Analysis of zz-www.sudokuoftheday.co.uk-20060723-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006
level: medium
position: 5.87........5.........1.56...9...4.3....7..2931.4.....7....8..4.34..7.1...5..12.. initial
Autosolve
position: 5.87....11..5.........1.56...91..4.3..6.7.12931.4.....7.1..8..4.34..7.1...5.412.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G2: 3,9 => CTR => G2: 7,8 * DIS # G7: 6 => CTR => G7: 3,9 * DIS # B4: 2,8 => CTR => B4: 5,7 * PRF # B5: 4,8 => SOL * DIS # B5: 5 => CTR => B5: 4,8 * DIS # B4: 2,7 => CTR => B4: 5,8 * DIS # C3: 2,7 => CTR => C3: 3 * DIS # D3: 2,9 => CTR => D3: 3,8 * DIS # D7: 2,9 => CTR => D7: 3,6 * DIS # E7: 2,9 => CTR => E7: 3,5 * DIS # B3: 2,9 => CTR => B3: 4,7 * DIS # H9: 8,9 => CTR => H9: 3,7 * CNT 12 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G2: 3,9 => CTR => G2: 7,8 * DIS G2: 7,8 # G7: 6 => CTR => G7: 3,9 * DIS G2: 7,8 + G7: 3,9 # B4: 2,8 => CTR => B4: 5,7 * DIS G2: 7,8 + G7: 3,9 + B4: 5,7 # A8: 2,8 => CTR => A8: 6,9 * PRF G2: 7,8 + G7: 3,9 + B4: 5,7 + A8: 6,9 # B5: 4,8 => SOL * STA G2: 7,8 + G7: 3,9 + B4: 5,7 + A8: 6,9 + B5: 4,8 * CNT 5 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5.87........5.........1.56...9...4.3....7..2931.4.....7....8..4.34..7.1...5..12.. | initial |
| 5.87....11..5.........1.56...91..4.3..6.7.12931.4.....7.1..8..4.34..7.1...5.412.. | autosolve |
| 568724391192563748473819562259186473846375129317492685721638954934257816685941237 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) G1: 3,9 A4: 2,8 A5: 4,8 C6: 2,7 D5: 3,8 F5: 3,5 B7: 2,9 B9: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I2,I3: 2.. / I2 = 2 => 10 pairs (_) / I3 = 2 => 0 pairs (*) B7,A8: 2.. / B7 = 2 => 8 pairs (_) / A8 = 2 => 0 pairs (X) C2,C3: 3.. / C2 = 3 => 0 pairs (X) / C3 = 3 => 9 pairs (_) D5,F5: 3.. / D5 = 3 => 0 pairs (*) / F5 = 3 => 0 pairs (X) D9,H9: 3.. / D9 = 3 => 0 pairs (X) / H9 = 3 => 21 pairs (_) H1,H2: 4.. / H1 = 4 => 8 pairs (_) / H2 = 4 => 11 pairs (_) A5,B5: 4.. / A5 = 4 => 9 pairs (_) / B5 = 4 => 0 pairs (*) A3,A5: 4.. / A3 = 4 => 0 pairs (*) / A5 = 4 => 0 pairs (X) B4,B5: 5.. / B4 = 5 => 0 pairs (*) / B5 = 5 => 0 pairs (X) E7,E8: 5.. / E7 = 5 => 0 pairs (X) / E8 = 5 => 19 pairs (_) H7,I8: 5.. / H7 = 5 => 19 pairs (_) / I8 = 5 => 0 pairs (X) B5,F5: 5.. / B5 = 5 => 0 pairs (X) / F5 = 5 => 0 pairs (_) E7,H7: 5.. / E7 = 5 => 0 pairs (X) / H7 = 5 => 19 pairs (_) E8,I8: 5.. / E8 = 5 => 19 pairs (_) / I8 = 5 => 0 pairs (X) I6,I8: 5.. / I6 = 5 => 19 pairs (_) / I8 = 5 => 0 pairs (X) B1,B2: 6.. / B1 = 6 => 9 pairs (_) / B2 = 6 => 8 pairs (_) E4,F4: 6.. / E4 = 6 => 9 pairs (_) / F4 = 6 => 12 pairs (_) G6,I6: 6.. / G6 = 6 => 17 pairs (_) / I6 = 6 => 0 pairs (X) A8,A9: 6.. / A8 = 6 => 14 pairs (_) / A9 = 6 => 12 pairs (_) D7,G7: 6.. / D7 = 6 => 13 pairs (_) / G7 = 6 => 0 pairs (X) B4,C6: 7.. / B4 = 7 => 0 pairs (X) / C6 = 7 => 21 pairs (_) H9,I9: 7.. / H9 = 7 => 0 pairs (X) / I9 = 7 => 13 pairs (_) B4,H4: 7.. / B4 = 7 => 0 pairs (X) / H4 = 7 => 21 pairs (_) G2,G6: 7.. / G2 = 7 => 14 pairs (_) / G6 = 7 => 0 pairs (X) E2,D3: 8.. / E2 = 8 => 0 pairs (X) / D3 = 8 => 0 pairs (_) D3,I3: 8.. / D3 = 8 => 0 pairs (*) / I3 = 8 => 0 pairs (X) D3,D5: 8.. / D3 = 8 => 0 pairs (*) / D5 = 8 => 0 pairs (X) E6,F6: 9.. / E6 = 9 => 11 pairs (_) / F6 = 9 => 10 pairs (_) * DURATION: 0:00:30.572054 START: 00:55:09.192649 END: 00:55:39.764703 2019-05-01 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,B7,B9,C6,D5,F5,G1) * 5.87....11..5.........1.56...91..4.3..6.7.12931.4.....7.1..8..4.34..7.1...5.412.. * PAIR G1: 3,9 BLK 3 H1: 3,9,4 # reduction candidate for 3,9 H1: 3,9 # 11 pairs G2: 3,9,7,8 # reduction candidate for 3,9 G2: 3,9 => CTR * 5.87...411.35..97...731.5688791..4534568731293124957867.1.58634.34.27815.85.41297 G2: 7,8 # 9 pairs H2: 3,9,4,7,8 # reduction candidate for 3,9 H2: 3,9 # 10 pairs * PAIR G1: 3,9 ROW 1 E1: 3,9,2,6 # reduction candidate for 3,9 E1: 3,9 # 11 pairs F1: 3,9,2,4,6 # reduction candidate for 3,9 F1: 3,9 # 11 pairs * PAIR G1: 3,9 COL G G7: 3,9,6 # reduction candidate for 3,9 G7: 6 => CTR * 5.873.9411..58.372..3.1.568..91..4.345687312931.4....67.1.586.4.34..7.15..5.412.7 G7: 3,9 # 13 pairs * PAIR A4: 2,8 BLK 4 B4: 2,8,5,7 # reduction candidate for 2,8 B4: 2,8 => CTR * 5.87..3.11.358.7.2972314568..91654734568731293174..6..7.1.38.54.34.57.166.5941237 B4: 5,7 # 9 pairs * PAIR A4: 2,8 ROW 4 E4: 2,8,6 # reduction candidate for 2,8 E4: 2,8 # 12 pairs E4: 6 # 9 pairs * PAIR A4: 2,8 COL A A8: 2,8,6,9 # reduction candidate for 2,8 A8: 2,8 # 14 pairs A8: 6,9 # 10 pairs * PAIR A5: 4,8 BLK 4 B5: 4,8,5 # reduction candidate for 4,8 B5: 4,8 => SOLVED * 568724391192563748473819562259186473846375129317492685721638954934257816685941237 B5: 5 => CTR * 5.87..3.11.358...2...31.568..91.54734568731293174..6857.1638954934257816685941237 * PAIR C6: 2,7 BLK 4 B4: 2,7,5,8 # reduction candidate for 2,7 B4: 2,7 => CTR * 5.87..3.11.358...2...31.5688.91.54734568731293174..6857.1638954934257816685941237 B4: 5,8 # 20 pairs * PAIR C6: 2,7 COL C C2: 2,7,3 # reduction candidate for 2,7 C2: 2,7 # 9 pairs C3: 2,7,3 # reduction candidate for 2,7 C3: 2,7 => CTR * 5.87..3.11.358.7.2...31.5688.91.5473..687312931.4..685721638954934257816685941237 C3: 3 # 9 pairs * PAIR D5: 3,8 COL D D3: 3,8,2,9 # reduction candidate for 3,8 D3: 2,9 => CTR * 5.873.9411.758.3.2..3.1.568..916.4.3456873129312495...7.1..8..4.34..7.15..5.412.. D3: 3,8 # 17 pairs * PAIR B7: 2,9 BLK 7 A8: 2,9,6,8 # reduction candidate for 2,9 A8: 2,9 # 17 pairs A8: 6,8 # 10 pairs * PAIR B7: 2,9 ROW 7 D7: 2,9,3,6 # reduction candidate for 2,9 D7: 2,9 => CTR * 5.873.9411..58.372..3.1.568..91..4.345687312931.4....67.1.58634.346.7.156.53412.7 D7: 3,6 # 9 pairs E7: 2,9,3,5 # reduction candidate for 2,9 E7: 2,9 => CTR * 5.87..9.11..58.7.2..3.1.56...91..4.3..687312931.4..6857.16.8354.34.57816685341297 E7: 3,5 # 9 pairs * PAIR B7: 2,9 COL B B1: 2,9,4,6 # reduction candidate for 2,9 B1: 2,9 # 13 pairs B2: 2,9,4,6,7 # reduction candidate for 2,9 B2: 2,9 # 15 pairs B3: 2,9,4,7 # reduction candidate for 2,9 B3: 2,9 => CTR * 5.87....11..5.......7.1.56..791.54838.6.7.12931.4....57.1.38.54.34.57.1..85.41237 B3: 4,7 # 9 pairs * PAIR B9: 8,9 BLK 7 A8: 8,9,2,6 # reduction candidate for 8,9 A8: 8,9 # 16 pairs A9: 8,9,6 # reduction candidate for 8,9 A9: 8,9 # 14 pairs * PAIR B9: 8,9 ROW 9 H9: 8,9,3,7 # reduction candidate for 8,9 H9: 8,9 => CTR * 5.873.9411.758.3.2..3.1.568..91..4.3456873129312495..67.1..8..4.34..7.156.53412.7 H9: 3,7 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060723-absurd-base-pr-000.dot * REASONING * DIS # G2: 3,9 => CTR => G2: 7,8 * DIS # G7: 6 => CTR => G7: 3,9 * DIS # B4: 2,8 => CTR => B4: 5,7 * PRF # B5: 4,8 => SOL * DIS # B5: 5 => CTR => B5: 4,8 * DIS # B4: 2,7 => CTR => B4: 5,8 * DIS # C3: 2,7 => CTR => C3: 3 * DIS # D3: 2,9 => CTR => D3: 3,8 * DIS # D7: 2,9 => CTR => D7: 3,6 * DIS # E7: 2,9 => CTR => E7: 3,5 * DIS # B3: 2,9 => CTR => B3: 4,7 * DIS # H9: 8,9 => CTR => H9: 3,7 * CNT 12 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,B7,B9,C6,D5,F5,G1) * 5.87....11..5.........1.56...91..4.3..6.7.12931.4.....7.1..8..4.34..7.1...5.412.. * PAIR G1: 3,9 BLK 3 H1: 3,9,4 # reduction candidate for 3,9 H1: 3,9 # 11 pairs G2: 3,9,7,8 # reduction candidate for 3,9 G2: 3,9 => CTR * 5.87...411.35..97...731.5688791..4534568731293124957867.1.58634.34.27815.85.41297 H2: 3,9,4 # reduction candidate for 3,9 H2: 3,9 # 10 pairs * PAIR G1: 3,9 ROW 1 E1: 3,9,2,6 # reduction candidate for 3,9 E1: 3,9 # 13 pairs F1: 3,9,2,4,6 # reduction candidate for 3,9 F1: 3,9 # 13 pairs * PAIR G1: 3,9 COL G G7: 3,9,6 # reduction candidate for 3,9 G7: 6 => CTR * 5.87..3.11..53....9...1.56...91..4.3..6.7.12931.4....67.1.586348346279156953412.. * PAIR RESTART * PAIR G1: 3,9 BLK 3 H1: 3,9,4 # reduction candidate for 3,9 H1: 3,9 # 15 pairs H2: 3,9,4 # reduction candidate for 3,9 H2: 3,9 # 14 pairs * PAIR G1: 3,9 ROW 1 E1: 3,9,2,6 # reduction candidate for 3,9 E1: 3,9 # 17 pairs F1: 3,9,2,4,6 # reduction candidate for 3,9 F1: 3,9 # 17 pairs * PAIR A4: 2,8 BLK 4 B4: 2,8,5,7 # reduction candidate for 2,8 B4: 2,8 => CTR * 5.87..3.11.358.7.29723145682891654734568731293174.....7.1638954.34257.166.5941237 * PAIR A4: 2,8 ROW 4 E4: 2,8,6 # reduction candidate for 2,8 E4: 2,8 # 17 pairs E4: 6 # 15 pairs * PAIR A4: 2,8 COL A A8: 2,8,6,9 # reduction candidate for 2,8 A8: 2,8 => CTR * 5287..9.116.58974294.21.568..91..4.34.687312931.4.....7.16.8..4.349.7.1.685341297 * PAIR RESTART * PAIR A4: 2,8 ROW 4 E4: 2,8,6 # reduction candidate for 2,8 E4: 2,8 # 19 pairs E4: 6 # 17 pairs * PAIR A5: 4,8 BLK 4 B5: 4,8,5 # reduction candidate for 4,8 B5: 4,8 => SOLVED * 568724391192563748473819562259186473846375129317492685721638954934257816685941237 * DURATION: 0:00:13.155721 START: 00:56:01.984637 END: 00:56:15.140358 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060723-absurd-base-pr-001.dot * REASONING * DIS # G2: 3,9 => CTR => G2: 7,8 * DIS G2: 7,8 # G7: 6 => CTR => G7: 3,9 * DIS G2: 7,8 + G7: 3,9 # B4: 2,8 => CTR => B4: 5,7 * DIS G2: 7,8 + G7: 3,9 + B4: 5,7 # A8: 2,8 => CTR => A8: 6,9 * PRF G2: 7,8 + G7: 3,9 + B4: 5,7 + A8: 6,9 # B5: 4,8 => SOL * STA G2: 7,8 + G7: 3,9 + B4: 5,7 + A8: 6,9 + B5: 4,8 * CNT 5 HDP CHAINS / 18 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060723, absurd
Solution
position: 568724391192563748473819562259186473846375129317492685721638954934257816685941237 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 # H1: 3,9 => UNS * DIS # G2: 3,9 => CTR => G2: 7,8 * INC # G2: 7,8 => UNS * INC # H2: 3,9 => UNS * INC # E1: 3,9 => UNS * INC # F1: 3,9 => UNS * INC # G7: 3,9 => UNS * DIS # G7: 6 => CTR => G7: 3,9 * DIS # B4: 2,8 => CTR => B4: 5,7 * INC # B4: 5,7 => UNS * INC # E4: 2,8 => UNS * INC # E4: 6 => UNS * INC # A8: 2,8 => UNS * INC # A8: 6,9 => UNS * PRF # B5: 4,8 => SOL * DIS # B5: 5 => CTR => B5: 4,8 * DIS # B4: 2,7 => CTR => B4: 5,8 * INC # B4: 5,8 => UNS * INC # C2: 2,7 => UNS * DIS # C3: 2,7 => CTR => C3: 3 * INC # C3: 3 => UNS * INC # D3: 3,8 => UNS * DIS # D3: 2,9 => CTR => D3: 3,8 * INC # A8: 2,9 => UNS * INC # A8: 6,8 => UNS * DIS # D7: 2,9 => CTR => D7: 3,6 * INC # D7: 3,6 => UNS * DIS # E7: 2,9 => CTR => E7: 3,5 * INC # E7: 3,5 => UNS * INC # B1: 2,9 => UNS * INC # B2: 2,9 => UNS * DIS # B3: 2,9 => CTR => B3: 4,7 * INC # B3: 4,7 => UNS * INC # A8: 8,9 => UNS * INC # A9: 8,9 => UNS * DIS # H9: 8,9 => CTR => H9: 3,7 * INC # H9: 3,7 => UNS * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # H1: 3,9 => UNS * DIS # G2: 3,9 => CTR => G2: 7,8 * INC G2: 7,8 # H2: 3,9 => UNS * INC G2: 7,8 # E1: 3,9 => UNS * INC G2: 7,8 # F1: 3,9 => UNS * INC G2: 7,8 # G7: 3,9 => UNS * DIS G2: 7,8 # G7: 6 => CTR => G7: 3,9 * INC G2: 7,8 + G7: 3,9 # H1: 3,9 => UNS * INC G2: 7,8 + G7: 3,9 # H2: 3,9 => UNS * INC G2: 7,8 + G7: 3,9 # E1: 3,9 => UNS * INC G2: 7,8 + G7: 3,9 # F1: 3,9 => UNS * DIS G2: 7,8 + G7: 3,9 # B4: 2,8 => CTR => B4: 5,7 * INC G2: 7,8 + G7: 3,9 + B4: 5,7 # E4: 2,8 => UNS * INC G2: 7,8 + G7: 3,9 + B4: 5,7 # E4: 6 => UNS * DIS G2: 7,8 + G7: 3,9 + B4: 5,7 # A8: 2,8 => CTR => A8: 6,9 * INC G2: 7,8 + G7: 3,9 + B4: 5,7 + A8: 6,9 # E4: 2,8 => UNS * INC G2: 7,8 + G7: 3,9 + B4: 5,7 + A8: 6,9 # E4: 6 => UNS * PRF G2: 7,8 + G7: 3,9 + B4: 5,7 + A8: 6,9 # B5: 4,8 => SOL * STA G2: 7,8 + G7: 3,9 + B4: 5,7 + A8: 6,9 + B5: 4,8 * CNT 18 HDP CHAINS / 18 HYP OPENED