2,9 * PRF # D2: 5,6 => SOL * DIS # D2: 4 => CTR => D2: 5,6 * CNT 30 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,C5,C8,D4,D8,D9,E4,F7) * .4.2.......8...3....918...2..3..1......745.3..549....7.92...7..6....9.1448......3 * PAIR C5: 1,6 BLK 4 B5: 1,6,2 # reduction candidate for 1,6 B5: 1,6 # 12 pairs B5: 2 # 10 pairs * PAIR C5: 1,6 ROW 5 G5: 1,6,2,8,9 # reduction candidate for 1,6 G5: 1,6 # 13 pairs I5: 1,6,8,9 # reduction candidate for 1,6 I5: 1,6 # 13 pairs * PAIR C5: 1,6 COL C C1: 1,6,5,7 # reduction candidate for 1,6 C1: 1,6 => CTR * .4.2.......84..3....918...2.73621......745.3.2549381671923647..635879214487512693 * PAIR RESTART * PAIR D4: 6,8 BLK 5 F6: 6,8,2,3 # reduction candidate for 6,8 F6: 6,8 => CTR * .452.......85..3....918...2.73821.....6745.3..54936.27592.1.7..6...59214481672..3 F6: 2,3 => SOLVED * 147293685268574391539186472723861549916745238854932167392418756675329814481657923 * DURATION: 0:00:06.436573 START: 04:28:30.648403 END: 04:28:37.084976 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190312-absurd-base-pr-001.dot * REASONING * DIS # C1: 1,6 => CTR => C1: 5,7 * DIS C1: 5,7 # F6: 6,8 => CTR => F6: 2,3 * PRF C1: 5,7 + F6: 2,3 => SOL * STA C1: 5,7 + F6: 2,3 * CNT 3 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190312, absurd
Solution
position: 147293685268574391539186472723861549916745238854932167392418756675329814481657923 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 # B5: 1,6 => UNS * INC # B5: 2 => UNS * INC # G5: 1,6 => UNS * INC # I5: 1,6 => UNS * DIS # C1: 1,6 => CTR => C1: 5,7 * INC # C1: 5,7 => UNS * DIS # F6: 6,8 => CTR => F6: 2,3 * PRF # F6: 2,3 => SOL * DIS # G4: 6,8 => CTR => G4: 2,4,5,9 * INC # G4: 2,4,5,9 => UNS * DIS # H4: 6,8 => CTR => H4: 2,4,5,9 * INC # H4: 2,4,5,9 => UNS * DIS # I4: 6,8 => CTR => I4: 5,9 * INC # I4: 5,9 => UNS * DIS # E6: 2,6 => CTR => E6: 3 * INC # E6: 3 => UNS * PRF # F6: 2,6 => SOL * DIS # F6: 3,8 => CTR => F6: 2,6 * PRF # B4: 2,6 => SOL * DIS # B4: 7 => CTR => B4: 2,6 * DIS # G4: 2,6 => CTR => G4: 4,5,8,9 * INC # G4: 4,5,8,9 => UNS * DIS # H4: 2,6 => CTR => H4: 4,5,8,9 * INC # H4: 4,5,8,9 => UNS * DIS # E9: 2,6 => CTR => E9: 1,5,7 * INC # E9: 1,5,7 => UNS * PRF # B3: 3,7 => SOL * DIS # B3: 6 => CTR => B3: 3,7 * DIS # C9: 5,7 => CTR => C9: 1 * INC # C9: 1 => UNS * DIS # E8: 5,7 => CTR => E8: 2 * PRF # E8: 2 => SOL * INC # C1: 5,7 => UNS * DIS # C1: 1,6 => CTR => C1: 5,7 * PRF # D7: 4,8 => SOL * DIS # D7: 3 => CTR => D7: 4,8 * DIS # D7: 3,8 => CTR => D7: 4 * PRF # D7: 4 => SOL * DIS # E7: 5,6 => CTR => E7: 1 * INC # E7: 1 => UNS * PRF # E9: 5,6 => SOL * INC # E9: 1,2,7 => UNS * DIS # G9: 5,6 => CTR => G9: 2,9 * INC # G9: 2,9 => UNS * DIS # H9: 5,6 => CTR => H9: 2,9 * INC # H9: 2,9 => UNS * PRF # D2: 5,6 => SOL * DIS # D2: 4 => CTR => D2: 5,6 * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B5: 1,6 => UNS * INC # B5: 2 => UNS * INC # G5: 1,6 => UNS * INC # I5: 1,6 => UNS * DIS # C1: 1,6 => CTR => C1: 5,7 * DIS C1: 5,7 # F6: 6,8 => CTR => F6: 2,3 * PRF C1: 5,7 + F6: 2,3 => SOL * STA C1: 5,7 + F6: 2,3 * CNT 7 HDP CHAINS / 6 HYP OPENED