Analysis of zz-www.sudokuwiki.org-0127-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=127
level: medium
position: .......1...6.4....3..61...7....954...7.....8......4.2.2.....87...8...5....95....4 initial
Autosolve
position: ..7.5..1...6.47.5.3..61..47...7954...7.....8......472.2.....87...8...59...95....4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C4: 1,3 => CTR => C4: 2 * PRF # C5: 1,3 => SOL * DIS # B6: 1,3 => CTR => B6: 6,9 * DIS # I6: 1,3 => CTR => I6: 5,6,9 * DIS # I5: 3,6 => CTR => I5: 1,5,9 * PRF # I6: 3,6 => SOL * PRF # B4: 3,6 => SOL * DIS # F7: 3,6 => CTR => F7: 1,9 * DIS # E8: 3,6 => CTR => E8: 2,7 * DIS # E9: 3,6 => CTR => E9: 2,7,8 * DIS # F9: 3,6 => CTR => F9: 1,2,8 * DIS # B7: 3,6 => CTR => B7: 1,4,5 * DIS # I8: 3,6 => CTR => I8: 1,2 * DIS # G9: 3,6 => CTR => G9: 1,2 * DIS # E9: 3,6 => CTR => E9: 2,7,8 * DIS # F9: 3,6 => CTR => F9: 1,2,8 * CNT 16 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C4: 1,3 => CTR => C4: 2 * PRF C4: 2 # C5: 1,3 => SOL * STA C4: 2 + C5: 1,3 * CNT 2 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......1...6.4....3..61...7....954...7.....8......4.2.2.....87...8...5....95....4 | initial |
| ..7.5..1...6.47.5.3..61..47...7954...7.....8......472.2.....87...8...59...95....4 | autosolve |
| 947352618126847359385619247862795431471236985593184726254961873618473592739528164 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) C3: 2,5 G3: 2,9 C6: 1,3 H4: 3,6 E7: 3,6 H9: 3,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,B2: 1.. / A2 = 1 => 8 pairs (_) / B2 = 1 => 10 pairs (_) G5,G9: 1.. / G5 = 1 => 0 pairs (X) / G9 = 1 => 11 pairs (_) B4,C4: 2.. / B4 = 2 => 0 pairs (X) / C4 = 2 => 5 pairs (_) I8,G9: 2.. / I8 = 2 => 8 pairs (_) / G9 = 2 => 0 pairs (X) C3,C4: 2.. / C3 = 2 => 0 pairs (X) / C4 = 2 => 5 pairs (_) H4,H9: 3.. / H4 = 3 => 9 pairs (_) / H9 = 3 => 9 pairs (_) A1,B1: 4.. / A1 = 4 => 6 pairs (_) / B1 = 4 => 7 pairs (_) A5,C5: 4.. / A5 = 4 => 0 pairs (*) / C5 = 4 => 0 pairs (X) D7,D8: 4.. / D7 = 4 => 7 pairs (_) / D8 = 4 => 10 pairs (_) C5,C7: 4.. / C5 = 4 => 6 pairs (_) / C7 = 4 => 0 pairs (*) B3,C3: 5.. / B3 = 5 => 0 pairs (X) / C3 = 5 => 5 pairs (_) A5,A6: 5.. / A5 = 5 => 6 pairs (_) / A6 = 5 => 6 pairs (_) I5,I6: 5.. / I5 = 5 => 6 pairs (_) / I6 = 5 => 6 pairs (_) B7,C7: 5.. / B7 = 5 => 5 pairs (_) / C7 = 5 => 0 pairs (X) A5,I5: 5.. / A5 = 5 => 6 pairs (_) / I5 = 5 => 6 pairs (_) A6,I6: 5.. / A6 = 5 => 6 pairs (_) / I6 = 5 => 6 pairs (_) B3,B7: 5.. / B3 = 5 => 0 pairs (X) / B7 = 5 => 5 pairs (_) C3,C7: 5.. / C3 = 5 => 5 pairs (_) / C7 = 5 => 0 pairs (X) G1,I1: 6.. / G1 = 6 => 6 pairs (_) / I1 = 6 => 20 pairs (_) H4,H9: 6.. / H4 = 6 => 9 pairs (_) / H9 = 6 => 9 pairs (_) A8,A9: 7.. / A8 = 7 => 0 pairs (X) / A9 = 7 => 6 pairs (_) E8,E9: 7.. / E8 = 7 => 6 pairs (_) / E9 = 7 => 0 pairs (X) A8,E8: 7.. / A8 = 7 => 0 pairs (X) / E8 = 7 => 6 pairs (_) A9,E9: 7.. / A9 = 7 => 6 pairs (_) / E9 = 7 => 0 pairs (X) I1,I2: 8.. / I1 = 8 => 7 pairs (_) / I2 = 8 => 7 pairs (_) A4,B4: 8.. / A4 = 8 => 8 pairs (_) / B4 = 8 => 17 pairs (_) D6,E6: 8.. / D6 = 8 => 13 pairs (_) / E6 = 8 => 10 pairs (_) E9,F9: 8.. / E9 = 8 => 13 pairs (_) / F9 = 8 => 10 pairs (_) B3,F3: 8.. / B3 = 8 => 8 pairs (_) / F3 = 8 => 13 pairs (_) E6,E9: 8.. / E6 = 8 => 10 pairs (_) / E9 = 8 => 13 pairs (_) D7,F7: 9.. / D7 = 9 => 10 pairs (_) / F7 = 9 => 7 pairs (_) * DURATION: 0:00:39.215546 START: 05:51:47.495611 END: 05:52:26.711157 2017-05-01 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,C6,E7,G3,H4,H9) * ..7.5..1...6.47.5.3..61..47...7954...7.....8......472.2.....87...8...59...95....4 * PAIR C3: 2,5 BLK 1 B3: 2,5,8,9 # reduction candidate for 2,5 B3: 2,5 # 21 pairs B3: 8,9 # 6 pairs * PAIR G3: 2,9 BLK 3 G1: 2,9,3,6 # reduction candidate for 2,9 G1: 2,9 # 22 pairs I1: 2,9,3,6,8 # reduction candidate for 2,9 I1: 2,9 # 11 pairs G2: 2,9,3 # reduction candidate for 2,9 G2: 2,9 # 14 pairs I2: 2,9,3,8 # reduction candidate for 2,9 I2: 2,9 # 10 pairs * PAIR G3: 2,9 ROW 3 B3: 2,9,5,8 # reduction candidate for 2,9 B3: 2,9 # 16 pairs F3: 2,9,8 # reduction candidate for 2,9 F3: 2,9 # 8 pairs * PAIR C6: 1,3 BLK 4 B4: 1,3,2,6,8 # reduction candidate for 1,3 B4: 1,3 # 11 pairs C4: 1,3,2 # reduction candidate for 1,3 C4: 1,3 => CTR * ..7.5..1...6.47.5.35261894782.7954...74.2.38....83472.2.5.6.873..8.7.59.7.958.164 C4: 2 # 5 pairs C5: 1,3,4 # reduction candidate for 1,3 C5: 1,3 => SOLVED * 947352618126847359385619247862795431471236985593184726254961873618473592739528164 C5: 4 # 6 pairs B6: 1,3,6,9 # reduction candidate for 1,3 B6: 1,3 => CTR * ..7.5..1...6.47.5.3..61..47..2795431.74....8....86472.2...3.876..8...59...95....4 B6: 6,9 # 7 pairs * PAIR C6: 1,3 ROW 6 D6: 1,3,8 # reduction candidate for 1,3 D6: 1,3 # 10 pairs I6: 1,3,5,6,9 # reduction candidate for 1,3 I6: 1,3 => CTR * ..7.5.61...6.4735.3..619247..27954..674.2.9855938647212.193687...8.7.59.7.958.1.4 I6: 5,6,9 # 6 pairs * PAIR C6: 1,3 COL C C7: 1,3,4,5 # reduction candidate for 1,3 C7: 4,5 # 9 pairs C7: 1,3 # 7 pairs * PAIR H4: 3,6 BLK 6 I4: 3,6,1 # reduction candidate for 3,6 I4: 3,6 # 13 pairs G5: 3,6,1,9 # reduction candidate for 3,6 G5: 3,6 # 20 pairs I5: 3,6,1,5,9 # reduction candidate for 3,6 I5: 3,6 => CTR * ..7.5361.1.6.4735.395618247..27954.1574.2.98.913864725251439876..8...592..95821.4 I5: 1,5,9 # 6 pairs I6: 3,6,1,5,9 # reduction candidate for 3,6 I6: 3,6 => SOLVED * 947352618126847359385619247862795431471236985593184726254961873618473592739528164 I6: 1,5,9 # 6 pairs * PAIR H4: 3,6 ROW 4 B4: 3,6,1,2,8 # reduction candidate for 3,6 B4: 3,6 => SOLVED * 947352618126847359385619247862795431471236985593184726254961873618473592739528164 B4: 1,2,8 # 6 pairs * PAIR E7: 3,6 BLK 8 F7: 3,6,1,9 # reduction candidate for 3,6 F7: 3,6 => CTR * ..7.5..1...6.47.5.38561..478..7954...7....18....18472.2..9..871..84..59...95.8..4 F7: 1,9 # 7 pairs E8: 3,6,2,7 # reduction candidate for 3,6 E8: 3,6 => CTR * ..7.5..1...6.47.5.3856129478.27954...7..2.18....18472.2514.987.7482.159.6395782.4 E8: 2,7 # 7 pairs F8: 3,6,1,2 # reduction candidate for 3,6 F8: 3,6 # 9 pairs E9: 3,6,2,7,8 # reduction candidate for 3,6 E9: 3,6 => CTR * ..7.5..1...6.47.5.3856129478.27954...7..2618....18472.2514.987...827159.7.95.82.4 E9: 2,7,8 # 6 pairs F9: 3,6,1,2,8 # reduction candidate for 3,6 F9: 3,6 => CTR * ..7.5..1...6.47.5.3..61.947...7954...7....18......472.2.....87...8...59...958.2.4 F9: 1,2,8 # 6 pairs * PAIR E7: 3,6 ROW 7 B7: 3,6,1,4,5 # reduction candidate for 3,6 B7: 3,6 => CTR * ..7.5..1...6.47.5.3526189478217954...74...18...386472.265439871..817.59.71958...4 B7: 1,4,5 # 6 pairs I7: 3,6,1 # reduction candidate for 3,6 I7: 3,6 # 10 pairs * PAIR E7: 3,6 COL E E5: 3,6,2 # reduction candidate for 3,6 E5: 3,6 # 13 pairs E6: 3,6,8 # reduction candidate for 3,6 E6: 3,6 # 13 pairs * PAIR H9: 3,6 BLK 9 I7: 3,6,1 # reduction candidate for 3,6 I7: 3,6 # 10 pairs I8: 3,6,1,2 # reduction candidate for 3,6 I8: 3,6 => CTR * ..7.5.61...6.4735.3856129478..7954...7....18....18472.2.....871..8...59...95.82.4 I8: 1,2 # 7 pairs G9: 3,6,1,2 # reduction candidate for 3,6 G9: 3,6 => CTR * ..7.5..1...6.47.5.38561..478.27954...7....18...318472.2514.987...83.1592.395286.4 G9: 1,2 # 7 pairs * PAIR H9: 3,6 ROW 9 B9: 3,6,1 # reduction candidate for 3,6 B9: 3,6 # 9 pairs E9: 3,6,2,7,8 # reduction candidate for 3,6 E9: 3,6 => CTR * ..7.5..1...6.47.5.3856129478.27954...7..2618....18472.2514.987...827159.7.95.82.4 E9: 2,7,8 # 6 pairs F9: 3,6,1,2,8 # reduction candidate for 3,6 F9: 3,6 => CTR * ..7.5..1...6.47.5.3..61.947...7954...7....18......472.2.....87...8...59...958.2.4 F9: 1,2,8 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0127-base-pr-000.dot * REASONING * DIS # C4: 1,3 => CTR => C4: 2 * PRF # C5: 1,3 => SOL * DIS # B6: 1,3 => CTR => B6: 6,9 * DIS # I6: 1,3 => CTR => I6: 5,6,9 * DIS # I5: 3,6 => CTR => I5: 1,5,9 * PRF # I6: 3,6 => SOL * PRF # B4: 3,6 => SOL * DIS # F7: 3,6 => CTR => F7: 1,9 * DIS # E8: 3,6 => CTR => E8: 2,7 * DIS # E9: 3,6 => CTR => E9: 2,7,8 * DIS # F9: 3,6 => CTR => F9: 1,2,8 * DIS # B7: 3,6 => CTR => B7: 1,4,5 * DIS # I8: 3,6 => CTR => I8: 1,2 * DIS # G9: 3,6 => CTR => G9: 1,2 * DIS # E9: 3,6 => CTR => E9: 2,7,8 * DIS # F9: 3,6 => CTR => F9: 1,2,8 * CNT 16 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,C6,E7,G3,H4,H9) * ..7.5..1...6.47.5.3..61..47...7954...7.....8......472.2.....87...8...59...95....4 * PAIR C3: 2,5 BLK 1 B3: 2,5,8,9 # reduction candidate for 2,5 B3: 2,5 # 21 pairs B3: 8,9 # 6 pairs * PAIR G3: 2,9 BLK 3 G1: 2,9,3,6 # reduction candidate for 2,9 G1: 2,9 # 22 pairs I1: 2,9,3,6,8 # reduction candidate for 2,9 I1: 2,9 # 11 pairs G2: 2,9,3 # reduction candidate for 2,9 G2: 2,9 # 14 pairs I2: 2,9,3,8 # reduction candidate for 2,9 I2: 2,9 # 10 pairs * PAIR G3: 2,9 ROW 3 B3: 2,9,5,8 # reduction candidate for 2,9 B3: 2,9 # 16 pairs F3: 2,9,8 # reduction candidate for 2,9 F3: 2,9 # 8 pairs * PAIR C6: 1,3 BLK 4 B4: 1,3,2,6,8 # reduction candidate for 1,3 B4: 1,3 # 11 pairs C4: 1,3,2 # reduction candidate for 1,3 C4: 1,3 => CTR * ..7.5..1...6.47.5.35261894782.7954...74.2.38....83472.2.5.6.873..8.7.59.7.958.164 C5: 1,3,4 # reduction candidate for 1,3 C5: 1,3 => SOLVED * 947352618126847359385619247862795431471236985593184726254961873618473592739528164 * DURATION: 0:00:10.028616 START: 05:53:04.374487 END: 05:53:14.403103 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0127-base-pr-001.dot * REASONING * DIS # C4: 1,3 => CTR => C4: 2 * PRF C4: 2 # C5: 1,3 => SOL * STA C4: 2 + C5: 1,3 * CNT 2 HDP CHAINS / 11 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=127
Solution
position: 947352618126847359385619247862795431471236985593184726254961873618473592739528164 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 # B3: 2,5 => UNS * INC # B3: 8,9 => UNS * INC # G1: 2,9 => UNS * INC # I1: 2,9 => UNS * INC # G2: 2,9 => UNS * INC # I2: 2,9 => UNS * INC # B3: 2,9 => UNS * INC # F3: 2,9 => UNS * INC # B4: 1,3 => UNS * DIS # C4: 1,3 => CTR => C4: 2 * INC # C4: 2 => UNS * PRF # C5: 1,3 => SOL * INC # C5: 4 => UNS * DIS # B6: 1,3 => CTR => B6: 6,9 * INC # B6: 6,9 => UNS * INC # D6: 1,3 => UNS * DIS # I6: 1,3 => CTR => I6: 5,6,9 * INC # I6: 5,6,9 => UNS * INC # C7: 1,3 => UNS * INC # C7: 4,5 => UNS * INC # I4: 3,6 => UNS * INC # G5: 3,6 => UNS * DIS # I5: 3,6 => CTR => I5: 1,5,9 * INC # I5: 1,5,9 => UNS * PRF # I6: 3,6 => SOL * INC # I6: 1,5,9 => UNS * PRF # B4: 3,6 => SOL * INC # B4: 1,2,8 => UNS * DIS # F7: 3,6 => CTR => F7: 1,9 * INC # F7: 1,9 => UNS * DIS # E8: 3,6 => CTR => E8: 2,7 * INC # E8: 2,7 => UNS * INC # F8: 3,6 => UNS * DIS # E9: 3,6 => CTR => E9: 2,7,8 * INC # E9: 2,7,8 => UNS * DIS # F9: 3,6 => CTR => F9: 1,2,8 * INC # F9: 1,2,8 => UNS * DIS # B7: 3,6 => CTR => B7: 1,4,5 * INC # B7: 1,4,5 => UNS * INC # I7: 3,6 => UNS * INC # E5: 3,6 => UNS * INC # E6: 3,6 => UNS * INC # I7: 3,6 => UNS * DIS # I8: 3,6 => CTR => I8: 1,2 * INC # I8: 1,2 => UNS * DIS # G9: 3,6 => CTR => G9: 1,2 * INC # G9: 1,2 => UNS * INC # B9: 3,6 => UNS * DIS # E9: 3,6 => CTR => E9: 2,7,8 * INC # E9: 2,7,8 => UNS * DIS # F9: 3,6 => CTR => F9: 1,2,8 * INC # F9: 1,2,8 => UNS * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B3: 2,5 => UNS * INC # B3: 8,9 => UNS * INC # G1: 2,9 => UNS * INC # I1: 2,9 => UNS * INC # G2: 2,9 => UNS * INC # I2: 2,9 => UNS * INC # B3: 2,9 => UNS * INC # F3: 2,9 => UNS * INC # B4: 1,3 => UNS * DIS # C4: 1,3 => CTR => C4: 2 * PRF C4: 2 # C5: 1,3 => SOL * STA C4: 2 + C5: 1,3 * CNT 11 HDP CHAINS / 11 HYP OPENED