Analysis of zz-www.sudokuoftheday.co.uk-20060721-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: .....7..4..4.3.792.........9...61..8..8..3.51.2....4....1.9452...715........28..7 initial
Autosolve
position: ..2..7..4.14.35792.....2..59...612.8..82.395112...94....179452.2.7156..9...328..7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 6,8 => CTR => A1: 3,5 * DIS # B1: 6,8 => CTR => B1: 3,5,9 * DIS # A3: 6,8 => CTR => A3: 3,7 * DIS # B3: 6,8 => CTR => B3: 3,7,9 * DIS # A7: 3 => CTR => A7: 6,8 * DIS # B1: 6,9 => CTR => B1: 3,5,8 * DIS # D3: 6,9 => CTR => D3: 4,8 * DIS # E3: 1,8 => CTR => E3: 4 * PRF # E3: 4 => SOL * DIS # D1: 6,8 => CTR => D1: 9 * PRF # D3: 6,8 => SOL * DIS # B5: 4,7 => CTR => B5: 6 * DIS # B5: 4,7 => CTR => B5: 6 * DIS # H6: 6 => CTR => H6: 3,7 * DIS # H6: 3,6 => CTR => H6: 7 * PRF # H6: 7 => SOL * DIS # H8: 8 => CTR => H8: 3,4 * DIS # B9: 6,9 => CTR => B9: 4,5 * DIS # B7: 3,6 => CTR => B7: 8 * DIS # H8: 3,8 => CTR => H8: 4 * DIS # H9: 4 => CTR => H9: 1,6 * CNT 21 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 # A1: 6,8 => CTR => A1: 3,5 * DIS A1: 3,5 # B1: 6,8 => CTR => B1: 3,5,9 * DIS A1: 3,5 + B1: 3,5,9 # A3: 6,8 => CTR => A3: 3,7 * DIS A1: 3,5 + B1: 3,5,9 + A3: 3,7 # B3: 6,8 => CTR => B3: 3,7,9 * DIS A1: 3,5 + B1: 3,5,9 + A3: 3,7 + B3: 3,7,9 # E3: 1,8 => CTR => E3: 4 * PRF A1: 3,5 + B1: 3,5,9 + A3: 3,7 + B3: 3,7,9 + E3: 4 => SOL * STA A1: 3,5 + B1: 3,5,9 + A3: 3,7 + B3: 3,7,9 + E3: 4 * CNT 6 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....7..4..4.3.792.........9...61..8..8..3.51.2....4....1.9452...715........28..7 | initial |
| ..2..7..4.14.35792.....2..59...612.8..82.395112...94....179452.2.7156..9...328..7 | autosolve |
| 352917684814635792796842315975461238468273951123589476681794523237156849549328167 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A2: 6,8 C3: 6,9 E1: 1,8 D2: 6,8 B4: 4,7 C4: 3,5 C6: 3,5 D4: 4,5 E5: 4,7 D6: 5,8 E6: 7,8 H4: 3,7 I6: 3,6 B8: 3,4 C9: 6,9 I7: 3,6 G8: 3,8 G9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,E3: 1.. / E1 = 1 => 18 pairs (_) / E3 = 1 => 0 pairs (X) G9,H9: 1.. / G9 = 1 => 18 pairs (_) / H9 = 1 => 22 pairs (_) C4,C6: 3.. / C4 = 3 => 0 pairs (X) / C6 = 3 => 0 pairs (_) C4,H4: 3.. / C4 = 3 => 0 pairs (X) / H4 = 3 => 0 pairs (_) I6,I7: 3.. / I6 = 3 => 0 pairs (X) / I7 = 3 => 22 pairs (_) D3,E3: 4.. / D3 = 4 => 0 pairs (X) / E3 = 4 => 0 pairs (_) D4,E5: 4.. / D4 = 4 => 0 pairs (*) / E5 = 4 => 0 pairs (X) H8,H9: 4.. / H8 = 4 => 22 pairs (_) / H9 = 4 => 0 pairs (X) B4,D4: 4.. / B4 = 4 => 0 pairs (X) / D4 = 4 => 0 pairs (_) B8,H8: 4.. / B8 = 4 => 0 pairs (X) / H8 = 4 => 22 pairs (_) A5,A9: 4.. / A5 = 4 => 0 pairs (*) / A9 = 4 => 0 pairs (X) D3,D4: 4.. / D3 = 4 => 0 pairs (X) / D4 = 4 => 0 pairs (_) E3,E5: 4.. / E3 = 4 => 0 pairs (*) / E5 = 4 => 0 pairs (X) A1,B1: 5.. / A1 = 5 => 20 pairs (_) / B1 = 5 => 0 pairs (*) C4,C6: 5.. / C4 = 5 => 0 pairs (*) / C6 = 5 => 0 pairs (X) D4,D6: 5.. / D4 = 5 => 0 pairs (X) / D6 = 5 => 0 pairs (_) A9,B9: 5.. / A9 = 5 => 0 pairs (*) / B9 = 5 => 0 pairs (X) C4,D4: 5.. / C4 = 5 => 0 pairs (*) / D4 = 5 => 0 pairs (X) C6,D6: 5.. / C6 = 5 => 0 pairs (X) / D6 = 5 => 0 pairs (_) A1,A9: 5.. / A1 = 5 => 20 pairs (_) / A9 = 5 => 0 pairs (*) B1,B9: 5.. / B1 = 5 => 0 pairs (*) / B9 = 5 => 0 pairs (X) A5,B5: 6.. / A5 = 6 => 0 pairs (X) / B5 = 6 => 20 pairs (_) H6,I6: 6.. / H6 = 6 => 0 pairs (X) / I6 = 6 => 22 pairs (_) A2,D2: 6.. / A2 = 6 => 0 pairs (X) / D2 = 6 => 18 pairs (_) C3,C9: 6.. / C3 = 6 => 18 pairs (_) / C9 = 6 => 0 pairs (X) I6,I7: 6.. / I6 = 6 => 22 pairs (_) / I7 = 6 => 0 pairs (X) A3,B3: 7.. / A3 = 7 => 19 pairs (_) / B3 = 7 => 0 pairs (X) E5,E6: 7.. / E5 = 7 => 0 pairs (*) / E6 = 7 => 0 pairs (X) H4,H6: 7.. / H4 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) B4,H4: 7.. / B4 = 7 => 0 pairs (*) / H4 = 7 => 0 pairs (X) E6,H6: 7.. / E6 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) A3,A5: 7.. / A3 = 7 => 19 pairs (_) / A5 = 7 => 0 pairs (X) D6,E6: 8.. / D6 = 8 => 0 pairs (X) / E6 = 8 => 0 pairs (_) A7,B7: 8.. / A7 = 8 => 0 pairs (X) / B7 = 8 => 19 pairs (_) G8,H8: 8.. / G8 = 8 => 18 pairs (_) / H8 = 8 => 0 pairs (X) A2,D2: 8.. / A2 = 8 => 18 pairs (_) / D2 = 8 => 0 pairs (X) D1,D3: 9.. / D1 = 9 => 18 pairs (_) / D3 = 9 => 0 pairs (X) B9,C9: 9.. / B9 = 9 => 0 pairs (X) / C9 = 9 => 18 pairs (_) B1,D1: 9.. / B1 = 9 => 0 pairs (X) / D1 = 9 => 18 pairs (_) C3,C9: 9.. / C3 = 9 => 0 pairs (X) / C9 = 9 => 18 pairs (_) * DURATION: 0:00:49.255870 START: 00:51:47.929202 END: 00:52:37.185072 2019-05-01 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B4,B8,C3,C4,C6,C9,D2,D4,D6,E1,E5,E6,G8,G9,H4,I6,I7) * ..2..7..4.14.35792.....2..59...612.8..82.395112...94....179452.2.7156..9...328..7 * PAIR A2: 6,8 BLK 1 A1: 6,8,3,5 # reduction candidate for 6,8 A1: 6,8 => CTR * .529.7..4.14.35792.....2..59...612.846827395112..89476681794523237156849549328..7 A1: 3,5 # 19 pairs B1: 6,8,3,5,9 # reduction candidate for 6,8 B1: 6,8 => CTR * 5.29.7..4.14.35792.96..2..59...612.8..82.395112...94....179452.2.7156..9.59328..7 B1: 3,5,9 # 18 pairs A3: 6,8,3,7 # reduction candidate for 6,8 A3: 6,8 => CTR * ..2..7..4.14.35792.7...2..594.5612787682439511258794....179452.237156849459328..7 A3: 3,7 # 19 pairs B3: 6,8,3,7,9 # reduction candidate for 6,8 B3: 6,8 => CTR * .529.7..4.14.357927.9..2..59...612.846827395112..89476..17945232.7156..9.96328147 B3: 3,7,9 # 18 pairs * PAIR A2: 6,8 COL A A7: 6,8,3 # reduction candidate for 6,8 A7: 3 => CTR * ..2..7..4.14.35792.....2..597.461238..82.395112...94..381794526247156..9...328147 A7: 6,8 # 24 pairs * PAIR C3: 6,9 BLK 1 B1: 6,9,3,5,8 # reduction candidate for 6,9 B1: 6,9 => CTR * 592..7..4814635792..6942..59..4612.8..827395112.589476.81794523237156849459328..7 B1: 3,5,8 # 18 pairs B3: 6,9,3,7,8 # reduction candidate for 6,9 B3: 6,9 # 22 pairs * PAIR C3: 6,9 ROW 3 D3: 6,9,4,8 # reduction candidate for 6,9 D3: 6,9 => CTR * 352917684.14835792789642315975461238..8273951123589476861794523237156849...328..7 D3: 4,8 # 18 pairs * PAIR E1: 1,8 BLK 2 E3: 1,8,4 # reduction candidate for 1,8 E3: 1,8 => CTR * 5.29.7..48146357923..4.2..594.561278..82439511258794....179452.237156849459328..7 E3: 4 => SOLVED * 352917684814635792796842315975461238468273951123589476681794523237156849549328167 * PAIR E1: 1,8 ROW 1 G1: 1,8,3,6 # reduction candidate for 1,8 G1: 1,8 # 25 pairs H1: 1,8,3,6 # reduction candidate for 1,8 H1: 1,8 # 21 pairs * PAIR D2: 6,8 BLK 2 D1: 6,8,9 # reduction candidate for 6,8 D1: 6,8 => CTR * 592.17..4814.35792..6942..59..4612.8..827395112.589476..1794523237156849.59328..7 D1: 9 # 18 pairs D3: 6,8,4,9 # reduction candidate for 6,8 D3: 6,8 => SOLVED * 352917684814635792796842315975461238468273951123589476681794523237156849549328167 D3: 4,9 # 19 pairs * PAIR B4: 4,7 BLK 4 A5: 4,7,6 # reduction candidate for 4,7 A5: 4,7 # 20 pairs B5: 4,7,6 # reduction candidate for 4,7 B5: 4,7 => CTR * 5.2..7..48146357927.6..2..59...612.86.82.395112...94..3.179452.2.7156..9459328..7 B5: 6 # 20 pairs * PAIR E5: 4,7 ROW 5 A5: 4,7,6 # reduction candidate for 4,7 A5: 4,7 # 20 pairs B5: 4,7,6 # reduction candidate for 4,7 B5: 4,7 => CTR * 5.2..7..48146357927.6..2..59...612.86.82.395112...94..3.179452.2.7156..9459328..7 B5: 6 # 20 pairs * PAIR H4: 3,7 BLK 6 H6: 3,7,6 # reduction candidate for 3,7 H6: 6 => CTR * ..2..7..4.14.35792.....2..5943561278..8243951125879463..17945262371568.9...328147 H6: 3,7 # 22 pairs * PAIR I6: 3,6 BLK 6 H6: 3,6,7 # reduction candidate for 3,6 H6: 3,6 => CTR * 5.2..7..4814635792376..2..5943561278..82439511258794....179452.237156849459328..7 H6: 7 => SOLVED * 352917684814635792796842315975461238468273951123589476681794523237156849549328167 * PAIR B8: 3,4 ROW 8 H8: 3,4,8 # reduction candidate for 3,4 H8: 8 => CTR * ..2..7..4.14.35792.....2..597.461238468273951123589476..179452.247156389...328.47 H8: 3,4 # 18 pairs * PAIR C9: 6,9 BLK 7 B9: 6,9,4,5 # reduction candidate for 6,9 B9: 6,9 => CTR * .529.7..4.14.35792.....2..59...612.846827395112..894766817945232.7156..95..328.47 B9: 4,5 # 20 pairs * PAIR I7: 3,6 ROW 7 A7: 3,6,8 # reduction candidate for 3,6 A7: 3,6 # 19 pairs B7: 3,6,8 # reduction candidate for 3,6 B7: 3,6 => CTR * ..2..7..4614835792..9..2..59...612.8.682.395112.58947683179452.2.7156..9...328..7 B7: 8 # 19 pairs * PAIR G8: 3,8 BLK 9 H8: 3,8,4 # reduction candidate for 3,8 H8: 3,8 => CTR * ..2..7..4.14.35792.....2..597.4612384682739511235894766.179452.247156..9...328.47 H8: 4 # 22 pairs * PAIR G8: 3,8 COL G G1: 3,8,1,6 # reduction candidate for 3,8 G1: 3,8 # 20 pairs G3: 3,8,1,6 # reduction candidate for 3,8 G3: 3,8 # 20 pairs * PAIR G9: 1,6 BLK 9 H9: 1,6,4 # reduction candidate for 1,6 H9: 4 => CTR * ..2..7..4.14.35792.....2..59...612.846827395112..894766817945232.7156..9...328147 H9: 1,6 # 22 pairs * PAIR G9: 1,6 COL G G1: 1,6,3,8 # reduction candidate for 1,6 G1: 1,6 # 20 pairs G3: 1,6,3,8 # reduction candidate for 1,6 G3: 1,6 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060721-absurd-base-pr-000.dot * REASONING * DIS # A1: 6,8 => CTR => A1: 3,5 * DIS # B1: 6,8 => CTR => B1: 3,5,9 * DIS # A3: 6,8 => CTR => A3: 3,7 * DIS # B3: 6,8 => CTR => B3: 3,7,9 * DIS # A7: 3 => CTR => A7: 6,8 * DIS # B1: 6,9 => CTR => B1: 3,5,8 * DIS # D3: 6,9 => CTR => D3: 4,8 * DIS # E3: 1,8 => CTR => E3: 4 * PRF # E3: 4 => SOL * DIS # D1: 6,8 => CTR => D1: 9 * PRF # D3: 6,8 => SOL * DIS # B5: 4,7 => CTR => B5: 6 * DIS # B5: 4,7 => CTR => B5: 6 * DIS # H6: 6 => CTR => H6: 3,7 * DIS # H6: 3,6 => CTR => H6: 7 * PRF # H6: 7 => SOL * DIS # H8: 8 => CTR => H8: 3,4 * DIS # B9: 6,9 => CTR => B9: 4,5 * DIS # B7: 3,6 => CTR => B7: 8 * DIS # H8: 3,8 => CTR => H8: 4 * DIS # H9: 4 => CTR => H9: 1,6 * CNT 21 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B4,B8,C3,C4,C6,C9,D2,D4,D6,E1,E5,E6,G8,G9,H4,I6,I7) * ..2..7..4.14.35792.....2..59...612.8..82.395112...94....179452.2.7156..9...328..7 * PAIR A2: 6,8 BLK 1 A1: 6,8,3,5 # reduction candidate for 6,8 A1: 6,8 => CTR * .529.7..4.14.35792.....2..59...612.846827395112..89476681794523237156849549328..7 B1: 6,8,3,5,9 # reduction candidate for 6,8 B1: 6,8 => CTR * 5.29.7..4.14.35792.96..2..59...612.8..82.395112...94....179452.2.7156..9.59328..7 A3: 6,8,3,7 # reduction candidate for 6,8 A3: 6,8 => CTR * ..2..7..4.14.35792.7...2..594.5612787682439511258794...8179452.237156849459328..7 B3: 6,8,3,7,9 # reduction candidate for 6,8 B3: 6,8 => CTR * .529.7..4.14.357927.9..2..59...612.846827395112..89476..17945232.7156..9.96328147 * PAIR E1: 1,8 BLK 2 E3: 1,8,4 # reduction candidate for 1,8 E3: 1,8 => CTR * ..2..7..4814635792..64.2..594.561278..82439511258794...8179452.237156849459328..7 E3: 4 => SOLVED * 352917684814635792796842315975461238468273951123589476681794523237156849549328167 * DURATION: 0:00:05.327898 START: 00:53:08.360477 END: 00:53:13.688375 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060721-absurd-base-pr-001.dot * REASONING * DIS # A1: 6,8 => CTR => A1: 3,5 * DIS A1: 3,5 # B1: 6,8 => CTR => B1: 3,5,9 * DIS A1: 3,5 + B1: 3,5,9 # A3: 6,8 => CTR => A3: 3,7 * DIS A1: 3,5 + B1: 3,5,9 + A3: 3,7 # B3: 6,8 => CTR => B3: 3,7,9 * DIS A1: 3,5 + B1: 3,5,9 + A3: 3,7 + B3: 3,7,9 # E3: 1,8 => CTR => E3: 4 * PRF A1: 3,5 + B1: 3,5,9 + A3: 3,7 + B3: 3,7,9 + E3: 4 => SOL * STA A1: 3,5 + B1: 3,5,9 + A3: 3,7 + B3: 3,7,9 + E3: 4 * CNT 6 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060721, absurd
Solution
position: 352917684814635792796842315975461238468273951123589476681794523237156849549328167 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 # A1: 6,8 => CTR => A1: 3,5 * INC # A1: 3,5 => UNS * DIS # B1: 6,8 => CTR => B1: 3,5,9 * INC # B1: 3,5,9 => UNS * DIS # A3: 6,8 => CTR => A3: 3,7 * INC # A3: 3,7 => UNS * DIS # B3: 6,8 => CTR => B3: 3,7,9 * INC # B3: 3,7,9 => UNS * INC # A7: 6,8 => UNS * DIS # A7: 3 => CTR => A7: 6,8 * DIS # B1: 6,9 => CTR => B1: 3,5,8 * INC # B1: 3,5,8 => UNS * INC # B3: 6,9 => UNS * DIS # D3: 6,9 => CTR => D3: 4,8 * INC # D3: 4,8 => UNS * DIS # E3: 1,8 => CTR => E3: 4 * PRF # E3: 4 => SOL * INC # G1: 1,8 => UNS * INC # H1: 1,8 => UNS * DIS # D1: 6,8 => CTR => D1: 9 * INC # D1: 9 => UNS * PRF # D3: 6,8 => SOL * INC # D3: 4,9 => UNS * INC # A5: 4,7 => UNS * DIS # B5: 4,7 => CTR => B5: 6 * INC # B5: 6 => UNS * INC # A5: 4,7 => UNS * DIS # B5: 4,7 => CTR => B5: 6 * INC # B5: 6 => UNS * INC # H6: 3,7 => UNS * DIS # H6: 6 => CTR => H6: 3,7 * DIS # H6: 3,6 => CTR => H6: 7 * PRF # H6: 7 => SOL * INC # H8: 3,4 => UNS * DIS # H8: 8 => CTR => H8: 3,4 * DIS # B9: 6,9 => CTR => B9: 4,5 * INC # B9: 4,5 => UNS * INC # A7: 3,6 => UNS * DIS # B7: 3,6 => CTR => B7: 8 * INC # B7: 8 => UNS * DIS # H8: 3,8 => CTR => H8: 4 * INC # H8: 4 => UNS * INC # G1: 3,8 => UNS * INC # G3: 3,8 => UNS * INC # H9: 1,6 => UNS * DIS # H9: 4 => CTR => H9: 1,6 * INC # G1: 1,6 => UNS * INC # G3: 1,6 => UNS * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 6,8 => CTR => A1: 3,5 * DIS A1: 3,5 # B1: 6,8 => CTR => B1: 3,5,9 * DIS A1: 3,5 + B1: 3,5,9 # A3: 6,8 => CTR => A3: 3,7 * DIS A1: 3,5 + B1: 3,5,9 + A3: 3,7 # B3: 6,8 => CTR => B3: 3,7,9 * DIS A1: 3,5 + B1: 3,5,9 + A3: 3,7 + B3: 3,7,9 # E3: 1,8 => CTR => E3: 4 * PRF A1: 3,5 + B1: 3,5,9 + A3: 3,7 + B3: 3,7,9 + E3: 4 => SOL * STA A1: 3,5 + B1: 3,5,9 + A3: 3,7 + B3: 3,7,9 + E3: 4 * CNT 6 HDP CHAINS / 5 HYP OPENED