Analysis of zz-www.sudokuoftheday.co.uk-20190416-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: 9.3........8..45....2..9..78...9.6..21.47.8.5....8.2.4...3.546.3.5..7............ initial
Autosolve
position: 9.3...1.6..8.34529..2..93.78...9.6.121.47.8.5....8.2.47..3.546.3.5..791....9..753 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 1,6 => CTR => A3: 4,5 * DIS # D2: 1 => CTR => D2: 6,7 * PRF # F9: 2,8 => SOL * DIS # F9: 1,6 => CTR => F9: 2,8 * DIS # B6: 6,9 => CTR => B6: 3,5 * PRF # B6: 3,5 => SOL * DIS # C6: 6,9 => CTR => C6: 7 * DIS # B6: 5,6 => CTR => B6: 3,9 * DIS # D6: 1 => CTR => D6: 5,6 * DIS # A3: 1,4 => CTR => A3: 5,6 * DIS # F6: 3,6 => CTR => F6: 1 * DIS # H6: 3,7 => CTR => H6: 9 * PRF # H6: 9 => SOL * DIS # H6: 7 => CTR => H6: 3,9 * DIS # B8: 4,6 => CTR => B8: 2,8 * PRF # B8: 2,8 => SOL * DIS # B9: 4,6 => CTR => B9: 2,8 * PRF # C9: 4,6 => SOL * DIS # C9: 1 => CTR => C9: 4,6 * DIS # E9: 4,6 => CTR => E9: 1,2 * DIS # A3: 4,6 => CTR => A3: 1,5 * DIS # F9: 1,2 => CTR => F9: 6,8 * DIS # B7: 2,8 => CTR => B7: 9 * PRF # B7: 9 => SOL * PRF # B8: 2,8 => SOL * DIS # B8: 4,6 => CTR => B8: 2,8 * DIS # D8: 2,8 => CTR => D8: 6 * PRF # D8: 6 => SOL * CNT 28 HDP CHAINS / 45 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 1,6 => CTR => A3: 4,5 * DIS A3: 4,5 # D1: 7 => CTR => D1: 2,8 * DIS A3: 4,5 + D1: 2,8 # C6: 6,9 => CTR => C6: 7 * DIS A3: 4,5 + D1: 2,8 + C6: 7 # F6: 3,6 => CTR => F6: 1 * PRF A3: 4,5 + D1: 2,8 + C6: 7 + F6: 1 => SOL * STA A3: 4,5 + D1: 2,8 + C6: 7 + F6: 1 * CNT 5 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9.3........8..45....2..9..78...9.6..21.47.8.5....8.2.4...3.546.3.5..7............ | initial |
| 9.3...1.6..8.34529..2..93.78...9.6.121.47.8.5....8.2.47..3.546.3.5..791....9..753 | autosolve |
| 973852146168734529542169387854293671219476835637581294791325468385647912426918753 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) A2: 1,6 B2: 6,7 E1: 2,5 F1: 2,8 H1: 4,8 H3: 4,8 C4: 4,7 C5: 6,9 A6: 5,6 D4: 2,5 F4: 2,3 F5: 3,6 H4: 3,7 H5: 3,9 C7: 1,9 A9: 4,6 E7: 1,2 I7: 2,8 I8: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 1.. / A2 = 1 => 19 pairs (_) / A3 = 1 => 0 pairs (X) D6,F6: 1.. / D6 = 1 => 0 pairs (X) / F6 = 1 => 23 pairs (_) C7,C9: 1.. / C7 = 1 => 0 pairs (*) / C9 = 1 => 0 pairs (X) A2,D2: 1.. / A2 = 1 => 19 pairs (_) / D2 = 1 => 0 pairs (X) C7,E7: 1.. / C7 = 1 => 0 pairs (*) / E7 = 1 => 0 pairs (X) F6,F9: 1.. / F6 = 1 => 23 pairs (_) / F9 = 1 => 0 pairs (X) D4,F4: 2.. / D4 = 2 => 0 pairs (*) / F4 = 2 => 0 pairs (X) I7,I8: 2.. / I7 = 2 => 0 pairs (X) / I8 = 2 => 20 pairs (_) B4,B6: 3.. / B4 = 3 => 0 pairs (X) / B6 = 3 => 0 pairs (_) F5,H5: 3.. / F5 = 3 => 0 pairs (X) / H5 = 3 => 0 pairs (_) H1,H3: 4.. / H1 = 4 => 19 pairs (_) / H3 = 4 => 0 pairs (X) B4,C4: 4.. / B4 = 4 => 0 pairs (X) / C4 = 4 => 20 pairs (_) E8,E9: 4.. / E8 = 4 => 19 pairs (_) / E9 = 4 => 0 pairs (X) B1,H1: 4.. / B1 = 4 => 0 pairs (X) / H1 = 4 => 19 pairs (_) B8,E8: 4.. / B8 = 4 => 0 pairs (X) / E8 = 4 => 19 pairs (_) A3,A9: 4.. / A3 = 4 => 0 pairs (X) / A9 = 4 => 19 pairs (_) C4,C9: 4.. / C4 = 4 => 20 pairs (_) / C9 = 4 => 0 pairs (X) E1,E3: 5.. / E1 = 5 => 21 pairs (_) / E3 = 5 => 0 pairs (X) D4,D6: 5.. / D4 = 5 => 0 pairs (X) / D6 = 5 => 0 pairs (_) B1,E1: 5.. / B1 = 5 => 0 pairs (X) / E1 = 5 => 21 pairs (_) B4,D4: 5.. / B4 = 5 => 0 pairs (*) / D4 = 5 => 0 pairs (X) A3,A6: 5.. / A3 = 5 => 0 pairs (*) / A6 = 5 => 0 pairs (X) C5,F5: 6.. / C5 = 6 => 0 pairs (X) / F5 = 6 => 0 pairs (_) B1,B2: 7.. / B1 = 7 => 22 pairs (_) / B2 = 7 => 20 pairs (_) D1,D2: 7.. / D1 = 7 => 20 pairs (_) / D2 = 7 => 22 pairs (_) C4,C6: 7.. / C4 = 7 => 0 pairs (X) / C6 = 7 => 20 pairs (_) H4,H6: 7.. / H4 = 7 => 20 pairs (_) / H6 = 7 => 0 pairs (X) B1,D1: 7.. / B1 = 7 => 22 pairs (_) / D1 = 7 => 20 pairs (_) B2,D2: 7.. / B2 = 7 => 20 pairs (_) / D2 = 7 => 22 pairs (_) C4,H4: 7.. / C4 = 7 => 0 pairs (X) / H4 = 7 => 20 pairs (_) C6,H6: 7.. / C6 = 7 => 20 pairs (_) / H6 = 7 => 0 pairs (X) H1,H3: 8.. / H1 = 8 => 0 pairs (X) / H3 = 8 => 19 pairs (_) D8,F9: 8.. / D8 = 8 => 0 pairs (X) / F9 = 8 => 0 pairs (_) I7,I8: 8.. / I7 = 8 => 20 pairs (_) / I8 = 8 => 0 pairs (X) D3,H3: 8.. / D3 = 8 => 0 pairs (X) / H3 = 8 => 19 pairs (_) B7,I7: 8.. / B7 = 8 => 0 pairs (X) / I7 = 8 => 20 pairs (_) B9,F9: 8.. / B9 = 8 => 0 pairs (X) / F9 = 8 => 0 pairs (_) F1,F9: 8.. / F1 = 8 => 0 pairs (X) / F9 = 8 => 0 pairs (_) H5,H6: 9.. / H5 = 9 => 0 pairs (X) / H6 = 9 => 0 pairs (_) B7,C7: 9.. / B7 = 9 => 0 pairs (*) / C7 = 9 => 0 pairs (X) C5,H5: 9.. / C5 = 9 => 0 pairs (*) / H5 = 9 => 0 pairs (X) B6,B7: 9.. / B6 = 9 => 0 pairs (X) / B7 = 9 => 0 pairs (_) * DURATION: 0:00:49.478077 START: 05:20:20.695686 END: 05:21:10.173763 2019-05-01 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A9,B2,C4,C5,C7,D4,E1,E7,F1,F4,F5,H1,H3,H4,H5,I7,I8) * 9.3...1.6..8.34529..2..93.78...9.6.121.47.8.5....8.2.47..3.546.3.5..791....9..753 * PAIR A2: 1,6 BLK 1 A3: 1,6,4,5 # reduction candidate for 1,6 A3: 1,6 => CTR * 9.3..8146..8.34529.42.5938783459267121.47.8.55.7.8.2.47..3.546.3.584791248.9..753 A3: 4,5 # 21 pairs * PAIR A2: 1,6 ROW 2 D2: 1,6,7 # reduction candidate for 1,6 D2: 7 # 22 pairs D2: 1,6 # 20 pairs * PAIR B2: 6,7 ROW 2 D2: 6,7,1 # reduction candidate for 6,7 D2: 1 => CTR * 9.37.81.6.781345291.2..93.78...9.6.121.47.8.55..6812.47..3.546.3.5..791.4..9.6753 D2: 6,7 # 19 pairs * PAIR F1: 2,8 BLK 2 D1: 2,8,7 # reduction candidate for 2,8 D1: 2,8 # 22 pairs D1: 7 # 20 pairs * PAIR F1: 2,8 COL F F9: 2,8,1,6 # reduction candidate for 2,8 F9: 2,8 => SOLVED * 973852146168734529542169387854293671219476835637581294791325468385647912426918753 F9: 1,6 => CTR * 9.3258146..8734529..2..93878..5926.121.47.8.5....8.2.47293154683.5847912.81926753 * PAIR C5: 6,9 BLK 4 B6: 6,9,3,5 # reduction candidate for 6,9 B6: 6,9 => CTR * 9.3258146..8734529.52..938783459267121.47.8.55.7.8.2.4729315468345867912.8.92.753 B6: 3,5 => SOLVED * 973852146168734529542169387854293671219476835637581294791325468385647912426918753 C6: 6,9,7 # reduction candidate for 6,9 C6: 6,9 => CTR * 9.3...1.6..8.34529..2..93.78.7.9.63121.473895.39.8.2747913254683.5..7912.249.8753 C6: 7 # 20 pairs * PAIR A6: 5,6 BLK 4 B6: 5,6,3,9 # reduction candidate for 5,6 B6: 5,6 => CTR * 9.3...1.6..8.34529..2..93.783459267121.47.8.5..7.8.2947913254683.5..7912.269.8753 B6: 3,9 # 20 pairs * PAIR A6: 5,6 ROW 6 D6: 5,6,1 # reduction candidate for 5,6 D6: 1 => CTR * 9.3..81461.8.34529..26193878..5926.121.47.8.5...18.2.47.13254683.58.7912...9.1753 D6: 5,6 # 23 pairs * PAIR A6: 5,6 COL A A3: 5,6,1,4 # reduction candidate for 5,6 A3: 1,4 => CTR * 9.3258146..8734529.52..93878..5926.121.47.8.55...8.2.47293154683.5847912.81926753 A3: 5,6 # 20 pairs * PAIR F5: 3,6 BLK 5 F6: 3,6,1 # reduction candidate for 3,6 F6: 3,6 => CTR * 9.3..81461.8.34529..26193878..5926.121.47.8.5...18.2.47.13254683.58.7912...9.1753 F6: 1 # 23 pairs * PAIR H4: 3,7 BLK 6 H6: 3,7,9 # reduction candidate for 3,7 H6: 3,7 => CTR * 9.3258146..8734529.52..93878..5926.12164738955...8.2.47293154683.5847912.81926753 H6: 9 => SOLVED * 973852146168734529542169387854293671219476835637581294791325468385647912426918753 * PAIR H5: 3,9 BLK 6 H6: 3,9,7 # reduction candidate for 3,9 H6: 7 => CTR * 9.3...1.6..8.34529..2..93.78.7.9.631216473895539.8.2747913254683.5..7912.249.8753 H6: 3,9 # 20 pairs * PAIR A9: 4,6 BLK 7 B8: 4,6,2,8 # reduction candidate for 4,6 B8: 4,6 => CTR * 9.3..8146..8.34529..2.693878345926712164738955976812347.931546.3658479124819.6753 B8: 2,8 => SOLVED * 973852146168734529542169387854293671219476835637581294791325468385647912426918753 B9: 4,6,2,8 # reduction candidate for 4,6 B9: 4,6 => CTR * 9.3..21.6..8.34529..2..93.78..29367121.476835.375812947913.546.3.5..791....9.8753 B9: 2,8 # 20 pairs C9: 4,6,1 # reduction candidate for 4,6 C9: 4,6 => SOLVED * 973852146168734529542169387854293671219476835637581294791325468385647912426918753 C9: 1 => CTR * 9.3..8146..8.34529..2.693878345926712164738955976812347.931546.3658479124819.6753 * PAIR A9: 4,6 ROW 9 E9: 4,6,1,2 # reduction candidate for 4,6 E9: 4,6 => CTR * 9.3...1.6..8.34529..2..93.78.429367121.476835.3..8.2.47..3.546.3.5..791....9..753 E9: 1,2 # 28 pairs * PAIR A9: 4,6 COL A A3: 4,6,1,5 # reduction candidate for 4,6 A3: 4,6 => CTR * 9.32581461.8734529.52..93878..5926.121.47.8.55...8.2.47293154683.5847912.81926753 A3: 1,5 # 20 pairs * PAIR E7: 1,2 BLK 8 E9: 1,2,4,6 # reduction candidate for 1,2 E9: 1,2 # 28 pairs F9: 1,2,6,8 # reduction candidate for 1,2 F9: 1,2 => CTR * 9.3.28146..8.34529..2.593878.429367121.47.8.5....8.2.47293154683.58.7912.819.2753 F9: 6,8 # 24 pairs * PAIR I7: 2,8 ROW 7 B7: 2,8,9 # reduction candidate for 2,8 B7: 2,8 => CTR * 9.3..8146..8.34529..2.693878345926712164738955976812347.931546.3658479124819.6753 B7: 9 => SOLVED * 973852146168734529542169387854293671219476835637581294791325468385647912426918753 * PAIR I8: 2,8 ROW 8 B8: 2,8,4,6 # reduction candidate for 2,8 B8: 2,8 => SOLVED * 973852146168734529542169387854293671219476835637581294791325468385647912426918753 B8: 4,6 => CTR * 9.3..8146..8.34529..2.693878345926712164738955976812347.931546.3658479124819.6753 D8: 2,8,6 # reduction candidate for 2,8 D8: 2,8 => CTR * 9.3258146..8734529.5216938783459267121647389559768123472931546.3.58.7912.81926753 D8: 6 => SOLVED * 973852146168734529542169387854293671219476835637581294791325468385647912426918753 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190416-absurd-base-pr-000.dot * REASONING * DIS # A3: 1,6 => CTR => A3: 4,5 * DIS # D2: 1 => CTR => D2: 6,7 * PRF # F9: 2,8 => SOL * DIS # F9: 1,6 => CTR => F9: 2,8 * DIS # B6: 6,9 => CTR => B6: 3,5 * PRF # B6: 3,5 => SOL * DIS # C6: 6,9 => CTR => C6: 7 * DIS # B6: 5,6 => CTR => B6: 3,9 * DIS # D6: 1 => CTR => D6: 5,6 * DIS # A3: 1,4 => CTR => A3: 5,6 * DIS # F6: 3,6 => CTR => F6: 1 * DIS # H6: 3,7 => CTR => H6: 9 * PRF # H6: 9 => SOL * DIS # H6: 7 => CTR => H6: 3,9 * DIS # B8: 4,6 => CTR => B8: 2,8 * PRF # B8: 2,8 => SOL * DIS # B9: 4,6 => CTR => B9: 2,8 * PRF # C9: 4,6 => SOL * DIS # C9: 1 => CTR => C9: 4,6 * DIS # E9: 4,6 => CTR => E9: 1,2 * DIS # A3: 4,6 => CTR => A3: 1,5 * DIS # F9: 1,2 => CTR => F9: 6,8 * DIS # B7: 2,8 => CTR => B7: 9 * PRF # B7: 9 => SOL * PRF # B8: 2,8 => SOL * DIS # B8: 4,6 => CTR => B8: 2,8 * DIS # D8: 2,8 => CTR => D8: 6 * PRF # D8: 6 => SOL * CNT 28 HDP CHAINS / 45 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A9,B2,C4,C5,C7,D4,E1,E7,F1,F4,F5,H1,H3,H4,H5,I7,I8) * 9.3...1.6..8.34529..2..93.78...9.6.121.47.8.5....8.2.47..3.546.3.5..791....9..753 * PAIR A2: 1,6 BLK 1 A3: 1,6,4,5 # reduction candidate for 1,6 A3: 1,6 => CTR * 9.3..8146..8.34529.42.5938783459267121.47.8.55.7.8.2.47..3.546.3.584791248.9..753 * PAIR F1: 2,8 BLK 2 D1: 2,8,7 # reduction candidate for 2,8 D1: 7 => CTR * 9.37..1.6178634529462.593878.4.9.67121.47.8.55.718.2.47..3.546.3.5.6791....94.753 * PAIR C5: 6,9 BLK 4 C6: 6,9,7 # reduction candidate for 6,9 C6: 6,9 => CTR * 973.5.146168734529..2..93878.7.9.63121.473895.39.862747913254683.5..79126249..753 * PAIR F5: 3,6 BLK 5 F6: 3,6,1 # reduction candidate for 3,6 F6: 3,6 => CTR * 973.58146168734529..26193878.459267121.47.8.5..718.2.47.13254683.5867912...9.1753 F6: 1 => SOLVED * 973852146168734529542169387854293671219476835637581294791325468385647912426918753 * DURATION: 0:00:06.877145 START: 05:21:41.197584 END: 05:21:48.074729 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190416-absurd-base-pr-001.dot * REASONING * DIS # A3: 1,6 => CTR => A3: 4,5 * DIS A3: 4,5 # D1: 7 => CTR => D1: 2,8 * DIS A3: 4,5 + D1: 2,8 # C6: 6,9 => CTR => C6: 7 * DIS A3: 4,5 + D1: 2,8 + C6: 7 # F6: 3,6 => CTR => F6: 1 * PRF A3: 4,5 + D1: 2,8 + C6: 7 + F6: 1 => SOL * STA A3: 4,5 + D1: 2,8 + C6: 7 + F6: 1 * CNT 5 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190416, absurd
Solution
position: 973852146168734529542169387854293671219476835637581294791325468385647912426918753 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:
* DIS # A3: 1,6 => CTR => A3: 4,5 * INC # A3: 4,5 => UNS * INC # D2: 1,6 => UNS * INC # D2: 7 => UNS * INC # D2: 6,7 => UNS * DIS # D2: 1 => CTR => D2: 6,7 * INC # D1: 2,8 => UNS * INC # D1: 7 => UNS * PRF # F9: 2,8 => SOL * DIS # F9: 1,6 => CTR => F9: 2,8 * DIS # B6: 6,9 => CTR => B6: 3,5 * PRF # B6: 3,5 => SOL * DIS # C6: 6,9 => CTR => C6: 7 * INC # C6: 7 => UNS * DIS # B6: 5,6 => CTR => B6: 3,9 * INC # B6: 3,9 => UNS * INC # D6: 5,6 => UNS * DIS # D6: 1 => CTR => D6: 5,6 * INC # A3: 5,6 => UNS * DIS # A3: 1,4 => CTR => A3: 5,6 * DIS # F6: 3,6 => CTR => F6: 1 * INC # F6: 1 => UNS * DIS # H6: 3,7 => CTR => H6: 9 * PRF # H6: 9 => SOL * INC # H6: 3,9 => UNS * DIS # H6: 7 => CTR => H6: 3,9 * DIS # B8: 4,6 => CTR => B8: 2,8 * PRF # B8: 2,8 => SOL * DIS # B9: 4,6 => CTR => B9: 2,8 * INC # B9: 2,8 => UNS * PRF # C9: 4,6 => SOL * DIS # C9: 1 => CTR => C9: 4,6 * DIS # E9: 4,6 => CTR => E9: 1,2 * INC # E9: 1,2 => UNS * DIS # A3: 4,6 => CTR => A3: 1,5 * INC # A3: 1,5 => UNS * INC # E9: 1,2 => UNS * DIS # F9: 1,2 => CTR => F9: 6,8 * INC # F9: 6,8 => UNS * DIS # B7: 2,8 => CTR => B7: 9 * PRF # B7: 9 => SOL * PRF # B8: 2,8 => SOL * DIS # B8: 4,6 => CTR => B8: 2,8 * DIS # D8: 2,8 => CTR => D8: 6 * PRF # D8: 6 => SOL * CNT 45 HDP CHAINS / 45 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A3: 1,6 => CTR => A3: 4,5 * INC A3: 4,5 # D1: 2,8 => UNS * DIS A3: 4,5 # D1: 7 => CTR => D1: 2,8 * DIS A3: 4,5 + D1: 2,8 # C6: 6,9 => CTR => C6: 7 * DIS A3: 4,5 + D1: 2,8 + C6: 7 # F6: 3,6 => CTR => F6: 1 * PRF A3: 4,5 + D1: 2,8 + C6: 7 + F6: 1 => SOL * STA A3: 4,5 + D1: 2,8 + C6: 7 + F6: 1 * CNT 6 HDP CHAINS / 5 HYP OPENED