Analysis of zz-www.sudokuwiki.org-0283-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=283
level: medium
position: ....47..9..4.3...8.1.2....6..3....97.2....6..6.....5..5..1.......8.96.7......4... initial
Autosolve
position: ....47..9..4.31..8.1.2....6..3.6..97.2....6..6.....5..5..1.......8.96.7......4... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H1: 2,5 => CTR => H1: 1,3 * DIS # I8: 3,4 => CTR => I8: 1,2,5 * CNT 2 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H1: 2,5 => CTR => H1: 1,3 * DIS H1: 1,3 # A8: 3,4 => CTR => A8: 1,2 * DIS H1: 1,3 + A8: 1,2 # G8: 3,4 => CTR => G8: 1,2 * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 # I8: 3,4 => CTR => I8: 5 * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 # F3: 5,8 => CTR => F3: 9 * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 # E9: 2,7 => CTR => E9: 5,8 * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 # G1: 2 => CTR => G1: 1,3 * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 # H9: 1,3 => CTR => H9: 2,6,8 * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 # F4: 5,8 => CTR => F4: 2 * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 + F4: 2 # A9: 1,2 => CTR => A9: 9 * PRF H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 + F4: 2 + A9: 9 => SOL * STA H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 + F4: 2 + A9: 9 * CNT 11 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....47..9..4.3...8.1.2....6..3....97.2....6..6.....5..5..1.......8.96.7......4... | initial |
| ....47..9..4.31..8.1.2....6..3.6..97.2....6..6.....5..5..1.......8.96.7......4... | autosolve |
| 862547319794631258315289746153862497427915683689473521576128934248396175931754862 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) E3: 5,8 G2: 2,7 H2: 2,5 B8: 3,4 D8: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,H1: 1.. / G1 = 1 => 0 pairs (X) / H1 = 1 => 6 pairs (_) E5,E6: 1.. / E5 = 1 => 6 pairs (_) / E6 = 1 => 7 pairs (_) A4,G4: 1.. / A4 = 1 => 8 pairs (_) / G4 = 1 => 13 pairs (_) F4,G4: 2.. / F4 = 2 => 6 pairs (_) / G4 = 2 => 14 pairs (_) G3,H3: 4.. / G3 = 4 => 6 pairs (_) / H3 = 4 => 6 pairs (_) B4,C5: 5.. / B4 = 5 => 7 pairs (_) / C5 = 5 => 8 pairs (_) I8,I9: 5.. / I8 = 5 => 7 pairs (_) / I9 = 5 => 9 pairs (_) D8,I8: 5.. / D8 = 5 => 9 pairs (_) / I8 = 5 => 7 pairs (_) D1,D2: 6.. / D1 = 6 => 7 pairs (_) / D2 = 6 => 8 pairs (_) H7,H9: 6.. / H7 = 6 => 5 pairs (_) / H9 = 6 => 5 pairs (_) B2,D2: 6.. / B2 = 6 => 7 pairs (_) / D2 = 6 => 8 pairs (_) G2,G3: 7.. / G2 = 7 => 6 pairs (_) / G3 = 7 => 11 pairs (_) D2,F3: 9.. / D2 = 9 => 9 pairs (_) / F3 = 9 => 8 pairs (_) G7,G9: 9.. / G7 = 9 => 5 pairs (_) / G9 = 9 => 5 pairs (_) * DURATION: 0:00:09.543885 START: 14:48:37.088320 END: 14:48:46.632205 2019-04-28 * CP COUNT: (14) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,D8,E3,G2,H2) * ....47..9..4.31..8.1.2....6..3.6..97.2....6..6.....5..5..1.......8.96.7......4... * PAIR E3: 5,8 BLK 2 D1: 5,8,6 # reduction candidate for 5,8 D1: 5,8 # 8 pairs F3: 5,8,9 # reduction candidate for 5,8 F3: 5,8 # 9 pairs * PAIR E3: 5,8 COL E E5: 5,8,1,7 # reduction candidate for 5,8 E5: 5,8 # 17 pairs E9: 5,8,2,7 # reduction candidate for 5,8 E9: 5,8 # 9 pairs * PAIR G2: 2,7 ROW 2 A2: 2,7,9 # reduction candidate for 2,7 A2: 9 # 9 pairs A2: 2,7 # 8 pairs * PAIR H2: 2,5 BLK 3 H1: 2,5,1,3 # reduction candidate for 2,5 H1: 2,5 => CTR * ..2.47159954631728.17259..61.3.6529742597.613679.125845.6183.422485963717.1.24..5 H1: 1,3 # 6 pairs * PAIR B8: 3,4 BLK 7 B7: 3,4,6,7,9 # reduction candidate for 3,4 B7: 3,4 # 8 pairs A8: 3,4,1,2 # reduction candidate for 3,4 A8: 3,4 # 13 pairs * PAIR B8: 3,4 ROW 8 G8: 3,4,1,2 # reduction candidate for 3,4 G8: 3,4 # 13 pairs I8: 3,4,1,2,5 # reduction candidate for 3,4 I8: 3,4 => CTR * ..2.47319..4.3125831.2..7461.3.62.97425...6..6.....5..5.61.....2.859617...1..4.65 I8: 1,2,5 # 5 pairs * PAIR D8: 3,5 BLK 8 D9: 3,5,7,8 # reduction candidate for 3,5 D9: 3,5 # 12 pairs D9: 7,8 # 6 pairs * PAIR D8: 3,5 ROW 8 I8: 3,5,1,2,4 # reduction candidate for 3,5 I8: 1,2,4 # 9 pairs I8: 3,5 # 8 pairs * PAIR D8: 3,5 COL D D5: 3,5,4,7,8,9 # reduction candidate for 3,5 D5: 3,5 # 12 pairs D5: 4,7,8,9 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0283-base-pr-000.dot * REASONING * DIS # H1: 2,5 => CTR => H1: 1,3 * DIS # I8: 3,4 => CTR => I8: 1,2,5 * CNT 2 HDP CHAINS / 19 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,D8,E3,G2,H2) * ....47..9..4.31..8.1.2....6..3.6..97.2....6..6.....5..5..1.......8.96.7......4... * PAIR E3: 5,8 BLK 2 D1: 5,8,6 # reduction candidate for 5,8 D1: 5,8 # 8 pairs F3: 5,8,9 # reduction candidate for 5,8 F3: 5,8 # 9 pairs * PAIR E3: 5,8 COL E E5: 5,8,1,7 # reduction candidate for 5,8 E5: 5,8 # 17 pairs E9: 5,8,2,7 # reduction candidate for 5,8 E9: 5,8 # 9 pairs * PAIR G2: 2,7 ROW 2 A2: 2,7,9 # reduction candidate for 2,7 A2: 9 # 9 pairs A2: 2,7 # 8 pairs * PAIR H2: 2,5 BLK 3 H1: 2,5,1,3 # reduction candidate for 2,5 H1: 2,5 => CTR * ..2.47159954631728.17259..61.3.6529742597.613679.125845.6183.422485963717.1.24..5 * PAIR B8: 3,4 BLK 7 B7: 3,4,6,7,9 # reduction candidate for 3,4 B7: 3,4 # 9 pairs A8: 3,4,1,2 # reduction candidate for 3,4 A8: 3,4 => CTR * ..5.47.19..4.31.58.1.2....6153.62.97.2....6..6.....52.5..1.......8596172..1..4..5 * RESTART * PAIR B8: 3,4 BLK 7 B7: 3,4,6,7,9 # reduction candidate for 3,4 B7: 3,4 # 9 pairs B7: 6,7,9 # 7 pairs * PAIR B8: 3,4 ROW 8 G8: 3,4,1,2 # reduction candidate for 3,4 G8: 3,4 => CTR * ..5.47..9..4.31.58.1.2....6.53.62197.2....6..6.....52.5..1.....1.8596.72.....4.15 I8: 3,4,5 # reduction candidate for 3,4 I8: 3,4 => CTR * ..2.47319..4.3125831.2..7461.3.62.97425...6..6.....5..5.61.....2.859617...1..4.65 * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A8,B4,E3,F7,G2,G8,H1,H2) * ....47..9..4.31..8.1.2....6..3.6..97.2....6..6.....5..5..1......48396.75.....4... * PAIR E3: 5,8 BLK 2 D1: 5,8,6 # reduction candidate for 5,8 D1: 5,8 # 11 pairs F3: 5,8,9 # reduction candidate for 5,8 F3: 5,8 => CTR * ..26473197649312583192857461.3.62.97425..96..697.135..5.61.89.42483961759.1.54862 * RESTART * PAIR E3: 5,8 BLK 2 D1: 5,8,6 # reduction candidate for 5,8 D1: 6 # 17 pairs D1: 5,8 # 11 pairs * PAIR E3: 5,8 COL E E9: 5,8,2,7 # reduction candidate for 5,8 E9: 2,7 => CTR * ...847..9..4631.58817259..6..346..9742....6..67.9..5..5..178....48396.757..524... * PAIR RESTART * PAIR E3: 5,8 BLK 2 D1: 5,8,6 # reduction candidate for 5,8 D1: 6 # 17 pairs D1: 5,8 # 15 pairs * PAIR H1: 1,3 BLK 3 G1: 1,3,2 # reduction candidate for 1,3 G1: 2 => CTR * ....47219294631758.1.2.9..6..3.62.97.2...56..6....35..5..128...148396.75.....4... * PAIR H1: 1,3 COL H H5: 1,3,4,8 # reduction candidate for 1,3 H5: 1,3 # 21 pairs H6: 1,3,2,4,8 # reduction candidate for 1,3 H6: 1,3 # 22 pairs H9: 1,3,2,6,8 # reduction candidate for 1,3 H9: 1,3 => CTR * ....47319..4.31728317289..6..3.6.197.2....6.36....35.253.128964148396275...754831 * PAIR RESTART * PAIR H1: 1,3 COL H H5: 1,3,4,8 # reduction candidate for 1,3 H5: 1,3 # 21 pairs H6: 1,3,2,4,8 # reduction candidate for 1,3 H6: 1,3 # 22 pairs * PAIR B4: 5,8 ROW 4 F4: 5,8,2 # reduction candidate for 5,8 F4: 5,8 => CTR * 8.2.47319..4.317283172894561.346.29742597.6.16798125..5.61289..2483961757...54..2 * PAIR RESTART * PAIR A8: 1,2 BLK 7 A9: 1,2,9 # reduction candidate for 1,2 A9: 1,2 => CTR * 862547..9..4631.58315289746453862197.2...568368...35245..128....48396.75...754... A9: 9 => SOLVED * 862547319794631258315289746153862497427915683689473521576128934248396175931754862 * DURATION: 0:00:18.839125 START: 14:48:54.609115 END: 14:49:13.448240 2019-04-28 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0283-base-pr-001.dot * REASONING * DIS # H1: 2,5 => CTR => H1: 1,3 * DIS H1: 1,3 # A8: 3,4 => CTR => A8: 1,2 * DIS H1: 1,3 + A8: 1,2 # G8: 3,4 => CTR => G8: 1,2 * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 # I8: 3,4 => CTR => I8: 5 * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 # F3: 5,8 => CTR => F3: 9 * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 # E9: 2,7 => CTR => E9: 5,8 * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 # G1: 2 => CTR => G1: 1,3 * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 # H9: 1,3 => CTR => H9: 2,6,8 * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 # F4: 5,8 => CTR => F4: 2 * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 + F4: 2 # A9: 1,2 => CTR => A9: 9 * PRF H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 + F4: 2 + A9: 9 => SOL * STA H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 + F4: 2 + A9: 9 * CNT 11 HDP CHAINS / 30 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=283
Solution
position: 862547319794631258315289746153862497427915683689473521576128934248396175931754862 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 # D1: 5,8 => UNS * INC # F3: 5,8 => UNS * INC # E5: 5,8 => UNS * INC # E9: 5,8 => UNS * INC # A2: 2,7 => UNS * INC # A2: 9 => UNS * DIS # H1: 2,5 => CTR => H1: 1,3 * INC # H1: 1,3 => UNS * INC # B7: 3,4 => UNS * INC # A8: 3,4 => UNS * INC # G8: 3,4 => UNS * DIS # I8: 3,4 => CTR => I8: 1,2,5 * INC # I8: 1,2,5 => UNS * INC # D9: 3,5 => UNS * INC # D9: 7,8 => UNS * INC # I8: 3,5 => UNS * INC # I8: 1,2,4 => UNS * INC # D5: 3,5 => UNS * INC # D5: 4,7,8,9 => UNS * CNT 19 HDP CHAINS / 19 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D1: 5,8 => UNS * INC # F3: 5,8 => UNS * INC # E5: 5,8 => UNS * INC # E9: 5,8 => UNS * INC # A2: 2,7 => UNS * INC # A2: 9 => UNS * DIS # H1: 2,5 => CTR => H1: 1,3 * INC H1: 1,3 # B7: 3,4 => UNS * DIS H1: 1,3 # A8: 3,4 => CTR => A8: 1,2 * INC H1: 1,3 + A8: 1,2 # B7: 3,4 => UNS * INC H1: 1,3 + A8: 1,2 # B7: 6,7,9 => UNS * DIS H1: 1,3 + A8: 1,2 # G8: 3,4 => CTR => G8: 1,2 * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 # I8: 3,4 => CTR => I8: 5 * INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 # D1: 5,8 => UNS * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 # F3: 5,8 => CTR => F3: 9 * INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 # D1: 5,8 => UNS * INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 # D1: 6 => UNS * INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 # E9: 5,8 => UNS * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 # E9: 2,7 => CTR => E9: 5,8 * INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 # D1: 5,8 => UNS * INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 # D1: 6 => UNS * INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 # G1: 1,3 => UNS * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 # G1: 2 => CTR => G1: 1,3 * INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 # H5: 1,3 => UNS * INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 # H6: 1,3 => UNS * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 # H9: 1,3 => CTR => H9: 2,6,8 * INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 # H5: 1,3 => UNS * INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 # H6: 1,3 => UNS * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 # F4: 5,8 => CTR => F4: 2 * DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 + F4: 2 # A9: 1,2 => CTR => A9: 9 * PRF H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 + F4: 2 + A9: 9 => SOL * STA H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 + F4: 2 + A9: 9 * CNT 31 HDP CHAINS / 30 HYP OPENED