Analysis of zz-menneske-no-06903973-base.sdk
Contents
Original Sudoku
level: medium
position: ...1.4.6.8........3....6..5.45..2.....2...57.....3...9....7.......9....8..6....2. initial
Autosolve
position: ...1.4.6.86.......3....6..5.45..2....32...57.....3.2.9....7.......9....8..6....2. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D6: 6,7 => CTR => D6: 4,5 * PRF # A4: 6,7 => SOL * DIS # H7: 1,4 => CTR => H7: 3,5,9 * DIS # H8: 1,4 => CTR => H8: 3,5 * CNT 4 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D6: 6,7 => CTR => D6: 4,5 * DIS D6: 4,5 # I5: 1,4 => CTR => I5: 6 * DIS D6: 4,5 + I5: 6 # B1: 7,9 => CTR => B1: 2,5 * DIS D6: 4,5 + I5: 6 + B1: 2,5 # G1: 7,9 => CTR => G1: 3,8 * PRF D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # I9: 1 => SOL * STA D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 + I9: 1 * CNT 5 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...1.4.6.8........3....6..5.45..2.....2...57.....3...9....7.......9....8..6....2. | initial |
| ...1.4.6.86.......3....6..5.45..2....32...57.....3.2.9....7.......9....8..6....2. | autosolve |
| 259184367867359412314726895745692183932418576681537249198275634423961758576843921 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) C1: 7,9 D4: 6,7 H6: 1,4 D7: 2,6 E8: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I1,I2: 2.. / I1 = 2 => 0 pairs (X) / I2 = 2 => 7 pairs (_) D7,E8: 2.. / D7 = 2 => 5 pairs (_) / E8 = 2 => 0 pairs (X) D2,F2: 3.. / D2 = 3 => 5 pairs (_) / F2 = 3 => 0 pairs (X) G1,I1: 3.. / G1 = 3 => 8 pairs (_) / I1 = 3 => 11 pairs (_) C7,C8: 3.. / C7 = 3 => 9 pairs (_) / C8 = 3 => 6 pairs (_) D2,D9: 3.. / D2 = 3 => 5 pairs (_) / D9 = 3 => 0 pairs (X) C2,C3: 4.. / C2 = 4 => 6 pairs (_) / C3 = 4 => 5 pairs (_) I5,H6: 4.. / I5 = 4 => 0 pairs (X) / H6 = 4 => 6 pairs (_) A7,A8: 4.. / A7 = 4 => 5 pairs (_) / A8 = 4 => 5 pairs (_) D9,E9: 4.. / D9 = 4 => 9 pairs (_) / E9 = 4 => 7 pairs (_) D6,H6: 4.. / D6 = 4 => 0 pairs (X) / H6 = 4 => 6 pairs (_) E5,E9: 4.. / E5 = 4 => 9 pairs (_) / E9 = 4 => 7 pairs (_) A1,B1: 5.. / A1 = 5 => 8 pairs (_) / B1 = 5 => 6 pairs (_) D6,F6: 5.. / D6 = 5 => 8 pairs (_) / F6 = 5 => 12 pairs (_) H7,H8: 5.. / H7 = 5 => 5 pairs (_) / H8 = 5 => 6 pairs (_) E2,E9: 5.. / E2 = 5 => 5 pairs (_) / E9 = 5 => 0 pairs (X) D7,E8: 6.. / D7 = 6 => 0 pairs (X) / E8 = 6 => 5 pairs (_) A6,D6: 6.. / A6 = 6 => 6 pairs (_) / D6 = 6 => 0 pairs (X) E8,G8: 6.. / E8 = 6 => 5 pairs (_) / G8 = 6 => 0 pairs (X) A4,D4: 7.. / A4 = 7 => 0 pairs (*) / D4 = 7 => 0 pairs (X) F2,F6: 7.. / F2 = 7 => 11 pairs (_) / F6 = 7 => 0 pairs (*) B6,C6: 8.. / B6 = 8 => 7 pairs (_) / C6 = 8 => 6 pairs (_) G4,H4: 8.. / G4 = 8 => 8 pairs (_) / H4 = 8 => 9 pairs (_) E1,G1: 8.. / E1 = 8 => 7 pairs (_) / G1 = 8 => 14 pairs (_) C6,C7: 8.. / C6 = 8 => 6 pairs (_) / C7 = 8 => 7 pairs (_) H3,H4: 8.. / H3 = 8 => 8 pairs (_) / H4 = 8 => 9 pairs (_) A4,A5: 9.. / A4 = 9 => 11 pairs (_) / A5 = 9 => 0 pairs (*) A4,E4: 9.. / A4 = 9 => 11 pairs (_) / E4 = 9 => 0 pairs (*) B9,G9: 9.. / B9 = 9 => 5 pairs (_) / G9 = 9 => 5 pairs (_) F2,F5: 9.. / F2 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) * DURATION: 0:00:42.927739 START: 06:40:06.875162 END: 06:40:49.802901 2017-05-01 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,D4,D7,E8,H6) * ...1.4.6.86.......3....6..5.45..2....32...57.....3.2.9....7.......9....8..6....2. * PAIR C1: 7,9 BLK 1 B1: 7,9,2,5 # reduction candidate for 7,9 B1: 7,9 # 18 pairs C2: 7,9,1,4 # reduction candidate for 7,9 C2: 7,9 # 19 pairs B3: 7,9,1,2 # reduction candidate for 7,9 B3: 7,9 # 15 pairs C3: 7,9,1,4 # reduction candidate for 7,9 C3: 7,9 # 15 pairs * PAIR C1: 7,9 ROW 1 G1: 7,9,3,8 # reduction candidate for 7,9 G1: 7,9 # 16 pairs G1: 3,8 # 6 pairs * PAIR D4: 6,7 BLK 5 D6: 6,7,4,5 # reduction candidate for 6,7 D6: 6,7 => CTR * 25.1.4.6.86.357..23..826..5945712.8.632489571...6352495..27.634423961758..654..2. D6: 4,5 # 7 pairs * PAIR D4: 6,7 ROW 4 A4: 6,7,1,9 # reduction candidate for 6,7 A4: 6,7 => SOLVED * 259184367867359412314726895745692183932418576681537249198275634423961758576843921 A4: 1,9 # 11 pairs * PAIR H6: 1,4 BLK 6 I5: 1,4,6 # reduction candidate for 1,4 I5: 6 # 17 pairs I5: 1,4 # 15 pairs * PAIR H6: 1,4 COL H H2: 1,4,9 # reduction candidate for 1,4 H2: 1,4 # 9 pairs H3: 1,4,8,9 # reduction candidate for 1,4 H3: 1,4 # 20 pairs H7: 1,4,3,5,9 # reduction candidate for 1,4 H7: 1,4 => CTR * 7..184.6.86.357.923..296.859457.283.1328.957.6...3.2.9...67....4..92.658..6....2. H7: 3,5,9 # 5 pairs H8: 1,4,3,5 # reduction candidate for 1,4 H8: 1,4 => CTR * .59184.6.86.357.923..296.859457628311328495766..531249.2167895....92.6.85.641..2. H8: 3,5 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06903973-base-pr-000.dot * REASONING * DIS # D6: 6,7 => CTR => D6: 4,5 * PRF # A4: 6,7 => SOL * DIS # H7: 1,4 => CTR => H7: 3,5,9 * DIS # H8: 1,4 => CTR => H8: 3,5 * CNT 4 HDP CHAINS / 18 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,D4,D7,E8,H6) * ...1.4.6.86.......3....6..5.45..2....32...57.....3.2.9....7.......9....8..6....2. * PAIR C1: 7,9 BLK 1 B1: 7,9,2,5 # reduction candidate for 7,9 B1: 7,9 # 18 pairs C2: 7,9,1,4 # reduction candidate for 7,9 C2: 7,9 # 19 pairs B3: 7,9,1,2 # reduction candidate for 7,9 B3: 7,9 # 15 pairs C3: 7,9,1,4 # reduction candidate for 7,9 C3: 7,9 # 15 pairs * PAIR C1: 7,9 ROW 1 G1: 7,9,3,8 # reduction candidate for 7,9 G1: 7,9 # 16 pairs G1: 3,8 # 6 pairs * PAIR D4: 6,7 BLK 5 D6: 6,7,4,5 # reduction candidate for 6,7 D6: 6,7 => CTR * 25.1.4.6.86.357..23..826..5945712.8.632489571...6352495..27.634423961758..654..2. * PAIR H6: 1,4 BLK 6 I5: 1,4,6 # reduction candidate for 1,4 I5: 1,4 => CTR * ..91.436786.357..23...96..5945712...132..95746..435219....7.......96.7.87.654..2. * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A4,A5,C1,D3,D4,D5,D7,D9,E4,E5,E8,E9,F2,F6,H2,I1,I4) * ...1.4.6.86.35...23....6..5.45..2....32...5766..53.249....7...44..9....8..6....2. * PAIR C1: 7,9 BLK 1 B1: 7,9,2,5 # reduction candidate for 7,9 B1: 7,9 => CTR * 5..12486386.35...232.786..5745692.81932...5766..5372492...7...44..9....8..6....2. C2: 7,9,1,4 # reduction candidate for 7,9 C2: 7,9 # 28 pairs B3: 7,9,1,2 # reduction candidate for 7,9 B3: 7,9 # 25 pairs C3: 7,9,1,4 # reduction candidate for 7,9 C3: 7,9 # 27 pairs * PAIR C1: 7,9 ROW 1 G1: 7,9,3,8 # reduction candidate for 7,9 G1: 7,9 => CTR * 25918476386.359.1237...6..5745692..1932...5766..537249...27.6.442796...8..6....27 * PAIR RESTART * PAIR C1: 7,9 BLK 1 C2: 7,9,1,4 # reduction candidate for 7,9 C2: 7,9 # 30 pairs B3: 7,9,1,2 # reduction candidate for 7,9 B3: 7,9 # 26 pairs C3: 7,9,1,4 # reduction candidate for 7,9 C3: 7,9 # 28 pairs * PAIR F2: 7,9 ROW 2 C2: 7,9,1,4 # reduction candidate for 7,9 C2: 7,9 # 30 pairs G2: 7,9,1,4 # reduction candidate for 7,9 G2: 7,9 # 22 pairs * PAIR D3: 2,7 ROW 3 B3: 2,7,1,9 # reduction candidate for 2,7 B3: 2,7 # 26 pairs B3: 1,9 # 26 pairs * PAIR I1: 3,7 COL I I9: 3,7,1 # reduction candidate for 3,7 I9: 1 => SOLVED * 259184367867359412314726895745692183932418576681537249198275634423961758576843921 * DURATION: 0:00:25.664267 START: 06:41:05.464669 END: 06:41:31.128936 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06903973-base-pr-001.dot * REASONING * DIS # D6: 6,7 => CTR => D6: 4,5 * DIS D6: 4,5 # I5: 1,4 => CTR => I5: 6 * DIS D6: 4,5 + I5: 6 # B1: 7,9 => CTR => B1: 2,5 * DIS D6: 4,5 + I5: 6 + B1: 2,5 # G1: 7,9 => CTR => G1: 3,8 * PRF D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # I9: 1 => SOL * STA D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 + I9: 1 * CNT 5 HDP CHAINS / 22 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6903973 umulig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: ...1.4.6.86.......3....6..5.45..2....32...57.....3.2.9....7.......9....8..6....2. C1: 7,9 B1: 2,5,7,9 # reduction candidate for 7,9 C2: 1,4,7,9 # reduction candidate for 7,9 B3: 1,2,7,9 # reduction candidate for 7,9 C3: 1,4,7,9 # reduction candidate for 7,9 G1: 3,7,8,9 # reduction candidate for 7,9 D4: 6,7 D6: 4,5,6,7 # reduction candidate for 6,7 D6: 6,7 => CTR * 25.1.4.6.86.357..23..826..5945712.8.632489571...6352495..27.634423961758..654..2. H6: 1,4 I5: 1,4,6 # reduction candidate for 1,4 I5: 1,4 => CTR * ..91.436786.357..23...96..5945712...132..95746..435219....7.......96.7.87.654..2. D7: 2,6 E8: 2,6 * ROUND 2: ...1.4.6.86.35...23....6..5.45..2....32...5766..53.249....7...44..9....8..6....2. C1: 7,9 B1: 2,5,7,9 # reduction candidate for 7,9 B1: 7,9 => CTR * 5..12486386.35...232.786..5745692.81932...5766..5372492...7...44..9....8..6....2. C2: 1,4,7,9 # reduction candidate for 7,9 B3: 1,2,7,9 # reduction candidate for 7,9 C3: 1,4,7,9 # reduction candidate for 7,9 G1: 3,7,8,9 # reduction candidate for 7,9 G1: 7,9 => CTR * 25918476386.359.1237...6..5745692..1932...5766..537249...27.6.442796...8..6....27 F2: 7,9 C2: 1,4,7,9 # reduction candidate for 7,9 G2: 1,4,7,9 # reduction candidate for 7,9 D3: 2,7 B3: 1,2,7,9 # reduction candidate for 2,7 I1: 3,7 I9: 1,3,7 # reduction candidate for 3,7 I9: 1 => SOLVED * 259184367867359412314726895745692183932418576681537249198275634423961758576843921 * SOLVED!
Solution
position: 259184367867359412314726895745692183932418576681537249198275634423961758576843921 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 # B1: 7,9 => UNS * INC # C2: 7,9 => UNS * INC # B3: 7,9 => UNS * INC # C3: 7,9 => UNS * INC # G1: 7,9 => UNS * INC # G1: 3,8 => UNS * DIS # D6: 6,7 => CTR => D6: 4,5 * INC # D6: 4,5 => UNS * PRF # A4: 6,7 => SOL * INC # A4: 1,9 => UNS * INC # I5: 1,4 => UNS * INC # I5: 6 => UNS * INC # H2: 1,4 => UNS * INC # H3: 1,4 => UNS * DIS # H7: 1,4 => CTR => H7: 3,5,9 * INC # H7: 3,5,9 => UNS * DIS # H8: 1,4 => CTR => H8: 3,5 * INC # H8: 3,5 => UNS * CNT 18 HDP CHAINS / 18 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 7,9 => UNS * INC # C2: 7,9 => UNS * INC # B3: 7,9 => UNS * INC # C3: 7,9 => UNS * INC # G1: 7,9 => UNS * INC # G1: 3,8 => UNS * DIS # D6: 6,7 => CTR => D6: 4,5 * DIS D6: 4,5 # I5: 1,4 => CTR => I5: 6 * DIS D6: 4,5 + I5: 6 # B1: 7,9 => CTR => B1: 2,5 * INC D6: 4,5 + I5: 6 + B1: 2,5 # C2: 7,9 => UNS * INC D6: 4,5 + I5: 6 + B1: 2,5 # B3: 7,9 => UNS * INC D6: 4,5 + I5: 6 + B1: 2,5 # C3: 7,9 => UNS * DIS D6: 4,5 + I5: 6 + B1: 2,5 # G1: 7,9 => CTR => G1: 3,8 * INC D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # C2: 7,9 => UNS * INC D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # B3: 7,9 => UNS * INC D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # C3: 7,9 => UNS * INC D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # C2: 7,9 => UNS * INC D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # G2: 7,9 => UNS * INC D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # B3: 2,7 => UNS * INC D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # B3: 1,9 => UNS * INC D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # I9: 3,7 => UNS * PRF D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 # I9: 1 => SOL * STA D6: 4,5 + I5: 6 + B1: 2,5 + G1: 3,8 + I9: 1 * CNT 22 HDP CHAINS / 22 HYP OPENED