Analysis of xx-top500-324-base.sdk
Contents
Original Sudoku
level: medium
position: .......127...6...........5..8.2.....6.....4.....1.9....19..........3.8..5.2...... initial
Autosolve
position: .......127...6...........5..8.2.6...6.....4.....1.9...819......4...3.8..532...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 3,9 => CTR => A3: 1,2 * DIS # D1: 3,9 => CTR => D1: 4,5,7,8 * DIS # G1: 3,9 => CTR => G1: 6,7 * PRF # A4: 3,9 => SOL * DIS # A4: 1 => CTR => A4: 3,9 * DIS # G1: 3,9 => CTR => G1: 6,7 * DIS # G4: 3,9 => CTR => G4: 1,5,7 * DIS # H6: 2,3 => CTR => H6: 6,7,8 * DIS # A3: 2,3 => CTR => A3: 1,9 * PRF # A3: 1,9 => SOL * DIS # I8: 5,9 => CTR => I8: 1 * PRF # I8: 1 => SOL * DIS # H5: 7,8 => CTR => H5: 2,9 * CNT 13 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 3,9 => CTR => A3: 1,2 * DIS A3: 1,2 # D1: 3,9 => CTR => D1: 4,5,7,8 * DIS A3: 1,2 + D1: 4,5,7,8 # G1: 3,9 => CTR => G1: 6,7 * PRF A3: 1,2 + D1: 4,5,7,8 + G1: 6,7 # A4: 3,9 => SOL * STA A3: 1,2 + D1: 4,5,7,8 + G1: 6,7 + A4: 3,9 * CNT 4 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......127...6...........5..8.2.....6.....4.....1.9....19..........3.8..5.2...... | initial |
| .......127...6...........5..8.2.6...6.....4.....1.9...819......4...3.8..532...... | autosolve |
| 346895712725361984198427356984256173651783429273149568819674235467532891532918647 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) A1: 3,9 G2: 3,9 A6: 2,3 B8: 6,7 C8: 6,7 D8: 5,9 H8: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,F2: 1.. / C2 = 1 => 0 pairs (X) / F2 = 1 => 0 pairs (_) C5,I5: 1.. / C5 = 1 => 0 pairs (*) / I5 = 1 => 0 pairs (X) F8,I8: 1.. / F8 = 1 => 0 pairs (X) / I8 = 1 => 0 pairs (_) A3,A4: 1.. / A3 = 1 => 0 pairs (*) / A4 = 1 => 0 pairs (X) E3,E9: 1.. / E3 = 1 => 0 pairs (X) / E9 = 1 => 0 pairs (_) G4,G9: 1.. / G4 = 1 => 0 pairs (*) / G9 = 1 => 0 pairs (X) B2,F2: 2.. / B2 = 2 => 0 pairs (*) / F2 = 2 => 0 pairs (X) B5,H5: 2.. / B5 = 2 => 0 pairs (X) / H5 = 2 => 0 pairs (_) F8,H8: 2.. / F8 = 2 => 0 pairs (*) / H8 = 2 => 0 pairs (X) A3,A6: 2.. / A3 = 2 => 0 pairs (X) / A6 = 2 => 0 pairs (_) E3,E7: 2.. / E3 = 2 => 0 pairs (*) / E7 = 2 => 0 pairs (X) G6,G7: 2.. / G6 = 2 => 0 pairs (X) / G7 = 2 => 0 pairs (_) D5,F5: 3.. / D5 = 3 => 7 pairs (_) / F5 = 3 => 7 pairs (_) E4,E6: 4.. / E4 = 4 => 7 pairs (_) / E6 = 4 => 8 pairs (_) C4,E4: 4.. / C4 = 4 => 8 pairs (_) / E4 = 4 => 7 pairs (_) B8,C8: 6.. / B8 = 6 => 6 pairs (_) / C8 = 6 => 5 pairs (_) D7,D9: 6.. / D7 = 6 => 7 pairs (_) / D9 = 6 => 7 pairs (_) B8,C8: 7.. / B8 = 7 => 5 pairs (_) / C8 = 7 => 6 pairs (_) A4,B5: 9.. / A4 = 9 => 0 pairs (*) / B5 = 9 => 0 pairs (X) * DURATION: 0:00:26.860477 START: 13:58:02.029217 END: 13:58:28.889694 2017-05-04 * CP COUNT: (19) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B8,C8,D8,G2,H8) * .......127...6...........5..8.2.6...6.....4.....1.9...819......4...3.8..532...... * PAIR A1: 3,9 BLK 1 A3: 3,9,1,2 # reduction candidate for 3,9 A3: 3,9 => CTR * .......127...6...........5.18.2.6...69....4212..1.9...819...2..4...3.8..532...... A3: 1,2 # 8 pairs * PAIR A1: 3,9 ROW 1 D1: 3,9,4,5,7,8 # reduction candidate for 3,9 D1: 3,9 => CTR * 9..3...127...62...2......5.18.2.6...62...34.13..1.92..819.2....4...3182.532.9.1.. D1: 4,5,7,8 # 7 pairs G1: 3,9,6,7 # reduction candidate for 3,9 G1: 3,9 => CTR * 9.....31275..629..24.....5.18.2.6...62....4.137.1.92..819.2....46..3.82.532...... G1: 6,7 # 8 pairs * PAIR A1: 3,9 COL A A4: 3,9,1 # reduction candidate for 3,9 A4: 3,9 => SOLVED * 346895712725361984198427356984256173651783429273149568819674235467532891532918647 A4: 1 => CTR * .......127...6...........5.18.2.6...69....421...1.9...819...2..4...3.8..532...... * PAIR G2: 3,9 BLK 3 G1: 3,9,6,7 # reduction candidate for 3,9 G1: 3,9 => CTR * 9.....31275..629..24.....5.18.2.6...62....4.137.1.92..819.2....46..3.82.532...... G1: 6,7 # 8 pairs H2: 3,9,4,8 # reduction candidate for 3,9 H2: 3,9 # 13 pairs I2: 3,9,4,8 # reduction candidate for 3,9 I2: 3,9 # 13 pairs G3: 3,9,6,7 # reduction candidate for 3,9 G3: 3,9 # 12 pairs I3: 3,9,4,6,7,8 # reduction candidate for 3,9 I3: 3,9 # 13 pairs * PAIR G2: 3,9 ROW 2 D2: 3,9,4,5,8 # reduction candidate for 3,9 D2: 3,9 # 12 pairs D2: 4,5,8 # 7 pairs * PAIR G2: 3,9 COL G G4: 3,9,1,5,7 # reduction candidate for 3,9 G4: 3,9 => CTR * .......127...6........1..5.18.2.6...69....421...1.9...819.2....4...3.8..532...1.. G4: 1,5,7 # 7 pairs * PAIR A6: 2,3 ROW 6 G6: 2,3,5,6,7 # reduction candidate for 2,3 G6: 2,3 # 8 pairs H6: 2,3,6,7,8 # reduction candidate for 2,3 H6: 2,3 => CTR * .......1272..6..4.....2..57.8.2.61..6.....4.....1.9...819...2..4...32891532...7.4 H6: 6,7,8 # 7 pairs * PAIR A6: 2,3 COL A A3: 2,3,1,9 # reduction candidate for 2,3 A3: 2,3 => CTR * .......127...6...........5.18.2.6...69....421...1.9...819...2..4...3.8..532...... A3: 1,9 => SOLVED * 346895712725361984198427356984256173651783429273149568819674235467532891532918647 * PAIR D8: 5,9 ROW 8 I8: 5,9,1 # reduction candidate for 5,9 I8: 5,9 => CTR * .......127.1.6........1..5.18.2.6...6.....4.....1.9...819......4...3182.532...... I8: 1 => SOLVED * 346895712725361984198427356984256173651783429273149568819674235467532891532918647 * PAIR D8: 5,9 COL D D1: 5,9,3,4,7,8 # reduction candidate for 5,9 D1: 5,9 # 10 pairs D2: 5,9,3,4,8 # reduction candidate for 5,9 D2: 5,9 # 8 pairs * PAIR H8: 2,9 COL H H5: 2,9,7,8 # reduction candidate for 2,9 H5: 7,8 => CTR * 9......127...62...2......5.18.2.6...62....4.93..1.9...819.2....4...3.82.532...19. H5: 2,9 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-324-base-pr-000.dot * REASONING * DIS # A3: 3,9 => CTR => A3: 1,2 * DIS # D1: 3,9 => CTR => D1: 4,5,7,8 * DIS # G1: 3,9 => CTR => G1: 6,7 * PRF # A4: 3,9 => SOL * DIS # A4: 1 => CTR => A4: 3,9 * DIS # G1: 3,9 => CTR => G1: 6,7 * DIS # G4: 3,9 => CTR => G4: 1,5,7 * DIS # H6: 2,3 => CTR => H6: 6,7,8 * DIS # A3: 2,3 => CTR => A3: 1,9 * PRF # A3: 1,9 => SOL * DIS # I8: 5,9 => CTR => I8: 1 * PRF # I8: 1 => SOL * DIS # H5: 7,8 => CTR => H5: 2,9 * CNT 13 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B8,C8,D8,G2,H8) * .......127...6...........5..8.2.6...6.....4.....1.9...819......4...3.8..532...... * PAIR A1: 3,9 BLK 1 A3: 3,9,1,2 # reduction candidate for 3,9 A3: 3,9 => CTR * .......127...6...........5.18.2.6...69....4212..1.9...819...2..4...3.8..532...... * PAIR A1: 3,9 ROW 1 D1: 3,9,4,5,7,8 # reduction candidate for 3,9 D1: 3,9 => CTR * 9..3...127...62...2......5.18.2.6...62...34.13..1.92..819.2....4...3182.532.9.1.. G1: 3,9,6,7 # reduction candidate for 3,9 G1: 3,9 => CTR * 9.....31275..629..24.....5.18.2.6...62....4.137.1.92..819.2....46..3.82.532...... * RESTART * PAIR A1: 3,9 COL A A4: 3,9,1 # reduction candidate for 3,9 A4: 3,9 => SOLVED * 346895712725361984198427356984256173651783429273149568819674235467532891532918647 * DURATION: 0:00:05.399289 START: 13:58:48.546233 END: 13:58:53.945522 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-324-base-pr-001.dot * REASONING * DIS # A3: 3,9 => CTR => A3: 1,2 * DIS A3: 1,2 # D1: 3,9 => CTR => D1: 4,5,7,8 * DIS A3: 1,2 + D1: 4,5,7,8 # G1: 3,9 => CTR => G1: 6,7 * PRF A3: 1,2 + D1: 4,5,7,8 + G1: 6,7 # A4: 3,9 => SOL * STA A3: 1,2 + D1: 4,5,7,8 + G1: 6,7 + A4: 3,9 * CNT 4 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 324 solution: 346895712725361984198427356984256173651783429273149568819674235467532891532918647 info: 2963 FNBHWY S8.f 11 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 346895712725361984198427356984256173651783429273149568819674235467532891532918647 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:
* DIS # A3: 3,9 => CTR => A3: 1,2 * INC # A3: 1,2 => UNS * DIS # D1: 3,9 => CTR => D1: 4,5,7,8 * INC # D1: 4,5,7,8 => UNS * DIS # G1: 3,9 => CTR => G1: 6,7 * INC # G1: 6,7 => UNS * PRF # A4: 3,9 => SOL * DIS # A4: 1 => CTR => A4: 3,9 * DIS # G1: 3,9 => CTR => G1: 6,7 * INC # G1: 6,7 => UNS * INC # H2: 3,9 => UNS * INC # I2: 3,9 => UNS * INC # G3: 3,9 => UNS * INC # I3: 3,9 => UNS * INC # D2: 3,9 => UNS * INC # D2: 4,5,8 => UNS * DIS # G4: 3,9 => CTR => G4: 1,5,7 * INC # G4: 1,5,7 => UNS * INC # G6: 2,3 => UNS * DIS # H6: 2,3 => CTR => H6: 6,7,8 * INC # H6: 6,7,8 => UNS * DIS # A3: 2,3 => CTR => A3: 1,9 * PRF # A3: 1,9 => SOL * DIS # I8: 5,9 => CTR => I8: 1 * PRF # I8: 1 => SOL * INC # D1: 5,9 => UNS * INC # D2: 5,9 => UNS * INC # H5: 2,9 => UNS * DIS # H5: 7,8 => CTR => H5: 2,9 * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A3: 3,9 => CTR => A3: 1,2 * DIS A3: 1,2 # D1: 3,9 => CTR => D1: 4,5,7,8 * DIS A3: 1,2 + D1: 4,5,7,8 # G1: 3,9 => CTR => G1: 6,7 * PRF A3: 1,2 + D1: 4,5,7,8 + G1: 6,7 # A4: 3,9 => SOL * STA A3: 1,2 + D1: 4,5,7,8 + G1: 6,7 + A4: 3,9 * CNT 4 HDP CHAINS / 4 HYP OPENED