Analysis of zz-www.sudokuoftheday.co.uk-20060902-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006
level: medium
position: ..6....74......1....81....25..69...7..9..23.........4.1.3..8.257...56..19..4..... initial
Autosolve
position: .16....74......1....81....25..69...78.9..23.66......491.3978.257...56..19..4..7.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F3: 3,4 => CTR => F3: 5,7,9 * DIS # E2: 3,8 => CTR => E2: 2,4,6 * PRF # D6: 5,7 => SOL * DIS # F4: 3 => CTR => F4: 1,4 * DIS # C4: 1 => CTR => C4: 2,4 * DIS # B9: 2,5 => CTR => B9: 6,8 * DIS # E9: 1 => CTR => E9: 2,3 * DIS # E9: 1,3 => CTR => E9: 2 * DIS # F4: 1,3 => CTR => F4: 4 * PRF # F4: 4 => SOL * PRF # F6: 1,3 => SOL * DIS # H9: 3,8 => CTR => H9: 6 * CNT 12 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F3: 3,4 => CTR => F3: 5,7,9 * DIS F3: 5,7,9 # E3: 6 => CTR => E3: 3,4 * DIS F3: 5,7,9 + E3: 3,4 # H2: 5,9 => CTR => H2: 3,8 * PRF F3: 5,7,9 + E3: 3,4 + H2: 3,8 # D6: 5,7 => SOL * STA F3: 5,7,9 + E3: 3,4 + H2: 3,8 + D6: 5,7 * CNT 4 HDP CHAINS / 17 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..6....74......1....81....25..69...7..9..23.........4.1.3..8.257...56..19..4..... | initial |
| .16....74......1....81....25..69...78.9..23.66......491.3978.257...56..19..4..7.. | autosolve |
| 216839574497265138358147692532694817849712356671583249163978425724356981985421763 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A1: 2,3 C2: 5,7 A3: 3,4 I2: 3,8 B5: 4,7 D5: 5,7 E5: 1,4 G4: 2,8 H4: 1,8 H5: 1,5 G6: 2,5 B7: 4,6 C8: 2,4 C9: 2,5 D8: 2,3 F9: 1,3 G7: 4,6 I9: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C4,C6: 1.. / C4 = 1 => 0 pairs (X) / C6 = 1 => 23 pairs (_) H4,H5: 1.. / H4 = 1 => 0 pairs (*) / H5 = 1 => 0 pairs (X) E9,F9: 1.. / E9 = 1 => 0 pairs (X) / F9 = 1 => 19 pairs (_) E5,H5: 1.. / E5 = 1 => 0 pairs (*) / H5 = 1 => 0 pairs (X) A1,A2: 2.. / A1 = 2 => 20 pairs (_) / A2 = 2 => 19 pairs (_) G4,G6: 2.. / G4 = 2 => 0 pairs (X) / G6 = 2 => 0 pairs (_) D8,E9: 2.. / D8 = 2 => 0 pairs (X) / E9 = 2 => 22 pairs (_) B4,B6: 3.. / B4 = 3 => 23 pairs (_) / B6 = 3 => 0 pairs (X) B4,F4: 3.. / B4 = 3 => 23 pairs (_) / F4 = 3 => 0 pairs (X) D8,H8: 3.. / D8 = 3 => 22 pairs (_) / H8 = 3 => 0 pairs (X) I2,I9: 3.. / I2 = 3 => 20 pairs (_) / I9 = 3 => 23 pairs (_) A2,A3: 4.. / A2 = 4 => 19 pairs (_) / A3 = 4 => 19 pairs (_) F4,E5: 4.. / F4 = 4 => 0 pairs (*) / E5 = 4 => 0 pairs (X) G7,G8: 4.. / G7 = 4 => 20 pairs (_) / G8 = 4 => 0 pairs (X) B5,E5: 4.. / B5 = 4 => 0 pairs (*) / E5 = 4 => 0 pairs (X) B7,G7: 4.. / B7 = 4 => 0 pairs (X) / G7 = 4 => 20 pairs (_) C4,C8: 4.. / C4 = 4 => 0 pairs (X) / C8 = 4 => 23 pairs (_) H5,G6: 5.. / H5 = 5 => 0 pairs (*) / G6 = 5 => 0 pairs (X) B9,C9: 5.. / B9 = 5 => 0 pairs (X) / C9 = 5 => 19 pairs (_) D5,H5: 5.. / D5 = 5 => 0 pairs (X) / H5 = 5 => 0 pairs (_) C2,C9: 5.. / C2 = 5 => 0 pairs (X) / C9 = 5 => 19 pairs (_) E2,E3: 6.. / E2 = 6 => 20 pairs (_) / E3 = 6 => 0 pairs (X) B7,B9: 6.. / B7 = 6 => 20 pairs (_) / B9 = 6 => 0 pairs (X) G7,H9: 6.. / G7 = 6 => 0 pairs (X) / H9 = 6 => 20 pairs (_) E2,H2: 6.. / E2 = 6 => 20 pairs (_) / H2 = 6 => 0 pairs (X) B7,G7: 6.. / B7 = 6 => 20 pairs (_) / G7 = 6 => 0 pairs (X) B9,H9: 6.. / B9 = 6 => 0 pairs (X) / H9 = 6 => 20 pairs (_) G3,G7: 6.. / G3 = 6 => 20 pairs (_) / G7 = 6 => 0 pairs (X) B3,F3: 7.. / B3 = 7 => 0 pairs (X) / F3 = 7 => 19 pairs (_) B5,D5: 7.. / B5 = 7 => 0 pairs (X) / D5 = 7 => 0 pairs (_) C2,C6: 7.. / C2 = 7 => 19 pairs (_) / C6 = 7 => 0 pairs (X) D6,E6: 8.. / D6 = 8 => 20 pairs (_) / E6 = 8 => 21 pairs (_) G4,H4: 8.. / G4 = 8 => 0 pairs (*) / H4 = 8 => 0 pairs (X) B8,B9: 8.. / B8 = 8 => 20 pairs (_) / B9 = 8 => 24 pairs (_) I2,I9: 8.. / I2 = 8 => 23 pairs (_) / I9 = 8 => 20 pairs (_) B2,B3: 9.. / B2 = 9 => 19 pairs (_) / B3 = 9 => 21 pairs (_) G8,H8: 9.. / G8 = 9 => 22 pairs (_) / H8 = 9 => 22 pairs (_) F1,G1: 9.. / F1 = 9 => 19 pairs (_) / G1 = 9 => 0 pairs (X) * DURATION: 0:00:43.732563 START: 02:17:58.679235 END: 02:18:42.411798 2019-05-01 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B5,B7,C2,C8,C9,D5,D8,E5,F9,G4,G6,G7,H4,H5,I2,I9) * .16....74......1....81....25..69...78.9..23.66......491.3978.257...56..19..4..7.. * PAIR A1: 2,3 BLK 1 A2: 2,3,4 # reduction candidate for 2,3 A2: 4 # 19 pairs A2: 2,3 # 19 pairs * PAIR A1: 2,3 ROW 1 D1: 2,3,5,8 # reduction candidate for 2,3 D1: 2,3 # 26 pairs E1: 2,3,8 # reduction candidate for 2,3 E1: 2,3 # 21 pairs * PAIR C2: 5,7 BLK 1 B2: 5,7,9 # reduction candidate for 5,7 B2: 5,7 # 21 pairs B3: 5,7,9 # reduction candidate for 5,7 B3: 5,7 # 19 pairs * PAIR C2: 5,7 ROW 2 D2: 5,7,2,3,8 # reduction candidate for 5,7 D2: 5,7 # 25 pairs F2: 5,7,3,4,9 # reduction candidate for 5,7 F2: 5,7 # 20 pairs * PAIR A3: 3,4 BLK 1 A2: 3,4,2 # reduction candidate for 3,4 A2: 3,4 # 20 pairs A2: 2 # 19 pairs * PAIR A3: 3,4 ROW 3 E3: 3,4,6 # reduction candidate for 3,4 E3: 3,4 # 20 pairs F3: 3,4,5,7,9 # reduction candidate for 3,4 F3: 3,4 => CTR * .16....74......1...781....25..69...78497123566......491.3978.257...56..19..4..7.. F3: 5,7,9 # 18 pairs * PAIR I2: 3,8 BLK 3 H2: 3,8,5,6,9 # reduction candidate for 3,8 H2: 3,8 # 22 pairs H2: 5,6,9 # 18 pairs * PAIR I2: 3,8 ROW 2 D2: 3,8,2,5,7 # reduction candidate for 3,8 D2: 3,8 # 20 pairs E2: 3,8,2,4,6 # reduction candidate for 3,8 E2: 3,8 => CTR * .16....74......16...816...25..69...78.9.423166.....5491.39786257...564919654217.. E2: 2,4,6 # 18 pairs * PAIR D5: 5,7 BLK 5 D6: 5,7,3,8 # reduction candidate for 5,7 D6: 5,7 => SOLVED * 216839574497265138358147692532694817849712356671583249163978425724356981985421763 D6: 3,8 # 20 pairs F6: 5,7,1,3 # reduction candidate for 5,7 F6: 5,7 # 20 pairs * PAIR D5: 5,7 COL D D2: 5,7,2,3,8 # reduction candidate for 5,7 D2: 5,7 # 25 pairs D2: 2,3,8 # 18 pairs * PAIR E5: 1,4 BLK 5 F4: 1,4,3 # reduction candidate for 1,4 F4: 3 => CTR * .16....74......1....81....25.1693287879542316632.175491.3978.257.4.56..19.54.17.. F4: 1,4 # 23 pairs * PAIR C8: 2,4 BLK 7 B8: 2,4,8 # reduction candidate for 2,4 B8: 2,4 # 24 pairs B8: 8 # 20 pairs * PAIR C8: 2,4 COL C C4: 2,4,1 # reduction candidate for 2,4 C4: 1 => CTR * 316285974257.6.1.8..813.652541693287879542316632...5491639784257.4356891985421763 C4: 2,4 # 23 pairs * PAIR C9: 2,5 BLK 7 B9: 2,5,6,8 # reduction candidate for 2,5 B9: 2,5 => CTR * .16.29.742...641.34.813.6.254.693..787954231663..81.491639784257842569319..4..768 B9: 6,8 # 22 pairs * PAIR D8: 2,3 BLK 8 E9: 2,3,1 # reduction candidate for 2,3 E9: 1 => CTR * .16....74......1.3..81....253.69...78.9.423166.....5491.3978.257842569319..413768 E9: 2,3 # 19 pairs * PAIR D8: 2,3 COL D D1: 2,3,5,8 # reduction candidate for 2,3 D1: 2,3 # 26 pairs D2: 2,3,5,7,8 # reduction candidate for 2,3 D2: 2,3 # 20 pairs * PAIR F9: 1,3 BLK 8 E9: 1,3,2 # reduction candidate for 1,3 E9: 1,3 => CTR * .16.29.742...641.34.813.6.254.693..787954231663..81.491639784257842569319..4..768 E9: 2 # 22 pairs * PAIR F9: 1,3 COL F F4: 1,3,4 # reduction candidate for 1,3 F4: 1,3 => CTR * .16..5974..7...1.8..81.76.25..69.2878795423166..78.5491639784257...568919854..7.. F4: 4 => SOLVED * 216839574497265138358147692532694817849712356671583249163978425724356981985421763 F6: 1,3,5,7 # reduction candidate for 1,3 F6: 1,3 => SOLVED * 216839574497265138358147692532694817849712356671583249163978425724356981985421763 F6: 5,7 # 20 pairs * PAIR I9: 3,8 BLK 9 H8: 3,8,9 # reduction candidate for 3,8 H8: 3,8 # 22 pairs H9: 3,8,6 # reduction candidate for 3,8 H9: 3,8 => CTR * .16....74..7...1....81.7..25.4693.17879..23.66......491.39786257...564919654217.. H9: 6 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060902-absurd-base-pr-000.dot * REASONING * DIS # F3: 3,4 => CTR => F3: 5,7,9 * DIS # E2: 3,8 => CTR => E2: 2,4,6 * PRF # D6: 5,7 => SOL * DIS # F4: 3 => CTR => F4: 1,4 * DIS # C4: 1 => CTR => C4: 2,4 * DIS # B9: 2,5 => CTR => B9: 6,8 * DIS # E9: 1 => CTR => E9: 2,3 * DIS # E9: 1,3 => CTR => E9: 2 * DIS # F4: 1,3 => CTR => F4: 4 * PRF # F4: 4 => SOL * PRF # F6: 1,3 => SOL * DIS # H9: 3,8 => CTR => H9: 6 * CNT 12 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B5,B7,C2,C8,C9,D5,D8,E5,F9,G4,G6,G7,H4,H5,I2,I9) * .16....74......1....81....25..69...78.9..23.66......491.3978.257...56..19..4..7.. * PAIR A1: 2,3 BLK 1 A2: 2,3,4 # reduction candidate for 2,3 A2: 4 # 19 pairs A2: 2,3 # 19 pairs * PAIR A1: 2,3 ROW 1 D1: 2,3,5,8 # reduction candidate for 2,3 D1: 2,3 # 26 pairs E1: 2,3,8 # reduction candidate for 2,3 E1: 2,3 # 21 pairs * PAIR C2: 5,7 BLK 1 B2: 5,7,9 # reduction candidate for 5,7 B2: 5,7 # 21 pairs B3: 5,7,9 # reduction candidate for 5,7 B3: 5,7 # 19 pairs * PAIR C2: 5,7 ROW 2 D2: 5,7,2,3,8 # reduction candidate for 5,7 D2: 5,7 # 25 pairs F2: 5,7,3,4,9 # reduction candidate for 5,7 F2: 5,7 # 20 pairs * PAIR A3: 3,4 BLK 1 A2: 3,4,2 # reduction candidate for 3,4 A2: 3,4 # 20 pairs A2: 2 # 19 pairs * PAIR A3: 3,4 ROW 3 E3: 3,4,6 # reduction candidate for 3,4 E3: 3,4 # 20 pairs F3: 3,4,5,7,9 # reduction candidate for 3,4 F3: 3,4 => CTR * .16....74......1...781....25..69...78497123566......491.3978.257...56..19..4..7.. * RESTART * PAIR A3: 3,4 ROW 3 E3: 3,4,6 # reduction candidate for 3,4 E3: 6 => CTR * .16....74..7...1684.8167.325.4693817879..23.66......491.39786257..356491965421783 * PAIR RESTART * PAIR I2: 3,8 BLK 3 H2: 3,8,5,9 # reduction candidate for 3,8 H2: 5,9 => CTR * .16.298742..8641.34.81....25..69.2878.9..23166...8.5491.3978.2578..56..19..413768 * PAIR D5: 5,7 BLK 5 D6: 5,7,3,8 # reduction candidate for 5,7 D6: 5,7 => SOLVED * 216839574497265138358147692532694817849712356671583249163978425724356981985421763 * DURATION: 0:00:11.393258 START: 02:19:10.953092 END: 02:19:22.346350 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060902-absurd-base-pr-001.dot * REASONING * DIS # F3: 3,4 => CTR => F3: 5,7,9 * DIS F3: 5,7,9 # E3: 6 => CTR => E3: 3,4 * DIS F3: 5,7,9 + E3: 3,4 # H2: 5,9 => CTR => H2: 3,8 * PRF F3: 5,7,9 + E3: 3,4 + H2: 3,8 # D6: 5,7 => SOL * STA F3: 5,7,9 + E3: 3,4 + H2: 3,8 + D6: 5,7 * CNT 4 HDP CHAINS / 17 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006, 20060902, absurd
Solution
position: 216839574497265138358147692532694817849712356671583249163978425724356981985421763 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 # A2: 2,3 => UNS * INC # A2: 4 => UNS * INC # D1: 2,3 => UNS * INC # E1: 2,3 => UNS * INC # B2: 5,7 => UNS * INC # B3: 5,7 => UNS * INC # D2: 5,7 => UNS * INC # F2: 5,7 => UNS * INC # A2: 3,4 => UNS * INC # A2: 2 => UNS * INC # E3: 3,4 => UNS * DIS # F3: 3,4 => CTR => F3: 5,7,9 * INC # F3: 5,7,9 => UNS * INC # H2: 3,8 => UNS * INC # H2: 5,6,9 => UNS * INC # D2: 3,8 => UNS * DIS # E2: 3,8 => CTR => E2: 2,4,6 * INC # E2: 2,4,6 => UNS * PRF # D6: 5,7 => SOL * INC # D6: 3,8 => UNS * INC # F6: 5,7 => UNS * INC # D2: 5,7 => UNS * INC # D2: 2,3,8 => UNS * INC # F4: 1,4 => UNS * DIS # F4: 3 => CTR => F4: 1,4 * INC # B8: 2,4 => UNS * INC # B8: 8 => UNS * INC # C4: 2,4 => UNS * DIS # C4: 1 => CTR => C4: 2,4 * DIS # B9: 2,5 => CTR => B9: 6,8 * INC # B9: 6,8 => UNS * INC # E9: 2,3 => UNS * DIS # E9: 1 => CTR => E9: 2,3 * INC # D1: 2,3 => UNS * INC # D2: 2,3 => UNS * DIS # E9: 1,3 => CTR => E9: 2 * INC # E9: 2 => UNS * DIS # F4: 1,3 => CTR => F4: 4 * PRF # F4: 4 => SOL * PRF # F6: 1,3 => SOL * INC # F6: 5,7 => UNS * INC # H8: 3,8 => UNS * DIS # H9: 3,8 => CTR => H9: 6 * INC # H9: 6 => UNS * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 2,3 => UNS * INC # A2: 4 => UNS * INC # D1: 2,3 => UNS * INC # E1: 2,3 => UNS * INC # B2: 5,7 => UNS * INC # B3: 5,7 => UNS * INC # D2: 5,7 => UNS * INC # F2: 5,7 => UNS * INC # A2: 3,4 => UNS * INC # A2: 2 => UNS * INC # E3: 3,4 => UNS * DIS # F3: 3,4 => CTR => F3: 5,7,9 * INC F3: 5,7,9 # E3: 3,4 => UNS * DIS F3: 5,7,9 # E3: 6 => CTR => E3: 3,4 * INC F3: 5,7,9 + E3: 3,4 # H2: 3,8 => UNS * DIS F3: 5,7,9 + E3: 3,4 # H2: 5,9 => CTR => H2: 3,8 * PRF F3: 5,7,9 + E3: 3,4 + H2: 3,8 # D6: 5,7 => SOL * STA F3: 5,7,9 + E3: 3,4 + H2: 3,8 + D6: 5,7 * CNT 17 HDP CHAINS / 17 HYP OPENED