Analysis of zz-www.sudokuwiki.org-0023-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=23
level: medium
position: .....8.1.3......85...6..9.4.1.5..2......6......5..2.697.6..1...19.4....7.8.2..... initial
Autosolve
position: .....8.1.3......85...6..9.461.5..2......6......5..2.697.6..1...19.4....7.8.2..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A5: 4,8 => CTR => A5: 2,9 * DIS # H9: 4,5 => CTR => H9: 3,9 * PRF # G9: 3,4 => SOL * CNT 3 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A5: 4,8 => CTR => A5: 2,9 * DIS A5: 2,9 # H9: 4,5 => CTR => H9: 3,9 * PRF A5: 2,9 + H9: 3,9 # G9: 3,4 => SOL * STA A5: 2,9 + H9: 3,9 + G9: 3,4 * CNT 3 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....8.1.3......85...6..9.4.1.5..2......6......5..2.697.6..1...19.4....7.8.2..... | initial |
| .....8.1.3......85...6..9.461.5..2......6......5..2.697.6..1...19.4....7.8.2..... | autosolve |
| 924758316361924785857613924618549273239167548475832169746391852192485637583276491 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) G2: 6,7 A6: 4,8 I4: 3,8 C8: 2,3 A9: 4,5 C9: 3,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 1.. / C2 = 1 => 8 pairs (_) / C3 = 1 => 7 pairs (_) G9,I9: 1.. / G9 = 1 => 7 pairs (_) / I9 = 1 => 15 pairs (_) C3,E3: 1.. / C3 = 1 => 7 pairs (_) / E3 = 1 => 8 pairs (_) I5,I9: 1.. / I5 = 1 => 7 pairs (_) / I9 = 1 => 15 pairs (_) I1,H3: 2.. / I1 = 2 => 8 pairs (_) / H3 = 2 => 12 pairs (_) B7,C8: 2.. / B7 = 2 => 0 pairs (X) / C8 = 2 => 6 pairs (_) C8,H8: 2.. / C8 = 2 => 6 pairs (_) / H8 = 2 => 0 pairs (X) I1,I7: 2.. / I1 = 2 => 8 pairs (_) / I7 = 2 => 12 pairs (_) G5,H5: 5.. / G5 = 5 => 6 pairs (_) / H5 = 5 => 9 pairs (_) B7,A9: 5.. / B7 = 5 => 10 pairs (_) / A9 = 5 => 6 pairs (_) B1,B2: 6.. / B1 = 6 => 7 pairs (_) / B2 = 6 => 9 pairs (_) F8,F9: 6.. / F8 = 6 => 8 pairs (_) / F9 = 6 => 16 pairs (_) B2,G2: 6.. / B2 = 6 => 9 pairs (_) / G2 = 6 => 7 pairs (_) F8,G8: 6.. / F8 = 6 => 8 pairs (_) / G8 = 6 => 16 pairs (_) I1,I9: 6.. / I1 = 6 => 14 pairs (_) / I9 = 6 => 7 pairs (_) E9,F9: 7.. / E9 = 7 => 6 pairs (_) / F9 = 7 => 11 pairs (_) A3,C3: 8.. / A3 = 8 => 7 pairs (_) / C3 = 8 => 9 pairs (_) E8,G8: 8.. / E8 = 8 => 7 pairs (_) / G8 = 8 => 10 pairs (_) H7,H9: 9.. / H7 = 9 => 13 pairs (_) / H9 = 9 => 6 pairs (_) A1,A5: 9.. / A1 = 9 => 7 pairs (_) / A5 = 9 => 7 pairs (_) * DURATION: 0:00:20.822054 START: 03:50:34.355599 END: 03:50:55.177653 2017-05-01 * CP COUNT: (20) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,C8,C9,G2,I4) * .....8.1.3......85...6..9.461.5..2......6......5..2.697.6..1...19.4....7.8.2..... * PAIR G2: 6,7 BLK 3 G1: 6,7,3 # reduction candidate for 6,7 G1: 6,7 # 9 pairs G1: 3 # 9 pairs * PAIR G2: 6,7 ROW 2 B2: 6,7,2,4 # reduction candidate for 6,7 B2: 6,7 # 9 pairs B2: 2,4 # 8 pairs * PAIR A6: 4,8 BLK 4 C4: 4,8,3,7,9 # reduction candidate for 4,8 C4: 4,8 # 9 pairs A5: 4,8,2,9 # reduction candidate for 4,8 A5: 4,8 => CTR * 95473861236192478527861593461.54.278..7869..18.5172.697463.1...19.4.6..758.2.71.6 A5: 2,9 # 7 pairs C5: 4,8,2,3,7,9 # reduction candidate for 4,8 C5: 4,8 # 9 pairs * PAIR A6: 4,8 ROW 6 E6: 4,8,1,3,7 # reduction candidate for 4,8 E6: 4,8 # 9 pairs G6: 4,8,1,3,7 # reduction candidate for 4,8 G6: 4,8 # 8 pairs * PAIR I4: 3,8 BLK 6 G5: 3,8,1,4,5,7 # reduction candidate for 3,8 G5: 3,8 # 13 pairs I5: 3,8,1 # reduction candidate for 3,8 I5: 3,8 # 15 pairs G6: 3,8,1,4,7 # reduction candidate for 3,8 G6: 3,8 # 9 pairs * PAIR I4: 3,8 ROW 4 C4: 3,8,4,7,9 # reduction candidate for 3,8 C4: 3,8 # 8 pairs E4: 3,8,4,7,9 # reduction candidate for 3,8 E4: 3,8 # 8 pairs * PAIR I4: 3,8 COL I I7: 3,8,2 # reduction candidate for 3,8 I7: 2 # 12 pairs I7: 3,8 # 8 pairs * PAIR C8: 2,3 BLK 7 B7: 2,3,4,5 # reduction candidate for 2,3 B7: 4,5 # 7 pairs B7: 2,3 # 7 pairs * PAIR C8: 2,3 ROW 8 H8: 2,3,5 # reduction candidate for 2,3 H8: 2,3 # 9 pairs H8: 5 # 7 pairs * PAIR C8: 2,3 COL C C5: 2,3,4,7,8,9 # reduction candidate for 2,3 C5: 2,3 # 9 pairs C5: 4,7,8,9 # 6 pairs * PAIR A9: 4,5 BLK 7 B7: 4,5,2,3 # reduction candidate for 4,5 B7: 4,5 # 7 pairs B7: 2,3 # 7 pairs * PAIR A9: 4,5 ROW 9 G9: 4,5,1,3,6 # reduction candidate for 4,5 G9: 4,5 # 18 pairs H9: 4,5,3,9 # reduction candidate for 4,5 H9: 4,5 => CTR * .5...8.1.36..2.78587163592461.5..2...2..6.45.435.128697463815921924563.75832...4. H9: 3,9 # 7 pairs * PAIR A9: 4,5 COL A A1: 4,5,2,9 # reduction candidate for 4,5 A1: 4,5 # 12 pairs A1: 2,9 # 7 pairs * PAIR C9: 3,4 BLK 7 B7: 3,4,2,5 # reduction candidate for 3,4 B7: 3,4 # 7 pairs B7: 2,5 # 7 pairs * PAIR C9: 3,4 ROW 9 G9: 3,4,1,5,6 # reduction candidate for 3,4 G9: 3,4 => SOLVED * 924758316361924785857613924618549273239167548475832169746391852192485637583276491 G9: 1,5,6 # 6 pairs H9: 3,4,5,9 # reduction candidate for 3,4 H9: 3,4 # 16 pairs * PAIR C9: 3,4 COL C C4: 3,4,7,8,9 # reduction candidate for 3,4 C4: 3,4 # 8 pairs C5: 3,4,2,7,8,9 # reduction candidate for 3,4 C5: 3,4 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0023-base-pr-000.dot * REASONING * DIS # A5: 4,8 => CTR => A5: 2,9 * DIS # H9: 4,5 => CTR => H9: 3,9 * PRF # G9: 3,4 => SOL * CNT 3 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,C8,C9,G2,I4) * .....8.1.3......85...6..9.461.5..2......6......5..2.697.6..1...19.4....7.8.2..... * PAIR G2: 6,7 BLK 3 G1: 6,7,3 # reduction candidate for 6,7 G1: 6,7 # 9 pairs G1: 3 # 9 pairs * PAIR G2: 6,7 ROW 2 B2: 6,7,2,4 # reduction candidate for 6,7 B2: 6,7 # 9 pairs B2: 2,4 # 8 pairs * PAIR A6: 4,8 BLK 4 C4: 4,8,3,7,9 # reduction candidate for 4,8 C4: 4,8 # 9 pairs A5: 4,8,2,9 # reduction candidate for 4,8 A5: 4,8 => CTR * 95473861236192478527861593461.54.278..7869..18.5172.697463.1...19.4.6..758.2.71.6 C5: 4,8,2,3,7,9 # reduction candidate for 4,8 C5: 4,8 # 9 pairs * PAIR A6: 4,8 ROW 6 E6: 4,8,1,3,7 # reduction candidate for 4,8 E6: 4,8 # 10 pairs G6: 4,8,1,3,7 # reduction candidate for 4,8 G6: 4,8 # 9 pairs * PAIR RESTART * PAIR A6: 4,8 BLK 4 C4: 4,8,3,7,9 # reduction candidate for 4,8 C4: 4,8 # 9 pairs C5: 4,8,2,3,7,9 # reduction candidate for 4,8 C5: 4,8 # 9 pairs * PAIR A6: 4,8 ROW 6 E6: 4,8,1,3,7 # reduction candidate for 4,8 E6: 4,8 # 10 pairs G6: 4,8,1,3,7 # reduction candidate for 4,8 G6: 4,8 # 9 pairs * PAIR I4: 3,8 BLK 6 G5: 3,8,1,4,5,7 # reduction candidate for 3,8 G5: 3,8 # 14 pairs I5: 3,8,1 # reduction candidate for 3,8 I5: 3,8 # 15 pairs G6: 3,8,1,4,7 # reduction candidate for 3,8 G6: 3,8 # 10 pairs * PAIR I4: 3,8 ROW 4 C4: 3,8,4,7,9 # reduction candidate for 3,8 C4: 3,8 # 9 pairs E4: 3,8,4,7,9 # reduction candidate for 3,8 E4: 3,8 # 9 pairs * PAIR I4: 3,8 COL I I7: 3,8,2 # reduction candidate for 3,8 I7: 2 # 12 pairs I7: 3,8 # 9 pairs * PAIR C8: 2,3 BLK 7 B7: 2,3,4,5 # reduction candidate for 2,3 B7: 4,5 # 8 pairs B7: 2,3 # 8 pairs * PAIR C8: 2,3 ROW 8 H8: 2,3,5 # reduction candidate for 2,3 H8: 2,3 # 10 pairs H8: 5 # 8 pairs * PAIR C8: 2,3 COL C C5: 2,3,4,7,8,9 # reduction candidate for 2,3 C5: 2,3 # 10 pairs C5: 4,7,8,9 # 7 pairs * PAIR A9: 4,5 BLK 7 B7: 4,5,2,3 # reduction candidate for 4,5 B7: 4,5 # 8 pairs B7: 2,3 # 8 pairs * PAIR A9: 4,5 ROW 9 G9: 4,5,1,3,6 # reduction candidate for 4,5 G9: 4,5 # 18 pairs H9: 4,5,3,9 # reduction candidate for 4,5 H9: 4,5 => CTR * .5...8.1.36..2.78587163592461.5..2...2..6.45.435.128697463815921924563.75832...4. * RESTART * PAIR A9: 4,5 ROW 9 G9: 4,5,1,3,6 # reduction candidate for 4,5 G9: 4,5 # 18 pairs G9: 1,3,6 # 8 pairs * PAIR A9: 4,5 COL A A1: 4,5,2,9 # reduction candidate for 4,5 A1: 4,5 # 13 pairs A1: 2,9 # 10 pairs * PAIR RESTART * PAIR A9: 4,5 BLK 7 B7: 4,5,2,3 # reduction candidate for 4,5 B7: 4,5 # 9 pairs B7: 2,3 # 8 pairs * PAIR A9: 4,5 ROW 9 G9: 4,5,1,3,6 # reduction candidate for 4,5 G9: 4,5 # 18 pairs G9: 1,3,6 # 8 pairs * PAIR A9: 4,5 COL A A1: 4,5,2,9 # reduction candidate for 4,5 A1: 4,5 # 13 pairs A1: 2,9 # 10 pairs * PAIR C9: 3,4 BLK 7 B7: 3,4,2,5 # reduction candidate for 3,4 B7: 3,4 # 9 pairs B7: 2,5 # 9 pairs * PAIR C9: 3,4 ROW 9 G9: 3,4,1,5,6 # reduction candidate for 3,4 G9: 3,4 => SOLVED * 924758316361924785857613924618549273239167548475832169746391852192485637583276491 * DURATION: 0:00:27.585014 START: 03:51:17.579723 END: 03:51:45.164737 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0023-base-pr-001.dot * REASONING * DIS # A5: 4,8 => CTR => A5: 2,9 * DIS A5: 2,9 # H9: 4,5 => CTR => H9: 3,9 * PRF A5: 2,9 + H9: 3,9 # G9: 3,4 => SOL * STA A5: 2,9 + H9: 3,9 + G9: 3,4 * CNT 3 HDP CHAINS / 43 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=23
Solution
position: 924758316361924785857613924618549273239167548475832169746391852192485637583276491 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 # G1: 6,7 => UNS * INC # G1: 3 => UNS * INC # B2: 6,7 => UNS * INC # B2: 2,4 => UNS * INC # C4: 4,8 => UNS * DIS # A5: 4,8 => CTR => A5: 2,9 * INC # A5: 2,9 => UNS * INC # C5: 4,8 => UNS * INC # E6: 4,8 => UNS * INC # G6: 4,8 => UNS * INC # G5: 3,8 => UNS * INC # I5: 3,8 => UNS * INC # G6: 3,8 => UNS * INC # C4: 3,8 => UNS * INC # E4: 3,8 => UNS * INC # I7: 3,8 => UNS * INC # I7: 2 => UNS * INC # B7: 2,3 => UNS * INC # B7: 4,5 => UNS * INC # H8: 2,3 => UNS * INC # H8: 5 => UNS * INC # C5: 2,3 => UNS * INC # C5: 4,7,8,9 => UNS * INC # B7: 4,5 => UNS * INC # B7: 2,3 => UNS * INC # G9: 4,5 => UNS * DIS # H9: 4,5 => CTR => H9: 3,9 * INC # H9: 3,9 => UNS * INC # A1: 4,5 => UNS * INC # A1: 2,9 => UNS * INC # B7: 3,4 => UNS * INC # B7: 2,5 => UNS * PRF # G9: 3,4 => SOL * INC # G9: 1,5,6 => UNS * INC # H9: 3,4 => UNS * INC # C4: 3,4 => UNS * INC # C5: 3,4 => UNS * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G1: 6,7 => UNS * INC # G1: 3 => UNS * INC # B2: 6,7 => UNS * INC # B2: 2,4 => UNS * INC # C4: 4,8 => UNS * DIS # A5: 4,8 => CTR => A5: 2,9 * INC A5: 2,9 # C5: 4,8 => UNS * INC A5: 2,9 # E6: 4,8 => UNS * INC A5: 2,9 # G6: 4,8 => UNS * INC A5: 2,9 # C4: 4,8 => UNS * INC A5: 2,9 # C5: 4,8 => UNS * INC A5: 2,9 # E6: 4,8 => UNS * INC A5: 2,9 # G6: 4,8 => UNS * INC A5: 2,9 # G5: 3,8 => UNS * INC A5: 2,9 # I5: 3,8 => UNS * INC A5: 2,9 # G6: 3,8 => UNS * INC A5: 2,9 # C4: 3,8 => UNS * INC A5: 2,9 # E4: 3,8 => UNS * INC A5: 2,9 # I7: 3,8 => UNS * INC A5: 2,9 # I7: 2 => UNS * INC A5: 2,9 # B7: 2,3 => UNS * INC A5: 2,9 # B7: 4,5 => UNS * INC A5: 2,9 # H8: 2,3 => UNS * INC A5: 2,9 # H8: 5 => UNS * INC A5: 2,9 # C5: 2,3 => UNS * INC A5: 2,9 # C5: 4,7,8,9 => UNS * INC A5: 2,9 # B7: 4,5 => UNS * INC A5: 2,9 # B7: 2,3 => UNS * INC A5: 2,9 # G9: 4,5 => UNS * DIS A5: 2,9 # H9: 4,5 => CTR => H9: 3,9 * INC A5: 2,9 + H9: 3,9 # G9: 4,5 => UNS * INC A5: 2,9 + H9: 3,9 # G9: 1,3,6 => UNS * INC A5: 2,9 + H9: 3,9 # A1: 4,5 => UNS * INC A5: 2,9 + H9: 3,9 # A1: 2,9 => UNS * INC A5: 2,9 + H9: 3,9 # B7: 4,5 => UNS * INC A5: 2,9 + H9: 3,9 # B7: 2,3 => UNS * INC A5: 2,9 + H9: 3,9 # G9: 4,5 => UNS * INC A5: 2,9 + H9: 3,9 # G9: 1,3,6 => UNS * INC A5: 2,9 + H9: 3,9 # A1: 4,5 => UNS * INC A5: 2,9 + H9: 3,9 # A1: 2,9 => UNS * INC A5: 2,9 + H9: 3,9 # B7: 3,4 => UNS * INC A5: 2,9 + H9: 3,9 # B7: 2,5 => UNS * PRF A5: 2,9 + H9: 3,9 # G9: 3,4 => SOL * STA A5: 2,9 + H9: 3,9 + G9: 3,4 * CNT 43 HDP CHAINS / 43 HYP OPENED