Analysis of xx-top500-212-base.sdk
Contents
Original Sudoku
level: medium
position: .21.3.......6...5.........96..5...........2......4.......72.1..4......3.58....... initial
Autosolve
position: .21.35......6...52...2...196..5.2...1.....2..2...4.5.....72.1.5412.5..3.587....2. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E2: 7,8 => CTR => E2: 1,9 * DIS # F2: 7,8 => CTR => F2: 1,9 * DIS # F3: 7,8 => CTR => F3: 4 * PRF # F3: 4 => SOL * PRF # A3: 7,8 => SOL * DIS # A3: 3 => CTR => A3: 7,8 * DIS # G3: 7,8 => CTR => G3: 3,4 * DIS # E5: 7,8 => CTR => E5: 6,9 * DIS # A2: 3,9 => CTR => A2: 7,8 * DIS # F3: 7 => CTR => F3: 4,8 * DIS # F8: 8,9 => CTR => F8: 6 * PRF # D1: 8,9 => SOL * DIS # D1: 4 => CTR => D1: 8,9 * DIS # D5: 8,9 => CTR => D5: 3 * DIS # D6: 8,9 => CTR => D6: 1,3 * DIS # G9: 4,6 => CTR => G9: 9 * DIS # F9: 4,6 => CTR => F9: 1,3,9 * CNT 17 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E2: 7,8 => CTR => E2: 1,9 * DIS E2: 1,9 # F2: 7,8 => CTR => F2: 1,9 * PRF E2: 1,9 + F2: 1,9 => SOL * STA E2: 1,9 + F2: 1,9 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .21.3.......6...5.........96..5...........2......4.......72.1..4......3.58....... | initial |
| .21.35......6...52...2...196..5.2...1.....2..2...4.5.....72.1.5412.5..3.587....2. | autosolve |
| 921835674734691852856274319673582491145369287298147563369728145412956738587413926 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) B3: 5,6 C3: 5,6 E3: 7,8 A7: 3,9 F7: 4,8 D8: 8,9 H7: 4,8 I9: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,F2: 1.. / E2 = 1 => 0 pairs (X) / F2 = 1 => 8 pairs (_) I4,I6: 1.. / I4 = 1 => 10 pairs (_) / I6 = 1 => 0 pairs (X) E4,I4: 1.. / E4 = 1 => 0 pairs (X) / I4 = 1 => 10 pairs (_) D6,D9: 1.. / D6 = 1 => 10 pairs (_) / D9 = 1 => 0 pairs (X) G2,G3: 3.. / G2 = 3 => 0 pairs (X) / G3 = 3 => 0 pairs (_) D9,F9: 3.. / D9 = 3 => 0 pairs (X) / F9 = 3 => 8 pairs (_) A3,G3: 3.. / A3 = 3 => 0 pairs (X) / G3 = 3 => 0 pairs (_) B2,C2: 4.. / B2 = 4 => 9 pairs (_) / C2 = 4 => 9 pairs (_) D1,F3: 4.. / D1 = 4 => 0 pairs (X) / F3 = 4 => 0 pairs (_) F3,G3: 4.. / F3 = 4 => 0 pairs (*) / G3 = 4 => 0 pairs (X) F7,H7: 4.. / F7 = 4 => 0 pairs (X) / H7 = 4 => 0 pairs (_) D1,D9: 4.. / D1 = 4 => 0 pairs (X) / D9 = 4 => 0 pairs (_) B3,C3: 5.. / B3 = 5 => 7 pairs (_) / C3 = 5 => 7 pairs (_) B5,C5: 5.. / B5 = 5 => 7 pairs (_) / C5 = 5 => 7 pairs (_) B3,B5: 5.. / B3 = 5 => 7 pairs (_) / B5 = 5 => 7 pairs (_) C3,C5: 5.. / C3 = 5 => 7 pairs (_) / C5 = 5 => 7 pairs (_) B3,C3: 6.. / B3 = 6 => 7 pairs (_) / C3 = 6 => 7 pairs (_) B7,C7: 6.. / B7 = 6 => 7 pairs (_) / C7 = 6 => 7 pairs (_) B3,B7: 6.. / B3 = 6 => 7 pairs (_) / B7 = 6 => 7 pairs (_) C3,C7: 6.. / C3 = 6 => 7 pairs (_) / C7 = 6 => 7 pairs (_) E5,E9: 6.. / E5 = 6 => 9 pairs (_) / E9 = 6 => 0 pairs (X) G8,I8: 7.. / G8 = 7 => 13 pairs (_) / I8 = 7 => 8 pairs (_) F7,H7: 8.. / F7 = 8 => 0 pairs (*) / H7 = 8 => 0 pairs (X) G8,G9: 9.. / G8 = 9 => 0 pairs (X) / G9 = 9 => 9 pairs (_) A1,D1: 9.. / A1 = 9 => 0 pairs (*) / D1 = 9 => 0 pairs (X) * DURATION: 0:00:37.650363 START: 10:04:25.647893 END: 10:05:03.298256 2017-05-04 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B3,C3,D8,E3,F7,H7,I9) * .21.35......6...52...2...196..5.2...1.....2..2...4.5.....72.1.5412.5..3.587....2. * PAIR E3: 7,8 BLK 2 E2: 7,8,1,9 # reduction candidate for 7,8 E2: 7,8 => CTR * .21935......6.1.52...2.4.196..5.2...1.....2..2...4.5.....7281.5412.5..3.587....2. E2: 1,9 # 9 pairs F2: 7,8,1,9 # reduction candidate for 7,8 F2: 7,8 => CTR * .21935......61..52...2.4.196..5.2..11.....2..2...4.5.....7281.5412.5..3.587....2. F2: 1,9 # 9 pairs F3: 7,8,4 # reduction candidate for 7,8 F3: 7,8 => CTR * 921435......6..3523..2..4196..5.2...1.....2..2...4.5.....72.1.5412.5..3.587....2. F3: 4 => SOLVED * 921835674734691852856274319673582491145369287298147563369728145412956738587413926 * PAIR E3: 7,8 ROW 3 A3: 7,8,3 # reduction candidate for 7,8 A3: 7,8 => SOLVED * 921835674734691852856274319673582491145369287298147563369728145412956738587413926 A3: 3 => CTR * .21935......6..3523..2.4.196..5.2...1.....2..2...4.5..9..7281.5412.5..3.587....2. G3: 7,8,3,4 # reduction candidate for 7,8 G3: 7,8 => CTR * .21.35......6..3523..2.4.196..5.2...1.....2..2...4.5..9..728145412956.3.587413926 G3: 3,4 # 9 pairs * PAIR E3: 7,8 COL E E4: 7,8,1,9 # reduction candidate for 7,8 E4: 7,8 # 13 pairs E5: 7,8,6,9 # reduction candidate for 7,8 E5: 7,8 => CTR * 921435......6..3523..2..4196..5.2...1.....2..2...4.5.....724185412.5..3.587.6.924 E5: 6,9 # 9 pairs * PAIR A7: 3,9 BLK 7 B7: 3,9,6 # reduction candidate for 3,9 B7: 3,9 # 7 pairs C7: 3,9,6 # reduction candidate for 3,9 C7: 3,9 # 7 pairs * PAIR A7: 3,9 COL A A2: 3,9,7,8 # reduction candidate for 3,9 A2: 3,9 => CTR * .21935......6...52...2.43196..5.2...1.....2..2...4.5.....7281.5412.5..3.587....2. A2: 7,8 # 9 pairs * PAIR F7: 4,8 COL F F3: 4,8,7 # reduction candidate for 4,8 F3: 7 => CTR * 921435...7..6..352...2.74196..5.2...1.....2..2...4.5.....72.1.5412.5..3.587....2. F3: 4,8 # 10 pairs * PAIR D8: 8,9 BLK 8 F8: 8,9,6 # reduction candidate for 8,9 F8: 8,9 => CTR * 921435......6..3523..2..4196..5.2...1.....2..2...4.5.....724185412.5..3.587...924 F8: 6 # 10 pairs * PAIR D8: 8,9 ROW 8 G8: 8,9,6,7 # reduction candidate for 8,9 G8: 8,9 # 10 pairs G8: 6,7 # 10 pairs * PAIR D8: 8,9 COL D D1: 8,9,4 # reduction candidate for 8,9 D1: 8,9 => SOLVED * 921835674734691852856274319673582491145369287298147563369728145412956738587413926 D1: 4 => CTR * 921435......6...52...2..4196..5.2...1.....2..2...4.5..3..72.1.5412.5..3.587....2. D5: 8,9,3 # reduction candidate for 8,9 D5: 8,9 => CTR * 921435......6...52...2..4196..5.2...1.....2..2...4.5..3..72.1.5412.5..3.587....2. D5: 3 # 10 pairs D6: 8,9,1,3 # reduction candidate for 8,9 D6: 8,9 => CTR * 921435......6..3523..2..4196..5.2...1..3..2..2...4.5.....724185412.5..3.5871.3.24 D6: 1,3 # 9 pairs * PAIR H7: 4,8 COL H H1: 4,8,6,7 # reduction candidate for 4,8 H1: 4,8 # 11 pairs H4: 4,8,7,9 # reduction candidate for 4,8 H4: 4,8 # 10 pairs H5: 4,8,6,7,9 # reduction candidate for 4,8 H5: 4,8 # 11 pairs * PAIR I9: 4,6 BLK 9 G9: 4,6,9 # reduction candidate for 4,6 G9: 4,6 => CTR * 921435......6..3523..2..4196..5.2...1...6.2..2...4.5.....724185412856937587...624 G9: 9 # 9 pairs * PAIR I9: 4,6 ROW 9 F9: 4,6,1,3,9 # reduction candidate for 4,6 F9: 4,6 => CTR * 921435......6913523..2..4196..5.2..11...6.2..2..14.5.....72.1.5412.5..3.58731.92. F9: 1,3,9 # 8 pairs * PAIR I9: 4,6 COL I I1: 4,6,7,8 # reduction candidate for 4,6 I1: 4,6 # 10 pairs I5: 4,6,3,7,8 # reduction candidate for 4,6 I5: 4,6 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-212-base-pr-000.dot * REASONING * DIS # E2: 7,8 => CTR => E2: 1,9 * DIS # F2: 7,8 => CTR => F2: 1,9 * DIS # F3: 7,8 => CTR => F3: 4 * PRF # F3: 4 => SOL * PRF # A3: 7,8 => SOL * DIS # A3: 3 => CTR => A3: 7,8 * DIS # G3: 7,8 => CTR => G3: 3,4 * DIS # E5: 7,8 => CTR => E5: 6,9 * DIS # A2: 3,9 => CTR => A2: 7,8 * DIS # F3: 7 => CTR => F3: 4,8 * DIS # F8: 8,9 => CTR => F8: 6 * PRF # D1: 8,9 => SOL * DIS # D1: 4 => CTR => D1: 8,9 * DIS # D5: 8,9 => CTR => D5: 3 * DIS # D6: 8,9 => CTR => D6: 1,3 * DIS # G9: 4,6 => CTR => G9: 9 * DIS # F9: 4,6 => CTR => F9: 1,3,9 * CNT 17 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B3,C3,D8,E3,F7,H7,I9) * .21.35......6...52...2...196..5.2...1.....2..2...4.5.....72.1.5412.5..3.587....2. * PAIR E3: 7,8 BLK 2 E2: 7,8,1,9 # reduction candidate for 7,8 E2: 7,8 => CTR * .21935......6.1.52...2.4.196..5.2...1.....2..2...4.5.....7281.5412.5..3.587....2. F2: 7,8,1,9 # reduction candidate for 7,8 F2: 7,8 => CTR * .21935......61..52...2.4.196..5.2..11.....2..2...4.5.....7281.5412.5..3.587....2. F2: 1,9 => SOLVED * 921835674734691852856274319673582491145369287298147563369728145412956738587413926 * DURATION: 0:00:02.611457 START: 10:05:34.413393 END: 10:05:37.024850 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-212-base-pr-001.dot * REASONING * DIS # E2: 7,8 => CTR => E2: 1,9 * DIS E2: 1,9 # F2: 7,8 => CTR => F2: 1,9 * PRF E2: 1,9 + F2: 1,9 => SOL * STA E2: 1,9 + F2: 1,9 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 212 solution: 921835674734691852856274319673582491145369287298147563369728145412956738587413926 info: 1945 FNBHWXY S8.f 17063 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 921835674734691852856274319673582491145369287298147563369728145412956738587413926 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 # E2: 7,8 => CTR => E2: 1,9 * INC # E2: 1,9 => UNS * DIS # F2: 7,8 => CTR => F2: 1,9 * INC # F2: 1,9 => UNS * DIS # F3: 7,8 => CTR => F3: 4 * PRF # F3: 4 => SOL * PRF # A3: 7,8 => SOL * DIS # A3: 3 => CTR => A3: 7,8 * DIS # G3: 7,8 => CTR => G3: 3,4 * INC # G3: 3,4 => UNS * INC # E4: 7,8 => UNS * DIS # E5: 7,8 => CTR => E5: 6,9 * INC # E5: 6,9 => UNS * INC # B7: 3,9 => UNS * INC # C7: 3,9 => UNS * DIS # A2: 3,9 => CTR => A2: 7,8 * INC # A2: 7,8 => UNS * INC # F3: 4,8 => UNS * DIS # F3: 7 => CTR => F3: 4,8 * DIS # F8: 8,9 => CTR => F8: 6 * INC # F8: 6 => UNS * INC # G8: 8,9 => UNS * INC # G8: 6,7 => UNS * PRF # D1: 8,9 => SOL * DIS # D1: 4 => CTR => D1: 8,9 * DIS # D5: 8,9 => CTR => D5: 3 * INC # D5: 3 => UNS * DIS # D6: 8,9 => CTR => D6: 1,3 * INC # D6: 1,3 => UNS * INC # H1: 4,8 => UNS * INC # H4: 4,8 => UNS * INC # H5: 4,8 => UNS * DIS # G9: 4,6 => CTR => G9: 9 * INC # G9: 9 => UNS * DIS # F9: 4,6 => CTR => F9: 1,3,9 * INC # F9: 1,3,9 => UNS * INC # I1: 4,6 => UNS * INC # I5: 4,6 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E2: 7,8 => CTR => E2: 1,9 * DIS E2: 1,9 # F2: 7,8 => CTR => F2: 1,9 * PRF E2: 1,9 + F2: 1,9 => SOL * STA E2: 1,9 + F2: 1,9 * CNT 3 HDP CHAINS / 2 HYP OPENED