Analysis of xx-top500-422-base.sdk
Contents
Original Sudoku
level: medium
position: 6.27........8..13........9.4.....7...3..9........1....5..4..6...1.....2.......... initial
Autosolve
position: 692731...7..829136.8..4.2974.....7...3..9........1....5..4..6...1.9...2....1..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D4: 5,6 => CTR => D4: 2,3 * DIS # F4: 5,6 => CTR => F4: 8 * DIS # F9: 5,6 => CTR => F9: 2,3,8 * DIS # B9: 2,7 => CTR => B9: 4,6 * DIS # B6: 2,7 => CTR => B6: 5,6 * DIS # C7: 3,8 => CTR => C7: 7,9 * PRF # C8: 3,8 => SOL * DIS # A9: 3,8 => CTR => A9: 2,9 * DIS # E9: 7,8 => CTR => E9: 5,6 * DIS # C7: 7,8 => CTR => C7: 3,9 * DIS # H7: 7,8 => CTR => H7: 1 * CNT 11 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D4: 5,6 => CTR => D4: 2,3 * DIS D4: 2,3 # F4: 5,6 => CTR => F4: 8 * DIS D4: 2,3 + F4: 8 # F9: 5,6 => CTR => F9: 2,3 * DIS D4: 2,3 + F4: 8 + F9: 2,3 # B9: 2,7 => CTR => B9: 4,6 * DIS D4: 2,3 + F4: 8 + F9: 2,3 + B9: 4,6 # B6: 2,7 => CTR => B6: 5,6 * DIS D4: 2,3 + F4: 8 + F9: 2,3 + B9: 4,6 + B6: 5,6 # H5: 4,5 => CTR => H5: 6 * PRF D4: 2,3 + F4: 8 + F9: 2,3 + B9: 4,6 + B6: 5,6 + H5: 6 => SOL * STA D4: 2,3 + F4: 8 + F9: 2,3 + B9: 4,6 + B6: 5,6 + H5: 6 * CNT 7 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6.27........8..13........9.4.....7...3..9........1....5..4..6...1.....2.......... | initial |
| 692731...7..829136.8..4.2974.....7...3..9........1....5..4..6...1.9...2....1..... | autosolve |
| 692731845754829136183645297421368759835297461967514382579482613318976524246153978 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) B2: 4,5 C2: 4,5 A3: 1,3 C3: 1,3 D3: 5,6 F3: 5,6 F5: 4,7 F6: 4,7 B7: 2,7 A8: 3,8 E7: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,C3: 1.. / A3 = 1 => 10 pairs (_) / C3 = 1 => 10 pairs (_) H7,I7: 1.. / H7 = 1 => 14 pairs (_) / I7 = 1 => 0 pairs (X) A3,A5: 1.. / A3 = 1 => 10 pairs (_) / A5 = 1 => 10 pairs (_) F7,F9: 2.. / F7 = 2 => 14 pairs (_) / F9 = 2 => 0 pairs (X) B7,F7: 2.. / B7 = 2 => 0 pairs (X) / F7 = 2 => 14 pairs (_) A3,C3: 3.. / A3 = 3 => 10 pairs (_) / C3 = 3 => 10 pairs (_) D4,D6: 3.. / D4 = 3 => 11 pairs (_) / D6 = 3 => 0 pairs (X) D4,I4: 3.. / D4 = 3 => 11 pairs (_) / I4 = 3 => 0 pairs (X) B2,C2: 4.. / B2 = 4 => 9 pairs (_) / C2 = 4 => 10 pairs (_) F5,F6: 4.. / F5 = 4 => 14 pairs (_) / F6 = 4 => 9 pairs (_) B2,B9: 4.. / B2 = 4 => 9 pairs (_) / B9 = 4 => 10 pairs (_) B2,C2: 5.. / B2 = 5 => 10 pairs (_) / C2 = 5 => 9 pairs (_) D3,F3: 5.. / D3 = 5 => 16 pairs (_) / F3 = 5 => 14 pairs (_) D3,F3: 6.. / D3 = 6 => 14 pairs (_) / F3 = 6 => 16 pairs (_) F5,F6: 7.. / F5 = 7 => 9 pairs (_) / F6 = 7 => 14 pairs (_) H7,H9: 7.. / H7 = 7 => 0 pairs (X) / H9 = 7 => 12 pairs (_) C5,F5: 7.. / C5 = 7 => 14 pairs (_) / F5 = 7 => 9 pairs (_) C8,E8: 7.. / C8 = 7 => 0 pairs (X) / E8 = 7 => 14 pairs (_) E4,F4: 8.. / E4 = 8 => 0 pairs (X) / F4 = 8 => 13 pairs (_) C4,I4: 9.. / C4 = 9 => 0 pairs (X) / I4 = 9 => 14 pairs (_) C7,I7: 9.. / C7 = 9 => 14 pairs (_) / I7 = 9 => 0 pairs (X) A6,A9: 9.. / A6 = 9 => 14 pairs (_) / A9 = 9 => 0 pairs (X) G6,G9: 9.. / G6 = 9 => 0 pairs (X) / G9 = 9 => 14 pairs (_) * DURATION: 0:00:36.891989 START: 17:13:33.946153 END: 17:14:10.838142 2017-05-04 * CP COUNT: (23) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B2,B7,C2,C3,D3,E7,F3,F5,F6) * 692731...7..829136.8..4.2974.....7...3..9........1....5..4..6...1.9...2....1..... * PAIR D3: 5,6 COL D D4: 5,6,2,3 # reduction candidate for 5,6 D4: 5,6 => CTR * 692731...7..829136.8..4.297429...713.3.29....8..31....5..4..6...1.9...2....1..... D4: 2,3 # 12 pairs D5: 5,6,2 # reduction candidate for 5,6 D5: 5,6 # 14 pairs D6: 5,6,2,3 # reduction candidate for 5,6 D6: 5,6 # 17 pairs * PAIR F3: 5,6 COL F F4: 5,6,8 # reduction candidate for 5,6 F4: 5,6 => CTR * 692731...7..829136.8..4.2974.9.8.71..3..97....7..14...52.47.68..1796..2....152.7. F4: 8 # 13 pairs F8: 5,6,3,8 # reduction candidate for 5,6 F8: 5,6 # 15 pairs F9: 5,6,2,3,8 # reduction candidate for 5,6 F9: 5,6 => CTR * 692731...7..829136.8..4.2974....87...3..9........1....57.48261.816973.2....1...7. F9: 2,3,8 # 11 pairs * PAIR B7: 2,7 BLK 7 B9: 2,7,4,6 # reduction candidate for 2,7 B9: 2,7 => CTR * 692731...745829136.8..4.2974.9...71..3..9........1....5..4..6...1.9...2....1..... B9: 4,6 # 12 pairs * PAIR B7: 2,7 COL B B6: 2,7,5,6 # reduction candidate for 2,7 B6: 2,7 => CTR * 692731...7..829136.8..4.2974.9...71..3..9........1....5..4..6...1.9...2....1..... B6: 5,6 # 16 pairs * PAIR A8: 3,8 BLK 7 C7: 3,8,7,9 # reduction candidate for 3,8 C7: 3,8 => CTR * 692731...7..829136.8..4.2974.93..7.1.3..9...22...1.9.35..4..619.1.9...2.9..1...7. C7: 7,9 # 12 pairs C8: 3,8,4,6,7 # reduction candidate for 3,8 C8: 3,8 => SOLVED * 692731845754829136183645297421368759835297461967514382579482613318976524246153978 C8: 4,6,7 # 11 pairs A9: 3,8,2,9 # reduction candidate for 3,8 A9: 3,8 => CTR * 692731...7..829136.8..4.2974.....7.923..9....9...1...25.94..6...1.9...2....1..9.. A9: 2,9 # 12 pairs C9: 3,8,4,6,7,9 # reduction candidate for 3,8 C9: 3,8 # 16 pairs * PAIR A8: 3,8 ROW 8 F8: 3,8,5,6 # reduction candidate for 3,8 F8: 3,8 # 19 pairs G8: 3,8,4,5 # reduction candidate for 3,8 G8: 3,8 # 17 pairs I8: 3,8,4,5 # reduction candidate for 3,8 I8: 3,8 # 19 pairs * PAIR E7: 7,8 BLK 8 E8: 7,8,5,6 # reduction candidate for 7,8 E8: 7,8 # 15 pairs E9: 7,8,5,6 # reduction candidate for 7,8 E9: 7,8 => CTR * 692731...7..829136.83.4.2974.9..871..31.97....7..14...5284.36...179...2....1.2... E9: 5,6 # 12 pairs * PAIR E7: 7,8 ROW 7 C7: 7,8,3,9 # reduction candidate for 7,8 C7: 7,8 => CTR * 692731...7..829136.8..4.2974.9...7.1.3..9........1.9.352.4.3619.1.9...2.9..1.2.7. C7: 3,9 # 12 pairs H7: 7,8,1 # reduction candidate for 7,8 H7: 7,8 => CTR * 692731...7..829136.8..4.2974.....7.9.3..9....9...1....5294.36.1.1.9...2....1.29.. H7: 1 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-422-base-pr-000.dot * REASONING * DIS # D4: 5,6 => CTR => D4: 2,3 * DIS # F4: 5,6 => CTR => F4: 8 * DIS # F9: 5,6 => CTR => F9: 2,3,8 * DIS # B9: 2,7 => CTR => B9: 4,6 * DIS # B6: 2,7 => CTR => B6: 5,6 * DIS # C7: 3,8 => CTR => C7: 7,9 * PRF # C8: 3,8 => SOL * DIS # A9: 3,8 => CTR => A9: 2,9 * DIS # E9: 7,8 => CTR => E9: 5,6 * DIS # C7: 7,8 => CTR => C7: 3,9 * DIS # H7: 7,8 => CTR => H7: 1 * CNT 11 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B2,B7,C2,C3,D3,E7,F3,F5,F6) * 692731...7..829136.8..4.2974.....7...3..9........1....5..4..6...1.9...2....1..... * PAIR D3: 5,6 COL D D4: 5,6,2,3 # reduction candidate for 5,6 D4: 5,6 => CTR * 692731...7..829136.8..4.297429...713.3.29....8..31....5..4..6...1.9...2....1..... D5: 5,6,2 # reduction candidate for 5,6 D5: 5,6 # 14 pairs D6: 5,6,2,3 # reduction candidate for 5,6 D6: 5,6 # 17 pairs * PAIR RESTART * PAIR D3: 5,6 COL D D5: 5,6,2 # reduction candidate for 5,6 D5: 5,6 # 14 pairs D6: 5,6,2,3 # reduction candidate for 5,6 D6: 5,6 # 17 pairs * PAIR F3: 5,6 COL F F4: 5,6,8 # reduction candidate for 5,6 F4: 5,6 => CTR * 692731...7..829136.8..4.2974.9.8.71..3..97....7..14...52.47.68..1796..2....152.7. F8: 5,6,3 # reduction candidate for 5,6 F8: 5,6 # 16 pairs F9: 5,6,2,3 # reduction candidate for 5,6 F9: 5,6 => CTR * 692731...7..829136.8..4.2974....87...3..9........1....57.48261.816973.2....1...7. * RESTART * PAIR RESTART * PAIR B7: 2,7 BLK 7 B9: 2,7,4,6 # reduction candidate for 2,7 B9: 2,7 => CTR * 692731...745829136.8..4.2974.9..871..3..9........1....5..4..6...1.9...2....1..... * PAIR B7: 2,7 COL B B6: 2,7,5,6 # reduction candidate for 2,7 B6: 2,7 => CTR * 692731...7..829136.8..4.2974.9..871..3..9........1....5..4..6...1.9...2....1..... * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (B2,B6,B9,C2,C5,D3,D6,E4,E9,F3,F8,G5,H1,H4) * 692731...7..829136183.4.2974213.87.983.297..19.7.1438257948261331.97..2.2..1.397. * PAIR H1: 4,5 BLK 3 G1: 4,5,8 # reduction candidate for 4,5 G1: 4,5 # 18 pairs I1: 4,5,8 # reduction candidate for 4,5 I1: 4,5 # 16 pairs * PAIR H1: 4,5 COL H H5: 4,5,6 # reduction candidate for 4,5 H5: 4,5 => CTR * 692731...7..829136183.4.2974213.8769836297..195761438257948261331.976.2.26.15397. H5: 6 => SOLVED * 692731845754829136183645297421368759835297461967514382579482613318976524246153978 * DURATION: 0:00:17.958487 START: 17:14:36.458440 END: 17:14:54.416927 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-422-base-pr-001.dot * REASONING * DIS # D4: 5,6 => CTR => D4: 2,3 * DIS D4: 2,3 # F4: 5,6 => CTR => F4: 8 * DIS D4: 2,3 + F4: 8 # F9: 5,6 => CTR => F9: 2,3 * DIS D4: 2,3 + F4: 8 + F9: 2,3 # B9: 2,7 => CTR => B9: 4,6 * DIS D4: 2,3 + F4: 8 + F9: 2,3 + B9: 4,6 # B6: 2,7 => CTR => B6: 5,6 * DIS D4: 2,3 + F4: 8 + F9: 2,3 + B9: 4,6 + B6: 5,6 # H5: 4,5 => CTR => H5: 6 * PRF D4: 2,3 + F4: 8 + F9: 2,3 + B9: 4,6 + B6: 5,6 + H5: 6 => SOL * STA D4: 2,3 + F4: 8 + F9: 2,3 + B9: 4,6 + B6: 5,6 + H5: 6 * CNT 7 HDP CHAINS / 13 HYP OPENED
Header Info
Top 500 Minimum 17 422 solution: 692731845754829136183645297421368759835297461967514382579482613318976524246153978 info: 95114 FNBHWXK S8.f 35424 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 692731845754829136183645297421368759835297461967514382579482613318976524246153978 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 # D4: 5,6 => CTR => D4: 2,3 * INC # D4: 2,3 => UNS * INC # D5: 5,6 => UNS * INC # D6: 5,6 => UNS * DIS # F4: 5,6 => CTR => F4: 8 * INC # F4: 8 => UNS * INC # F8: 5,6 => UNS * DIS # F9: 5,6 => CTR => F9: 2,3,8 * INC # F9: 2,3,8 => UNS * DIS # B9: 2,7 => CTR => B9: 4,6 * INC # B9: 4,6 => UNS * DIS # B6: 2,7 => CTR => B6: 5,6 * INC # B6: 5,6 => UNS * DIS # C7: 3,8 => CTR => C7: 7,9 * INC # C7: 7,9 => UNS * PRF # C8: 3,8 => SOL * INC # C8: 4,6,7 => UNS * DIS # A9: 3,8 => CTR => A9: 2,9 * INC # A9: 2,9 => UNS * INC # C9: 3,8 => UNS * INC # F8: 3,8 => UNS * INC # G8: 3,8 => UNS * INC # I8: 3,8 => UNS * INC # E8: 7,8 => UNS * DIS # E9: 7,8 => CTR => E9: 5,6 * INC # E9: 5,6 => UNS * DIS # C7: 7,8 => CTR => C7: 3,9 * INC # C7: 3,9 => UNS * DIS # H7: 7,8 => CTR => H7: 1 * INC # H7: 1 => UNS * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D4: 5,6 => CTR => D4: 2,3 * INC D4: 2,3 # D5: 5,6 => UNS * INC D4: 2,3 # D6: 5,6 => UNS * INC D4: 2,3 # D5: 5,6 => UNS * INC D4: 2,3 # D6: 5,6 => UNS * DIS D4: 2,3 # F4: 5,6 => CTR => F4: 8 * INC D4: 2,3 + F4: 8 # F8: 5,6 => UNS * DIS D4: 2,3 + F4: 8 # F9: 5,6 => CTR => F9: 2,3 * DIS D4: 2,3 + F4: 8 + F9: 2,3 # B9: 2,7 => CTR => B9: 4,6 * DIS D4: 2,3 + F4: 8 + F9: 2,3 + B9: 4,6 # B6: 2,7 => CTR => B6: 5,6 * INC D4: 2,3 + F4: 8 + F9: 2,3 + B9: 4,6 + B6: 5,6 # G1: 4,5 => UNS * INC D4: 2,3 + F4: 8 + F9: 2,3 + B9: 4,6 + B6: 5,6 # I1: 4,5 => UNS * DIS D4: 2,3 + F4: 8 + F9: 2,3 + B9: 4,6 + B6: 5,6 # H5: 4,5 => CTR => H5: 6 * PRF D4: 2,3 + F4: 8 + F9: 2,3 + B9: 4,6 + B6: 5,6 + H5: 6 => SOL * STA D4: 2,3 + F4: 8 + F9: 2,3 + B9: 4,6 + B6: 5,6 + H5: 6 * CNT 14 HDP CHAINS / 13 HYP OPENED