Analysis of zz-www.sudokuwiki.org-0038-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=38
level: medium
position: ....2..7..5..97...6.73..2..4.......5.16...32.7.......6..2..94.3...47..1..8..5.... initial
Autosolve
position: ....2..7.25..97.346.73..2..4.......5.16...32.7......46.72..94.3.6.47..1..84.5.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D2: 6 => CTR => D2: 1,8 * DIS # D2: 1 => CTR => D2: 6,8 * DIS # D4: 8,9 => CTR => D4: 1,2,6,7 * DIS # H3: 8,9 => CTR => H3: 5 * DIS # I9: 2 => CTR => I9: 7,9 * 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 # D2: 6 => CTR => D2: 1,8 * DIS D2: 1,8 # C1: 1,8 => CTR => C1: 3,9 * DIS D2: 1,8 + C1: 3,9 # B1: 3 => CTR => B1: 4,9 * DIS D2: 1,8 + C1: 3,9 + B1: 4,9 # F5: 5 => CTR => F5: 4,8 * DIS D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 # G6: 1 => CTR => G6: 8,9 * DIS D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 + G6: 8,9 # H3: 8,9 => CTR => H3: 5 * PRF D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 + G6: 8,9 + H3: 5 => SOL * STA D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 + G6: 8,9 + H3: 5 * CNT 7 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....2..7..5..97...6.73..2..4.......5.16...32.7.......6..2..94.3...47..1..8..5.... | initial |
| ....2..7.25..97.346.73..2..4.......5.16...32.7......46.72..94.3.6.47..1..84.5.... | autosolve |
| 843625971251897634697341258428736195916584327735912846572169483369478512184253769 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) C2: 1,8 B3: 4,9 G2: 6,8 E5: 4,8 H4: 8,9 A7: 1,5 G9: 7,9 H9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,C2: 1.. / C1 = 1 => 0 pairs (X) / C2 = 1 => 9 pairs (_) I1,I3: 1.. / I1 = 1 => 10 pairs (_) / I3 = 1 => 12 pairs (_) G4,G6: 1.. / G4 = 1 => 9 pairs (_) / G6 = 1 => 9 pairs (_) A7,A9: 1.. / A7 = 1 => 0 pairs (X) / A9 = 1 => 14 pairs (_) C2,D2: 1.. / C2 = 1 => 9 pairs (_) / D2 = 1 => 0 pairs (X) B4,B6: 2.. / B4 = 2 => 9 pairs (_) / B6 = 2 => 11 pairs (_) I8,I9: 2.. / I8 = 2 => 13 pairs (_) / I9 = 2 => 0 pairs (X) F8,I8: 2.. / F8 = 2 => 0 pairs (X) / I8 = 2 => 13 pairs (_) E4,E6: 3.. / E4 = 3 => 15 pairs (_) / E6 = 3 => 9 pairs (_) F8,F9: 3.. / F8 = 3 => 0 pairs (X) / F9 = 3 => 10 pairs (_) A9,F9: 3.. / A9 = 3 => 0 pairs (X) / F9 = 3 => 10 pairs (_) B1,B3: 4.. / B1 = 4 => 14 pairs (_) / B3 = 4 => 14 pairs (_) E5,F5: 4.. / E5 = 4 => 9 pairs (_) / F5 = 4 => 18 pairs (_) B1,F1: 4.. / B1 = 4 => 14 pairs (_) / F1 = 4 => 14 pairs (_) E3,E5: 4.. / E3 = 4 => 18 pairs (_) / E5 = 4 => 9 pairs (_) G1,H3: 5.. / G1 = 5 => 0 pairs (X) / H3 = 5 => 14 pairs (_) A5,C6: 5.. / A5 = 5 => 0 pairs (X) / C6 = 5 => 10 pairs (_) H7,G8: 5.. / H7 = 5 => 0 pairs (X) / G8 = 5 => 14 pairs (_) F3,H3: 5.. / F3 = 5 => 0 pairs (X) / H3 = 5 => 14 pairs (_) A7,H7: 5.. / A7 = 5 => 14 pairs (_) / H7 = 5 => 0 pairs (X) C6,C8: 5.. / C6 = 5 => 10 pairs (_) / C8 = 5 => 0 pairs (X) G1,G8: 5.. / G1 = 5 => 0 pairs (X) / G8 = 5 => 14 pairs (_) H3,H7: 5.. / H3 = 5 => 14 pairs (_) / H7 = 5 => 0 pairs (X) G1,G2: 6.. / G1 = 6 => 0 pairs (X) / G2 = 6 => 8 pairs (_) H7,H9: 6.. / H7 = 6 => 0 pairs (X) / H9 = 6 => 9 pairs (_) D2,G2: 6.. / D2 = 6 => 0 pairs (X) / G2 = 6 => 8 pairs (_) E4,E7: 6.. / E4 = 6 => 10 pairs (_) / E7 = 6 => 10 pairs (_) D4,D5: 7.. / D4 = 7 => 8 pairs (_) / D5 = 7 => 13 pairs (_) G4,I5: 7.. / G4 = 7 => 13 pairs (_) / I5 = 7 => 8 pairs (_) G9,I9: 7.. / G9 = 7 => 8 pairs (_) / I9 = 7 => 13 pairs (_) D4,G4: 7.. / D4 = 7 => 8 pairs (_) / G4 = 7 => 13 pairs (_) D5,I5: 7.. / D5 = 7 => 13 pairs (_) / I5 = 7 => 8 pairs (_) G4,G9: 7.. / G4 = 7 => 13 pairs (_) / G9 = 7 => 8 pairs (_) I5,I9: 7.. / I5 = 7 => 8 pairs (_) / I9 = 7 => 13 pairs (_) A1,A5: 8.. / A1 = 8 => 12 pairs (_) / A5 = 8 => 18 pairs (_) * DURATION: 0:00:46.161570 START: 04:09:07.810506 END: 04:09:53.972076 2017-05-01 * CP COUNT: (35) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B3,C2,E5,G2,G9,H4,H9) * ....2..7.25..97.346.73..2..4.......5.16...32.7......46.72..94.3.6.47..1..84.5.... * PAIR C2: 1,8 BLK 1 C1: 1,8,3,9 # reduction candidate for 1,8 C1: 1,8 # 18 pairs C1: 3,9 # 12 pairs * PAIR C2: 1,8 ROW 2 D2: 1,8,6 # reduction candidate for 1,8 D2: 6 => CTR * 8...2.67.2516978346.738.25.428..6.95.16...3287.5..2146572.69483.6.478512184253967 D2: 1,8 # 8 pairs * PAIR B3: 4,9 BLK 1 B1: 4,9,3 # reduction candidate for 4,9 B1: 3 # 21 pairs B1: 4,9 # 14 pairs * PAIR G2: 6,8 BLK 3 G1: 6,8,5,9 # reduction candidate for 6,8 G1: 6,8 # 22 pairs G1: 5,9 # 9 pairs * PAIR G2: 6,8 ROW 2 D2: 6,8,1 # reduction candidate for 6,8 D2: 1 => CTR * 341526879258197634697384251439261.85816.4532.7.5.3..46572819463963472518184653.92 D2: 6,8 # 9 pairs * PAIR E5: 4,8 BLK 5 F5: 4,8,5 # reduction candidate for 4,8 F5: 4,8 # 15 pairs F5: 5 # 14 pairs * PAIR E5: 4,8 COL E E3: 4,8,1 # reduction candidate for 4,8 E3: 1 # 12 pairs E3: 4,8 # 11 pairs * PAIR H4: 8,9 BLK 6 G4: 8,9,1,7 # reduction candidate for 8,9 G4: 8,9 # 20 pairs I5: 8,9,7 # reduction candidate for 8,9 I5: 8,9 # 13 pairs G6: 8,9,1 # reduction candidate for 8,9 G6: 8,9 # 9 pairs * PAIR H4: 8,9 ROW 4 C4: 8,9,3 # reduction candidate for 8,9 C4: 8,9 # 11 pairs D4: 8,9,1,2,6,7 # reduction candidate for 8,9 D4: 8,9 => CTR * .3..2457.25..97634647385291423916785516748329798532146172869453.65473812384251967 D4: 1,2,6,7 # 8 pairs * PAIR H4: 8,9 COL H H3: 8,9,5 # reduction candidate for 8,9 H3: 8,9 => CTR * 8..62457.2518976346.73.52..4.......5.16...32.7......46172..9453.6.47..1..84.5..6. H3: 5 # 14 pairs * PAIR G9: 7,9 BLK 9 I9: 7,9,2 # reduction candidate for 7,9 I9: 2 => CTR * ...526.7.25..976346.73..25.42.76..858169453277.5238146572..9463.6.472518184653792 I9: 7,9 # 13 pairs * PAIR G9: 7,9 COL G G4: 7,9,1,8 # reduction candidate for 7,9 G4: 7,9 # 11 pairs G4: 1,8 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0038-base-pr-000.dot * REASONING * DIS # D2: 6 => CTR => D2: 1,8 * DIS # D2: 1 => CTR => D2: 6,8 * DIS # D4: 8,9 => CTR => D4: 1,2,6,7 * DIS # H3: 8,9 => CTR => H3: 5 * DIS # I9: 2 => CTR => I9: 7,9 * CNT 5 HDP CHAINS / 26 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B3,C2,E5,G2,G9,H4,H9) * ....2..7.25..97.346.73..2..4.......5.16...32.7......46.72..94.3.6.47..1..84.5.... * PAIR C2: 1,8 BLK 1 C1: 1,8,3,9 # reduction candidate for 1,8 C1: 1,8 # 18 pairs C1: 3,9 # 12 pairs * PAIR C2: 1,8 ROW 2 D2: 1,8,6 # reduction candidate for 1,8 D2: 6 => CTR * 8...2.67.2516978346.738.25.428..6.95.16...3287.5..2146572.69483.6.478512184253967 * PAIR RESTART * PAIR C2: 1,8 BLK 1 C1: 1,8,3,9 # reduction candidate for 1,8 C1: 1,8 => CTR * 34.5268792581976346973842514.9.6..858169453277.5.38.46572..946396347.518184653.92 * PAIR B3: 4,9 BLK 1 B1: 4,9,3 # reduction candidate for 4,9 B1: 3 => CTR * 8396245712518976346473152..4.3.6...5516.4832.7.853..46172.89453.6547..1..84.5..6. * PAIR E5: 4,8 BLK 5 F5: 4,8,5 # reduction candidate for 4,8 F5: 5 => CTR * 8.3.2..7.2518976346.73..2..4.......5.16.453287.5....46.72..94.3.6947.812.84.5...7 * PAIR H4: 8,9 BLK 6 G6: 8,9,1 # reduction candidate for 8,9 G6: 1 => CTR * 8.352697.2518976346.73..2..4......85.16...3297.89.5146.72.894.3.6547.812.84.5...7 * PAIR H4: 8,9 COL H H3: 8,9,5 # reduction candidate for 8,9 H3: 8,9 => CTR * 8.31265792518976346973452..4..7..1.5.16...3277......46172689453.6.47..1..84.5.76. H3: 5 => SOLVED * 843625971251897634697341258428736195916584327735912846572169483369478512184253769 * DURATION: 0:00:14.007945 START: 04:10:13.941014 END: 04:10:27.948959 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0038-base-pr-001.dot * REASONING * DIS # D2: 6 => CTR => D2: 1,8 * DIS D2: 1,8 # C1: 1,8 => CTR => C1: 3,9 * DIS D2: 1,8 + C1: 3,9 # B1: 3 => CTR => B1: 4,9 * DIS D2: 1,8 + C1: 3,9 + B1: 4,9 # F5: 5 => CTR => F5: 4,8 * DIS D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 # G6: 1 => CTR => G6: 8,9 * DIS D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 + G6: 8,9 # H3: 8,9 => CTR => H3: 5 * PRF D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 + G6: 8,9 + H3: 5 => SOL * STA D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 + G6: 8,9 + H3: 5 * CNT 7 HDP CHAINS / 12 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=38
Solution
position: 843625971251897634697341258428736195916584327735912846572169483369478512184253769 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 # C1: 1,8 => UNS * INC # C1: 3,9 => UNS * INC # D2: 1,8 => UNS * DIS # D2: 6 => CTR => D2: 1,8 * INC # B1: 4,9 => UNS * INC # B1: 3 => UNS * INC # G1: 6,8 => UNS * INC # G1: 5,9 => UNS * INC # D2: 6,8 => UNS * DIS # D2: 1 => CTR => D2: 6,8 * INC # F5: 4,8 => UNS * INC # F5: 5 => UNS * INC # E3: 4,8 => UNS * INC # E3: 1 => UNS * INC # G4: 8,9 => UNS * INC # I5: 8,9 => UNS * INC # G6: 8,9 => UNS * INC # C4: 8,9 => UNS * DIS # D4: 8,9 => CTR => D4: 1,2,6,7 * INC # D4: 1,2,6,7 => UNS * DIS # H3: 8,9 => CTR => H3: 5 * INC # H3: 5 => UNS * INC # I9: 7,9 => UNS * DIS # I9: 2 => CTR => I9: 7,9 * INC # G4: 7,9 => UNS * INC # G4: 1,8 => UNS * CNT 26 HDP CHAINS / 26 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 1,8 => UNS * INC # C1: 3,9 => UNS * INC # D2: 1,8 => UNS * DIS # D2: 6 => CTR => D2: 1,8 * DIS D2: 1,8 # C1: 1,8 => CTR => C1: 3,9 * INC D2: 1,8 + C1: 3,9 # B1: 4,9 => UNS * DIS D2: 1,8 + C1: 3,9 # B1: 3 => CTR => B1: 4,9 * INC D2: 1,8 + C1: 3,9 + B1: 4,9 # F5: 4,8 => UNS * DIS D2: 1,8 + C1: 3,9 + B1: 4,9 # F5: 5 => CTR => F5: 4,8 * INC D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 # G6: 8,9 => UNS * DIS D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 # G6: 1 => CTR => G6: 8,9 * DIS D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 + G6: 8,9 # H3: 8,9 => CTR => H3: 5 * PRF D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 + G6: 8,9 + H3: 5 => SOL * STA D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 + G6: 8,9 + H3: 5 * CNT 13 HDP CHAINS / 12 HYP OPENED