Analysis of zz-www.sudokuwiki.org-0058-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=58
level: medium
position: ..18.....28....7.....1...9.5....9.7...8.2.4...3.6....2.2...3.....4.....5...9.61.. initial
Autosolve
position: ..18.....28....7.....1...9.5.2..9.7...8.2.4...3.6....2.2...3.....42....5...9.612. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 4,5 => CTR => E1: 3,6,7,9 * DIS # E2: 4,5 => CTR => E2: 3,6,9 * DIS # E3: 4,5 => CTR => E3: 3,6,7 * PRF # A6: 7,9 => SOL * DIS # C9: 5,7 => CTR => C9: 3 * PRF # E9: 5,7 => SOL * CNT 6 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E1: 4,5 => CTR => E1: 3,6,7,9 * DIS E1: 3,6,7,9 # E2: 4,5 => CTR => E2: 3,6,9 * DIS E1: 3,6,7,9 + E2: 3,6,9 # E3: 4,5 => CTR => E3: 3,6,7 * PRF E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 # A6: 7,9 => SOL * STA E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 + A6: 7,9 * CNT 4 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..18.....28....7.....1...9.5....9.7...8.2.4...3.6....2.2...3.....4.....5...9.61.. | initial |
| ..18.....28....7.....1...9.5.2..9.7...8.2.4...3.6....2.2...3.....42....5...9.612. | autosolve |
| 371892546289564713465137298542389671618725439937641852126453987794218365853976124 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) F2: 4,5 C6: 7,9 D4: 3,4 B9: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H2,I2: 1.. / H2 = 1 => 5 pairs (_) / I2 = 1 => 4 pairs (_) A7,E7: 1.. / A7 = 1 => 4 pairs (_) / E7 = 1 => 11 pairs (_) F1,F3: 2.. / F1 = 2 => 4 pairs (_) / F3 = 2 => 4 pairs (_) G1,G3: 2.. / G1 = 2 => 4 pairs (_) / G3 = 2 => 4 pairs (_) F1,G1: 2.. / F1 = 2 => 4 pairs (_) / G1 = 2 => 4 pairs (_) F3,G3: 2.. / F3 = 2 => 4 pairs (_) / G3 = 2 => 4 pairs (_) B4,A6: 4.. / B4 = 4 => 12 pairs (_) / A6 = 4 => 6 pairs (_) E9,I9: 4.. / E9 = 4 => 5 pairs (_) / I9 = 4 => 0 pairs (*) I7,I9: 7.. / I7 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) D5,D7: 7.. / D5 = 7 => 7 pairs (_) / D7 = 7 => 8 pairs (_) G3,I3: 8.. / G3 = 8 => 7 pairs (_) / I3 = 8 => 4 pairs (_) F6,F8: 8.. / F6 = 8 => 9 pairs (_) / F8 = 8 => 6 pairs (_) E1,E2: 9.. / E1 = 9 => 5 pairs (_) / E2 = 9 => 4 pairs (_) I5,G6: 9.. / I5 = 9 => 5 pairs (_) / G6 = 9 => 0 pairs (X) C2,E2: 9.. / C2 = 9 => 5 pairs (_) / E2 = 9 => 4 pairs (_) I5,I7: 9.. / I5 = 9 => 5 pairs (_) / I7 = 9 => 0 pairs (X) * DURATION: 0:00:17.095149 START: 04:28:23.702931 END: 04:28:40.798080 2017-05-01 * CP COUNT: (16) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,C6,D4,F2) * ..18.....28....7.....1...9.5.2..9.7...8.2.4...3.6....2.2...3.....42....5...9.612. * PAIR F2: 4,5 BLK 2 E1: 4,5,3,6,7,9 # reduction candidate for 4,5 E1: 4,5 => CTR * ..185....28.3947.....16..9.5.2439.7...872.4..4376..9.2.295.36....42..385...9.612. E1: 3,6,7,9 # 4 pairs F1: 4,5,2,7 # reduction candidate for 4,5 F1: 4,5 # 15 pairs D2: 4,5,3 # reduction candidate for 4,5 D2: 4,5 # 10 pairs E2: 4,5,3,6,9 # reduction candidate for 4,5 E2: 4,5 => CTR * ..189....2893547.....16..985.2439671..8.2.4..4376..9.2.26..3849..42....5...946127 E2: 3,6,9 # 4 pairs E3: 4,5,3,6,7 # reduction candidate for 4,5 E3: 4,5 => CTR * ..18..5..28.3.47.....15..9.5.2439.7...872.4..4376..9.2.2.5.3..9..42....5...9.6127 E3: 3,6,7 # 4 pairs F3: 4,5,2,7 # reduction candidate for 4,5 F3: 4,5 # 15 pairs * PAIR F2: 4,5 ROW 2 H2: 4,5,1,3,6 # reduction candidate for 4,5 H2: 4,5 # 14 pairs H2: 1,3,6 # 4 pairs * PAIR F2: 4,5 COL F F6: 4,5,1,7,8 # reduction candidate for 4,5 F6: 4,5 # 13 pairs F6: 1,7,8 # 5 pairs * PAIR C6: 7,9 BLK 4 A5: 7,9,1,6 # reduction candidate for 7,9 A5: 7,9 # 7 pairs B5: 7,9,1,6 # reduction candidate for 7,9 B5: 7,9 # 7 pairs A6: 7,9,1,4 # reduction candidate for 7,9 A6: 7,9 => SOLVED * 371892546289564713465137298542389671618725439937641852126453987794218365853976124 A6: 1,4 # 5 pairs * PAIR C6: 7,9 COL C C7: 7,9,5,6 # reduction candidate for 7,9 C7: 7,9 # 6 pairs C7: 5,6 # 5 pairs * PAIR D4: 3,4 BLK 5 E4: 3,4,1,8 # reduction candidate for 3,4 E4: 3,4 # 12 pairs E4: 1,8 # 11 pairs * PAIR D4: 3,4 COL D D2: 3,4,5 # reduction candidate for 3,4 D2: 5 # 10 pairs D2: 3,4 # 8 pairs * PAIR B9: 5,7 BLK 7 C7: 5,7,6,9 # reduction candidate for 5,7 C7: 5,7 # 12 pairs C9: 5,7,3 # reduction candidate for 5,7 C9: 5,7 => CTR * ..18...4.28.5.47..4..1...9.542319.7...8725439.3.648..2.2.453..7..42....5...986124 C9: 3 # 5 pairs * PAIR B9: 5,7 ROW 9 E9: 5,7,4,8 # reduction candidate for 5,7 E9: 5,7 => SOLVED * 371892546289564713465137298542389671618725439937641852126453987794218365853976124 E9: 4,8 # 5 pairs * PAIR B9: 5,7 COL B B1: 5,7,4,6,9 # reduction candidate for 5,7 B1: 5,7 # 6 pairs B3: 5,7,4,6 # reduction candidate for 5,7 B3: 5,7 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0058-base-pr-000.dot * REASONING * DIS # E1: 4,5 => CTR => E1: 3,6,7,9 * DIS # E2: 4,5 => CTR => E2: 3,6,9 * DIS # E3: 4,5 => CTR => E3: 3,6,7 * PRF # A6: 7,9 => SOL * DIS # C9: 5,7 => CTR => C9: 3 * PRF # E9: 5,7 => SOL * CNT 6 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,C6,D4,F2) * ..18.....28....7.....1...9.5.2..9.7...8.2.4...3.6....2.2...3.....42....5...9.612. * PAIR F2: 4,5 BLK 2 E1: 4,5,3,6,7,9 # reduction candidate for 4,5 E1: 4,5 => CTR * ..185....28.3947.....16..9.5.2439.7...872.4..4376..9.2.295.36....42..385...9.612. F1: 4,5,2,7 # reduction candidate for 4,5 F1: 4,5 # 15 pairs D2: 4,5,3 # reduction candidate for 4,5 D2: 4,5 # 10 pairs E2: 4,5,3,6,9 # reduction candidate for 4,5 E2: 4,5 => CTR * ..189....2893547.....16..985.2439671..8.2.4..4376..9.2.26..3849..42....5...946127 E3: 4,5,3,6,7 # reduction candidate for 4,5 E3: 4,5 => CTR * ..18..5..28.3.47.....15..9.5.2439.7...872.4..4376..9.2.2.5.3..9..42....5...9.6127 F3: 4,5,2,7 # reduction candidate for 4,5 F3: 4,5 # 15 pairs * PAIR F2: 4,5 ROW 2 H2: 4,5,1,3,6 # reduction candidate for 4,5 H2: 4,5 # 17 pairs H2: 1,3,6 # 4 pairs * PAIR F2: 4,5 COL F F6: 4,5,1,7,8 # reduction candidate for 4,5 F6: 4,5 # 16 pairs F6: 1,7,8 # 5 pairs * PAIR RESTART * PAIR F2: 4,5 BLK 2 F1: 4,5,2,7 # reduction candidate for 4,5 F1: 4,5 # 15 pairs D2: 4,5,3 # reduction candidate for 4,5 D2: 4,5 # 10 pairs F3: 4,5,2,7 # reduction candidate for 4,5 F3: 4,5 # 15 pairs * PAIR F2: 4,5 ROW 2 H2: 4,5,1,3,6 # reduction candidate for 4,5 H2: 4,5 # 17 pairs H2: 1,3,6 # 4 pairs * PAIR F2: 4,5 COL F F6: 4,5,1,7,8 # reduction candidate for 4,5 F6: 4,5 # 16 pairs F6: 1,7,8 # 5 pairs * PAIR C6: 7,9 BLK 4 A5: 7,9,1,6 # reduction candidate for 7,9 A5: 7,9 # 7 pairs B5: 7,9,1,6 # reduction candidate for 7,9 B5: 7,9 # 7 pairs A6: 7,9,1,4 # reduction candidate for 7,9 A6: 7,9 => SOLVED * 371892546289564713465137298542389671618725439937641852126453987794218365853976124 * DURATION: 0:00:15.971616 START: 04:28:59.399511 END: 04:29:15.371127 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0058-base-pr-001.dot * REASONING * DIS # E1: 4,5 => CTR => E1: 3,6,7,9 * DIS E1: 3,6,7,9 # E2: 4,5 => CTR => E2: 3,6,9 * DIS E1: 3,6,7,9 + E2: 3,6,9 # E3: 4,5 => CTR => E3: 3,6,7 * PRF E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 # A6: 7,9 => SOL * STA E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 + A6: 7,9 * CNT 4 HDP CHAINS / 20 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=58
Solution
position: 371892546289564713465137298542389671618725439937641852126453987794218365853976124 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 # E1: 4,5 => CTR => E1: 3,6,7,9 * INC # E1: 3,6,7,9 => UNS * INC # F1: 4,5 => UNS * INC # D2: 4,5 => UNS * DIS # E2: 4,5 => CTR => E2: 3,6,9 * INC # E2: 3,6,9 => UNS * DIS # E3: 4,5 => CTR => E3: 3,6,7 * INC # E3: 3,6,7 => UNS * INC # F3: 4,5 => UNS * INC # H2: 4,5 => UNS * INC # H2: 1,3,6 => UNS * INC # F6: 4,5 => UNS * INC # F6: 1,7,8 => UNS * INC # A5: 7,9 => UNS * INC # B5: 7,9 => UNS * PRF # A6: 7,9 => SOL * INC # A6: 1,4 => UNS * INC # C7: 7,9 => UNS * INC # C7: 5,6 => UNS * INC # E4: 3,4 => UNS * INC # E4: 1,8 => UNS * INC # D2: 3,4 => UNS * INC # D2: 5 => UNS * INC # C7: 5,7 => UNS * DIS # C9: 5,7 => CTR => C9: 3 * INC # C9: 3 => UNS * PRF # E9: 5,7 => SOL * INC # E9: 4,8 => UNS * INC # B1: 5,7 => UNS * INC # B3: 5,7 => UNS * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E1: 4,5 => CTR => E1: 3,6,7,9 * INC E1: 3,6,7,9 # F1: 4,5 => UNS * INC E1: 3,6,7,9 # D2: 4,5 => UNS * DIS E1: 3,6,7,9 # E2: 4,5 => CTR => E2: 3,6,9 * DIS E1: 3,6,7,9 + E2: 3,6,9 # E3: 4,5 => CTR => E3: 3,6,7 * INC E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 # F3: 4,5 => UNS * INC E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 # H2: 4,5 => UNS * INC E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 # H2: 1,3,6 => UNS * INC E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 # F6: 4,5 => UNS * INC E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 # F6: 1,7,8 => UNS * INC E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 # F1: 4,5 => UNS * INC E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 # D2: 4,5 => UNS * INC E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 # F3: 4,5 => UNS * INC E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 # H2: 4,5 => UNS * INC E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 # H2: 1,3,6 => UNS * INC E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 # F6: 4,5 => UNS * INC E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 # F6: 1,7,8 => UNS * INC E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 # A5: 7,9 => UNS * INC E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 # B5: 7,9 => UNS * PRF E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 # A6: 7,9 => SOL * STA E1: 3,6,7,9 + E2: 3,6,9 + E3: 3,6,7 + A6: 7,9 * CNT 20 HDP CHAINS / 20 HYP OPENED