Analysis of zz-www.sudokuoftheday.co.uk-20060328-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006
level: medium
position: ..57...8.9.3.2.....1..56............54...2..6.79...5....76.32..........7..24..83. initial
Autosolve
position: ..57...8.9.3.2....71..56.....65.....54...2..6.79.6.5....76.32.....2....7..24..83. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 4 => CTR => A1: 2,6 * PRF # C8: 1 => SOL * DIS # F2: 1,8 => CTR => F2: 4 * DIS # D5: 1,8 => CTR => D5: 3,9 * DIS # D6: 1,8 => CTR => D6: 3 * DIS # D5: 1,8 => CTR => D5: 3,9 * DIS # C8: 4 => CTR => C8: 1,8 * CNT 7 HDP CHAINS / 17 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 4 => CTR => A1: 2,6 * DIS A1: 2,6 # A4: 1,8 => CTR => A4: 2,3 * DIS A1: 2,6 + A4: 2,3 # E5: 1,8 => CTR => E5: 7 * PRF A1: 2,6 + A4: 2,3 + E5: 7 => SOL * STA A1: 2,6 + A4: 2,3 + E5: 7 * CNT 4 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..57...8.9.3.2.....1..56............54...2..6.79...5....76.32..........7..24..83. | initial |
| ..57...8.9.3.2....71..56.....65.....54...2..6.79.6.5....76.32.....2....7..24..83. | autosolve |
| 265739184983124675714856923326541798548972316179368542497683251831295467652417839 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) B1: 2,6 B2: 6,8 C3: 4,8 D2: 1,8 C5: 1,8 A9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C5,C8: 1.. / C5 = 1 => 9 pairs (_) / C8 = 1 => 0 pairs (*) A1,B1: 2.. / A1 = 2 => 17 pairs (_) / B1 = 2 => 7 pairs (_) H3,I3: 2.. / H3 = 2 => 10 pairs (_) / I3 = 2 => 7 pairs (_) B1,B4: 2.. / B1 = 2 => 7 pairs (_) / B4 = 2 => 17 pairs (_) E1,D3: 3.. / E1 = 3 => 10 pairs (_) / D3 = 3 => 0 pairs (X) A8,B8: 3.. / A8 = 3 => 6 pairs (_) / B8 = 3 => 9 pairs (_) B4,B8: 3.. / B4 = 3 => 6 pairs (_) / B8 = 3 => 9 pairs (_) A1,C3: 4.. / A1 = 4 => 0 pairs (X) / C3 = 4 => 18 pairs (_) C3,C8: 4.. / C3 = 4 => 18 pairs (_) / C8 = 4 => 0 pairs (X) E1,E4: 4.. / E1 = 4 => 0 pairs (X) / E4 = 4 => 7 pairs (_) H2,I2: 5.. / H2 = 5 => 0 pairs (X) / I2 = 5 => 7 pairs (_) F8,F9: 5.. / F8 = 5 => 6 pairs (_) / F9 = 5 => 8 pairs (_) A9,B9: 6.. / A9 = 6 => 7 pairs (_) / B9 = 6 => 0 pairs (X) G8,H8: 6.. / G8 = 6 => 0 pairs (X) / H8 = 6 => 6 pairs (_) A1,A9: 6.. / A1 = 6 => 0 pairs (X) / A9 = 6 => 7 pairs (_) H2,H8: 6.. / H2 = 6 => 0 pairs (X) / H8 = 6 => 6 pairs (_) G2,H2: 7.. / G2 = 7 => 6 pairs (_) / H2 = 7 => 9 pairs (_) E9,F9: 7.. / E9 = 7 => 6 pairs (_) / F9 = 7 => 9 pairs (_) F4,F9: 7.. / F4 = 7 => 6 pairs (_) / F9 = 7 => 9 pairs (_) B2,C3: 8.. / B2 = 8 => 18 pairs (_) / C3 = 8 => 0 pairs (X) I4,I6: 8.. / I4 = 8 => 7 pairs (_) / I6 = 8 => 8 pairs (_) C3,D3: 8.. / C3 = 8 => 0 pairs (X) / D3 = 8 => 18 pairs (_) D3,D5: 9.. / D3 = 9 => 0 pairs (X) / D5 = 9 => 8 pairs (_) * DURATION: 0:00:22.023382 START: 21:58:49.765319 END: 21:59:11.788701 2019-04-30 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B1,B2,C3,C5,D2) * ..57...8.9.3.2....71..56.....65.....54...2..6.79.6.5....76.32.....2....7..24..83. * PAIR B1: 2,6 BLK 1 A1: 2,6,4 # reduction candidate for 2,6 A1: 4 => CTR * 4257..68.963824...718.564....654....541.82..6.7916.5....76.32....42...676.24..83. A1: 2,6 # 18 pairs * PAIR C3: 4,8 COL C C8: 4,8,1 # reduction candidate for 4,8 C8: 1 => SOLVED * 265739184983124675714856923326541798548972316179368542497683251831295467652417839 C8: 4,8 # 9 pairs * PAIR D2: 1,8 BLK 2 F2: 1,8,4 # reduction candidate for 1,8 F2: 1,8 => CTR * ..57...8.9.3.2....714856.....65.....54.9.2..6.7936.5....76.32.....2....7..24..83. F2: 4 # 10 pairs * PAIR D2: 1,8 COL D D5: 1,8,3,9 # reduction candidate for 1,8 D5: 1,8 => CTR * 4.573..8.9.3.2....718956.....654....5418.23.6.793615....76.32....42....7..24..83. D5: 3,9 # 7 pairs D6: 1,8,3 # reduction candidate for 1,8 D6: 1,8 => CTR * 4257..68.963821...718.56..22.65.7...541.82..6.7916452...76.32....42.8.67692475831 D6: 3 # 11 pairs * PAIR C5: 1,8 BLK 4 A4: 1,8,2,3 # reduction candidate for 1,8 A4: 1,8 # 9 pairs A6: 1,8,2,3 # reduction candidate for 1,8 A6: 1,8 # 9 pairs * PAIR C5: 1,8 ROW 5 D5: 1,8,3,9 # reduction candidate for 1,8 D5: 1,8 => CTR * 4.573..8.9.3.2....718956.....654....5418.23.6.793615....76.32....42....7..24..83. D5: 3,9 # 7 pairs E5: 1,8,3,7,9 # reduction candidate for 1,8 E5: 1,8 # 13 pairs * PAIR C5: 1,8 COL C C8: 1,8,4 # reduction candidate for 1,8 C8: 4 => CTR * 4257..68.963824...718.564....654....541.82..6.7916.5....76.32....42...676.24..83. C8: 1,8 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060328-absurd-base-pr-000.dot * REASONING * DIS # A1: 4 => CTR => A1: 2,6 * PRF # C8: 1 => SOL * DIS # F2: 1,8 => CTR => F2: 4 * DIS # D5: 1,8 => CTR => D5: 3,9 * DIS # D6: 1,8 => CTR => D6: 3 * DIS # D5: 1,8 => CTR => D5: 3,9 * DIS # C8: 4 => CTR => C8: 1,8 * CNT 7 HDP CHAINS / 17 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B1,B2,C3,C5,D2) * ..57...8.9.3.2....71..56.....65.....54...2..6.79.6.5....76.32.....2....7..24..83. * PAIR B1: 2,6 BLK 1 A1: 2,6,4 # reduction candidate for 2,6 A1: 4 => CTR * 4257..68.963824...718.564....654....541.82..6.7916.5....76.32....42...676.24..83. * PAIR C5: 1,8 BLK 4 A4: 1,8,2,3 # reduction candidate for 1,8 A4: 1,8 => CTR * 62573918498312467571485692313654..9254.9.23.6279361548..76.32..3..2..467..24..83. * RESTART * PAIR C5: 1,8 ROW 5 E5: 1,8,7 # reduction candidate for 1,8 E5: 1,8 => CTR * 265739481983124765714856923326547198541982376.7936.542.976.325443.295617.52471839 E5: 7 => SOLVED * 265739184983124675714856923326541798548972316179368542497683251831295467652417839 * DURATION: 0:00:05.039909 START: 21:59:21.487581 END: 21:59:26.527490 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060328-absurd-base-pr-001.dot * REASONING * DIS # A1: 4 => CTR => A1: 2,6 * DIS A1: 2,6 # A4: 1,8 => CTR => A4: 2,3 * DIS A1: 2,6 + A4: 2,3 # E5: 1,8 => CTR => E5: 7 * PRF A1: 2,6 + A4: 2,3 + E5: 7 => SOL * STA A1: 2,6 + A4: 2,3 + E5: 7 * CNT 4 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060328, absurd
Solution
position: 265739184983124675714856923326541798548972316179368542497683251831295467652417839 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 # A1: 2,6 => UNS * DIS # A1: 4 => CTR => A1: 2,6 * INC # C8: 4,8 => UNS * PRF # C8: 1 => SOL * DIS # F2: 1,8 => CTR => F2: 4 * INC # F2: 4 => UNS * DIS # D5: 1,8 => CTR => D5: 3,9 * INC # D5: 3,9 => UNS * DIS # D6: 1,8 => CTR => D6: 3 * INC # D6: 3 => UNS * INC # A4: 1,8 => UNS * INC # A6: 1,8 => UNS * DIS # D5: 1,8 => CTR => D5: 3,9 * INC # D5: 3,9 => UNS * INC # E5: 1,8 => UNS * INC # C8: 1,8 => UNS * DIS # C8: 4 => CTR => C8: 1,8 * CNT 17 HDP CHAINS / 17 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 2,6 => UNS * DIS # A1: 4 => CTR => A1: 2,6 * DIS A1: 2,6 # A4: 1,8 => CTR => A4: 2,3 * DIS A1: 2,6 + A4: 2,3 # E5: 1,8 => CTR => E5: 7 * PRF A1: 2,6 + A4: 2,3 + E5: 7 => SOL * STA A1: 2,6 + A4: 2,3 + E5: 7 * CNT 5 HDP CHAINS / 4 HYP OPENED