Analysis of zz-www.sudokuwiki.org-0013-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=13
level: medium
position: 9...4......61..2...2.9.7.311.3...58....8.1....87...1.271.6.8.2...8..43......1...8 initial
Autosolve
position: 9.1.4.8....61..2...2.9.7.311.3...58....8.1..3.87...1.271.638.2...8..431.....1...8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 4,5 => CTR => B2: 3,7 * PRF # C5: 4,5 => SOL * DIS # C9: 4,5 => CTR => C9: 2,9 * DIS # E3: 6 => CTR => E3: 5,8 * DIS # D1: 3,5 => CTR => D1: 2 * DIS # F1: 3,5 => CTR => F1: 2,6 * DIS # B2: 3,5 => CTR => B2: 4,7 * DIS # F6: 6,9 => CTR => F6: 3,5 * DIS # I7: 4,9 => CTR => I7: 5 * DIS # G9: 4,9 => CTR => G9: 6,7 * DIS # H9: 4,9 => CTR => H9: 5,6,7 * DIS # C7: 5 => CTR => C7: 4,9 * CNT 12 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 4,5 => CTR => B2: 3,7 * PRF B2: 3,7 # C5: 4,5 => SOL * STA B2: 3,7 + C5: 4,5 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9...4......61..2...2.9.7.311.3...58....8.1....87...1.271.6.8.2...8..43......1...8 | initial |
| 9.1.4.8....61..2...2.9.7.311.3...58....8.1..3.87...1.271.638.2...8..431.....1...8 | autosolve |
| 931246857876153294425987631193472586254861973687395142719638425568724319342519768 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) C3: 4,5 E2: 5,8 F2: 3,5 G3: 4,6 G7: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D1,F1: 2.. / D1 = 2 => 10 pairs (_) / F1 = 2 => 0 pairs (X) A5,C5: 2.. / A5 = 2 => 8 pairs (_) / C5 = 2 => 6 pairs (_) C5,C9: 2.. / C5 = 2 => 6 pairs (_) / C9 = 2 => 8 pairs (_) E4,E8: 2.. / E4 = 2 => 7 pairs (_) / E8 = 2 => 12 pairs (_) D6,F6: 3.. / D6 = 3 => 7 pairs (_) / F6 = 3 => 0 pairs (X) A9,B9: 3.. / A9 = 3 => 7 pairs (_) / B9 = 3 => 0 pairs (X) A2,A9: 3.. / A2 = 3 => 0 pairs (X) / A9 = 3 => 7 pairs (_) D1,D6: 3.. / D1 = 3 => 0 pairs (X) / D6 = 3 => 7 pairs (_) D4,D6: 4.. / D4 = 4 => 7 pairs (_) / D6 = 4 => 0 pairs (X) C7,I7: 5.. / C7 = 5 => 0 pairs (X) / I7 = 5 => 7 pairs (_) F1,E3: 6.. / F1 = 6 => 17 pairs (_) / E3 = 6 => 0 pairs (X) E3,G3: 6.. / E3 = 6 => 0 pairs (X) / G3 = 6 => 17 pairs (_) B1,B2: 7.. / B1 = 7 => 0 pairs (X) / B2 = 7 => 6 pairs (_) G5,G9: 7.. / G5 = 7 => 20 pairs (_) / G9 = 7 => 6 pairs (_) A2,A3: 8.. / A2 = 8 => 15 pairs (_) / A3 = 8 => 5 pairs (_) E2,E3: 8.. / E2 = 8 => 5 pairs (_) / E3 = 8 => 15 pairs (_) A2,E2: 8.. / A2 = 8 => 15 pairs (_) / E2 = 8 => 5 pairs (_) A3,E3: 8.. / A3 = 8 => 5 pairs (_) / E3 = 8 => 15 pairs (_) H2,I2: 9.. / H2 = 9 => 7 pairs (_) / I2 = 9 => 6 pairs (_) E8,F9: 9.. / E8 = 9 => 0 pairs (X) / F9 = 9 => 6 pairs (_) * DURATION: 0:00:27.854682 START: 03:37:07.506670 END: 03:37:35.361352 2017-05-01 * CP COUNT: (20) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,E2,F2,G3,G7) * 9.1.4.8....61..2...2.9.7.311.3...58....8.1..3.87...1.271.638.2...8..431.....1...8 * PAIR C3: 4,5 BLK 1 A2: 4,5,3,8 # reduction candidate for 4,5 A2: 4,5 # 8 pairs B2: 4,5,3,7 # reduction candidate for 4,5 B2: 4,5 => CTR * 9713428563461852798259674311.32765844.28.17.3.874.31.2714638925..8524317.3.71.648 B2: 3,7 # 6 pairs A3: 4,5,8 # reduction candidate for 4,5 A3: 4,5 # 15 pairs * PAIR C3: 4,5 COL C C5: 4,5,2,9 # reduction candidate for 4,5 C5: 4,5 => SOLVED * 931246857876153294425987631193472586254861973687395142719638425568724319342519768 C5: 2,9 # 6 pairs C7: 4,5,9 # reduction candidate for 4,5 C7: 4,5 # 8 pairs C9: 4,5,2,9 # reduction candidate for 4,5 C9: 4,5 => CTR * 931246857.761.32...2.9.76311.34..58...28.1..3.873..1.2719638425..8..431.3...12..8 C9: 2,9 # 6 pairs * PAIR E2: 5,8 BLK 2 E3: 5,8,6 # reduction candidate for 5,8 E3: 6 => CTR * 971342856..6185279825967431193276584..28.1..3.874.31.2714638925..8..4317...719648 E3: 5,8 # 17 pairs * PAIR E2: 5,8 ROW 2 A2: 5,8,3,4 # reduction candidate for 5,8 A2: 5,8 # 17 pairs A2: 3,4 # 6 pairs * PAIR F2: 3,5 BLK 2 D1: 3,5,2 # reduction candidate for 3,5 D1: 3,5 => CTR * 971342856..6185279825967431193276584..28.1..3.874.31.2714638925..8..4317...719648 D1: 2 # 10 pairs F1: 3,5,2,6 # reduction candidate for 3,5 F1: 3,5 => CTR * 9.124.8....618.2..8259674311.34..58....8.1..3.873..1.271463892...8..431.....1...8 F1: 2,6 # 6 pairs * PAIR F2: 3,5 ROW 2 A2: 3,5,4,8 # reduction candidate for 3,5 A2: 3,5 # 9 pairs B2: 3,5,4,7 # reduction candidate for 3,5 B2: 3,5 => CTR * 9713428564361852798259674311.3276584.4.8.17.3.874.31.2714638925.685.43173..71.648 B2: 4,7 # 6 pairs * PAIR F2: 3,5 COL F F6: 3,5,6,9 # reduction candidate for 3,5 F6: 6,9 => CTR * 9.1.4.8....618.2..8259674311.34..58....8.1..3.873..1.271.63892...8..431.....1...8 F6: 3,5 # 8 pairs * PAIR G3: 4,6 COL G G5: 4,6,7,9 # reduction candidate for 4,6 G5: 4,6 # 14 pairs G9: 4,6,7,9 # reduction candidate for 4,6 G9: 4,6 # 20 pairs * PAIR G7: 4,9 BLK 9 I7: 4,9,5 # reduction candidate for 4,9 I7: 4,9 => CTR * 9312468...761.32...249.76311.34..586.5.8.1..3.873..1.2715638.2..68..4315349512768 I7: 5 # 7 pairs G9: 4,9,6,7 # reduction candidate for 4,9 G9: 4,9 => CTR * 9312468...761.32.4.2.9.76311.347258.24.8.17.3.873.5142714638925.98.2431.352719468 G9: 6,7 # 6 pairs H9: 4,9,5,6,7 # reduction candidate for 4,9 H9: 4,9 => CTR * 9.1.4.857.761..294425987631143..6589269851473.87.9.162714638925.98..431...2.19748 H9: 5,6,7 # 5 pairs * PAIR G7: 4,9 ROW 7 C7: 4,9,5 # reduction candidate for 4,9 C7: 5 => CTR * 9312468...761.32...249.76311.34..586.5.8.1..3.873..1.2715638.2..68..4315349512768 C7: 4,9 # 7 pairs * PAIR G7: 4,9 COL G G5: 4,9,6,7 # reduction candidate for 4,9 G5: 4,9 # 16 pairs G5: 6,7 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0013-base-pr-000.dot * REASONING * DIS # B2: 4,5 => CTR => B2: 3,7 * PRF # C5: 4,5 => SOL * DIS # C9: 4,5 => CTR => C9: 2,9 * DIS # E3: 6 => CTR => E3: 5,8 * DIS # D1: 3,5 => CTR => D1: 2 * DIS # F1: 3,5 => CTR => F1: 2,6 * DIS # B2: 3,5 => CTR => B2: 4,7 * DIS # F6: 6,9 => CTR => F6: 3,5 * DIS # I7: 4,9 => CTR => I7: 5 * DIS # G9: 4,9 => CTR => G9: 6,7 * DIS # H9: 4,9 => CTR => H9: 5,6,7 * DIS # C7: 5 => CTR => C7: 4,9 * CNT 12 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,E2,F2,G3,G7) * 9.1.4.8....61..2...2.9.7.311.3...58....8.1..3.87...1.271.638.2...8..431.....1...8 * PAIR C3: 4,5 BLK 1 A2: 4,5,3,8 # reduction candidate for 4,5 A2: 4,5 # 8 pairs B2: 4,5,3,7 # reduction candidate for 4,5 B2: 4,5 => CTR * 9713428563461852798259674311.32765844.28.17.3.874.31.2714638925..8524317.3.71.648 A3: 4,5,8 # reduction candidate for 4,5 A3: 4,5 # 15 pairs * PAIR C3: 4,5 COL C C5: 4,5,2,9 # reduction candidate for 4,5 C5: 4,5 => SOLVED * 931246857876153294425987631193472586254861973687395142719638425568724319342519768 * DURATION: 0:00:05.198945 START: 03:38:02.440483 END: 03:38:07.639428 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0013-base-pr-001.dot * REASONING * DIS # B2: 4,5 => CTR => B2: 3,7 * PRF B2: 3,7 # C5: 4,5 => SOL * STA B2: 3,7 + C5: 4,5 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=13
Solution
position: 931246857876153294425987631193472586254861973687395142719638425568724319342519768 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: 4,5 => UNS * DIS # B2: 4,5 => CTR => B2: 3,7 * INC # B2: 3,7 => UNS * INC # A3: 4,5 => UNS * PRF # C5: 4,5 => SOL * INC # C5: 2,9 => UNS * INC # C7: 4,5 => UNS * DIS # C9: 4,5 => CTR => C9: 2,9 * INC # C9: 2,9 => UNS * INC # E3: 5,8 => UNS * DIS # E3: 6 => CTR => E3: 5,8 * INC # A2: 5,8 => UNS * INC # A2: 3,4 => UNS * DIS # D1: 3,5 => CTR => D1: 2 * INC # D1: 2 => UNS * DIS # F1: 3,5 => CTR => F1: 2,6 * INC # F1: 2,6 => UNS * INC # A2: 3,5 => UNS * DIS # B2: 3,5 => CTR => B2: 4,7 * INC # B2: 4,7 => UNS * INC # F6: 3,5 => UNS * DIS # F6: 6,9 => CTR => F6: 3,5 * INC # G5: 4,6 => UNS * INC # G9: 4,6 => UNS * DIS # I7: 4,9 => CTR => I7: 5 * INC # I7: 5 => UNS * DIS # G9: 4,9 => CTR => G9: 6,7 * INC # G9: 6,7 => UNS * DIS # H9: 4,9 => CTR => H9: 5,6,7 * INC # H9: 5,6,7 => UNS * INC # C7: 4,9 => UNS * DIS # C7: 5 => CTR => C7: 4,9 * INC # G5: 4,9 => UNS * INC # G5: 6,7 => UNS * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 4,5 => UNS * DIS # B2: 4,5 => CTR => B2: 3,7 * INC B2: 3,7 # A3: 4,5 => UNS * PRF B2: 3,7 # C5: 4,5 => SOL * STA B2: 3,7 + C5: 4,5 * CNT 4 HDP CHAINS / 4 HYP OPENED