Analysis of zz-www.sudokuwiki.org-0009-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=9
level: medium
position: ...9....8..6..5.....9.743..31..5..2.6.......3.9..2..67..541.7.....5..2..4....3... initial
Autosolve
position: ...9....8..6..5.....9.743..31..5..2.6...4...3.9.32..67..541.7.....5..2..4....3... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # I3: 1,5 => SOL * DIS # H9: 1,5 => CTR => H9: 8,9 * DIS # F5: 1,8 => CTR => F5: 7,9 * DIS # I2: 4,9 => CTR => I2: 1,2 * PRF # I8: 4,9 => SOL * DIS # I8: 6,9 => CTR => I8: 1,4 * DIS # I9: 6,9 => CTR => I9: 1,5 * CNT 7 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:
* PRF # I3: 1,5 => SOL * STA I3: 1,5 * CNT 1 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...9....8..6..5.....9.743..31..5..2.6.......3.9..2..67..541.7.....5..2..4....3... | initial |
| ...9....8..6..5.....9.743..31..5..2.6...4...3.9.32..67..541.7.....5..2..4....3... | autosolve |
| 541932678736185942289674351317856429652749813894321567925418736163597284478263195 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) E1: 3,6 E2: 3,8 H3: 1,5 A6: 5,8 C6: 4,8 F6: 1,8 I4: 4,9 I7: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F6,G6: 1.. / F6 = 1 => 9 pairs (_) / G6 = 1 => 11 pairs (_) I2,I3: 2.. / I2 = 2 => 9 pairs (_) / I3 = 2 => 19 pairs (_) B5,C5: 2.. / B5 = 2 => 11 pairs (_) / C5 = 2 => 8 pairs (_) F7,D9: 2.. / F7 = 2 => 14 pairs (_) / D9 = 2 => 12 pairs (_) F1,F7: 2.. / F1 = 2 => 12 pairs (_) / F7 = 2 => 14 pairs (_) E1,E2: 3.. / E1 = 3 => 11 pairs (_) / E2 = 3 => 20 pairs (_) H7,H8: 3.. / H7 = 3 => 8 pairs (_) / H8 = 3 => 0 pairs (X) B2,E2: 3.. / B2 = 3 => 11 pairs (_) / E2 = 3 => 20 pairs (_) B7,H7: 3.. / B7 = 3 => 0 pairs (X) / H7 = 3 => 8 pairs (_) C1,C8: 3.. / C1 = 3 => 0 pairs (X) / C8 = 3 => 10 pairs (_) B1,B2: 4.. / B1 = 4 => 8 pairs (_) / B2 = 4 => 22 pairs (_) C4,C6: 4.. / C4 = 4 => 0 pairs (X) / C6 = 4 => 8 pairs (_) H8,I8: 4.. / H8 = 4 => 9 pairs (_) / I8 = 4 => 0 pairs (*) C6,G6: 4.. / C6 = 4 => 8 pairs (_) / G6 = 4 => 0 pairs (X) B5,A6: 5.. / B5 = 5 => 14 pairs (_) / A6 = 5 => 7 pairs (_) A6,G6: 5.. / A6 = 5 => 7 pairs (_) / G6 = 5 => 14 pairs (_) I3,I9: 5.. / I3 = 5 => 0 pairs (X) / I9 = 5 => 8 pairs (_) G1,I3: 6.. / G1 = 6 => 17 pairs (_) / I3 = 6 => 13 pairs (_) D4,F4: 6.. / D4 = 6 => 13 pairs (_) / F4 = 6 => 11 pairs (_) D3,I3: 6.. / D3 = 6 => 17 pairs (_) / I3 = 6 => 13 pairs (_) G1,G9: 6.. / G1 = 6 => 17 pairs (_) / G9 = 6 => 13 pairs (_) H1,H2: 7.. / H1 = 7 => 8 pairs (_) / H2 = 7 => 8 pairs (_) F8,D9: 7.. / F8 = 7 => 8 pairs (_) / D9 = 7 => 0 pairs (X) F4,F5: 9.. / F4 = 9 => 14 pairs (_) / F5 = 9 => 8 pairs (_) A7,A8: 9.. / A7 = 9 => 0 pairs (*) / A8 = 9 => 0 pairs (X) E8,E9: 9.. / E8 = 9 => 0 pairs (*) / E9 = 9 => 0 pairs (X) * DURATION: 0:00:34.179305 START: 03:31:02.970380 END: 03:31:37.149685 2017-05-01 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,C6,E1,E2,F6,H3,I4,I7) * ...9....8..6..5.....9.743..31..5..2.6...4...3.9.32..67..541.7.....5..2..4....3... * PAIR E2: 3,8 ROW 2 B2: 3,8,2,4,7 # reduction candidate for 3,8 B2: 2,4,7 # 22 pairs B2: 3,8 # 10 pairs * PAIR H3: 1,5 BLK 3 G1: 1,5,4,6 # reduction candidate for 1,5 G1: 1,5 # 19 pairs H1: 1,5,4,7 # reduction candidate for 1,5 H1: 1,5 # 19 pairs I3: 1,5,2,6 # reduction candidate for 1,5 I3: 1,5 => SOLVED * 541932678736185942289674351317856429652749813894321567925418736163597284478263195 I3: 2,6 # 9 pairs * PAIR H3: 1,5 ROW 3 A3: 1,5,2,8 # reduction candidate for 1,5 A3: 1,5 # 11 pairs A3: 2,8 # 9 pairs * PAIR H3: 1,5 COL H H5: 1,5,8,9 # reduction candidate for 1,5 H5: 1,5 # 11 pairs H9: 1,5,8,9 # reduction candidate for 1,5 H9: 1,5 => CTR * ...93.6.8.36.85.....96743..31.856.2.6..749183894321567..541873....5.72..4....38.. H9: 8,9 # 9 pairs * PAIR A6: 5,8 BLK 4 B5: 5,8,2,7 # reduction candidate for 5,8 B5: 5,8 # 14 pairs B5: 2,7 # 8 pairs * PAIR A6: 5,8 ROW 6 G6: 5,8,1,4 # reduction candidate for 5,8 G6: 5,8 # 10 pairs G6: 1,4 # 8 pairs * PAIR A6: 5,8 COL A A3: 5,8,1,2 # reduction candidate for 5,8 A3: 5,8 # 10 pairs A3: 1,2 # 9 pairs * PAIR C6: 4,8 BLK 4 C4: 4,8,7 # reduction candidate for 4,8 C4: 4,8 # 13 pairs C4: 7 # 9 pairs * PAIR C6: 4,8 ROW 6 G6: 4,8,1,5 # reduction candidate for 4,8 G6: 4,8 # 13 pairs G6: 1,5 # 9 pairs * PAIR F6: 1,8 BLK 5 D5: 1,8,7 # reduction candidate for 1,8 D5: 1,8 # 11 pairs F5: 1,8,7,9 # reduction candidate for 1,8 F5: 1,8 => CTR * ...9.2..8..6..5..2..9.743.63176598246.274...3.9432..67..541673996.5.7241471293685 F5: 7,9 # 9 pairs * PAIR F6: 1,8 ROW 6 G6: 1,8,4,5 # reduction candidate for 1,8 G6: 4,5 # 12 pairs G6: 1,8 # 8 pairs * PAIR I4: 4,9 BLK 6 G4: 4,9,8 # reduction candidate for 4,9 G4: 8 # 10 pairs G4: 4,9 # 9 pairs * PAIR I4: 4,9 COL I I2: 4,9,1,2 # reduction candidate for 4,9 I2: 4,9 => CTR * 74.9326.8236185.7...96743.231..56.2.6.2749..3.9.321.67925418736863597241471263.95 I2: 1,2 # 9 pairs I8: 4,9,1,6 # reduction candidate for 4,9 I8: 4,9 => SOLVED * 541932678736185942289674351317856429652749813894321567925418736163597284478263195 I8: 1,6 # 10 pairs * PAIR I7: 6,9 BLK 9 I8: 6,9,1,4 # reduction candidate for 6,9 I8: 6,9 => CTR * 541932678736185492..96743..318.569246.2.49..3.94321.67..541873...3567249467293... I8: 1,4 # 9 pairs G9: 6,9,1,5,8 # reduction candidate for 6,9 G9: 6,9 # 12 pairs I9: 6,9,1,5 # reduction candidate for 6,9 I9: 6,9 => CTR * ...9326.8.36185..2..967431531..56.246.2.491.3.94321.67..541873...35.72414712.3... I9: 1,5 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0009-base-pr-000.dot * REASONING * PRF # I3: 1,5 => SOL * DIS # H9: 1,5 => CTR => H9: 8,9 * DIS # F5: 1,8 => CTR => F5: 7,9 * DIS # I2: 4,9 => CTR => I2: 1,2 * PRF # I8: 4,9 => SOL * DIS # I8: 6,9 => CTR => I8: 1,4 * DIS # I9: 6,9 => CTR => I9: 1,5 * CNT 7 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,C6,E1,E2,F6,H3,I4,I7) * ...9....8..6..5.....9.743..31..5..2.6...4...3.9.32..67..541.7.....5..2..4....3... * PAIR E2: 3,8 ROW 2 B2: 3,8,2,4,7 # reduction candidate for 3,8 B2: 2,4,7 # 22 pairs B2: 3,8 # 10 pairs * PAIR H3: 1,5 BLK 3 G1: 1,5,4,6 # reduction candidate for 1,5 G1: 1,5 # 19 pairs H1: 1,5,4,7 # reduction candidate for 1,5 H1: 1,5 # 19 pairs I3: 1,5,2,6 # reduction candidate for 1,5 I3: 1,5 => SOLVED * 541932678736185942289674351317856429652749813894321567925418736163597284478263195 * DURATION: 0:00:05.887398 START: 03:32:03.047539 END: 03:32:08.934937 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0009-base-pr-001.dot * REASONING * PRF # I3: 1,5 => SOL * STA I3: 1,5 * CNT 1 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=9
Solution
position: 541932678736185942289674351317856429652749813894321567925418736163597284478263195 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 # B2: 3,8 => UNS * INC # B2: 2,4,7 => UNS * INC # G1: 1,5 => UNS * INC # H1: 1,5 => UNS * PRF # I3: 1,5 => SOL * INC # I3: 2,6 => UNS * INC # A3: 1,5 => UNS * INC # A3: 2,8 => UNS * INC # H5: 1,5 => UNS * DIS # H9: 1,5 => CTR => H9: 8,9 * INC # H9: 8,9 => UNS * INC # B5: 5,8 => UNS * INC # B5: 2,7 => UNS * INC # G6: 5,8 => UNS * INC # G6: 1,4 => UNS * INC # A3: 5,8 => UNS * INC # A3: 1,2 => UNS * INC # C4: 4,8 => UNS * INC # C4: 7 => UNS * INC # G6: 4,8 => UNS * INC # G6: 1,5 => UNS * INC # D5: 1,8 => UNS * DIS # F5: 1,8 => CTR => F5: 7,9 * INC # F5: 7,9 => UNS * INC # G6: 1,8 => UNS * INC # G6: 4,5 => UNS * INC # G4: 4,9 => UNS * INC # G4: 8 => UNS * DIS # I2: 4,9 => CTR => I2: 1,2 * INC # I2: 1,2 => UNS * PRF # I8: 4,9 => SOL * INC # I8: 1,6 => UNS * DIS # I8: 6,9 => CTR => I8: 1,4 * INC # I8: 1,4 => UNS * INC # G9: 6,9 => UNS * DIS # I9: 6,9 => CTR => I9: 1,5 * INC # I9: 1,5 => UNS * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 3,8 => UNS * INC # B2: 2,4,7 => UNS * INC # G1: 1,5 => UNS * INC # H1: 1,5 => UNS * PRF # I3: 1,5 => SOL * STA I3: 1,5 * CNT 5 HDP CHAINS / 5 HYP OPENED