Analysis of zz-www.sudokuwiki.org-0027-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=27
level: medium
position: ...8.9..7.2.....6.....7...4..3...8..6...1...9..4.....25...46....6.....5.1..2.5... initial
Autosolve
position: ...8.9..7.2.....6.....7...4..3...8..6...1...9..4.....25...46....6.....5.1..2.5... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 3,4 => CTR => B1: 5 * PRF # B1: 5 => SOL * PRF # A8: 3,4 => SOL * DIS # A8: 2,7,8,9 => CTR => A8: 3,4 * DIS # E1: 3,5 => CTR => E1: 2,6 * DIS # D3: 3,5 => CTR => D3: 1,6 * DIS # G2: 3,5 => CTR => G2: 1,9 * DIS # I2: 3,5 => CTR => I2: 1,8 * CNT 8 HDP CHAINS / 15 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 3,4 => CTR => B1: 5 * PRF B1: 5 => SOL * STA B1: 5 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...8.9..7.2.....6.....7...4..3...8..6...1...9..4.....25...46....6.....5.1..2.5... | initial |
| ...8.9..7.2.....6.....7...4..3...8..6...1...9..4.....25...46....6.....5.1..2.5... | autosolve |
| 456829137721354968839671524213967845685412379974583612597146283362798451148235796 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (2) A1: 3,4 E2: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B4,B6: 1.. / B4 = 1 => 4 pairs (_) / B6 = 1 => 3 pairs (_) E1,F3: 2.. / E1 = 2 => 0 pairs (*) / F3 = 2 => 0 pairs (X) A4,C5: 2.. / A4 = 2 => 0 pairs (*) / C5 = 2 => 0 pairs (X) C5,F5: 2.. / C5 = 2 => 0 pairs (X) / F5 = 2 => 0 pairs (_) A4,A8: 2.. / A4 = 2 => 0 pairs (*) / A8 = 2 => 0 pairs (X) E1,E4: 2.. / E1 = 2 => 0 pairs (*) / E4 = 2 => 0 pairs (X) A1,B1: 4.. / A1 = 4 => 2 pairs (_) / B1 = 4 => 0 pairs (X) D2,F2: 4.. / D2 = 4 => 3 pairs (_) / F2 = 4 => 3 pairs (_) A8,B9: 4.. / A8 = 4 => 0 pairs (X) / B9 = 4 => 2 pairs (_) A8,G8: 4.. / A8 = 4 => 0 pairs (X) / G8 = 4 => 2 pairs (_) A1,A8: 4.. / A1 = 4 => 2 pairs (_) / A8 = 4 => 0 pairs (X) B1,B9: 4.. / B1 = 4 => 0 pairs (X) / B9 = 4 => 2 pairs (_) I2,I4: 5.. / I2 = 5 => 0 pairs (X) / I4 = 5 => 5 pairs (_) C1,C3: 6.. / C1 = 6 => 2 pairs (_) / C3 = 6 => 0 pairs (X) E1,D3: 6.. / E1 = 6 => 0 pairs (X) / D3 = 6 => 2 pairs (_) I4,G6: 6.. / I4 = 6 => 0 pairs (X) / G6 = 6 => 5 pairs (_) G9,I9: 6.. / G9 = 6 => 0 pairs (X) / I9 = 6 => 5 pairs (_) C1,E1: 6.. / C1 = 6 => 2 pairs (_) / E1 = 6 => 0 pairs (X) C3,D3: 6.. / C3 = 6 => 0 pairs (X) / D3 = 6 => 2 pairs (_) G6,G9: 6.. / G6 = 6 => 5 pairs (_) / G9 = 6 => 0 pairs (X) I4,I9: 6.. / I4 = 6 => 0 pairs (X) / I9 = 6 => 5 pairs (_) A2,C2: 7.. / A2 = 7 => 4 pairs (_) / C2 = 7 => 0 pairs (X) I2,H3: 8.. / I2 = 8 => 7 pairs (_) / H3 = 8 => 0 pairs (X) * DURATION: 0:00:25.993503 START: 03:57:09.227978 END: 03:57:35.221481 2017-05-01 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,E2) * ...8.9..7.2.....6.....7...4..3...8..6...1...9..4.....25...46....6.....5.1..2.5... * PAIR A1: 3,4 BLK 1 B1: 3,4,5 # reduction candidate for 3,4 B1: 3,4 => CTR * ..6829517.2.....6....67...42.3...8.56...12..9..4.....25...46....6.....5.1..2.5... B1: 5 => SOLVED * 456829137721354968839671524213967845685412379974583612597146283362798451148235796 * PAIR A1: 3,4 COL A A8: 3,4,2,7,8,9 # reduction candidate for 3,4 A8: 3,4 => SOLVED * 456829137721354968839671524213967845685412379974583612597146283362798451148235796 A8: 2,7,8,9 => CTR * 456829137.2..5.968.9.67.5242.396.8.5685.123.99.45836.253.7462.176219845314.2357.6 * PAIR E2: 3,5 BLK 2 E1: 3,5,2,6 # reduction candidate for 3,5 E1: 3,5 => CTR * 4.68.9..7.2.....65..5672.84..3.2.8.66.2.1...9..4.6...253..46...26....45.14.2.56.. E1: 2,6 # 3 pairs D2: 3,5,1,4 # reduction candidate for 3,5 D2: 3,5 # 11 pairs D3: 3,5,1,6 # reduction candidate for 3,5 D3: 3,5 => CTR * 451869..7.2.....6...6.72..4..3.2.8..6.2.1...9..4.....253..46...26....45.14.2.5... D3: 1,6 # 3 pairs * PAIR E2: 3,5 ROW 2 G2: 3,5,1,9 # reduction candidate for 3,5 G2: 3,5 => CTR * ..6829.17.2..5.368851673..421396.8.5685.12..9..45..6.25...46....6.....5.1..2.5..6 G2: 1,9 # 3 pairs I2: 3,5,1,8 # reduction candidate for 3,5 I2: 3,5 => CTR * ..6829..7.2..5.963.516732842.3...8.5685.12..9..45..6.25.9.46.28.62....511..2.5.96 I2: 1,8 # 6 pairs * PAIR E2: 3,5 COL E E6: 3,5,6,8,9 # reduction candidate for 3,5 E6: 3,5 # 7 pairs E6: 6,8,9 # 2 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0027-base-pr-000.dot * REASONING * DIS # B1: 3,4 => CTR => B1: 5 * PRF # B1: 5 => SOL * PRF # A8: 3,4 => SOL * DIS # A8: 2,7,8,9 => CTR => A8: 3,4 * DIS # E1: 3,5 => CTR => E1: 2,6 * DIS # D3: 3,5 => CTR => D3: 1,6 * DIS # G2: 3,5 => CTR => G2: 1,9 * DIS # I2: 3,5 => CTR => I2: 1,8 * CNT 8 HDP CHAINS / 15 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,E2) * ...8.9..7.2.....6.....7...4..3...8..6...1...9..4.....25...46....6.....5.1..2.5... * PAIR A1: 3,4 BLK 1 B1: 3,4,5 # reduction candidate for 3,4 B1: 3,4 => CTR * ..6829517.2.....6....67...42.3...8.56...12..9..4.....25...46....6.....5.1..2.5... B1: 5 => SOLVED * 456829137721354968839671524213967845685412379974583612597146283362798451148235796 * DURATION: 0:00:02.955386 START: 03:57:46.139749 END: 03:57:49.095135 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0027-base-pr-001.dot * REASONING * DIS # B1: 3,4 => CTR => B1: 5 * PRF B1: 5 => SOL * STA B1: 5 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=27
Solution
position: 456829137721354968839671524213967845685412379974583612597146283362798451148235796 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 # B1: 3,4 => CTR => B1: 5 * PRF # B1: 5 => SOL * PRF # A8: 3,4 => SOL * DIS # A8: 2,7,8,9 => CTR => A8: 3,4 * DIS # E1: 3,5 => CTR => E1: 2,6 * INC # E1: 2,6 => UNS * INC # D2: 3,5 => UNS * DIS # D3: 3,5 => CTR => D3: 1,6 * INC # D3: 1,6 => UNS * DIS # G2: 3,5 => CTR => G2: 1,9 * INC # G2: 1,9 => UNS * DIS # I2: 3,5 => CTR => I2: 1,8 * INC # I2: 1,8 => UNS * INC # E6: 3,5 => UNS * INC # E6: 6,8,9 => UNS * CNT 15 HDP CHAINS / 15 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 3,4 => CTR => B1: 5 * PRF B1: 5 => SOL * STA B1: 5 * CNT 2 HDP CHAINS / 1 HYP OPENED