Analysis of xx-top500-035-base.sdk
Contents
Original Sudoku
level: medium
position: ...5....2.1.....7...3........7...16....8..4..5..2.........1.3..86.......2........ initial
Autosolve
position: ...5...12.12...573.5312.8..327...1681968..4255..261739..5.1238.8613..2.723.7....1 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 6,9 => CTR => A1: 4,7 * DIS # F1: 6,9 => CTR => F1: 3,4,7 * DIS # H9: 4,9 => CTR => H9: 5 * DIS # B1: 7 => CTR => B1: 4,8 * DIS # C1: 4,8 => CTR => C1: 9 * PRF # C1: 9 => SOL * DIS # D2: 4,9 => CTR => D2: 6 * PRF # D2: 6 => SOL * PRF # D7: 4,9 => SOL * DIS # D7: 6 => CTR => D7: 4,9 * DIS # A7: 4,7 => CTR => A7: 9 * PRF # A7: 9 => SOL * DIS # B1: 4,7 => CTR => B1: 8 * DIS # A7: 7 => CTR => A7: 4,9 * DIS # E9: 4,9 => CTR => E9: 5,8 * DIS # F9: 4,9 => CTR => F9: 5,6,8 * DIS # H9: 4,9 => CTR => H9: 5 * DIS # C1: 8 => CTR => C1: 4,9 * PRF # D7: 4,6 => SOL * DIS # D7: 9 => CTR => D7: 4,6 * PRF # F9: 6,9 => SOL * DIS # F9: 4,5,8 => CTR => F9: 6,9 * CNT 22 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 6,9 => CTR => A1: 4,7 * DIS A1: 4,7 # F1: 6,9 => CTR => F1: 3,4,7 * PRF A1: 4,7 + F1: 3,4,7 => SOL * STA A1: 4,7 + F1: 3,4,7 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...5....2.1.....7...3........7...16....8..4..5..2.........1.3..86.......2........ | initial |
| ...5...12.12...573.5312.8..327...1681968..4255..261739..5.1238.8613..2.723.7....1 | autosolve |
| 789534612412698573653127894327945168196873425548261739975412386861359247234786951 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) E1: 3,7 G1: 6,9 H3: 4,9 I3: 4,6 B6: 4,8 C6: 4,8 D4: 4,9 E5: 3,7 F5: 3,7 B7: 4,7 C9: 4,9 I7: 4,6 G9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,F1: 3.. / E1 = 3 => 10 pairs (_) / F1 = 3 => 13 pairs (_) E5,F5: 3.. / E5 = 3 => 13 pairs (_) / F5 = 3 => 10 pairs (_) E1,E5: 3.. / E1 = 3 => 10 pairs (_) / E5 = 3 => 13 pairs (_) F1,F5: 3.. / F1 = 3 => 13 pairs (_) / F5 = 3 => 10 pairs (_) H3,I3: 4.. / H3 = 4 => 0 pairs (X) / I3 = 4 => 0 pairs (_) B6,C6: 4.. / B6 = 4 => 12 pairs (_) / C6 = 4 => 0 pairs (X) I3,I7: 4.. / I3 = 4 => 0 pairs (*) / I7 = 4 => 0 pairs (X) E4,F4: 5.. / E4 = 5 => 15 pairs (_) / F4 = 5 => 15 pairs (_) H8,H9: 5.. / H8 = 5 => 0 pairs (X) / H9 = 5 => 14 pairs (_) G1,I3: 6.. / G1 = 6 => 0 pairs (*) / I3 = 6 => 0 pairs (X) D7,F9: 6.. / D7 = 6 => 0 pairs (X) / F9 = 6 => 0 pairs (_) I7,G9: 6.. / I7 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) D7,I7: 6.. / D7 = 6 => 0 pairs (X) / I7 = 6 => 0 pairs (_) F9,G9: 6.. / F9 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) D2,D7: 6.. / D2 = 6 => 0 pairs (*) / D7 = 6 => 0 pairs (X) G1,G9: 6.. / G1 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) I3,I7: 6.. / I3 = 6 => 0 pairs (X) / I7 = 6 => 0 pairs (_) E5,F5: 7.. / E5 = 7 => 10 pairs (_) / F5 = 7 => 13 pairs (_) A7,B7: 7.. / A7 = 7 => 0 pairs (X) / B7 = 7 => 14 pairs (_) A3,F3: 7.. / A3 = 7 => 17 pairs (_) / F3 = 7 => 11 pairs (_) B1,B7: 7.. / B1 = 7 => 0 pairs (X) / B7 = 7 => 14 pairs (_) E1,E5: 7.. / E1 = 7 => 13 pairs (_) / E5 = 7 => 10 pairs (_) B1,C1: 8.. / B1 = 8 => 12 pairs (_) / C1 = 8 => 0 pairs (X) E2,F2: 8.. / E2 = 8 => 0 pairs (X) / F2 = 8 => 14 pairs (_) B6,C6: 8.. / B6 = 8 => 0 pairs (X) / C6 = 8 => 12 pairs (_) E9,F9: 8.. / E9 = 8 => 14 pairs (_) / F9 = 8 => 0 pairs (X) B1,B6: 8.. / B1 = 8 => 12 pairs (_) / B6 = 8 => 0 pairs (X) C1,C6: 8.. / C1 = 8 => 0 pairs (X) / C6 = 8 => 12 pairs (_) E2,E9: 8.. / E2 = 8 => 0 pairs (X) / E9 = 8 => 14 pairs (_) F2,F9: 8.. / F2 = 8 => 14 pairs (_) / F9 = 8 => 0 pairs (X) G1,H3: 9.. / G1 = 9 => 0 pairs (X) / H3 = 9 => 0 pairs (_) A7,C9: 9.. / A7 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) A7,D7: 9.. / A7 = 9 => 0 pairs (*) / D7 = 9 => 0 pairs (X) C1,C9: 9.. / C1 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) G1,G9: 9.. / G1 = 9 => 0 pairs (X) / G9 = 9 => 0 pairs (_) * DURATION: 0:00:59.272951 START: 03:52:07.172000 END: 03:53:06.444951 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,B7,C6,C9,D4,E1,E5,F5,G1,G9,H3,I3,I7) * ...5...12.12...573.5312.8..327...1681968..4255..261739..5.1238.8613..2.723.7....1 * PAIR E1: 3,7 BLK 2 F1: 3,7,4,6,9 # reduction candidate for 3,7 F1: 3,7 # 17 pairs F1: 4,6,9 # 11 pairs * PAIR G1: 6,9 ROW 1 A1: 6,9,4,7 # reduction candidate for 6,9 A1: 6,9 => CTR * ...5...12.12...573.5312.8..327...1681968..4255..261739..5.1238.8613..2.72397..6.1 A1: 4,7 # 14 pairs F1: 6,9,3,4,7 # reduction candidate for 6,9 F1: 6,9 => CTR * ...53..12.12...573.531278..327...1681968734255..261739..59123868613..29723.7....1 F1: 3,4,7 # 13 pairs * PAIR H3: 4,9 COL H H8: 4,9,5 # reduction candidate for 4,9 H8: 4,9 # 14 pairs H9: 4,9,5 # reduction candidate for 4,9 H9: 4,9 => CTR * ..95..612.12...573.5312.894327...1681968..4255.82617399.5.1238.8613..25723.7....1 H9: 5 # 14 pairs * PAIR B6: 4,8 COL B B1: 4,8,7 # reduction candidate for 4,8 B1: 7 => CTR * .7853..12.12...573.531278..327...1681968734255842617397459123868613..29723.7....1 B1: 4,8 # 14 pairs * PAIR C6: 4,8 COL C C1: 4,8,9 # reduction candidate for 4,8 C1: 4,8 => CTR * ...5...12.12...573.5312.8..327...1681968..4255..261739..5.1238.8613..2.72397..6.1 C1: 9 => SOLVED * 789534612412698573653127894327945168196873425548261739975412386861359247234786951 * PAIR D4: 4,9 BLK 5 E4: 4,9,5 # reduction candidate for 4,9 E4: 4,9 # 15 pairs F4: 4,9,5 # reduction candidate for 4,9 F4: 4,9 # 15 pairs * PAIR D4: 4,9 COL D D2: 4,9,6 # reduction candidate for 4,9 D2: 4,9 => CTR * ..95...12.12...573.5312.8..327...1681968..4255..261739..56123848613..2.72347..6.1 D2: 6 => SOLVED * 789534612412698573653127894327945168196873425548261739975412386861359247234786951 D7: 4,9,6 # reduction candidate for 4,9 D7: 4,9 => SOLVED * 789534612412698573653127894327945168196873425548261739975412386861359247234786951 D7: 6 => CTR * ..95...12.12...573.5312.8..327...1681968..4255..2617399756123848613..2.72347..6.1 * PAIR F5: 3,7 COL F F1: 3,7,4,6,9 # reduction candidate for 3,7 F1: 3,7 # 17 pairs F1: 4,6,9 # 11 pairs * PAIR B7: 4,7 BLK 7 A7: 4,7,9 # reduction candidate for 4,7 A7: 4,7 => CTR * ...5...12.12...573.5312.8..327...1681968..4255..261739..59123868613..29723.7....1 A7: 9 => SOLVED * 789534612412698573653127894327945168196873425548261739975412386861359247234786951 * PAIR B7: 4,7 COL B B1: 4,7,8 # reduction candidate for 4,7 B1: 4,7 => CTR * ..85...12.12...573.5312.8..327...1681968..425584261739..5.1238.8613..2.72397..6.1 B1: 8 # 12 pairs * PAIR C9: 4,9 BLK 7 A7: 4,9,7 # reduction candidate for 4,9 A7: 7 => CTR * ...5...12.12...573.5312.8..327...1681968..4255..2617397459123868613..29723.7....1 A7: 4,9 # 14 pairs * PAIR C9: 4,9 ROW 9 E9: 4,9,5,8 # reduction candidate for 4,9 E9: 4,9 => CTR * ...5..912.12.8.573.5312.846327...1681968..4255..261739..56123848613..29723.7.8651 E9: 5,8 # 14 pairs F9: 4,9,5,6,8 # reduction candidate for 4,9 F9: 4,9 => CTR * ..95...12.12..8573.5312.8..327...1681968..4255..261739..56123848613..2.7234789651 F9: 5,6,8 # 13 pairs H9: 4,9,5 # reduction candidate for 4,9 H9: 4,9 => CTR * ..95..612.12...573.5312.894327...1681968..4255.82617399.5.1238.8613..25723.7....1 H9: 5 # 14 pairs * PAIR C9: 4,9 COL C C1: 4,9,8 # reduction candidate for 4,9 C1: 8 => CTR * ..85...12.12...573.5312.8..327...1681968..425584261739..5.1238.8613..2.72397..6.1 C1: 4,9 # 12 pairs * PAIR I7: 4,6 ROW 7 D7: 4,6,9 # reduction candidate for 4,6 D7: 4,6 => SOLVED * 789534612412698573653127894327945168196873425548261739975412386861359247234786951 D7: 9 => CTR * ...5...12.126..573.5312.8..3274..1681968..4255..261739..59123868613..29723.7....1 * PAIR G9: 6,9 ROW 9 F9: 6,9,4,5,8 # reduction candidate for 6,9 F9: 6,9 => SOLVED * 789534612412698573653127894327945168196873425548261739975412386861359247234786951 F9: 4,5,8 => CTR * ..95...12.12...573.5312.8..327...1681968..4255..261739..56123848613..2.72347..6.1 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-035-base-pr-000.dot * REASONING * DIS # A1: 6,9 => CTR => A1: 4,7 * DIS # F1: 6,9 => CTR => F1: 3,4,7 * DIS # H9: 4,9 => CTR => H9: 5 * DIS # B1: 7 => CTR => B1: 4,8 * DIS # C1: 4,8 => CTR => C1: 9 * PRF # C1: 9 => SOL * DIS # D2: 4,9 => CTR => D2: 6 * PRF # D2: 6 => SOL * PRF # D7: 4,9 => SOL * DIS # D7: 6 => CTR => D7: 4,9 * DIS # A7: 4,7 => CTR => A7: 9 * PRF # A7: 9 => SOL * DIS # B1: 4,7 => CTR => B1: 8 * DIS # A7: 7 => CTR => A7: 4,9 * DIS # E9: 4,9 => CTR => E9: 5,8 * DIS # F9: 4,9 => CTR => F9: 5,6,8 * DIS # H9: 4,9 => CTR => H9: 5 * DIS # C1: 8 => CTR => C1: 4,9 * PRF # D7: 4,6 => SOL * DIS # D7: 9 => CTR => D7: 4,6 * PRF # F9: 6,9 => SOL * DIS # F9: 4,5,8 => CTR => F9: 6,9 * CNT 22 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,B7,C6,C9,D4,E1,E5,F5,G1,G9,H3,I3,I7) * ...5...12.12...573.5312.8..327...1681968..4255..261739..5.1238.8613..2.723.7....1 * PAIR E1: 3,7 BLK 2 F1: 3,7,4,6,9 # reduction candidate for 3,7 F1: 3,7 # 17 pairs F1: 4,6,9 # 11 pairs * PAIR G1: 6,9 ROW 1 A1: 6,9,4,7 # reduction candidate for 6,9 A1: 6,9 => CTR * ...5...12.12...573.5312.8..327...1681968..4255..261739..5.1238.8613..2.72397..6.1 F1: 6,9,3,4,7 # reduction candidate for 6,9 F1: 6,9 => CTR * ...53..12.12...573.531278..327...1681968734255..261739..59123868613..29723.7....1 F1: 3,4,7 => SOLVED * 789534612412698573653127894327945168196873425548261739975412386861359247234786951 * DURATION: 0:00:04.665905 START: 03:53:45.060012 END: 03:53:49.725917 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-035-base-pr-001.dot * REASONING * DIS # A1: 6,9 => CTR => A1: 4,7 * DIS A1: 4,7 # F1: 6,9 => CTR => F1: 3,4,7 * PRF A1: 4,7 + F1: 3,4,7 => SOL * STA A1: 4,7 + F1: 3,4,7 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 035 solution: 789534612412698573653127894327945168196873425548261739975412386861359247234786951 info: 1360 FNBHWXY S8.f 9541 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 789534612412698573653127894327945168196873425548261739975412386861359247234786951 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 # F1: 3,7 => UNS * INC # F1: 4,6,9 => UNS * DIS # A1: 6,9 => CTR => A1: 4,7 * INC # A1: 4,7 => UNS * DIS # F1: 6,9 => CTR => F1: 3,4,7 * INC # F1: 3,4,7 => UNS * INC # H8: 4,9 => UNS * DIS # H9: 4,9 => CTR => H9: 5 * INC # H9: 5 => UNS * INC # B1: 4,8 => UNS * DIS # B1: 7 => CTR => B1: 4,8 * DIS # C1: 4,8 => CTR => C1: 9 * PRF # C1: 9 => SOL * INC # E4: 4,9 => UNS * INC # F4: 4,9 => UNS * DIS # D2: 4,9 => CTR => D2: 6 * PRF # D2: 6 => SOL * PRF # D7: 4,9 => SOL * DIS # D7: 6 => CTR => D7: 4,9 * INC # F1: 3,7 => UNS * INC # F1: 4,6,9 => UNS * DIS # A7: 4,7 => CTR => A7: 9 * PRF # A7: 9 => SOL * DIS # B1: 4,7 => CTR => B1: 8 * INC # B1: 8 => UNS * INC # A7: 4,9 => UNS * DIS # A7: 7 => CTR => A7: 4,9 * DIS # E9: 4,9 => CTR => E9: 5,8 * INC # E9: 5,8 => UNS * DIS # F9: 4,9 => CTR => F9: 5,6,8 * INC # F9: 5,6,8 => UNS * DIS # H9: 4,9 => CTR => H9: 5 * INC # H9: 5 => UNS * INC # C1: 4,9 => UNS * DIS # C1: 8 => CTR => C1: 4,9 * PRF # D7: 4,6 => SOL * DIS # D7: 9 => CTR => D7: 4,6 * PRF # F9: 6,9 => SOL * DIS # F9: 4,5,8 => CTR => F9: 6,9 * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F1: 3,7 => UNS * INC # F1: 4,6,9 => UNS * DIS # A1: 6,9 => CTR => A1: 4,7 * DIS A1: 4,7 # F1: 6,9 => CTR => F1: 3,4,7 * PRF A1: 4,7 + F1: 3,4,7 => SOL * STA A1: 4,7 + F1: 3,4,7 * CNT 5 HDP CHAINS / 4 HYP OPENED