Analysis of zz-www.sudokuwiki.org-0089-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=89
level: medium
position: ......7....6.9..54...5.2.1...28....5.5.....3.8....64...8.3.9...91..4.6....4...... initial
Autosolve
position: ......7....6.9..54...5.2.1...28....5.5.....3.8...564...8.3.9.4.91..4.6....4...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F2: 1,7 => CTR => F2: 3,8 * DIS # D5: 1,7 => CTR => D5: 2,4,9 * DIS # D6: 1,7 => CTR => D6: 2,9 * DIS # G5: 1,9 => CTR => G5: 2,8 * PRF # A7: 5,7 => SOL * DIS # E7: 2,7 => CTR => E7: 1,6 * DIS # E9: 2,7 => CTR => E9: 1,6,8 * DIS # D5: 2,7 => CTR => D5: 1,4,9 * DIS # D6: 2,7 => CTR => D6: 1,9 * CNT 9 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 # F2: 1,7 => CTR => F2: 3,8 * PRF F2: 3,8 # A2: 2,3 => SOL * STA F2: 3,8 + A2: 2,3 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......7....6.9..54...5.2.1...28....5.5.....3.8....64...8.3.9...91..4.6....4...... | initial |
| ......7....6.9..54...5.2.1...28....5.5.....3.8...564...8.3.9.4.91..4.6....4...... | autosolve |
| 125634789376198254498572316742813965659427831831956427587369142913245678264781593 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) D2: 1,7 G4: 1,9 C7: 5,7 D8: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B6,C6: 3.. / B6 = 3 => 6 pairs (_) / C6 = 3 => 9 pairs (_) E4,F4: 3.. / E4 = 3 => 4 pairs (_) / F4 = 3 => 5 pairs (_) C8,I8: 3.. / C8 = 3 => 6 pairs (_) / I8 = 3 => 7 pairs (_) A3,B3: 4.. / A3 = 4 => 10 pairs (_) / B3 = 4 => 5 pairs (_) D1,F1: 4.. / D1 = 4 => 0 pairs (X) / F1 = 4 => 8 pairs (_) B3,B4: 4.. / B3 = 4 => 5 pairs (_) / B4 = 4 => 10 pairs (_) D1,D5: 4.. / D1 = 4 => 0 pairs (X) / D5 = 4 => 8 pairs (_) A1,C1: 5.. / A1 = 5 => 4 pairs (_) / C1 = 5 => 11 pairs (_) F8,F9: 5.. / F8 = 5 => 5 pairs (_) / F9 = 5 => 7 pairs (_) G7,G9: 5.. / G7 = 5 => 7 pairs (_) / G9 = 5 => 6 pairs (_) C8,F8: 5.. / C8 = 5 => 7 pairs (_) / F8 = 5 => 5 pairs (_) H4,I5: 6.. / H4 = 6 => 7 pairs (_) / I5 = 6 => 0 pairs (X) E3,I3: 6.. / E3 = 6 => 0 pairs (X) / I3 = 6 => 7 pairs (_) A5,I5: 6.. / A5 = 6 => 7 pairs (_) / I5 = 6 => 0 pairs (X) A7,E7: 6.. / A7 = 6 => 0 pairs (X) / E7 = 6 => 7 pairs (_) B4,B9: 6.. / B4 = 6 => 0 pairs (X) / B9 = 6 => 7 pairs (_) D1,D9: 6.. / D1 = 6 => 7 pairs (_) / D9 = 6 => 0 pairs (X) H1,H4: 6.. / H1 = 6 => 0 pairs (X) / H4 = 6 => 7 pairs (_) C1,C3: 8.. / C1 = 8 => 8 pairs (_) / C3 = 8 => 5 pairs (_) G5,I5: 8.. / G5 = 8 => 7 pairs (_) / I5 = 8 => 0 pairs (X) F2,G2: 8.. / F2 = 8 => 6 pairs (_) / G2 = 8 => 0 pairs (X) D5,D6: 9.. / D5 = 9 => 0 pairs (X) / D6 = 9 => 6 pairs (_) * DURATION: 0:00:28.104784 START: 05:03:34.247345 END: 05:04:02.352129 2017-05-01 * CP COUNT: (22) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C7,D2,D8,G4) * ......7....6.9..54...5.2.1...28....5.5.....3.8...564...8.3.9.4.91..4.6....4...... * PAIR D2: 1,7 BLK 2 F2: 1,7,3,8 # reduction candidate for 1,7 F2: 1,7 => CTR * .9.6.4723..6.9.854...5.2.16..28.3.6565.42..388..9564...8.369.4.91..4.6...64...... F2: 3,8 # 5 pairs * PAIR D2: 1,7 ROW 2 A2: 1,7,2,3 # reduction candidate for 1,7 A2: 2,3 # 11 pairs A2: 1,7 # 7 pairs * PAIR D2: 1,7 COL D D5: 1,7,2,4,9 # reduction candidate for 1,7 D5: 1,7 => CTR * .9.4..76.1.6798.54.4.562.1..628..195.5912.8368319564..68.3.9.4.91.24.68..7468..2. D5: 2,4,9 # 4 pairs D6: 1,7,2,9 # reduction candidate for 1,7 D6: 1,7 => CTR * ...4..76.1.6798.54347562918.628..195.5192.8368..156427685379.4.91.24.68...468.... D6: 2,9 # 5 pairs D9: 1,7,2,6 # reduction candidate for 1,7 D9: 1,7 # 8 pairs * PAIR G4: 1,9 BLK 6 G5: 1,9,2,8 # reduction candidate for 1,9 G5: 1,9 => CTR * 1256.47..3761982544985723167428.39656594271388319564..287369541913.4568..64...... G5: 2,8 # 5 pairs I5: 1,9,2,6,7,8 # reduction candidate for 1,9 I5: 1,9 # 18 pairs I6: 1,9,2,7 # reduction candidate for 1,9 I6: 1,9 # 8 pairs * PAIR G4: 1,9 COL G G9: 1,9,2,3,5,8 # reduction candidate for 1,9 G9: 1,9 # 10 pairs G9: 2,3,5,8 # 4 pairs * PAIR C7: 5,7 BLK 7 A7: 5,7,2,6 # reduction candidate for 5,7 A7: 5,7 => SOLVED * 125634789376198254498572316742813965659427831831956427587369142913245678264781593 A7: 2,6 # 5 pairs C8: 5,7,3 # reduction candidate for 5,7 C8: 5,7 # 7 pairs A9: 5,7,2,3,6 # reduction candidate for 5,7 A9: 5,7 # 9 pairs * PAIR D8: 2,7 BLK 8 E7: 2,7,1,6 # reduction candidate for 2,7 E7: 2,7 => CTR * 5.....76.1.6798.54347562918.628..195.5..2.8368...5642768537924191324568.2.46815.. E7: 1,6 # 5 pairs D9: 2,7,1,6 # reduction candidate for 2,7 D9: 2,7 # 18 pairs E9: 2,7,1,6,8 # reduction candidate for 2,7 E9: 2,7 => CTR * .9.6.472..2679.854...5.2316..28...6565.42..388319564...8.369.4191.24.6...6417.... E9: 1,6,8 # 4 pairs * PAIR D8: 2,7 ROW 8 H8: 2,7,8 # reduction candidate for 2,7 H8: 2,7 # 8 pairs I8: 2,7,3,8 # reduction candidate for 2,7 I8: 2,7 # 7 pairs * PAIR D8: 2,7 COL D D5: 2,7,1,4,9 # reduction candidate for 2,7 D5: 2,7 => CTR * ...4..76...619..54.4.562.1..628....5.59...8368..9564..68.3.9.4.91..4.6....46..... D5: 1,4,9 # 4 pairs D6: 2,7,1,9 # reduction candidate for 2,7 D6: 2,7 => CTR * ...4..76...619..54.4.562.1..628....5.5.9..8368...564..68.3.9.4.91..4.6....46..... D6: 1,9 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0089-base-pr-000.dot * REASONING * DIS # F2: 1,7 => CTR => F2: 3,8 * DIS # D5: 1,7 => CTR => D5: 2,4,9 * DIS # D6: 1,7 => CTR => D6: 2,9 * DIS # G5: 1,9 => CTR => G5: 2,8 * PRF # A7: 5,7 => SOL * DIS # E7: 2,7 => CTR => E7: 1,6 * DIS # E9: 2,7 => CTR => E9: 1,6,8 * DIS # D5: 2,7 => CTR => D5: 1,4,9 * DIS # D6: 2,7 => CTR => D6: 1,9 * CNT 9 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C7,D2,D8,G4) * ......7....6.9..54...5.2.1...28....5.5.....3.8...564...8.3.9.4.91..4.6....4...... * PAIR D2: 1,7 BLK 2 F2: 1,7,3,8 # reduction candidate for 1,7 F2: 1,7 => CTR * .9.6.4723..6.9.854...5.2.16..28.3.6565.42..388..9564...8.369.4.91..4.6...64...... * PAIR D2: 1,7 ROW 2 A2: 1,7,2,3 # reduction candidate for 1,7 A2: 2,3 => SOLVED * 125634789376198254498572316742813965659427831831956427587369142913245678264781593 * DURATION: 0:00:04.260860 START: 05:04:22.878167 END: 05:04:27.139027 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0089-base-pr-001.dot * REASONING * DIS # F2: 1,7 => CTR => F2: 3,8 * PRF F2: 3,8 # A2: 2,3 => SOL * STA F2: 3,8 + A2: 2,3 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=89
Solution
position: 125634789376198254498572316742813965659427831831956427587369142913245678264781593 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 # F2: 1,7 => CTR => F2: 3,8 * INC # F2: 3,8 => UNS * INC # A2: 1,7 => UNS * INC # A2: 2,3 => UNS * DIS # D5: 1,7 => CTR => D5: 2,4,9 * INC # D5: 2,4,9 => UNS * DIS # D6: 1,7 => CTR => D6: 2,9 * INC # D6: 2,9 => UNS * INC # D9: 1,7 => UNS * DIS # G5: 1,9 => CTR => G5: 2,8 * INC # G5: 2,8 => UNS * INC # I5: 1,9 => UNS * INC # I6: 1,9 => UNS * INC # G9: 1,9 => UNS * INC # G9: 2,3,5,8 => UNS * PRF # A7: 5,7 => SOL * INC # A7: 2,6 => UNS * INC # C8: 5,7 => UNS * INC # A9: 5,7 => UNS * DIS # E7: 2,7 => CTR => E7: 1,6 * INC # E7: 1,6 => UNS * INC # D9: 2,7 => UNS * DIS # E9: 2,7 => CTR => E9: 1,6,8 * INC # E9: 1,6,8 => UNS * INC # H8: 2,7 => UNS * INC # I8: 2,7 => UNS * DIS # D5: 2,7 => CTR => D5: 1,4,9 * INC # D5: 1,4,9 => UNS * DIS # D6: 2,7 => CTR => D6: 1,9 * INC # D6: 1,9 => UNS * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # F2: 1,7 => CTR => F2: 3,8 * INC F2: 3,8 # A2: 1,7 => UNS * PRF F2: 3,8 # A2: 2,3 => SOL * STA F2: 3,8 + A2: 2,3 * CNT 3 HDP CHAINS / 3 HYP OPENED