Analysis of zz-www.sudokuoftheday.co.uk-20190427-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019
level: medium
position: .......5...9.1....3..5...48.2..6.....153..6..6...97......9.....4...365....2.4.37. initial
Autosolve
position: .......5..59.1....3..5.9.48.2..65....153..6..6...97..5...952...4..7365..5.284137. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 1 => CTR => C3: 6,7 * PRF # B7: 6,7 => SOL * DIS # D2: 2,6 => CTR => D2: 4 * DIS # I1: 2,6 => CTR => I1: 1,3,7,9 * DIS # F2: 4 => CTR => F2: 3,8 * DIS # E1: 8 => CTR => E1: 2,7 * DIS # G3: 2,7 => CTR => G3: 1 * PRF # G1: 2,7 => SOL * DIS # I1: 2,7 => CTR => I1: 1,3,6,9 * DIS # I2: 2,7 => CTR => I2: 3,6 * DIS # G3: 2,7 => CTR => G3: 1 * DIS # A2: 8 => CTR => A2: 2,7 * DIS # A4: 7,9 => CTR => A4: 8 * DIS # I5: 2,4 => CTR => I5: 7,9 * DIS # D6: 1,4 => CTR => D6: 2 * DIS # E1: 2,8 => CTR => E1: 7 * DIS # F2: 3 => CTR => F2: 4,8 * DIS # I5: 2,9 => CTR => I5: 4,7 * DIS # H8: 1,8 => CTR => H8: 2,9 * PRF # H8: 8,9 => SOL * DIS # A7: 1,8 => CTR => A7: 7 * PRF # A7: 7 => SOL * DIS # C7: 1,8 => CTR => C7: 3,6,7 * DIS # H8: 1,8 => CTR => H8: 2,9 * CNT 24 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 1 => CTR => C3: 6,7 * PRF C3: 6,7 # B7: 6,7 => SOL * STA C3: 6,7 + B7: 6,7 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......5...9.1....3..5...48.2..6.....153..6..6...97......9.....4...365....2.4.37. | initial |
| .......5..59.1....3..5.9.48.2..65....153..6..6...97..5...952...4..7365..5.284137. | autosolve |
| 148673259259418763376529148827165934915384627634297815763952481481736592592841376 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B3: 6,7 D1: 2,6 F1: 3,8 E3: 2,7 G2: 2,7 A5: 7,9 D4: 1,4 E5: 2,8 F5: 4,8 H5: 2,9 B8: 8,9 C8: 1,8 B9: 6,9 I9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D4,D6: 1.. / D4 = 1 => 14 pairs (_) / D6 = 1 => 0 pairs (X) C3,G3: 1.. / C3 = 1 => 0 pairs (X) / G3 = 1 => 24 pairs (_) A1,A7: 1.. / A1 = 1 => 0 pairs (*) / A7 = 1 => 0 pairs (X) A1,A2: 2.. / A1 = 2 => 0 pairs (X) / A2 = 2 => 13 pairs (_) E5,D6: 2.. / E5 = 2 => 0 pairs (X) / D6 = 2 => 13 pairs (_) H8,I8: 2.. / H8 = 2 => 0 pairs (X) / I8 = 2 => 14 pairs (_) E3,G3: 2.. / E3 = 2 => 13 pairs (_) / G3 = 2 => 0 pairs (X) F1,F2: 3.. / F1 = 3 => 14 pairs (_) / F2 = 3 => 0 pairs (X) B7,C7: 3.. / B7 = 3 => 18 pairs (_) / C7 = 3 => 0 pairs (*) F1,I1: 3.. / F1 = 3 => 14 pairs (_) / I1 = 3 => 0 pairs (X) B6,B7: 3.. / B6 = 3 => 0 pairs (*) / B7 = 3 => 0 pairs (X) B1,C1: 4.. / B1 = 4 => 15 pairs (_) / C1 = 4 => 20 pairs (_) D2,F2: 4.. / D2 = 4 => 13 pairs (_) / F2 = 4 => 0 pairs (X) G7,I7: 4.. / G7 = 4 => 15 pairs (_) / I7 = 4 => 14 pairs (_) F5,I5: 4.. / F5 = 4 => 13 pairs (_) / I5 = 4 => 0 pairs (X) B1,B6: 4.. / B1 = 4 => 15 pairs (_) / B6 = 4 => 20 pairs (_) F2,F5: 4.. / F2 = 4 => 0 pairs (X) / F5 = 4 => 13 pairs (_) B3,C3: 6.. / B3 = 6 => 0 pairs (X) / C3 = 6 => 23 pairs (_) D1,D2: 6.. / D1 = 6 => 14 pairs (_) / D2 = 6 => 0 pairs (X) D1,I1: 6.. / D1 = 6 => 14 pairs (_) / I1 = 6 => 0 pairs (X) B9,I9: 6.. / B9 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) C3,C7: 6.. / C3 = 6 => 23 pairs (_) / C7 = 6 => 0 pairs (X) H2,H7: 6.. / H2 = 6 => 15 pairs (_) / H7 = 6 => 0 pairs (X) E1,E3: 7.. / E1 = 7 => 13 pairs (_) / E3 = 7 => 0 pairs (X) A5,I5: 7.. / A5 = 7 => 0 pairs (X) / I5 = 7 => 13 pairs (_) E5,F5: 8.. / E5 = 8 => 13 pairs (_) / F5 = 8 => 0 pairs (X) A2,F2: 8.. / A2 = 8 => 0 pairs (X) / F2 = 8 => 13 pairs (_) E1,E5: 8.. / E1 = 8 => 0 pairs (X) / E5 = 8 => 13 pairs (_) G1,I1: 9.. / G1 = 9 => 14 pairs (_) / I1 = 9 => 0 pairs (*) A4,A5: 9.. / A4 = 9 => 0 pairs (X) / A5 = 9 => 13 pairs (_) B8,B9: 9.. / B8 = 9 => 0 pairs (X) / B9 = 9 => 0 pairs (_) B9,I9: 9.. / B9 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) G1,G4: 9.. / G1 = 9 => 14 pairs (_) / G4 = 9 => 0 pairs (*) * DURATION: 0:00:36.475378 START: 05:38:14.105481 END: 05:38:50.580859 2019-05-01 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B3,B8,B9,C8,D1,D4,E3,E5,F1,F5,G2,H5,I9) * .......5..59.1....3..5.9.48.2..65....153..6..6...97..5...952...4..7365..5.284137. * PAIR B3: 6,7 BLK 1 C3: 6,7,1 # reduction candidate for 6,7 C3: 1 => CTR * .......5..59.1....3615.9.48.2..65....153..6..6...97..51.6952.8.4..7365..5.284137. C3: 6,7 # 24 pairs * PAIR B3: 6,7 COL B B7: 6,7,3,8 # reduction candidate for 6,7 B7: 6,7 => SOLVED * 148673259259418763376529148827165934915384627634297815763952481481736592592841376 B7: 3,8 # 18 pairs * PAIR D1: 2,6 BLK 2 D2: 2,6,4 # reduction candidate for 2,6 D2: 2,6 => CTR * ....83.5.859.14...3..579248.2..65...7153286946...97.251..9524.64.87365..5.284137. D2: 4 # 13 pairs * PAIR D1: 2,6 ROW 1 I1: 2,6,1,3,7,9 # reduction candidate for 2,6 I1: 2,6 => CTR * ...6739522594187..3..529148.2.165....1538462.6..297.15...952...4..7365..5.284137. I1: 1,3,7,9 # 14 pairs * PAIR F1: 3,8 BLK 2 F2: 3,8,4 # reduction candidate for 3,8 F2: 4 => CTR * 2..683.5.8592147..3..579248.2..65..77153286946...97.251..9524.64.87365..5.284137. F2: 3,8 # 13 pairs * PAIR E3: 2,7 BLK 2 E1: 2,7,8 # reduction candidate for 2,7 E1: 8 => CTR * ....83.5.859.14...3..579248.2..65....153286946...97.25...9524..4..7365.25.2841379 E1: 2,7 # 13 pairs * PAIR E3: 2,7 ROW 3 G3: 2,7,1 # reduction candidate for 2,7 G3: 2,7 => CTR * .......5..59.1....3.15.9.48.2..65....153..6..6...97..51.6952.8.4..7365..5.284137. G3: 1 # 24 pairs * PAIR G2: 2,7 BLK 3 G1: 2,7,1,9 # reduction candidate for 2,7 G1: 2,7 => SOLVED * 148673259259418763376529148827165934915384627634297815763952481481736592592841376 G1: 1,9 # 15 pairs I1: 2,7,1,3,6,9 # reduction candidate for 2,7 I1: 2,7 => CTR * ...6739522594187..3..529148.2.165....1538462.6..297.15...952...4..7365..5.284137. I1: 1,3,6,9 # 14 pairs I2: 2,7,3,6 # reduction candidate for 2,7 I2: 2,7 => CTR * 2416789538594132673..529148.2.165....153846..6..297.151..952.8.4.87365.15.284137. I2: 3,6 # 15 pairs G3: 2,7,1 # reduction candidate for 2,7 G3: 2,7 => CTR * .......5..59.1....3.15.9.48.2..65....153..6..6...97..51.6952.8.4..7365..5.284137. G3: 1 # 24 pairs * PAIR G2: 2,7 ROW 2 A2: 2,7,8 # reduction candidate for 2,7 A2: 8 => CTR * 2416..95.859.1....376529148.2..65....153846..68.297415137952864498736521562841379 A2: 2,7 # 13 pairs * PAIR A5: 7,9 BLK 4 A4: 7,9,8 # reduction candidate for 7,9 A4: 7,9 => CTR * 2.167.9538594132673765291489241657..7153846926.3297.15.37952..649.736521562841379 A4: 8 # 22 pairs * PAIR A5: 7,9 ROW 5 I5: 7,9,2,4 # reduction candidate for 7,9 I5: 2,4 => CTR * 2.167.95385941326737652914892.16573471538469268.297.15.37952...49.736521562841379 I5: 7,9 # 13 pairs * PAIR D4: 1,4 BLK 5 D6: 1,4,2 # reduction candidate for 1,4 D6: 1,4 => CTR * ....8395.859.14...3..57924892..65...7153286946...97.251..9524.64.87365..5.284137. D6: 2 # 13 pairs * PAIR D4: 1,4 ROW 4 G4: 1,4,7,8,9 # reduction candidate for 1,4 G4: 1,4 # 16 pairs I4: 1,4,3,7,9 # reduction candidate for 1,4 I4: 1,4 # 19 pairs * PAIR E5: 2,8 COL E E1: 2,8,7 # reduction candidate for 2,8 E1: 2,8 => CTR * .......5..59.1.7..361579248.2..65....153..6..6...97..51.6952.8.4..7365..5.284137. E1: 7 # 13 pairs * PAIR F5: 4,8 COL F F2: 4,8,3 # reduction candidate for 4,8 F2: 3 => CTR * 2..6789538594132673..529148.2.16578..153846..6..297..51..952...4.87365.15.284137. F2: 4,8 # 14 pairs * PAIR H5: 2,9 BLK 6 I5: 2,9,4,7 # reduction candidate for 2,9 I5: 2,9 => CTR * ..167.953.5941326737652914892.1657..7153846..6..297.15.37952...498736521562841379 I5: 4,7 # 15 pairs * PAIR H5: 2,9 COL H H8: 2,9,1,8 # reduction candidate for 2,9 H8: 1,8 => CTR * ......95..59.1....376529148.2..65....153846276..297.15...952..1491736582562841379 H8: 2,9 # 17 pairs * PAIR B8: 8,9 ROW 8 H8: 8,9,1,2 # reduction candidate for 8,9 H8: 8,9 => SOLVED * 148673259259418763376529148827165934915384627634297815763952481481736592592841376 H8: 1,2 # 16 pairs * PAIR C8: 1,8 BLK 7 A7: 1,8,7 # reduction candidate for 1,8 A7: 1,8 => CTR * 2.167.9538594132673765291489241657..7153846926.3297.15.37952..649.736521562841379 A7: 7 => SOLVED * 148673259259418763376529148827165934915384627634297815763952481481736592592841376 C7: 1,8,3,6,7 # reduction candidate for 1,8 C7: 1,8 => CTR * ......95..59.1....376529148.27.65...9153846276.3297.1573.952...49.736582562841379 C7: 3,6,7 # 14 pairs * PAIR C8: 1,8 ROW 8 H8: 1,8,2,9 # reduction candidate for 1,8 H8: 1,8 => CTR * ......95..59.1....376529148.2..65....153846276..297.15...952..1491736582562841379 H8: 2,9 # 17 pairs * PAIR C8: 1,8 COL C C1: 1,8,4,7 # reduction candidate for 1,8 C1: 1,8 # 27 pairs C1: 4,7 # 15 pairs * PAIR I9: 6,9 COL I I1: 6,9,1,2,3,7 # reduction candidate for 6,9 I1: 6,9 # 18 pairs I1: 1,2,3,7 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190427-absurd-base-pr-000.dot * REASONING * DIS # C3: 1 => CTR => C3: 6,7 * PRF # B7: 6,7 => SOL * DIS # D2: 2,6 => CTR => D2: 4 * DIS # I1: 2,6 => CTR => I1: 1,3,7,9 * DIS # F2: 4 => CTR => F2: 3,8 * DIS # E1: 8 => CTR => E1: 2,7 * DIS # G3: 2,7 => CTR => G3: 1 * PRF # G1: 2,7 => SOL * DIS # I1: 2,7 => CTR => I1: 1,3,6,9 * DIS # I2: 2,7 => CTR => I2: 3,6 * DIS # G3: 2,7 => CTR => G3: 1 * DIS # A2: 8 => CTR => A2: 2,7 * DIS # A4: 7,9 => CTR => A4: 8 * DIS # I5: 2,4 => CTR => I5: 7,9 * DIS # D6: 1,4 => CTR => D6: 2 * DIS # E1: 2,8 => CTR => E1: 7 * DIS # F2: 3 => CTR => F2: 4,8 * DIS # I5: 2,9 => CTR => I5: 4,7 * DIS # H8: 1,8 => CTR => H8: 2,9 * PRF # H8: 8,9 => SOL * DIS # A7: 1,8 => CTR => A7: 7 * PRF # A7: 7 => SOL * DIS # C7: 1,8 => CTR => C7: 3,6,7 * DIS # H8: 1,8 => CTR => H8: 2,9 * CNT 24 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B3,B8,B9,C8,D1,D4,E3,E5,F1,F5,G2,H5,I9) * .......5..59.1....3..5.9.48.2..65....153..6..6...97..5...952...4..7365..5.284137. * PAIR B3: 6,7 BLK 1 C3: 6,7,1 # reduction candidate for 6,7 C3: 1 => CTR * .......5..59.1....3615.9.48.2..65....153..6..6...97..51.6952.8.4..7365..5.284137. * PAIR B3: 6,7 COL B B7: 6,7,3 # reduction candidate for 6,7 B7: 6,7 => SOLVED * 148673259259418763376529148827165934915384627634297815763952481481736592592841376 * DURATION: 0:00:02.998335 START: 05:39:22.271352 END: 05:39:25.269687 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190427-absurd-base-pr-001.dot * REASONING * DIS # C3: 1 => CTR => C3: 6,7 * PRF C3: 6,7 # B7: 6,7 => SOL * STA C3: 6,7 + B7: 6,7 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190427, absurd
Solution
position: 148673259259418763376529148827165934915384627634297815763952481481736592592841376 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 # C3: 6,7 => UNS * DIS # C3: 1 => CTR => C3: 6,7 * PRF # B7: 6,7 => SOL * INC # B7: 3,8 => UNS * DIS # D2: 2,6 => CTR => D2: 4 * INC # D2: 4 => UNS * DIS # I1: 2,6 => CTR => I1: 1,3,7,9 * INC # I1: 1,3,7,9 => UNS * INC # F2: 3,8 => UNS * DIS # F2: 4 => CTR => F2: 3,8 * INC # E1: 2,7 => UNS * DIS # E1: 8 => CTR => E1: 2,7 * DIS # G3: 2,7 => CTR => G3: 1 * INC # G3: 1 => UNS * PRF # G1: 2,7 => SOL * INC # G1: 1,9 => UNS * DIS # I1: 2,7 => CTR => I1: 1,3,6,9 * INC # I1: 1,3,6,9 => UNS * DIS # I2: 2,7 => CTR => I2: 3,6 * INC # I2: 3,6 => UNS * DIS # G3: 2,7 => CTR => G3: 1 * INC # G3: 1 => UNS * INC # A2: 2,7 => UNS * DIS # A2: 8 => CTR => A2: 2,7 * DIS # A4: 7,9 => CTR => A4: 8 * INC # A4: 8 => UNS * INC # I5: 7,9 => UNS * DIS # I5: 2,4 => CTR => I5: 7,9 * DIS # D6: 1,4 => CTR => D6: 2 * INC # D6: 2 => UNS * INC # G4: 1,4 => UNS * INC # I4: 1,4 => UNS * DIS # E1: 2,8 => CTR => E1: 7 * INC # E1: 7 => UNS * INC # F2: 4,8 => UNS * DIS # F2: 3 => CTR => F2: 4,8 * DIS # I5: 2,9 => CTR => I5: 4,7 * INC # I5: 4,7 => UNS * INC # H8: 2,9 => UNS * DIS # H8: 1,8 => CTR => H8: 2,9 * PRF # H8: 8,9 => SOL * INC # H8: 1,2 => UNS * DIS # A7: 1,8 => CTR => A7: 7 * PRF # A7: 7 => SOL * DIS # C7: 1,8 => CTR => C7: 3,6,7 * INC # C7: 3,6,7 => UNS * DIS # H8: 1,8 => CTR => H8: 2,9 * INC # H8: 2,9 => UNS * INC # C1: 1,8 => UNS * INC # C1: 4,7 => UNS * INC # I1: 6,9 => UNS * INC # I1: 1,2,3,7 => UNS * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 6,7 => UNS * DIS # C3: 1 => CTR => C3: 6,7 * PRF C3: 6,7 # B7: 6,7 => SOL * STA C3: 6,7 + B7: 6,7 * CNT 3 HDP CHAINS / 3 HYP OPENED