Analysis of zz-www.sudokuwiki.org-0128-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=128
level: medium
position: 43..........65.9..9...2.3......495..2..8.........3..9..8...1.3...7........14...86 initial
Autosolve
position: 43..........6539..9...243..8.3.495..2..8....3...53.89..8...1.3...73.....3.14.5.86 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B3: 1,7 => SOL * PRF # H2: 1,7 => SOL * DIS # I2: 1,7 => CTR => I2: 2,4,8 * PRF # D1: 1,7 => SOL * PRF # B3: 1,7 => SOL * DIS # I3: 1,7 => CTR => I3: 5,8 * DIS # E5: 6,7 => CTR => E5: 1 * PRF # I7: 2,7 => SOL * PRF # G1: 2,7 => SOL * CNT 9 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B3: 1,7 => SOL * STA B3: 1,7 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 43..........65.9..9...2.3......495..2..8.........3..9..8...1.3...7........14...86 | initial |
| 43..........6539..9...243..8.3.495..2..8....3...53.89..8...1.3...73.....3.14.5.86 | autosolve |
| 436198725728653914915724368863249571259817643174536892582961437647382159391475286 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) A2: 1,7 C2: 2,8 F1: 7,8 D3: 1,7 B5: 5,9 C5: 5,9 A6: 1,7 C6: 4,6 F5: 6,7 A7: 5,6 A8: 5,6 B9: 2,9 E9: 7,9 G9: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D4,E5: 1.. / D4 = 1 => 0 pairs (X) / E5 = 1 => 16 pairs (_) A2,A6: 1.. / A2 = 1 => 16 pairs (_) / A6 = 1 => 15 pairs (_) E1,E5: 1.. / E1 = 1 => 0 pairs (X) / E5 = 1 => 16 pairs (_) D4,F6: 2.. / D4 = 2 => 18 pairs (_) / F6 = 2 => 28 pairs (_) D7,F8: 2.. / D7 = 2 => 28 pairs (_) / F8 = 2 => 18 pairs (_) F6,I6: 2.. / F6 = 2 => 28 pairs (_) / I6 = 2 => 18 pairs (_) B9,G9: 2.. / B9 = 2 => 20 pairs (_) / G9 = 2 => 16 pairs (_) D4,D7: 2.. / D4 = 2 => 18 pairs (_) / D7 = 2 => 28 pairs (_) F6,F8: 2.. / F6 = 2 => 28 pairs (_) / F8 = 2 => 18 pairs (_) H2,I2: 4.. / H2 = 4 => 26 pairs (_) / I2 = 4 => 14 pairs (_) B6,C6: 4.. / B6 = 4 => 23 pairs (_) / C6 = 4 => 15 pairs (_) G5,H5: 4.. / G5 = 4 => 17 pairs (_) / H5 = 4 => 14 pairs (_) C7,B8: 4.. / C7 = 4 => 23 pairs (_) / B8 = 4 => 15 pairs (_) B6,B8: 4.. / B6 = 4 => 23 pairs (_) / B8 = 4 => 15 pairs (_) C6,C7: 4.. / C6 = 4 => 15 pairs (_) / C7 = 4 => 23 pairs (_) B5,C5: 5.. / B5 = 5 => 13 pairs (_) / C5 = 5 => 17 pairs (_) A7,A8: 5.. / A7 = 5 => 15 pairs (_) / A8 = 5 => 30 pairs (_) A7,I7: 5.. / A7 = 5 => 15 pairs (_) / I7 = 5 => 30 pairs (_) B3,B5: 5.. / B3 = 5 => 17 pairs (_) / B5 = 5 => 13 pairs (_) A7,A8: 6.. / A7 = 6 => 30 pairs (_) / A8 = 6 => 15 pairs (_) B4,H4: 6.. / B4 = 6 => 19 pairs (_) / H4 = 6 => 18 pairs (_) A7,E7: 6.. / A7 = 6 => 30 pairs (_) / E7 = 6 => 15 pairs (_) G1,G5: 6.. / G1 = 6 => 15 pairs (_) / G5 = 6 => 0 pairs (*) E9,G9: 7.. / E9 = 7 => 16 pairs (_) / G9 = 7 => 20 pairs (_) A2,A6: 7.. / A2 = 7 => 15 pairs (_) / A6 = 7 => 16 pairs (_) C2,C3: 8.. / C2 = 8 => 14 pairs (_) / C3 = 8 => 19 pairs (_) E1,F1: 8.. / E1 = 8 => 0 pairs (X) / F1 = 8 => 16 pairs (_) I2,I3: 8.. / I2 = 8 => 19 pairs (_) / I3 = 8 => 14 pairs (_) E8,F8: 8.. / E8 = 8 => 16 pairs (_) / F8 = 8 => 0 pairs (X) C2,I2: 8.. / C2 = 8 => 14 pairs (_) / I2 = 8 => 19 pairs (_) C3,I3: 8.. / C3 = 8 => 19 pairs (_) / I3 = 8 => 14 pairs (_) E1,E8: 8.. / E1 = 8 => 0 pairs (X) / E8 = 8 => 16 pairs (_) F1,F8: 8.. / F1 = 8 => 16 pairs (_) / F8 = 8 => 0 pairs (X) D1,E1: 9.. / D1 = 9 => 15 pairs (_) / E1 = 9 => 0 pairs (*) B5,C5: 9.. / B5 = 9 => 17 pairs (_) / C5 = 9 => 13 pairs (_) I7,I8: 9.. / I7 = 9 => 15 pairs (_) / I8 = 9 => 16 pairs (_) B9,E9: 9.. / B9 = 9 => 16 pairs (_) / E9 = 9 => 20 pairs (_) C5,C7: 9.. / C5 = 9 => 13 pairs (_) / C7 = 9 => 17 pairs (_) D1,D7: 9.. / D1 = 9 => 15 pairs (_) / D7 = 9 => 0 pairs (*) * DURATION: 0:01:11.147033 START: 05:53:29.364285 END: 05:54:40.511318 2017-05-01 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A7,A8,B5,B9,C2,C5,C6,D3,E9,F1,F5,G9) * 43..........6539..9...243..8.3.495..2..8....3...53.89..8...1.3...73.....3.14.5.86 * PAIR A2: 1,7 BLK 1 B2: 1,7,2 # reduction candidate for 1,7 B2: 1,7 # 18 pairs B3: 1,7,5,6 # reduction candidate for 1,7 B3: 1,7 => SOLVED * 436198725728653914915724368863249571259817643174536892582961437647382159391475286 B3: 5,6 # 18 pairs * PAIR A2: 1,7 ROW 2 H2: 1,7,2,4 # reduction candidate for 1,7 H2: 1,7 => SOLVED * 436198725728653914915724368863249571259817643174536892582961437647382159391475286 H2: 2,4 # 15 pairs I2: 1,7,2,4,8 # reduction candidate for 1,7 I2: 1,7 => CTR * 435..86...2865394.9.6.243.88.32495..25981.4.3..453.892582961734647382159391475286 I2: 2,4,8 # 14 pairs * PAIR C2: 2,8 ROW 2 I2: 2,8,1,4,7 # reduction candidate for 2,8 I2: 2,8 # 26 pairs I2: 1,4,7 # 14 pairs * PAIR F1: 7,8 BLK 2 E1: 7,8,1,9 # reduction candidate for 7,8 E1: 1,9 # 18 pairs E1: 7,8 # 17 pairs * PAIR D3: 1,7 BLK 2 D1: 1,7,9 # reduction candidate for 1,7 D1: 1,7 => SOLVED * 436198725728653914915724368863249571259817643174536892582961437647382159391475286 D1: 9 # 15 pairs E1: 1,7,8,9 # reduction candidate for 1,7 E1: 1,7 # 18 pairs * PAIR D3: 1,7 ROW 3 B3: 1,7,5,6 # reduction candidate for 1,7 B3: 1,7 => SOLVED * 436198725728653914915724368863249571259817643174536892582961437647382159391475286 B3: 5,6 # 18 pairs H3: 1,7,5,6 # reduction candidate for 1,7 H3: 1,7 # 21 pairs I3: 1,7,5,8 # reduction candidate for 1,7 I3: 1,7 => CTR * 43....6....2653948968.2435.8.3.4956.2598..4.3..653.89..84..1.3...73..124321495786 I3: 5,8 # 15 pairs * PAIR D3: 1,7 COL D D4: 1,7,2 # reduction candidate for 1,7 D4: 1,7 # 28 pairs D4: 2 # 18 pairs * PAIR A6: 1,7 BLK 4 B4: 1,7,6 # reduction candidate for 1,7 B4: 1,7 # 18 pairs B6: 1,7,4,6 # reduction candidate for 1,7 B6: 1,7 # 19 pairs * PAIR A6: 1,7 ROW 6 I6: 1,7,2 # reduction candidate for 1,7 I6: 1,7 # 28 pairs I6: 2 # 18 pairs * PAIR C6: 4,6 BLK 4 B6: 4,6,1,7 # reduction candidate for 4,6 B6: 1,7 # 19 pairs B6: 4,6 # 18 pairs * PAIR F5: 6,7 BLK 5 E5: 6,7,1 # reduction candidate for 6,7 E5: 6,7 => CTR * 43.9186.....6539.49..7243.88.31495622..867..3...53289.68.2.1.355.7386..93.14.5.86 E5: 1 # 16 pairs F6: 6,7,2 # reduction candidate for 6,7 F6: 6,7 # 18 pairs * PAIR F5: 6,7 ROW 5 G5: 6,7,1,4 # reduction candidate for 6,7 G5: 6,7 # 17 pairs H5: 6,7,1,4 # reduction candidate for 6,7 H5: 6,7 # 20 pairs * PAIR B9: 2,9 BLK 7 C7: 2,9,4 # reduction candidate for 2,9 C7: 2,9 # 15 pairs B8: 2,9,4 # reduction candidate for 2,9 B8: 2,9 # 23 pairs * PAIR E9: 7,9 BLK 8 D7: 7,9,2 # reduction candidate for 7,9 D7: 7,9 # 18 pairs E7: 7,9,6 # reduction candidate for 7,9 E7: 7,9 # 30 pairs * PAIR E9: 7,9 COL E E1: 7,9,1,8 # reduction candidate for 7,9 E1: 7,9 # 18 pairs E1: 1,8 # 16 pairs * PAIR G9: 2,7 BLK 9 G7: 2,7,4 # reduction candidate for 2,7 G7: 2,7 # 17 pairs I7: 2,7,4,5,9 # reduction candidate for 2,7 I7: 2,7 => SOLVED * 436198725728653914915724368863249571259817643174536892582961437647382159391475286 I7: 4,5,9 # 14 pairs * PAIR G9: 2,7 COL G G1: 2,7,1,6 # reduction candidate for 2,7 G1: 2,7 => SOLVED * 436198725728653914915724368863249571259817643174536892582961437647382159391475286 G1: 1,6 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0128-base-pr-000.dot * REASONING * PRF # B3: 1,7 => SOL * PRF # H2: 1,7 => SOL * DIS # I2: 1,7 => CTR => I2: 2,4,8 * PRF # D1: 1,7 => SOL * PRF # B3: 1,7 => SOL * DIS # I3: 1,7 => CTR => I3: 5,8 * DIS # E5: 6,7 => CTR => E5: 1 * PRF # I7: 2,7 => SOL * PRF # G1: 2,7 => SOL * CNT 9 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A7,A8,B5,B9,C2,C5,C6,D3,E9,F1,F5,G9) * 43..........6539..9...243..8.3.495..2..8....3...53.89..8...1.3...73.....3.14.5.86 * PAIR A2: 1,7 BLK 1 B2: 1,7,2 # reduction candidate for 1,7 B2: 1,7 # 18 pairs B3: 1,7,5,6 # reduction candidate for 1,7 B3: 1,7 => SOLVED * 436198725728653914915724368863249571259817643174536892582961437647382159391475286 * DURATION: 0:00:03.452439 START: 05:55:24.370987 END: 05:55:27.823426 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0128-base-pr-001.dot * REASONING * PRF # B3: 1,7 => SOL * STA B3: 1,7 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=128
Solution
position: 436198725728653914915724368863249571259817643174536892582961437647382159391475286 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: 1,7 => UNS * PRF # B3: 1,7 => SOL * INC # B3: 5,6 => UNS * PRF # H2: 1,7 => SOL * INC # H2: 2,4 => UNS * DIS # I2: 1,7 => CTR => I2: 2,4,8 * INC # I2: 2,4,8 => UNS * INC # I2: 2,8 => UNS * INC # I2: 1,4,7 => UNS * INC # E1: 7,8 => UNS * INC # E1: 1,9 => UNS * PRF # D1: 1,7 => SOL * INC # D1: 9 => UNS * INC # E1: 1,7 => UNS * PRF # B3: 1,7 => SOL * INC # B3: 5,6 => UNS * INC # H3: 1,7 => UNS * DIS # I3: 1,7 => CTR => I3: 5,8 * INC # I3: 5,8 => UNS * INC # D4: 1,7 => UNS * INC # D4: 2 => UNS * INC # B4: 1,7 => UNS * INC # B6: 1,7 => UNS * INC # I6: 1,7 => UNS * INC # I6: 2 => UNS * INC # B6: 4,6 => UNS * INC # B6: 1,7 => UNS * DIS # E5: 6,7 => CTR => E5: 1 * INC # E5: 1 => UNS * INC # F6: 6,7 => UNS * INC # G5: 6,7 => UNS * INC # H5: 6,7 => UNS * INC # C7: 2,9 => UNS * INC # B8: 2,9 => UNS * INC # D7: 7,9 => UNS * INC # E7: 7,9 => UNS * INC # E1: 7,9 => UNS * INC # E1: 1,8 => UNS * INC # G7: 2,7 => UNS * PRF # I7: 2,7 => SOL * INC # I7: 4,5,9 => UNS * PRF # G1: 2,7 => SOL * INC # G1: 1,6 => UNS * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 1,7 => UNS * PRF # B3: 1,7 => SOL * STA B3: 1,7 * CNT 2 HDP CHAINS / 2 HYP OPENED