Analysis of zz-www.sudokuwiki.org-0121-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=121
level: medium
position: 5.........1.67..9...7.2.4.......1..9.3..6..2.1..7.......8.4.5...2..36.7....9....2 initial
Autosolve
position: 5.........1.67..9...7.2.4.......1..9.3..6..2.1..7....4..8.4.5..42..3697....9...42 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C6: 5,9 => CTR => C6: 2,6 * DIS # E6: 5,8 => CTR => E6: 9 * DIS # B4: 5,8 => CTR => B4: 4,6,7 * DIS # D8: 8 => CTR => D8: 1,5 * DIS # I1: 1,8 => CTR => I1: 3,6,7 * CNT 5 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C6: 5,9 => CTR => C6: 2,6 * DIS C6: 2,6 # E6: 5,8 => CTR => E6: 9 * DIS C6: 2,6 + E6: 9 # B4: 5,8 => CTR => B4: 4,6,7 * PRF C6: 2,6 + E6: 9 + B4: 4,6,7 # E9: 1 => SOL * STA C6: 2,6 + E6: 9 + B4: 4,6,7 + E9: 1 * CNT 4 HDP CHAINS / 15 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5.........1.67..9...7.2.4.......1..9.3..6..2.1..7.......8.4.5...2..36.7....9....2 | initial |
| 5.........1.67..9...7.2.4.......1..9.3..6..2.1..7....4..8.4.5..42..3697....9...42 | autosolve |
| 563489217214675893987123456842351769739864125156792384698247531421536978375918642 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) C5: 5,9 D4: 2,3 E4: 5,8 F6: 2,3 C8: 1,5 D7: 1,2 F7: 2,7 I8: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G5,I5: 1.. / G5 = 1 => 8 pairs (_) / I5 = 1 => 11 pairs (_) C8,C9: 1.. / C8 = 1 => 10 pairs (_) / C9 = 1 => 12 pairs (_) E1,E9: 1.. / E1 = 1 => 9 pairs (_) / E9 = 1 => 9 pairs (_) G1,G2: 2.. / G1 = 2 => 9 pairs (_) / G2 = 2 => 11 pairs (_) D4,F6: 2.. / D4 = 2 => 19 pairs (_) / F6 = 2 => 8 pairs (_) D7,F7: 2.. / D7 = 2 => 8 pairs (_) / F7 = 2 => 19 pairs (_) C1,G1: 2.. / C1 = 2 => 11 pairs (_) / G1 = 2 => 9 pairs (_) C6,F6: 2.. / C6 = 2 => 19 pairs (_) / F6 = 2 => 8 pairs (_) A2,A4: 2.. / A2 = 2 => 10 pairs (_) / A4 = 2 => 9 pairs (_) D4,D7: 2.. / D4 = 2 => 19 pairs (_) / D7 = 2 => 8 pairs (_) F6,F7: 2.. / F6 = 2 => 8 pairs (_) / F7 = 2 => 19 pairs (_) D4,F6: 3.. / D4 = 3 => 8 pairs (_) / F6 = 3 => 19 pairs (_) B4,C4: 4.. / B4 = 4 => 9 pairs (_) / C4 = 4 => 9 pairs (_) D5,F5: 4.. / D5 = 4 => 8 pairs (_) / F5 = 4 => 11 pairs (_) C2,F2: 4.. / C2 = 4 => 9 pairs (_) / F2 = 4 => 9 pairs (_) B1,B4: 4.. / B1 = 4 => 9 pairs (_) / B4 = 4 => 9 pairs (_) D1,D5: 4.. / D1 = 4 => 11 pairs (_) / D5 = 4 => 8 pairs (_) F2,I2: 5.. / F2 = 5 => 11 pairs (_) / I2 = 5 => 8 pairs (_) C8,D8: 5.. / C8 = 5 => 12 pairs (_) / D8 = 5 => 10 pairs (_) G1,I1: 7.. / G1 = 7 => 0 pairs (X) / I1 = 7 => 8 pairs (_) F7,F9: 7.. / F7 = 7 => 8 pairs (_) / F9 = 7 => 19 pairs (_) I1,I5: 7.. / I1 = 7 => 8 pairs (_) / I5 = 7 => 0 pairs (X) I8,G9: 8.. / I8 = 8 => 9 pairs (_) / G9 = 8 => 0 pairs (X) D8,I8: 8.. / D8 = 8 => 0 pairs (X) / I8 = 8 => 9 pairs (_) F5,E6: 9.. / F5 = 9 => 0 pairs (X) / E6 = 9 => 9 pairs (_) A7,B7: 9.. / A7 = 9 => 10 pairs (_) / B7 = 9 => 9 pairs (_) E1,E6: 9.. / E1 = 9 => 0 pairs (X) / E6 = 9 => 9 pairs (_) * DURATION: 0:00:34.639801 START: 05:42:49.701819 END: 05:43:24.341620 2017-05-01 * CP COUNT: (27) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,C8,D4,D7,E4,F6,F7,I8) * 5.........1.67..9...7.2.4.......1..9.3..6..2.1..7....4..8.4.5..42..3697....9...42 * PAIR C5: 5,9 BLK 4 B6: 5,9,6,8 # reduction candidate for 5,9 B6: 5,9 # 11 pairs C6: 5,9,2,6 # reduction candidate for 5,9 C6: 5,9 => CTR * 54........1.6748959871254..2743.16.9835469.2.1697.23.4.982475..42153697875.918.42 C6: 2,6 # 9 pairs * PAIR C5: 5,9 ROW 5 F5: 5,9,4,8 # reduction candidate for 5,9 F5: 5,9 # 12 pairs F5: 4,8 # 10 pairs * PAIR E4: 5,8 BLK 5 D5: 5,8,4 # reduction candidate for 5,8 D5: 5,8 # 11 pairs F5: 5,8,4,9 # reduction candidate for 5,8 F5: 5,8 # 10 pairs E6: 5,8,9 # reduction candidate for 5,8 E6: 5,8 => CTR * 54..93....1.6748959871254..2743.16.9835469.2.1697.23.4.982475..42153697875.918.42 E6: 9 # 9 pairs * PAIR E4: 5,8 ROW 4 B4: 5,8,4,6,7 # reduction candidate for 5,8 B4: 5,8 => CTR * 54......7813674295..7.2.4..254381769739465.2.186792354..82475..42..3697.37.958642 B4: 4,6,7 # 8 pairs H4: 5,8,3,6 # reduction candidate for 5,8 H4: 5,8 # 9 pairs * PAIR E4: 5,8 COL E E9: 5,8,1 # reduction candidate for 5,8 E9: 5,8 # 9 pairs E9: 1 # 9 pairs * PAIR C8: 1,5 BLK 7 C9: 1,5,3,6 # reduction candidate for 1,5 C9: 1,5 # 13 pairs C9: 3,6 # 11 pairs * PAIR C8: 1,5 ROW 8 D8: 1,5,8 # reduction candidate for 1,5 D8: 8 => CTR * 5...1.2.721.67.39...732.41....281739739564128182793654978142563425836971361957842 D8: 1,5 # 9 pairs * PAIR I8: 1,8 BLK 9 G9: 1,8,3,6 # reduction candidate for 1,8 G9: 1,8 # 19 pairs G9: 3,6 # 8 pairs * PAIR I8: 1,8 ROW 8 D8: 1,8,5 # reduction candidate for 1,8 D8: 1,8 # 12 pairs D8: 5 # 10 pairs * PAIR I8: 1,8 COL I I1: 1,8,3,6,7 # reduction candidate for 1,8 I1: 1,8 => CTR * 542...76..13674295..7.2.4..2743.16.9.3.46.1271..7.2..439824751642..369787..9..342 I1: 3,6,7 # 8 pairs I3: 1,8,3,5,6 # reduction candidate for 1,8 I3: 1,8 # 12 pairs I5: 1,8,5,7 # reduction candidate for 1,8 I5: 1,8 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0121-base-pr-000.dot * REASONING * DIS # C6: 5,9 => CTR => C6: 2,6 * DIS # E6: 5,8 => CTR => E6: 9 * DIS # B4: 5,8 => CTR => B4: 4,6,7 * DIS # D8: 8 => CTR => D8: 1,5 * DIS # I1: 1,8 => CTR => I1: 3,6,7 * CNT 5 HDP CHAINS / 26 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,C8,D4,D7,E4,F6,F7,I8) * 5.........1.67..9...7.2.4.......1..9.3..6..2.1..7....4..8.4.5..42..3697....9...42 * PAIR C5: 5,9 BLK 4 B6: 5,9,6,8 # reduction candidate for 5,9 B6: 5,9 # 11 pairs C6: 5,9,2,6 # reduction candidate for 5,9 C6: 5,9 => CTR * 54........1.6748959871254..2743.16.9835469.2.1697.23.4.982475..42153697875.918.42 * RESTART * PAIR C5: 5,9 BLK 4 B6: 5,9,6,8 # reduction candidate for 5,9 B6: 6,8 # 11 pairs B6: 5,9 # 11 pairs * PAIR C5: 5,9 ROW 5 F5: 5,9,4,8 # reduction candidate for 5,9 F5: 5,9 # 13 pairs F5: 4,8 # 11 pairs * PAIR E4: 5,8 BLK 5 D5: 5,8,4 # reduction candidate for 5,8 D5: 5,8 # 12 pairs F5: 5,8,4,9 # reduction candidate for 5,8 F5: 5,8 # 11 pairs E6: 5,8,9 # reduction candidate for 5,8 E6: 5,8 => CTR * 5...9.....1.67..9...7.2.4.......1..9.39.6..2.1..7....4..8.4.5..42..3697....91..42 * PAIR E4: 5,8 ROW 4 B4: 5,8,4,6,7 # reduction candidate for 5,8 B4: 5,8 => CTR * 54..19..7813674295..7523481254381769739465.2.1.6792354..82475..42..3697..7.958.42 H4: 5,8,3,6 # reduction candidate for 5,8 H4: 5,8 # 16 pairs * RESTART * PAIR E4: 5,8 ROW 4 H4: 5,8,3,6 # reduction candidate for 5,8 H4: 5,8 # 16 pairs H4: 3,6 # 11 pairs * PAIR E4: 5,8 COL E E9: 5,8,1 # reduction candidate for 5,8 E9: 1 => SOLVED * 563489217214675893987123456842351769739864125156792384698247531421536978375918642 * DURATION: 0:00:12.531465 START: 05:43:43.237252 END: 05:43:55.768717 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0121-base-pr-001.dot * REASONING * DIS # C6: 5,9 => CTR => C6: 2,6 * DIS C6: 2,6 # E6: 5,8 => CTR => E6: 9 * DIS C6: 2,6 + E6: 9 # B4: 5,8 => CTR => B4: 4,6,7 * PRF C6: 2,6 + E6: 9 + B4: 4,6,7 # E9: 1 => SOL * STA C6: 2,6 + E6: 9 + B4: 4,6,7 + E9: 1 * CNT 4 HDP CHAINS / 15 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=121
Solution
position: 563489217214675893987123456842351769739864125156792384698247531421536978375918642 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 # B6: 5,9 => UNS * DIS # C6: 5,9 => CTR => C6: 2,6 * INC # C6: 2,6 => UNS * INC # F5: 5,9 => UNS * INC # F5: 4,8 => UNS * INC # D5: 5,8 => UNS * INC # F5: 5,8 => UNS * DIS # E6: 5,8 => CTR => E6: 9 * INC # E6: 9 => UNS * DIS # B4: 5,8 => CTR => B4: 4,6,7 * INC # B4: 4,6,7 => UNS * INC # H4: 5,8 => UNS * INC # E9: 5,8 => UNS * INC # E9: 1 => UNS * INC # C9: 1,5 => UNS * INC # C9: 3,6 => UNS * INC # D8: 1,5 => UNS * DIS # D8: 8 => CTR => D8: 1,5 * INC # G9: 1,8 => UNS * INC # G9: 3,6 => UNS * INC # D8: 1,8 => UNS * INC # D8: 5 => UNS * DIS # I1: 1,8 => CTR => I1: 3,6,7 * INC # I1: 3,6,7 => UNS * INC # I3: 1,8 => UNS * INC # I5: 1,8 => UNS * CNT 26 HDP CHAINS / 26 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B6: 5,9 => UNS * DIS # C6: 5,9 => CTR => C6: 2,6 * INC C6: 2,6 # B6: 5,9 => UNS * INC C6: 2,6 # B6: 6,8 => UNS * INC C6: 2,6 # F5: 5,9 => UNS * INC C6: 2,6 # F5: 4,8 => UNS * INC C6: 2,6 # D5: 5,8 => UNS * INC C6: 2,6 # F5: 5,8 => UNS * DIS C6: 2,6 # E6: 5,8 => CTR => E6: 9 * DIS C6: 2,6 + E6: 9 # B4: 5,8 => CTR => B4: 4,6,7 * INC C6: 2,6 + E6: 9 + B4: 4,6,7 # H4: 5,8 => UNS * INC C6: 2,6 + E6: 9 + B4: 4,6,7 # H4: 5,8 => UNS * INC C6: 2,6 + E6: 9 + B4: 4,6,7 # H4: 3,6 => UNS * INC C6: 2,6 + E6: 9 + B4: 4,6,7 # E9: 5,8 => UNS * PRF C6: 2,6 + E6: 9 + B4: 4,6,7 # E9: 1 => SOL * STA C6: 2,6 + E6: 9 + B4: 4,6,7 + E9: 1 * CNT 15 HDP CHAINS / 15 HYP OPENED