Analysis of zz-www.sudokuwiki.org-0116-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=116
level: medium
position: ...8....398.....7...4..31...2.9....5....4....7....5.1...72..6...5..8..242....9... initial
Autosolve
position: ..28....3983....7...4..31...2.9....5..5.4....7....5.1...72..6...5..8..242....9... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E2: 2,6 => CTR => E2: 1,5 * DIS # I5: 2,6 => CTR => I5: 7,8,9 * PRF # B6: 3,6 => SOL * DIS # D9: 3,6 => CTR => D9: 1,4,5,7 * CNT 4 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E2: 2,6 => CTR => E2: 1,5 * DIS E2: 1,5 # I5: 2,6 => CTR => I5: 7,8,9 * PRF E2: 1,5 + I5: 7,8,9 # B6: 3,6 => SOL * STA E2: 1,5 + I5: 7,8,9 + B6: 3,6 * CNT 3 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...8....398.....7...4..31...2.9....5....4....7....5.1...72..6...5..8..242....9... | initial |
| ..28....3983....7...4..31...2.9....5..5.4....7....5.1...72..6...5..8..242....9... | autosolve |
| 512876943983412576674593182421968735395741268768325419837254691159687324246139857 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) A3: 5,6 B3: 6,7 E3: 2,9 I2: 2,6 H3: 8,9 D6: 3,6 F7: 1,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B1: 1.. / A1 = 1 => 11 pairs (_) / B1 = 1 => 9 pairs (_) I7,I9: 1.. / I7 = 1 => 13 pairs (_) / I9 = 1 => 9 pairs (_) F5,E6: 2.. / F5 = 2 => 13 pairs (_) / E6 = 2 => 8 pairs (_) E3,I3: 2.. / E3 = 2 => 14 pairs (_) / I3 = 2 => 7 pairs (_) F2,F5: 2.. / F2 = 2 => 8 pairs (_) / F5 = 2 => 13 pairs (_) A4,B6: 4.. / A4 = 4 => 9 pairs (_) / B6 = 4 => 16 pairs (_) F7,D9: 4.. / F7 = 4 => 9 pairs (_) / D9 = 4 => 11 pairs (_) B6,G6: 4.. / B6 = 4 => 16 pairs (_) / G6 = 4 => 9 pairs (_) B9,D9: 4.. / B9 = 4 => 9 pairs (_) / D9 = 4 => 11 pairs (_) A4,A7: 4.. / A4 = 4 => 9 pairs (_) / A7 = 4 => 16 pairs (_) D2,D9: 4.. / D2 = 4 => 9 pairs (_) / D9 = 4 => 11 pairs (_) H1,H4: 4.. / H1 = 4 => 9 pairs (_) / H4 = 4 => 19 pairs (_) A1,A3: 5.. / A1 = 5 => 8 pairs (_) / A3 = 5 => 10 pairs (_) A3,D3: 5.. / A3 = 5 => 10 pairs (_) / D3 = 5 => 8 pairs (_) E7,H7: 5.. / E7 = 5 => 7 pairs (_) / H7 = 5 => 9 pairs (_) H1,I2: 6.. / H1 = 6 => 0 pairs (X) / I2 = 6 => 6 pairs (_) B1,B3: 7.. / B1 = 7 => 9 pairs (_) / B3 = 7 => 8 pairs (_) B3,D3: 7.. / B3 = 7 => 8 pairs (_) / D3 = 7 => 9 pairs (_) I5,I9: 7.. / I5 = 7 => 8 pairs (_) / I9 = 7 => 14 pairs (_) H3,I3: 8.. / H3 = 8 => 8 pairs (_) / I3 = 8 => 15 pairs (_) F4,F5: 8.. / F4 = 8 => 8 pairs (_) / F5 = 8 => 11 pairs (_) A7,C9: 8.. / A7 = 8 => 11 pairs (_) / C9 = 8 => 16 pairs (_) E1,E3: 9.. / E1 = 9 => 14 pairs (_) / E3 = 9 => 7 pairs (_) B7,C8: 9.. / B7 = 9 => 10 pairs (_) / C8 = 9 => 9 pairs (_) C8,G8: 9.. / C8 = 9 => 9 pairs (_) / G8 = 9 => 10 pairs (_) C6,C8: 9.. / C6 = 9 => 10 pairs (_) / C8 = 9 => 9 pairs (_) * DURATION: 0:00:30.098905 START: 05:35:47.437472 END: 05:36:17.536377 2017-05-01 * CP COUNT: (26) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B3,D6,E3,F7,H3,I2) * ..28....3983....7...4..31...2.9....5..5.4....7....5.1...72..6...5..8..242....9... * PAIR A3: 5,6 BLK 1 A1: 5,6,1 # reduction candidate for 5,6 A1: 1 # 11 pairs A1: 5,6 # 9 pairs * PAIR A3: 5,6 ROW 3 D3: 5,6,7 # reduction candidate for 5,6 D3: 7 # 9 pairs D3: 5,6 # 8 pairs * PAIR B3: 6,7 BLK 1 B1: 6,7,1 # reduction candidate for 6,7 B1: 6,7 # 11 pairs B1: 1 # 9 pairs * PAIR B3: 6,7 ROW 3 D3: 6,7,5 # reduction candidate for 6,7 D3: 6,7 # 10 pairs D3: 5 # 8 pairs * PAIR E3: 2,9 ROW 3 I3: 2,9,8 # reduction candidate for 2,9 I3: 8 # 15 pairs I3: 2,9 # 8 pairs * PAIR I2: 2,6 ROW 2 E2: 2,6,1,5 # reduction candidate for 2,6 E2: 2,6 => CTR * ..28....39831.457...45.31...2.918745815742...749..52184972.16...5..8..242.84.9..1 E2: 1,5 # 8 pairs F2: 2,6,1,4 # reduction candidate for 2,6 F2: 2,6 # 10 pairs * PAIR I2: 2,6 COL I I5: 2,6,7,8,9 # reduction candidate for 2,6 I5: 2,6 => CTR * ..28...439834...76..4..31..42.9....5..5.4...27...2541...72.46.1.5..8..2424...9..7 I5: 7,8,9 # 7 pairs I6: 2,6,8,9 # reduction candidate for 2,6 I6: 2,6 # 21 pairs * PAIR H3: 8,9 BLK 3 I3: 8,9,2 # reduction candidate for 8,9 I3: 8,9 # 14 pairs I3: 2 # 7 pairs * PAIR H3: 8,9 COL H H5: 8,9,3,6 # reduction candidate for 8,9 H5: 8,9 # 14 pairs H7: 8,9,3,5 # reduction candidate for 8,9 H7: 8,9 # 12 pairs * PAIR D6: 3,6 BLK 5 E4: 3,6,1,7 # reduction candidate for 3,6 E4: 3,6 # 10 pairs D5: 3,6,1,7 # reduction candidate for 3,6 D5: 3,6 # 14 pairs E6: 3,6,2 # reduction candidate for 3,6 E6: 3,6 # 13 pairs * PAIR D6: 3,6 ROW 6 B6: 3,6,4,9 # reduction candidate for 3,6 B6: 3,6 => SOLVED * 512876943983412576674593182421968735395741268768325419837254691159687324246139857 B6: 4,9 # 8 pairs * PAIR D6: 3,6 COL D D8: 3,6,1,7 # reduction candidate for 3,6 D8: 3,6 # 12 pairs D9: 3,6,1,4,5,7 # reduction candidate for 3,6 D9: 3,6 => CTR * 5128..94398341257667459318242193..65..5.4.23.73..2541...72.46...59.8..242463.9.5. D9: 1,4,5,7 # 7 pairs * PAIR F7: 1,4 BLK 8 D9: 1,4,3,5,6,7 # reduction candidate for 1,4 D9: 1,4 # 11 pairs D9: 3,5,6,7 # 9 pairs * PAIR F7: 1,4 ROW 7 A7: 1,4,3,8 # reduction candidate for 1,4 A7: 1,4 # 16 pairs B7: 1,4,3,9 # reduction candidate for 1,4 B7: 1,4 # 20 pairs * PAIR F7: 1,4 COL F F2: 1,4,2,6 # reduction candidate for 1,4 F2: 1,4 # 17 pairs F2: 2,6 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0116-base-pr-000.dot * REASONING * DIS # E2: 2,6 => CTR => E2: 1,5 * DIS # I5: 2,6 => CTR => I5: 7,8,9 * PRF # B6: 3,6 => SOL * DIS # D9: 3,6 => CTR => D9: 1,4,5,7 * CNT 4 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B3,D6,E3,F7,H3,I2) * ..28....3983....7...4..31...2.9....5..5.4....7....5.1...72..6...5..8..242....9... * PAIR A3: 5,6 BLK 1 A1: 5,6,1 # reduction candidate for 5,6 A1: 1 # 11 pairs A1: 5,6 # 9 pairs * PAIR A3: 5,6 ROW 3 D3: 5,6,7 # reduction candidate for 5,6 D3: 7 # 9 pairs D3: 5,6 # 8 pairs * PAIR B3: 6,7 BLK 1 B1: 6,7,1 # reduction candidate for 6,7 B1: 6,7 # 11 pairs B1: 1 # 9 pairs * PAIR B3: 6,7 ROW 3 D3: 6,7,5 # reduction candidate for 6,7 D3: 6,7 # 10 pairs D3: 5 # 8 pairs * PAIR E3: 2,9 ROW 3 I3: 2,9,8 # reduction candidate for 2,9 I3: 8 # 15 pairs I3: 2,9 # 8 pairs * PAIR I2: 2,6 ROW 2 E2: 2,6,1,5 # reduction candidate for 2,6 E2: 2,6 => CTR * ..28....39831.457...45.31...2.918745815742...749..52184972.16...5..8..242.84.9..1 F2: 2,6,1,4 # reduction candidate for 2,6 F2: 2,6 # 10 pairs * RESTART * PAIR I2: 2,6 ROW 2 F2: 2,6,1,4 # reduction candidate for 2,6 F2: 1,4 # 19 pairs F2: 2,6 # 10 pairs * PAIR I2: 2,6 COL I I5: 2,6,7,8,9 # reduction candidate for 2,6 I5: 2,6 => CTR * ..28...439834...76..4..31..42.9....5..5.4...27...2541...72.46.1.5..8..2424...9..7 I6: 2,6,8,9 # reduction candidate for 2,6 I6: 2,6 # 21 pairs * RESTART * PAIR I2: 2,6 COL I I6: 2,6,8,9 # reduction candidate for 2,6 I6: 2,6 # 21 pairs I6: 8,9 # 8 pairs * PAIR RESTART * PAIR I2: 2,6 ROW 2 F2: 2,6,1,4 # reduction candidate for 2,6 F2: 1,4 # 21 pairs F2: 2,6 # 10 pairs * PAIR I2: 2,6 COL I I6: 2,6,8,9 # reduction candidate for 2,6 I6: 2,6 # 21 pairs I6: 8,9 # 8 pairs * PAIR H3: 8,9 BLK 3 I3: 8,9,2 # reduction candidate for 8,9 I3: 8,9 # 21 pairs I3: 2 # 8 pairs * PAIR H3: 8,9 COL H H5: 8,9,3,6 # reduction candidate for 8,9 H5: 8,9 # 15 pairs H7: 8,9,3,5 # reduction candidate for 8,9 H7: 8,9 # 12 pairs * PAIR D6: 3,6 BLK 5 E4: 3,6,1,7 # reduction candidate for 3,6 E4: 3,6 # 10 pairs D5: 3,6,1,7 # reduction candidate for 3,6 D5: 3,6 # 14 pairs E6: 3,6,2 # reduction candidate for 3,6 E6: 3,6 # 21 pairs * PAIR D6: 3,6 ROW 6 B6: 3,6,4,9 # reduction candidate for 3,6 B6: 3,6 => SOLVED * 512876943983412576674593182421968735395741268768325419837254691159687324246139857 * DURATION: 0:00:22.468963 START: 05:36:40.849638 END: 05:37:03.318601 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0116-base-pr-001.dot * REASONING * DIS # E2: 2,6 => CTR => E2: 1,5 * DIS E2: 1,5 # I5: 2,6 => CTR => I5: 7,8,9 * PRF E2: 1,5 + I5: 7,8,9 # B6: 3,6 => SOL * STA E2: 1,5 + I5: 7,8,9 + B6: 3,6 * CNT 3 HDP CHAINS / 30 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=116
Solution
position: 512876943983412576674593182421968735395741268768325419837254691159687324246139857 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 # A1: 5,6 => UNS * INC # A1: 1 => UNS * INC # D3: 5,6 => UNS * INC # D3: 7 => UNS * INC # B1: 6,7 => UNS * INC # B1: 1 => UNS * INC # D3: 6,7 => UNS * INC # D3: 5 => UNS * INC # I3: 2,9 => UNS * INC # I3: 8 => UNS * DIS # E2: 2,6 => CTR => E2: 1,5 * INC # E2: 1,5 => UNS * INC # F2: 2,6 => UNS * DIS # I5: 2,6 => CTR => I5: 7,8,9 * INC # I5: 7,8,9 => UNS * INC # I6: 2,6 => UNS * INC # I3: 8,9 => UNS * INC # I3: 2 => UNS * INC # H5: 8,9 => UNS * INC # H7: 8,9 => UNS * INC # E4: 3,6 => UNS * INC # D5: 3,6 => UNS * INC # E6: 3,6 => UNS * PRF # B6: 3,6 => SOL * INC # B6: 4,9 => UNS * INC # D8: 3,6 => UNS * DIS # D9: 3,6 => CTR => D9: 1,4,5,7 * INC # D9: 1,4,5,7 => UNS * INC # D9: 1,4 => UNS * INC # D9: 3,5,6,7 => UNS * INC # A7: 1,4 => UNS * INC # B7: 1,4 => UNS * INC # F2: 1,4 => UNS * INC # F2: 2,6 => UNS * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 5,6 => UNS * INC # A1: 1 => UNS * INC # D3: 5,6 => UNS * INC # D3: 7 => UNS * INC # B1: 6,7 => UNS * INC # B1: 1 => UNS * INC # D3: 6,7 => UNS * INC # D3: 5 => UNS * INC # I3: 2,9 => UNS * INC # I3: 8 => UNS * DIS # E2: 2,6 => CTR => E2: 1,5 * INC E2: 1,5 # F2: 2,6 => UNS * INC E2: 1,5 # F2: 2,6 => UNS * INC E2: 1,5 # F2: 1,4 => UNS * DIS E2: 1,5 # I5: 2,6 => CTR => I5: 7,8,9 * INC E2: 1,5 + I5: 7,8,9 # I6: 2,6 => UNS * INC E2: 1,5 + I5: 7,8,9 # I6: 2,6 => UNS * INC E2: 1,5 + I5: 7,8,9 # I6: 8,9 => UNS * INC E2: 1,5 + I5: 7,8,9 # F2: 2,6 => UNS * INC E2: 1,5 + I5: 7,8,9 # F2: 1,4 => UNS * INC E2: 1,5 + I5: 7,8,9 # I6: 2,6 => UNS * INC E2: 1,5 + I5: 7,8,9 # I6: 8,9 => UNS * INC E2: 1,5 + I5: 7,8,9 # I3: 8,9 => UNS * INC E2: 1,5 + I5: 7,8,9 # I3: 2 => UNS * INC E2: 1,5 + I5: 7,8,9 # H5: 8,9 => UNS * INC E2: 1,5 + I5: 7,8,9 # H7: 8,9 => UNS * INC E2: 1,5 + I5: 7,8,9 # E4: 3,6 => UNS * INC E2: 1,5 + I5: 7,8,9 # D5: 3,6 => UNS * INC E2: 1,5 + I5: 7,8,9 # E6: 3,6 => UNS * PRF E2: 1,5 + I5: 7,8,9 # B6: 3,6 => SOL * STA E2: 1,5 + I5: 7,8,9 + B6: 3,6 * CNT 30 HDP CHAINS / 30 HYP OPENED