Analysis of xx-top500-461-base.sdk
Contents
Original Sudoku
level: medium
position: ...6...1..72.......8..4....5..3.9.......7.8..6........3..9....5.4....7........... initial
Autosolve
position: .536...17.72.......8674....51.3.9...2.4.7.8..6........3.19.7..584.2..7..7........ autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 4,9 => CTR => A2: 1 * PRF # A2: 1 => SOL * PRF # G1: 4,9 => SOL * DIS # G1: 2 => CTR => G1: 4,9 * PRF # A2: 1,9 => SOL * DIS # A2: 4 => CTR => A2: 1,9 * PRF # E1: 2,8 => SOL * DIS # E1: 9 => CTR => E1: 2,8 * PRF # F6: 2,8 => SOL * DIS # E2: 1,5 => CTR => E2: 3,9 * DIS # F2: 1,5 => CTR => F2: 3 * PRF # F3: 1,5 => SOL * DIS # F3: 2,3 => CTR => F3: 1,5 * DIS # F5: 1,5 => CTR => F5: 6 * DIS # F6: 1,5 => CTR => F6: 2,4,8 * PRF # F6: 1,2,5 => SOL * DIS # G7: 2,6 => CTR => G7: 4 * PRF # G7: 4 => SOL * DIS # H7: 2,6 => CTR => H7: 4,8 * DIS # G9: 2,6 => CTR => G9: 1,3,9 * DIS # E9: 6,8 => CTR => E9: 1,3,5 * PRF # H7: 6,8 => SOL * DIS # H7: 2,4 => CTR => H7: 6,8 * PRF # F9: 4,8 => SOL * DIS # F9: 1,3,5,6 => CTR => F9: 4,8 * CNT 25 HDP CHAINS / 45 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 4,9 => CTR => A2: 1 * PRF A2: 1 => SOL * STA A2: 1 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...6...1..72.......8..4....5..3.9.......7.8..6........3..9....5.4....7........... | initial |
| .536...17.72.......8674....51.3.9...2.4.7.8..6........3.19.7..584.2..7..7........ | autosolve |
| 453628917172593648986741523517389264234176859698452371321967485849215736765834192 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A1: 4,9 A3: 1,9 F1: 2,8 D2: 1,5 C4: 7,8 B5: 3,9 B6: 3,9 C6: 7,8 D5: 1,5 D6: 4,8 B7: 2,6 C8: 5,9 B9: 2,6 C9: 5,9 E7: 6,8 D9: 4,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 1.. / A2 = 1 => 0 pairs (*) / A3 = 1 => 0 pairs (X) A3,F3: 1.. / A3 = 1 => 0 pairs (X) / F3 = 1 => 0 pairs (_) D2,D5: 1.. / D2 = 1 => 0 pairs (X) / D5 = 1 => 16 pairs (_) G6,G9: 1.. / G6 = 1 => 16 pairs (_) / G9 = 1 => 16 pairs (_) B7,B9: 2.. / B7 = 2 => 15 pairs (_) / B9 = 2 => 0 pairs (X) B5,B6: 3.. / B5 = 3 => 14 pairs (_) / B6 = 3 => 14 pairs (_) A1,A2: 4.. / A1 = 4 => 0 pairs (*) / A2 = 4 => 0 pairs (X) D6,F6: 4.. / D6 = 4 => 0 pairs (*) / F6 = 4 => 0 pairs (X) D9,F9: 4.. / D9 = 4 => 14 pairs (_) / F9 = 4 => 0 pairs (*) G7,H7: 4.. / G7 = 4 => 0 pairs (*) / H7 = 4 => 0 pairs (X) A1,G1: 4.. / A1 = 4 => 0 pairs (*) / G1 = 4 => 0 pairs (X) D6,D9: 4.. / D6 = 4 => 0 pairs (*) / D9 = 4 => 0 pairs (X) F6,F9: 4.. / F6 = 4 => 14 pairs (_) / F9 = 4 => 0 pairs (*) I2,I4: 4.. / I2 = 4 => 0 pairs (X) / I4 = 4 => 17 pairs (_) C8,C9: 5.. / C8 = 5 => 14 pairs (_) / C9 = 5 => 15 pairs (_) D2,D5: 5.. / D2 = 5 => 16 pairs (_) / D5 = 5 => 0 pairs (X) E4,F5: 6.. / E4 = 6 => 0 pairs (X) / F5 = 6 => 17 pairs (_) B7,B9: 6.. / B7 = 6 => 0 pairs (X) / B9 = 6 => 15 pairs (_) C4,C6: 7.. / C4 = 7 => 0 pairs (*) / C6 = 7 => 0 pairs (X) H4,H6: 7.. / H4 = 7 => 15 pairs (_) / H6 = 7 => 0 pairs (*) C4,H4: 7.. / C4 = 7 => 0 pairs (*) / H4 = 7 => 0 pairs (X) C6,H6: 7.. / C6 = 7 => 15 pairs (_) / H6 = 7 => 0 pairs (*) E1,F1: 8.. / E1 = 8 => 0 pairs (X) / F1 = 8 => 16 pairs (_) H2,I2: 8.. / H2 = 8 => 0 pairs (X) / I2 = 8 => 17 pairs (_) C4,C6: 8.. / C4 = 8 => 15 pairs (_) / C6 = 8 => 0 pairs (*) C4,E4: 8.. / C4 = 8 => 15 pairs (_) / E4 = 8 => 0 pairs (*) E7,H7: 8.. / E7 = 8 => 0 pairs (X) / H7 = 8 => 0 pairs (_) D6,D9: 8.. / D6 = 8 => 14 pairs (_) / D9 = 8 => 0 pairs (*) I2,I9: 8.. / I2 = 8 => 17 pairs (_) / I9 = 8 => 0 pairs (X) E1,E2: 9.. / E1 = 9 => 0 pairs (X) / E2 = 9 => 0 pairs (_) B5,B6: 9.. / B5 = 9 => 14 pairs (_) / B6 = 9 => 14 pairs (_) C8,C9: 9.. / C8 = 9 => 15 pairs (_) / C9 = 9 => 14 pairs (_) * DURATION: 0:01:04.731472 START: 18:28:25.755076 END: 18:29:30.486548 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B5,B6,B7,B9,C4,C6,C8,C9,D2,D5,D6,D9,E7,F1) * .536...17.72.......8674....51.3.9...2.4.7.8..6........3.19.7..584.2..7..7........ * PAIR A1: 4,9 BLK 1 A2: 4,9,1 # reduction candidate for 4,9 A2: 4,9 => CTR * 953628417472.9....18674....51.3.9..42.4.7.8..6........3.1987.4584.2..7..7..4..... A2: 1 => SOLVED * 453628917172593648986741523517389264234176859698452371321967485849215736765834192 * PAIR A1: 4,9 ROW 1 G1: 4,9,2 # reduction candidate for 4,9 G1: 4,9 => SOLVED * 453628917172593648986741523517389264234176859698452371321967485849215736765834192 G1: 2 => CTR * 453698217972......186742...51.3.9...2.4.7.8..6........3.19.7..584.2..7..7........ * PAIR A3: 1,9 BLK 1 A2: 1,9,4 # reduction candidate for 1,9 A2: 1,9 => SOLVED * 453628917172593648986741523517389264234176859698452371321967485849215736765834192 A2: 4 => CTR * 953628417472.9....18674....51.3.9..42.4.7.8..6........3.1987.4584.2..7..7..4..... * PAIR F1: 2,8 BLK 2 E1: 2,8,9 # reduction candidate for 2,8 E1: 2,8 => SOLVED * 453628917172593648986741523517389264234176859698452371321967485849215736765834192 E1: 9 => CTR * 453698217972......186742...51.3.9...2.4.7.8..6........3.19.7..584.2..7..7........ * PAIR F1: 2,8 COL F F6: 2,8,1,4,5 # reduction candidate for 2,8 F6: 2,8 => SOLVED * 453628917172593648986741523517389264234176859698452371321967485849215736765834192 F6: 1,4,5 # 17 pairs * PAIR D2: 1,5 BLK 2 E2: 1,5,3,9 # reduction candidate for 1,5 E2: 1,5 => CTR * 453698217972..3...186742...51.3.9...2.4.7.8..6........3.19.7..584.2..7..7........ E2: 3,9 # 17 pairs F2: 1,5,3 # reduction candidate for 1,5 F2: 1,5 => CTR * 953628417472.9.3..186743...51.3.9..42.4.7.8..6........3.1987.4584.2..7..7..4..... F2: 3 # 16 pairs F3: 1,5,2,3 # reduction candidate for 1,5 F3: 1,5 => SOLVED * 453628917172593648986741523517389264234176859698452371321967485849215736765834192 F3: 2,3 => CTR * 953628417472.9.3..186743...51.3.9..42.4.7.8..6........3.1987.4584.2..7..7..4..... * PAIR B5: 3,9 ROW 5 H5: 3,9,5,6 # reduction candidate for 3,9 H5: 3,9 # 18 pairs I5: 3,9,1,6 # reduction candidate for 3,9 I5: 3,9 # 18 pairs * PAIR B6: 3,9 ROW 6 G6: 3,9,1,2,5 # reduction candidate for 3,9 G6: 3,9 # 18 pairs H6: 3,9,2,5,7 # reduction candidate for 3,9 H6: 3,9 # 17 pairs I6: 3,9,1,2 # reduction candidate for 3,9 I6: 3,9 # 17 pairs * PAIR D5: 1,5 BLK 5 F5: 1,5,6 # reduction candidate for 1,5 F5: 1,5 => CTR * 453698217972....8.186742...5183694722.4.7.8..6.7824...3.198764584.2.67..76.4...28 F5: 6 # 17 pairs E6: 1,5,2,8 # reduction candidate for 1,5 E6: 1,5 # 18 pairs F6: 1,5,2,4,8 # reduction candidate for 1,5 F6: 1,5 => CTR * .53698217.72....48186742...51.3.96.42.4.768..6..4.....32196748584.2..76.76.8.4... F6: 2,4,8 # 16 pairs * PAIR D6: 4,8 BLK 5 F6: 4,8,1,2,5 # reduction candidate for 4,8 F6: 1,2,5 => SOLVED * 453628917172593648986741523517389264234176859698452371321967485849215736765834192 F6: 4,8 # 17 pairs * PAIR B7: 2,6 ROW 7 G7: 2,6,4 # reduction candidate for 2,6 G7: 2,6 => CTR * 453698217972.....4186742...5183.947.2.4.7.8..6.78.4...32198764584.2..7..76.4....8 G7: 4 => SOLVED * 453628917172593648986741523517389264234176859698452371321967485849215736765834192 H7: 2,6,4,8 # reduction candidate for 2,6 H7: 2,6 => CTR * 453698217.72...648.86742...5183.9.742.4.7.8..6.78.4...3.19874.584.2..7..7..4...8. H7: 4,8 # 17 pairs * PAIR B9: 2,6 ROW 9 G9: 2,6,1,3,9 # reduction candidate for 2,6 G9: 2,6 => CTR * .536...17.72.......8674....51.3.9...2.4.7.8..6.....1..3.19.7..584.2..7..7........ G9: 1,3,9 # 16 pairs H9: 2,6,3,8,9 # reduction candidate for 2,6 H9: 2,6 # 17 pairs I9: 2,6,1,3,8,9 # reduction candidate for 2,6 I9: 2,6 # 18 pairs * PAIR E7: 6,8 BLK 8 E9: 6,8,1,3,5 # reduction candidate for 6,8 E9: 6,8 => CTR * 453698217972......186742...518329.7.2.4.768..6.78.4...3.19.74.584.2..7..7..4..... E9: 1,3,5 # 16 pairs F9: 6,8,1,3,4,5 # reduction candidate for 6,8 F9: 6,8 # 16 pairs * PAIR E7: 6,8 ROW 7 H7: 6,8,2,4 # reduction candidate for 6,8 H7: 6,8 => SOLVED * 453628917172593648986741523517389264234176859698452371321967485849215736765834192 H7: 2,4 => CTR * 453698217972......186742...5183.9.7.2.4.7.8..6.78.4...3.1987..584.2..7..7..4..... * PAIR E7: 6,8 COL E E4: 6,8,2 # reduction candidate for 6,8 E4: 6,8 # 17 pairs E4: 2 # 17 pairs * PAIR D9: 4,8 BLK 8 F9: 4,8,1,3,5,6 # reduction candidate for 4,8 F9: 4,8 => SOLVED * 453628917172593648986741523517389264234176859698452371321967485849215736765834192 F9: 1,3,5,6 => CTR * 453698217972......186742...5183.9.7.2.4.7.8..6.78.4...3.19.7..584.2..7..7..4..... * INCONCLUSIVE * SAVE PR GRAPH xx-top500-461-base-pr-000.dot * REASONING * DIS # A2: 4,9 => CTR => A2: 1 * PRF # A2: 1 => SOL * PRF # G1: 4,9 => SOL * DIS # G1: 2 => CTR => G1: 4,9 * PRF # A2: 1,9 => SOL * DIS # A2: 4 => CTR => A2: 1,9 * PRF # E1: 2,8 => SOL * DIS # E1: 9 => CTR => E1: 2,8 * PRF # F6: 2,8 => SOL * DIS # E2: 1,5 => CTR => E2: 3,9 * DIS # F2: 1,5 => CTR => F2: 3 * PRF # F3: 1,5 => SOL * DIS # F3: 2,3 => CTR => F3: 1,5 * DIS # F5: 1,5 => CTR => F5: 6 * DIS # F6: 1,5 => CTR => F6: 2,4,8 * PRF # F6: 1,2,5 => SOL * DIS # G7: 2,6 => CTR => G7: 4 * PRF # G7: 4 => SOL * DIS # H7: 2,6 => CTR => H7: 4,8 * DIS # G9: 2,6 => CTR => G9: 1,3,9 * DIS # E9: 6,8 => CTR => E9: 1,3,5 * PRF # H7: 6,8 => SOL * DIS # H7: 2,4 => CTR => H7: 6,8 * PRF # F9: 4,8 => SOL * DIS # F9: 1,3,5,6 => CTR => F9: 4,8 * CNT 25 HDP CHAINS / 45 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B5,B6,B7,B9,C4,C6,C8,C9,D2,D5,D6,D9,E7,F1) * .536...17.72.......8674....51.3.9...2.4.7.8..6........3.19.7..584.2..7..7........ * PAIR A1: 4,9 BLK 1 A2: 4,9,1 # reduction candidate for 4,9 A2: 4,9 => CTR * 953628417472.9....18674....51.3.9..42.4.7.8..6........3.1987.4584.2..7..7..4..... A2: 1 => SOLVED * 453628917172593648986741523517389264234176859698452371321967485849215736765834192 * DURATION: 0:00:03.888392 START: 18:30:23.339287 END: 18:30:27.227679 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-461-base-pr-001.dot * REASONING * DIS # A2: 4,9 => CTR => A2: 1 * PRF A2: 1 => SOL * STA A2: 1 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 461 solution: 453628917172593648986741523517389264234176859698452371321967485849215736765834192 info: 95544 FNBTYK S8.f 10358 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 453628917172593648986741523517389264234176859698452371321967485849215736765834192 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 # A2: 4,9 => CTR => A2: 1 * PRF # A2: 1 => SOL * PRF # G1: 4,9 => SOL * DIS # G1: 2 => CTR => G1: 4,9 * PRF # A2: 1,9 => SOL * DIS # A2: 4 => CTR => A2: 1,9 * PRF # E1: 2,8 => SOL * DIS # E1: 9 => CTR => E1: 2,8 * PRF # F6: 2,8 => SOL * INC # F6: 1,4,5 => UNS * DIS # E2: 1,5 => CTR => E2: 3,9 * INC # E2: 3,9 => UNS * DIS # F2: 1,5 => CTR => F2: 3 * INC # F2: 3 => UNS * PRF # F3: 1,5 => SOL * DIS # F3: 2,3 => CTR => F3: 1,5 * INC # H5: 3,9 => UNS * INC # I5: 3,9 => UNS * INC # G6: 3,9 => UNS * INC # H6: 3,9 => UNS * INC # I6: 3,9 => UNS * DIS # F5: 1,5 => CTR => F5: 6 * INC # F5: 6 => UNS * INC # E6: 1,5 => UNS * DIS # F6: 1,5 => CTR => F6: 2,4,8 * INC # F6: 2,4,8 => UNS * INC # F6: 4,8 => UNS * PRF # F6: 1,2,5 => SOL * DIS # G7: 2,6 => CTR => G7: 4 * PRF # G7: 4 => SOL * DIS # H7: 2,6 => CTR => H7: 4,8 * INC # H7: 4,8 => UNS * DIS # G9: 2,6 => CTR => G9: 1,3,9 * INC # G9: 1,3,9 => UNS * INC # H9: 2,6 => UNS * INC # I9: 2,6 => UNS * DIS # E9: 6,8 => CTR => E9: 1,3,5 * INC # E9: 1,3,5 => UNS * INC # F9: 6,8 => UNS * PRF # H7: 6,8 => SOL * DIS # H7: 2,4 => CTR => H7: 6,8 * INC # E4: 6,8 => UNS * INC # E4: 2 => UNS * PRF # F9: 4,8 => SOL * DIS # F9: 1,3,5,6 => CTR => F9: 4,8 * CNT 45 HDP CHAINS / 45 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 4,9 => CTR => A2: 1 * PRF A2: 1 => SOL * STA A2: 1 * CNT 2 HDP CHAINS / 1 HYP OPENED