Analysis of zz-www.sudokuwiki.org-0118-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=118
level: medium
position: .5..3..4...82..6..9....5..1...8...36....2....48.......7..4....8..5..97...9..6..2. initial
Autosolve
position: .5..3..4...82..6..9....5..1...8...36....2....48.......7..4.2..8..5..97...9..6..2. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 6,7 => CTR => D1: 1,9 * DIS # F1: 6,7 => CTR => F1: 1,8 * DIS # B3: 6,7 => CTR => B3: 2,3,4 * DIS # C3: 6,7 => CTR => C3: 2,3,4 * DIS # D9: 1,5 => CTR => D9: 3,7 * DIS # D9: 1,3 => CTR => D9: 5,7 * DIS # A8: 1,6 => CTR => A8: 2,3,8 * DIS # B8: 1,6 => CTR => B8: 2,3,4 * CNT 8 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 6,7 => CTR => D1: 1,9 * DIS D1: 1,9 # F1: 6,7 => CTR => F1: 1,8 * DIS D1: 1,9 + F1: 1,8 # D9: 1,5 => CTR => D9: 3,7 * DIS D1: 1,9 + F1: 1,8 + D9: 3,7 # A8: 1,8 => CTR => A8: 2,3,6 * DIS D1: 1,9 + F1: 1,8 + D9: 3,7 + A8: 2,3,6 # B8: 1,6 => CTR => B8: 2,3,4 * PRF D1: 1,9 + F1: 1,8 + D9: 3,7 + A8: 2,3,6 + B8: 2,3,4 # H7: 9 => SOL * STA D1: 1,9 + F1: 1,8 + D9: 3,7 + A8: 2,3,6 + B8: 2,3,4 + H7: 9 * CNT 6 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5..3..4...82..6..9....5..1...8...36....2....48.......7..4....8..5..97...9..6..2. | initial |
| .5..3..4...82..6..9....5..1...8...36....2....48.......7..4.2..8..5..97...9..6..2. | autosolve |
| 156938247378214659924675381512847936639521874487396512763452198245189763891763425 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A2: 1,3 D3: 6,7 H3: 7,8 E7: 1,5 D8: 1,3 E8: 1,8 H8: 1,6 I8: 3,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A8,B8: 2.. / A8 = 2 => 11 pairs (_) / B8 = 2 => 9 pairs (_) I1,I6: 2.. / I1 = 2 => 11 pairs (_) / I6 = 2 => 9 pairs (_) I2,G3: 3.. / I2 = 3 => 24 pairs (_) / G3 = 3 => 11 pairs (_) B8,C9: 4.. / B8 = 4 => 17 pairs (_) / C9 = 4 => 8 pairs (_) B8,I8: 4.. / B8 = 4 => 17 pairs (_) / I8 = 4 => 8 pairs (_) C3,C9: 4.. / C3 = 4 => 17 pairs (_) / C9 = 4 => 8 pairs (_) H2,I2: 5.. / H2 = 5 => 8 pairs (_) / I2 = 5 => 15 pairs (_) A4,A5: 5.. / A4 = 5 => 8 pairs (_) / A5 = 5 => 9 pairs (_) E7,D9: 5.. / E7 = 5 => 7 pairs (_) / D9 = 5 => 0 pairs (X) H7,H8: 6.. / H7 = 6 => 0 pairs (X) / H8 = 6 => 7 pairs (_) D9,F9: 7.. / D9 = 7 => 7 pairs (_) / F9 = 7 => 14 pairs (_) F1,E3: 8.. / F1 = 8 => 9 pairs (_) / E3 = 8 => 18 pairs (_) G5,H5: 8.. / G5 = 8 => 9 pairs (_) / H5 = 8 => 9 pairs (_) A8,A9: 8.. / A8 = 8 => 18 pairs (_) / A9 = 8 => 9 pairs (_) E8,F9: 8.. / E8 = 8 => 9 pairs (_) / F9 = 8 => 18 pairs (_) F1,G1: 8.. / F1 = 8 => 9 pairs (_) / G1 = 8 => 18 pairs (_) A8,E8: 8.. / A8 = 8 => 18 pairs (_) / E8 = 8 => 9 pairs (_) A9,F9: 8.. / A9 = 8 => 9 pairs (_) / F9 = 8 => 18 pairs (_) E3,E8: 8.. / E3 = 8 => 18 pairs (_) / E8 = 8 => 9 pairs (_) F1,F9: 8.. / F1 = 8 => 9 pairs (_) / F9 = 8 => 18 pairs (_) H3,H5: 8.. / H3 = 8 => 9 pairs (_) / H5 = 8 => 9 pairs (_) D1,E2: 9.. / D1 = 9 => 15 pairs (_) / E2 = 9 => 9 pairs (_) G7,H7: 9.. / G7 = 9 => 11 pairs (_) / H7 = 9 => 8 pairs (_) * DURATION: 0:00:25.106729 START: 05:38:35.551006 END: 05:39:00.657735 2017-05-01 * CP COUNT: (23) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,D3,D8,E7,E8,H3,H8,I8) * .5..3..4...82..6..9....5..1...8...36....2....48.......7..4.2..8..5..97...9..6..2. * PAIR A2: 1,3 BLK 1 B2: 1,3,4,7 # reduction candidate for 1,3 B2: 1,3 # 17 pairs B2: 4,7 # 9 pairs * PAIR A2: 1,3 COL A A5: 1,3,5,6 # reduction candidate for 1,3 A5: 1,3 # 12 pairs A8: 1,3,2,6,8 # reduction candidate for 1,3 A8: 1,3 # 13 pairs A9: 1,3,8 # reduction candidate for 1,3 A9: 1,3 # 18 pairs * PAIR D3: 6,7 BLK 2 D1: 6,7,1,9 # reduction candidate for 6,7 D1: 6,7 => CTR * .5..38.4.3482916..9...45381...8.4.36....2....48.......7..4.2..8..5.897..894.67.2. D1: 1,9 # 9 pairs F1: 6,7,1,8 # reduction candidate for 6,7 F1: 6,7 => CTR * .5.93784237824165994268537121.8.45365.912.48748.5.....7..452..8825319764.94768.2. F1: 1,8 # 9 pairs * PAIR D3: 6,7 ROW 3 B3: 6,7,2,3,4 # reduction candidate for 6,7 B3: 6,7 => CTR * .5..38947148297653973645281...8..436....248..48.3.65.27..452398..5189764894763125 B3: 2,3,4 # 8 pairs C3: 6,7,2,3,4 # reduction candidate for 6,7 C3: 6,7 => CTR * .5..38947148297653937645281...8..436....248..48...65.27..452398325189764894763125 C3: 2,3,4 # 8 pairs * PAIR D3: 6,7 COL D D5: 6,7,1,3,5,9 # reduction candidate for 6,7 D5: 6,7 # 14 pairs D6: 6,7,1,3,5,9 # reduction candidate for 6,7 D6: 6,7 # 18 pairs * PAIR H3: 7,8 ROW 3 E3: 7,8,4 # reduction candidate for 7,8 E3: 7,8 # 9 pairs E3: 4 # 9 pairs * PAIR H3: 7,8 COL H H5: 7,8,1,5,9 # reduction candidate for 7,8 H5: 7,8 # 10 pairs H5: 1,5,9 # 9 pairs * PAIR E7: 1,5 BLK 8 D9: 1,5,3,7 # reduction candidate for 1,5 D9: 1,5 => CTR * .5..38.4...82..6539..645871...8.4.363..52648.486..35.27..452..8..53897.4894167325 D9: 3,7 # 8 pairs * PAIR E7: 1,5 ROW 7 G7: 1,5,3,9 # reduction candidate for 1,5 G7: 1,5 # 13 pairs H7: 1,5,6,9 # reduction candidate for 1,5 H7: 1,5 # 13 pairs * PAIR E7: 1,5 COL E E4: 1,5,4,7,9 # reduction candidate for 1,5 E4: 1,5 # 12 pairs E6: 1,5,7,9 # reduction candidate for 1,5 E6: 1,5 # 10 pairs * PAIR D8: 1,3 BLK 8 D9: 1,3,5,7 # reduction candidate for 1,3 D9: 1,3 => CTR * 15..38.4.3782..6599.4.75381...8...36....2.8.448.......7..452..8.45.897.3891367425 D9: 5,7 # 9 pairs F9: 1,3,7,8 # reduction candidate for 1,3 F9: 1,3 # 9 pairs * PAIR D8: 1,3 ROW 8 A8: 1,3,2,6,8 # reduction candidate for 1,3 A8: 1,3 # 13 pairs B8: 1,3,2,4,6 # reduction candidate for 1,3 B8: 1,3 # 11 pairs * PAIR D8: 1,3 COL D D5: 1,3,5,6,7,9 # reduction candidate for 1,3 D5: 1,3 # 10 pairs D6: 1,3,5,6,7,9 # reduction candidate for 1,3 D6: 1,3 # 10 pairs * PAIR E8: 1,8 BLK 8 F9: 1,8,3,7 # reduction candidate for 1,8 F9: 1,8 # 13 pairs F9: 3,7 # 10 pairs * PAIR E8: 1,8 ROW 8 A8: 1,8,2,3,6 # reduction candidate for 1,8 A8: 1,8 # 11 pairs A8: 2,3,6 # 9 pairs * PAIR H8: 1,6 BLK 9 H7: 1,6,5,9 # reduction candidate for 1,6 H7: 1,6 # 11 pairs H7: 5,9 # 8 pairs * PAIR H8: 1,6 ROW 8 A8: 1,6,2,3,8 # reduction candidate for 1,6 A8: 1,6 => CTR * .5..38.4...82..6539.26458712..8.4.36....2.48.48.......7..4.2..8.253897.4894.6.325 A8: 2,3,8 # 8 pairs B8: 1,6,2,3,4 # reduction candidate for 1,6 B8: 1,6 => CTR * 65..382491482976539..6458715..8.4.363.95264874869735127..4521982153897.4894.6.325 B8: 2,3,4 # 8 pairs * PAIR I8: 3,4 BLK 9 G9: 3,4,1,5 # reduction candidate for 3,4 G9: 3,4 # 11 pairs I9: 3,4,5 # reduction candidate for 3,4 I9: 3,4 # 13 pairs * PAIR I8: 3,4 ROW 8 B8: 3,4,1,2,6 # reduction candidate for 3,4 B8: 3,4 # 17 pairs B8: 1,2,6 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0118-base-pr-000.dot * REASONING * DIS # D1: 6,7 => CTR => D1: 1,9 * DIS # F1: 6,7 => CTR => F1: 1,8 * DIS # B3: 6,7 => CTR => B3: 2,3,4 * DIS # C3: 6,7 => CTR => C3: 2,3,4 * DIS # D9: 1,5 => CTR => D9: 3,7 * DIS # D9: 1,3 => CTR => D9: 5,7 * DIS # A8: 1,6 => CTR => A8: 2,3,8 * DIS # B8: 1,6 => CTR => B8: 2,3,4 * CNT 8 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,D3,D8,E7,E8,H3,H8,I8) * .5..3..4...82..6..9....5..1...8...36....2....48.......7..4.2..8..5..97...9..6..2. * PAIR A2: 1,3 BLK 1 B2: 1,3,4,7 # reduction candidate for 1,3 B2: 1,3 # 17 pairs B2: 4,7 # 9 pairs * PAIR A2: 1,3 COL A A5: 1,3,5,6 # reduction candidate for 1,3 A5: 1,3 # 12 pairs A8: 1,3,2,6,8 # reduction candidate for 1,3 A8: 1,3 # 13 pairs A9: 1,3,8 # reduction candidate for 1,3 A9: 1,3 # 18 pairs * PAIR D3: 6,7 BLK 2 D1: 6,7,1,9 # reduction candidate for 6,7 D1: 6,7 => CTR * .5..38.4.3482916..9...45381...8.4.36....2....48.......7..4.2..8..5.897..894.67.2. F1: 6,7,1,8 # reduction candidate for 6,7 F1: 6,7 => CTR * .5.93784237824165994268537121.8.45365.912.48748.5.....7..452..8825319764.94768.2. * PAIR H3: 7,8 ROW 3 E3: 7,8,4 # reduction candidate for 7,8 E3: 7,8 # 11 pairs E3: 4 # 10 pairs * PAIR H3: 7,8 COL H H5: 7,8,1,5,9 # reduction candidate for 7,8 H5: 7,8 # 11 pairs H5: 1,5,9 # 9 pairs * PAIR E7: 1,5 BLK 8 D9: 1,5,3,7 # reduction candidate for 1,5 D9: 1,5 => CTR * .57.38.4...827.65.9..6.5871...8...36....2.48.48.......7..4.2..8..53897.4894.67325 * PAIR D8: 1,3 BLK 8 F9: 1,3,7,8 # reduction candidate for 1,3 F9: 7,8 # 13 pairs F9: 1,3 # 9 pairs * PAIR D8: 1,3 ROW 8 A8: 1,3,2,6,8 # reduction candidate for 1,3 A8: 1,3 # 14 pairs B8: 1,3,2,4,6 # reduction candidate for 1,3 B8: 1,3 # 12 pairs * PAIR D8: 1,3 COL D D5: 1,3,5,7,9 # reduction candidate for 1,3 D5: 1,3 # 19 pairs D6: 1,3,5,7,9 # reduction candidate for 1,3 D6: 1,3 # 16 pairs * PAIR E8: 1,8 BLK 8 F9: 1,8,3,7 # reduction candidate for 1,8 F9: 3,7 # 17 pairs F9: 1,8 # 17 pairs * PAIR E8: 1,8 ROW 8 A8: 1,8,2,3,6 # reduction candidate for 1,8 A8: 1,8 => CTR * 657.3..4...82..6539326458712..8.45365...2.48.48.5.....7..452..8.25389764.9476..25 * PAIR RESTART * PAIR H8: 1,6 BLK 9 H7: 1,6,9 # reduction candidate for 1,6 H7: 1,6 # 15 pairs H7: 9 # 11 pairs * PAIR H8: 1,6 ROW 8 B8: 1,6,2,3,4 # reduction candidate for 1,6 B8: 1,6 => CTR * 6571382491482976539..6458715..8.4.363.95264874869735127..4521982153897.4894761325 * PAIR RESTART * PAIR H8: 1,6 BLK 9 H7: 1,6,9 # reduction candidate for 1,6 H7: 9 => SOLVED * 156938247378214659924675381512847936639521874487396512763452198245189763891763425 * DURATION: 0:00:22.261383 START: 05:39:29.225063 END: 05:39:51.486446 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0118-base-pr-001.dot * REASONING * DIS # D1: 6,7 => CTR => D1: 1,9 * DIS D1: 1,9 # F1: 6,7 => CTR => F1: 1,8 * DIS D1: 1,9 + F1: 1,8 # D9: 1,5 => CTR => D9: 3,7 * DIS D1: 1,9 + F1: 1,8 + D9: 3,7 # A8: 1,8 => CTR => A8: 2,3,6 * DIS D1: 1,9 + F1: 1,8 + D9: 3,7 + A8: 2,3,6 # B8: 1,6 => CTR => B8: 2,3,4 * PRF D1: 1,9 + F1: 1,8 + D9: 3,7 + A8: 2,3,6 + B8: 2,3,4 # H7: 9 => SOL * STA D1: 1,9 + F1: 1,8 + D9: 3,7 + A8: 2,3,6 + B8: 2,3,4 + H7: 9 * CNT 6 HDP CHAINS / 26 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=118
Solution
position: 156938247378214659924675381512847936639521874487396512763452198245189763891763425 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: 1,3 => UNS * INC # B2: 4,7 => UNS * INC # A5: 1,3 => UNS * INC # A8: 1,3 => UNS * INC # A9: 1,3 => UNS * DIS # D1: 6,7 => CTR => D1: 1,9 * INC # D1: 1,9 => UNS * DIS # F1: 6,7 => CTR => F1: 1,8 * INC # F1: 1,8 => UNS * DIS # B3: 6,7 => CTR => B3: 2,3,4 * INC # B3: 2,3,4 => UNS * DIS # C3: 6,7 => CTR => C3: 2,3,4 * INC # C3: 2,3,4 => UNS * INC # D5: 6,7 => UNS * INC # D6: 6,7 => UNS * INC # E3: 7,8 => UNS * INC # E3: 4 => UNS * INC # H5: 7,8 => UNS * INC # H5: 1,5,9 => UNS * DIS # D9: 1,5 => CTR => D9: 3,7 * INC # D9: 3,7 => UNS * INC # G7: 1,5 => UNS * INC # H7: 1,5 => UNS * INC # E4: 1,5 => UNS * INC # E6: 1,5 => UNS * DIS # D9: 1,3 => CTR => D9: 5,7 * INC # D9: 5,7 => UNS * INC # F9: 1,3 => UNS * INC # A8: 1,3 => UNS * INC # B8: 1,3 => UNS * INC # D5: 1,3 => UNS * INC # D6: 1,3 => UNS * INC # F9: 1,8 => UNS * INC # F9: 3,7 => UNS * INC # A8: 1,8 => UNS * INC # A8: 2,3,6 => UNS * INC # H7: 1,6 => UNS * INC # H7: 5,9 => UNS * DIS # A8: 1,6 => CTR => A8: 2,3,8 * INC # A8: 2,3,8 => UNS * DIS # B8: 1,6 => CTR => B8: 2,3,4 * INC # B8: 2,3,4 => UNS * INC # G9: 3,4 => UNS * INC # I9: 3,4 => UNS * INC # B8: 3,4 => UNS * INC # B8: 1,2,6 => UNS * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 1,3 => UNS * INC # B2: 4,7 => UNS * INC # A5: 1,3 => UNS * INC # A8: 1,3 => UNS * INC # A9: 1,3 => UNS * DIS # D1: 6,7 => CTR => D1: 1,9 * DIS D1: 1,9 # F1: 6,7 => CTR => F1: 1,8 * INC D1: 1,9 + F1: 1,8 # E3: 7,8 => UNS * INC D1: 1,9 + F1: 1,8 # E3: 4 => UNS * INC D1: 1,9 + F1: 1,8 # H5: 7,8 => UNS * INC D1: 1,9 + F1: 1,8 # H5: 1,5,9 => UNS * DIS D1: 1,9 + F1: 1,8 # D9: 1,5 => CTR => D9: 3,7 * INC D1: 1,9 + F1: 1,8 + D9: 3,7 # F9: 1,3 => UNS * INC D1: 1,9 + F1: 1,8 + D9: 3,7 # F9: 7,8 => UNS * INC D1: 1,9 + F1: 1,8 + D9: 3,7 # A8: 1,3 => UNS * INC D1: 1,9 + F1: 1,8 + D9: 3,7 # B8: 1,3 => UNS * INC D1: 1,9 + F1: 1,8 + D9: 3,7 # D5: 1,3 => UNS * INC D1: 1,9 + F1: 1,8 + D9: 3,7 # D6: 1,3 => UNS * INC D1: 1,9 + F1: 1,8 + D9: 3,7 # F9: 1,8 => UNS * INC D1: 1,9 + F1: 1,8 + D9: 3,7 # F9: 3,7 => UNS * DIS D1: 1,9 + F1: 1,8 + D9: 3,7 # A8: 1,8 => CTR => A8: 2,3,6 * INC D1: 1,9 + F1: 1,8 + D9: 3,7 + A8: 2,3,6 # H7: 1,6 => UNS * INC D1: 1,9 + F1: 1,8 + D9: 3,7 + A8: 2,3,6 # H7: 9 => UNS * DIS D1: 1,9 + F1: 1,8 + D9: 3,7 + A8: 2,3,6 # B8: 1,6 => CTR => B8: 2,3,4 * INC D1: 1,9 + F1: 1,8 + D9: 3,7 + A8: 2,3,6 + B8: 2,3,4 # H7: 1,6 => UNS * PRF D1: 1,9 + F1: 1,8 + D9: 3,7 + A8: 2,3,6 + B8: 2,3,4 # H7: 9 => SOL * STA D1: 1,9 + F1: 1,8 + D9: 3,7 + A8: 2,3,6 + B8: 2,3,4 + H7: 9 * CNT 26 HDP CHAINS / 26 HYP OPENED