Analysis of zz-www.sudokuoftheday.co.uk-20060618-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006
level: medium
position: ..3.2....1278..39.95....6......9.18.51...2..........3.74..5......1.349..3......7. initial
Autosolve
position: ..3.2....1278..39.95...36...3..9.18.51.3.2....7.....3.74..5...3..17349..395....7. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A1: 4 => SOL * DIS # A1: 6 => CTR => A1: 4,8 * PRF # I3: 1,2,7 => SOL * DIS # E5: 4,6 => CTR => E5: 7,8 * DIS # F4: 5,6 => CTR => F4: 7 * PRF # D1: 1,4 => SOL * DIS # E3: 1,4 => CTR => E3: 7 * DIS # H3: 1,4 => CTR => H3: 2 * PRF # I3: 1,4 => SOL * DIS # G1: 4,5 => CTR => G1: 7,8 * DIS # I1: 4,5 => CTR => I1: 1,7,8 * DIS # I4: 4,7 => CTR => I4: 2,5,6 * DIS # I5: 4,7 => CTR => I5: 6,9 * DIS # E5: 4,7 => CTR => E5: 6,8 * DIS # G1: 4,7 => CTR => G1: 5,8 * DIS # E5: 4,6 => CTR => E5: 7,8 * DIS # A8: 6,8 => CTR => A8: 2 * DIS # G9: 2,8 => CTR => G9: 4 * PRF # I9: 2,8 => SOL * CNT 19 HDP CHAINS / 57 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A1: 4 => SOL * STA A1: 4 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..3.2....1278..39.95....6......9.18.51...2..........3.74..5......1.349..3......7. | initial |
| ..3.2....1278..39.95...36...3..9.18.51.3.2....7.....3.74..5...3..17349..395....7. | autosolve |
| 463129857127865394958473621634597182519382746872641539746958213281734965395216478 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) B1: 6,8 C3: 4,8 E2: 4,6 F2: 5,6 D3: 1,4 I2: 4,5 G5: 4,7 H5: 4,6 B8: 6,8 G7: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H7,I9: 1.. / H7 = 1 => 17 pairs (_) / I9 = 1 => 19 pairs (_) H3,I3: 2.. / H3 = 2 => 12 pairs (_) / I3 = 2 => 0 pairs (X) C7,A8: 2.. / C7 = 2 => 0 pairs (X) / A8 = 2 => 13 pairs (_) D7,D9: 2.. / D7 = 2 => 0 pairs (X) / D9 = 2 => 11 pairs (_) A1,C3: 4.. / A1 = 4 => 0 pairs (*) / C3 = 4 => 0 pairs (X) G9,I9: 4.. / G9 = 4 => 11 pairs (_) / I9 = 4 => 0 pairs (X) E2,I2: 4.. / E2 = 4 => 0 pairs (X) / I2 = 4 => 0 pairs (_) H8,I8: 5.. / H8 = 5 => 11 pairs (_) / I8 = 5 => 0 pairs (*) F2,I2: 5.. / F2 = 5 => 0 pairs (*) / I2 = 5 => 0 pairs (X) G1,G6: 5.. / G1 = 5 => 0 pairs (X) / G6 = 5 => 16 pairs (_) H1,H8: 5.. / H1 = 5 => 0 pairs (*) / H8 = 5 => 0 pairs (X) A1,B1: 6.. / A1 = 6 => 0 pairs (X) / B1 = 6 => 11 pairs (_) E2,F2: 6.. / E2 = 6 => 0 pairs (*) / F2 = 6 => 0 pairs (X) B1,B8: 6.. / B1 = 6 => 11 pairs (_) / B8 = 6 => 0 pairs (X) F1,E3: 7.. / F1 = 7 => 0 pairs (X) / E3 = 7 => 10 pairs (_) F4,E5: 7.. / F4 = 7 => 10 pairs (_) / E5 = 7 => 0 pairs (X) E3,I3: 7.. / E3 = 7 => 10 pairs (_) / I3 = 7 => 0 pairs (X) F4,I4: 7.. / F4 = 7 => 10 pairs (_) / I4 = 7 => 0 pairs (X) E3,E5: 7.. / E3 = 7 => 10 pairs (_) / E5 = 7 => 0 pairs (X) F1,F4: 7.. / F1 = 7 => 0 pairs (X) / F4 = 7 => 10 pairs (_) G1,G5: 7.. / G1 = 7 => 0 pairs (X) / G5 = 7 => 9 pairs (_) C3,I3: 8.. / C3 = 8 => 0 pairs (*) / I3 = 8 => 0 pairs (X) C5,E5: 8.. / C5 = 8 => 0 pairs (X) / E5 = 8 => 11 pairs (_) B1,B8: 8.. / B1 = 8 => 0 pairs (X) / B8 = 8 => 11 pairs (_) D1,F1: 9.. / D1 = 9 => 12 pairs (_) / F1 = 9 => 12 pairs (_) C5,C6: 9.. / C5 = 9 => 13 pairs (_) / C6 = 9 => 10 pairs (_) I5,I6: 9.. / I5 = 9 => 10 pairs (_) / I6 = 9 => 13 pairs (_) D7,F7: 9.. / D7 = 9 => 12 pairs (_) / F7 = 9 => 12 pairs (_) C5,I5: 9.. / C5 = 9 => 13 pairs (_) / I5 = 9 => 10 pairs (_) C6,I6: 9.. / C6 = 9 => 10 pairs (_) / I6 = 9 => 13 pairs (_) D1,D7: 9.. / D1 = 9 => 12 pairs (_) / D7 = 9 => 12 pairs (_) F1,F7: 9.. / F1 = 9 => 12 pairs (_) / F7 = 9 => 12 pairs (_) * DURATION: 0:00:31.803165 START: 23:55:52.560254 END: 23:56:24.363419 2019-04-30 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B8,C3,D3,E2,F2,G5,G7,H5,I2) * ..3.2....1278..39.95...36...3..9.18.51.3.2....7.....3.74..5...3..17349..395....7. * PAIR B1: 6,8 BLK 1 A1: 6,8,4 # reduction candidate for 6,8 A1: 4 => SOLVED * 463129857127865394958473621634597182519382746872641539746958213281734965395216478 A1: 6,8 # 17 pairs * PAIR C3: 4,8 BLK 1 A1: 4,8,6 # reduction candidate for 4,8 A1: 6 => CTR * 683.2.5.71278.539495417362823649718551.3.274.47.5..23.7426598.38617349523952..47. A1: 4,8 # 11 pairs * PAIR C3: 4,8 ROW 3 I3: 4,8,1,2,7 # reduction candidate for 4,8 I3: 1,2,7 => SOLVED * 463129857127865394958473621634597182519382746872641539746958213281734965395216478 I3: 4,8 # 14 pairs * PAIR C3: 4,8 COL C C5: 4,8,6,9 # reduction candidate for 4,8 C5: 4,8 # 13 pairs C6: 4,8,2,6,9 # reduction candidate for 4,8 C6: 4,8 # 16 pairs * PAIR E2: 4,6 COL E E5: 4,6,7,8 # reduction candidate for 4,6 E5: 4,6 => CTR * ..3.2..171278..39.954173628.3..9718.5183.2749.79.18.3.74..51863..1734952395286471 E5: 7,8 # 11 pairs E6: 4,6,1,8 # reduction candidate for 4,6 E6: 4,6 # 14 pairs * PAIR F2: 5,6 COL F F4: 5,6,7 # reduction candidate for 5,6 F4: 5,6 => CTR * ..3.27...1278..39.95...36.7.3..9.18.51.372469.79....3.74..59..3..17349..395....74 F4: 7 # 10 pairs F6: 5,6,1,8 # reduction candidate for 5,6 F6: 5,6 # 14 pairs * PAIR D3: 1,4 BLK 2 D1: 1,4,5,9 # reduction candidate for 1,4 D1: 1,4 => SOLVED * 463129857127865394958473621634597182519382746872641539746958213281734965395216478 D1: 5,9 # 11 pairs E3: 1,4,7 # reduction candidate for 1,4 E3: 1,4 => CTR * ..3.27...1278..39.95...36.7.3..9.18.51.372469.79....3.74..59..3..17349..395....74 E3: 7 # 10 pairs * PAIR D3: 1,4 ROW 3 H3: 1,4,2 # reduction candidate for 1,4 H3: 1,4 => CTR * ..3.2.5..1278..39.95...36.2.3..9.18.51.3.2....7....23.74..5.8.3..17349..3952..47. H3: 2 # 12 pairs I3: 1,4,2,7,8 # reduction candidate for 1,4 I3: 1,4 => SOLVED * 463129857127865394958473621634597182519382746872641539746958213281734965395216478 I3: 2,7,8 # 10 pairs * PAIR D3: 1,4 COL D D6: 1,4,5,6 # reduction candidate for 1,4 D6: 1,4 # 14 pairs D6: 5,6 # 11 pairs * PAIR I2: 4,5 BLK 3 G1: 4,5,7,8 # reduction candidate for 4,5 G1: 4,5 => CTR * ..3.295171278.5394954173628.3..9718.51.3427...7..1..3.74..51.63..17349523952..471 G1: 7,8 # 17 pairs H1: 4,5,1 # reduction candidate for 4,5 H1: 4,5 # 17 pairs I1: 4,5,1,7,8 # reduction candidate for 4,5 I1: 4,5 => CTR * ..3.2..1.1278..39.95...362..3..9.18.51.3.274..7....53.74..5.2632617349583952..471 I1: 1,7,8 # 10 pairs * PAIR I2: 4,5 COL I I4: 4,5,2,6,7 # reduction candidate for 4,5 I4: 4,5 # 14 pairs I6: 4,5,2,6,9 # reduction candidate for 4,5 I6: 4,5 # 15 pairs * PAIR G5: 4,7 BLK 6 I4: 4,7,2,5,6 # reduction candidate for 4,7 I4: 4,7 => CTR * ..3.2....12784639595.1736...3..9718451438276987946153274..5..13..17349..395....7. I4: 2,5,6 # 10 pairs I5: 4,7,6,9 # reduction candidate for 4,7 I5: 4,7 => CTR * ..3925.41127846395954173628436597182519382.67.7.46153974.659813..173495.395.18.7. I5: 6,9 # 11 pairs * PAIR G5: 4,7 ROW 5 E5: 4,7,6,8 # reduction candidate for 4,7 E5: 4,7 => CTR * ..3.2....1278..39.954173628.3..9718.518342769.79....3.74..5..13..173495.395....7. E5: 6,8 # 11 pairs * PAIR G5: 4,7 COL G G1: 4,7,5,8 # reduction candidate for 4,7 G1: 4,7 => CTR * .63.2....127846395954173628.32.9718651.3.2....7....53.746.5..132817349..395....74 G1: 5,8 # 10 pairs * PAIR H5: 4,6 BLK 6 I4: 4,6,2,5,7 # reduction candidate for 4,6 I4: 4,6 # 12 pairs I5: 4,6,7,9 # reduction candidate for 4,6 I5: 4,6 # 13 pairs I6: 4,6,2,5,9 # reduction candidate for 4,6 I6: 4,6 # 12 pairs * PAIR H5: 4,6 ROW 5 C5: 4,6,8,9 # reduction candidate for 4,6 C5: 4,6 # 13 pairs E5: 4,6,7,8 # reduction candidate for 4,6 E5: 4,6 => CTR * ..3.2..171278..39.954173628.3..9718.5183.2749.79.18.3.74..51863..1734952395286471 E5: 7,8 # 11 pairs * PAIR B8: 6,8 BLK 7 C7: 6,8,2 # reduction candidate for 6,8 C7: 6,8 # 13 pairs A8: 6,8,2 # reduction candidate for 6,8 A8: 6,8 => CTR * ..3.2.5..1278.539495..736..23..9718.51.3.274..7..4.23.742.5.8.3..1734952395218476 A8: 2 # 13 pairs * PAIR B8: 6,8 ROW 8 I8: 6,8,2,5 # reduction candidate for 6,8 I8: 6,8 # 14 pairs I8: 2,5 # 12 pairs * PAIR G7: 2,8 BLK 9 I8: 2,8,5,6 # reduction candidate for 2,8 I8: 2,8 # 17 pairs G9: 2,8,4 # reduction candidate for 2,8 G9: 2,8 => CTR * .63.25.41127846395954173628.3.59718251.3.2467.7.461539746.5..13..1734956395....74 G9: 4 # 11 pairs I9: 2,8,1,4,6 # reduction candidate for 2,8 I9: 2,8 => SOLVED * 463129857127865394958473621634597182519382746872641539746958213281734965395216478 I9: 1,4,6 # 10 pairs * PAIR G7: 2,8 ROW 7 C7: 2,8,6 # reduction candidate for 2,8 C7: 2,8 # 16 pairs C7: 6 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060618-absurd-base-pr-000.dot * REASONING * PRF # A1: 4 => SOL * DIS # A1: 6 => CTR => A1: 4,8 * PRF # I3: 1,2,7 => SOL * DIS # E5: 4,6 => CTR => E5: 7,8 * DIS # F4: 5,6 => CTR => F4: 7 * PRF # D1: 1,4 => SOL * DIS # E3: 1,4 => CTR => E3: 7 * DIS # H3: 1,4 => CTR => H3: 2 * PRF # I3: 1,4 => SOL * DIS # G1: 4,5 => CTR => G1: 7,8 * DIS # I1: 4,5 => CTR => I1: 1,7,8 * DIS # I4: 4,7 => CTR => I4: 2,5,6 * DIS # I5: 4,7 => CTR => I5: 6,9 * DIS # E5: 4,7 => CTR => E5: 6,8 * DIS # G1: 4,7 => CTR => G1: 5,8 * DIS # E5: 4,6 => CTR => E5: 7,8 * DIS # A8: 6,8 => CTR => A8: 2 * DIS # G9: 2,8 => CTR => G9: 4 * PRF # I9: 2,8 => SOL * CNT 19 HDP CHAINS / 57 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B8,C3,D3,E2,F2,G5,G7,H5,I2) * ..3.2....1278..39.95...36...3..9.18.51.3.2....7.....3.74..5...3..17349..395....7. * PAIR B1: 6,8 BLK 1 A1: 6,8,4 # reduction candidate for 6,8 A1: 4 => SOLVED * 463129857127865394958473621634597182519382746872641539746958213281734965395216478 * DURATION: 0:00:02.396041 START: 23:56:56.221548 END: 23:56:58.617589 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060618-absurd-base-pr-001.dot * REASONING * PRF # A1: 4 => SOL * STA A1: 4 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060618, absurd
Solution
position: 463129857127865394958473621634597182519382746872641539746958213281734965395216478 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: 6,8 => UNS * PRF # A1: 4 => SOL * INC # A1: 4,8 => UNS * DIS # A1: 6 => CTR => A1: 4,8 * INC # I3: 4,8 => UNS * PRF # I3: 1,2,7 => SOL * INC # C5: 4,8 => UNS * INC # C6: 4,8 => UNS * DIS # E5: 4,6 => CTR => E5: 7,8 * INC # E5: 7,8 => UNS * INC # E6: 4,6 => UNS * DIS # F4: 5,6 => CTR => F4: 7 * INC # F4: 7 => UNS * INC # F6: 5,6 => UNS * PRF # D1: 1,4 => SOL * INC # D1: 5,9 => UNS * DIS # E3: 1,4 => CTR => E3: 7 * INC # E3: 7 => UNS * DIS # H3: 1,4 => CTR => H3: 2 * INC # H3: 2 => UNS * PRF # I3: 1,4 => SOL * INC # I3: 2,7,8 => UNS * INC # D6: 1,4 => UNS * INC # D6: 5,6 => UNS * DIS # G1: 4,5 => CTR => G1: 7,8 * INC # G1: 7,8 => UNS * INC # H1: 4,5 => UNS * DIS # I1: 4,5 => CTR => I1: 1,7,8 * INC # I1: 1,7,8 => UNS * INC # I4: 4,5 => UNS * INC # I6: 4,5 => UNS * DIS # I4: 4,7 => CTR => I4: 2,5,6 * INC # I4: 2,5,6 => UNS * DIS # I5: 4,7 => CTR => I5: 6,9 * INC # I5: 6,9 => UNS * DIS # E5: 4,7 => CTR => E5: 6,8 * INC # E5: 6,8 => UNS * DIS # G1: 4,7 => CTR => G1: 5,8 * INC # G1: 5,8 => UNS * INC # I4: 4,6 => UNS * INC # I5: 4,6 => UNS * INC # I6: 4,6 => UNS * INC # C5: 4,6 => UNS * DIS # E5: 4,6 => CTR => E5: 7,8 * INC # E5: 7,8 => UNS * INC # C7: 6,8 => UNS * DIS # A8: 6,8 => CTR => A8: 2 * INC # A8: 2 => UNS * INC # I8: 6,8 => UNS * INC # I8: 2,5 => UNS * INC # I8: 2,8 => UNS * DIS # G9: 2,8 => CTR => G9: 4 * INC # G9: 4 => UNS * PRF # I9: 2,8 => SOL * INC # I9: 1,4,6 => UNS * INC # C7: 2,8 => UNS * INC # C7: 6 => UNS * CNT 57 HDP CHAINS / 57 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 6,8 => UNS * PRF # A1: 4 => SOL * STA A1: 4 * CNT 2 HDP CHAINS / 2 HYP OPENED