Analysis of xx-top500-462-base.sdk
Contents
Original Sudoku
level: medium
position: ...28..3.1.5...6.....9......8....32.7...1.............4.....1.5.2.8.............. initial
Autosolve
position: 6..281539195...6828329...1..8....3217...128..21...8...4.8.2.1.5.218....33..1..2.8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G6: 4,7 => CTR => G6: 9 * DIS # C5: 4,6 => CTR => C5: 3,9 * DIS # D5: 4,6 => CTR => D5: 3,5 * DIS # B9: 6,7 => CTR => B9: 5 * DIS # F7: 6,7 => CTR => F7: 3,9 * DIS # H7: 6,7 => CTR => H7: 9 * PRF # E8: 5,9 => SOL * CNT 7 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G6: 4,7 => CTR => G6: 9 * DIS G6: 9 # I6: 4,7 => CTR => I6: 6 * PRF G6: 9 + I6: 6 => SOL * STA G6: 9 + I6: 6 * CNT 3 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...28..3.1.5...6.....9......8....32.7...1.............4.....1.5.2.8.............. | initial |
| 6..281539195...6828329...1..8....3217...128..21...8...4.8.2.1.5.218....33..1..2.8 | autosolve |
| 647281539195437682832965417584796321769312854213548976478623195921854763356179248 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) B1: 4,7 C1: 4,7 E3: 5,6 F3: 5,6 G3: 4,7 I3: 4,7 A4: 5,9 I5: 4,6 B7: 6,7 A8: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C5,C6: 3.. / C5 = 3 => 0 pairs (X) / C6 = 3 => 17 pairs (_) D7,F7: 3.. / D7 = 3 => 0 pairs (X) / F7 = 3 => 17 pairs (_) C5,D5: 3.. / C5 = 3 => 0 pairs (X) / D5 = 3 => 17 pairs (_) E2,E6: 3.. / E2 = 3 => 17 pairs (_) / E6 = 3 => 0 pairs (X) F2,F7: 3.. / F2 = 3 => 0 pairs (X) / F7 = 3 => 17 pairs (_) B1,C1: 4.. / B1 = 4 => 10 pairs (_) / C1 = 4 => 0 pairs (X) G3,I3: 4.. / G3 = 4 => 12 pairs (_) / I3 = 4 => 11 pairs (_) B1,B5: 4.. / B1 = 4 => 10 pairs (_) / B5 = 4 => 0 pairs (X) E3,F3: 5.. / E3 = 5 => 8 pairs (_) / F3 = 5 => 8 pairs (_) A4,B5: 5.. / A4 = 5 => 17 pairs (_) / B5 = 5 => 0 pairs (X) H5,H6: 5.. / H5 = 5 => 17 pairs (_) / H6 = 5 => 12 pairs (_) A8,B9: 5.. / A8 = 5 => 0 pairs (X) / B9 = 5 => 17 pairs (_) A4,D4: 5.. / A4 = 5 => 17 pairs (_) / D4 = 5 => 0 pairs (X) D6,H6: 5.. / D6 = 5 => 17 pairs (_) / H6 = 5 => 12 pairs (_) A4,A8: 5.. / A4 = 5 => 17 pairs (_) / A8 = 5 => 0 pairs (X) B5,B9: 5.. / B5 = 5 => 0 pairs (X) / B9 = 5 => 17 pairs (_) E3,F3: 6.. / E3 = 6 => 8 pairs (_) / F3 = 6 => 8 pairs (_) I5,I6: 6.. / I5 = 6 => 12 pairs (_) / I6 = 6 => 10 pairs (_) B1,C1: 7.. / B1 = 7 => 0 pairs (X) / C1 = 7 => 10 pairs (_) G3,I3: 7.. / G3 = 7 => 11 pairs (_) / I3 = 7 => 12 pairs (_) C1,C9: 7.. / C1 = 7 => 10 pairs (_) / C9 = 7 => 0 pairs (X) I3,I6: 7.. / I3 = 7 => 12 pairs (_) / I6 = 7 => 11 pairs (_) A8,C9: 9.. / A8 = 9 => 17 pairs (_) / C9 = 9 => 0 pairs (X) C5,H5: 9.. / C5 = 9 => 17 pairs (_) / H5 = 9 => 0 pairs (X) F7,H7: 9.. / F7 = 9 => 0 pairs (X) / H7 = 9 => 17 pairs (_) A4,A8: 9.. / A4 = 9 => 0 pairs (X) / A8 = 9 => 17 pairs (_) G6,G8: 9.. / G6 = 9 => 17 pairs (_) / G8 = 9 => 0 pairs (X) * DURATION: 0:00:46.958929 START: 18:30:43.106095 END: 18:31:30.065024 2017-05-04 * CP COUNT: (27) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B1,B7,C1,E3,F3,G3,I3,I5) * 6..281539195...6828329...1..8....3217...128..21...8...4.8.2.1.5.218....33..1..2.8 * PAIR E3: 5,6 COL E E8: 5,6,4,7,9 # reduction candidate for 5,6 E8: 5,6 # 11 pairs E9: 5,6,4,7,9 # reduction candidate for 5,6 E9: 5,6 # 11 pairs * PAIR F3: 5,6 COL F F8: 5,6,4,7,9 # reduction candidate for 5,6 F8: 5,6 # 11 pairs F9: 5,6,4,7,9 # reduction candidate for 5,6 F9: 5,6 # 11 pairs * PAIR G3: 4,7 COL G G6: 4,7,9 # reduction candidate for 4,7 G6: 4,7 => CTR * 647281539195.3.6828329...1.98.5..32175..1289.21..98.5.4.83291.55218..9.33.91..2.8 G6: 9 # 17 pairs G8: 4,7,9 # reduction candidate for 4,7 G8: 4,7 # 17 pairs * PAIR I3: 4,7 COL I I6: 4,7,6 # reduction candidate for 4,7 I6: 4,7 # 12 pairs I6: 6 # 10 pairs * PAIR I5: 4,6 BLK 6 I6: 4,6,7 # reduction candidate for 4,6 I6: 4,6 # 12 pairs I6: 7 # 11 pairs * PAIR I5: 4,6 ROW 5 B5: 4,6,5 # reduction candidate for 4,6 B5: 4,6 # 17 pairs C5: 4,6,3,9 # reduction candidate for 4,6 C5: 4,6 => CTR * 6..281539195...6828329...1..8....3217..31289.213.98.5.4.8.2.1.5.218....33..1..2.8 C5: 3,9 # 11 pairs D5: 4,6,3,5 # reduction candidate for 4,6 D5: 4,6 => CTR * 6.7281539195..36828329...1.98.5..3217.3.1289.21...8.5.4.8.291.5.218..9.33.91..2.8 D5: 3,5 # 11 pairs * PAIR B7: 6,7 BLK 7 B9: 6,7,5 # reduction candidate for 6,7 B9: 6,7 => CTR * 647281539195.3.6828329...1.98.5..32175..1289.21..98.5.4.83291.55218..9.33.91..2.8 B9: 5 # 17 pairs C9: 6,7,9 # reduction candidate for 6,7 C9: 6,7 # 17 pairs * PAIR B7: 6,7 ROW 7 D7: 6,7,3 # reduction candidate for 6,7 D7: 6,7 # 17 pairs F7: 6,7,3,9 # reduction candidate for 6,7 F7: 6,7 => CTR * 6..281539195..36828329...1..8....3217...128..21..38...4.832.195.218....33..1..2.8 F7: 3,9 # 11 pairs H7: 6,7,9 # reduction candidate for 6,7 H7: 6,7 => CTR * 6..281539195..36828329...1..8..9.3217.3.1289.219.38.5.4.83291.59218....335.1..2.8 H7: 9 # 17 pairs * PAIR A8: 5,9 ROW 8 E8: 5,9,4,6,7 # reduction candidate for 5,9 E8: 5,9 => SOLVED * 647281539195437682832965417584796321769312854213548976478623195921854763356179248 E8: 4,6,7 # 10 pairs F8: 5,9,4,6,7 # reduction candidate for 5,9 F8: 5,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-462-base-pr-000.dot * REASONING * DIS # G6: 4,7 => CTR => G6: 9 * DIS # C5: 4,6 => CTR => C5: 3,9 * DIS # D5: 4,6 => CTR => D5: 3,5 * DIS # B9: 6,7 => CTR => B9: 5 * DIS # F7: 6,7 => CTR => F7: 3,9 * DIS # H7: 6,7 => CTR => H7: 9 * PRF # E8: 5,9 => SOL * CNT 7 HDP CHAINS / 27 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B1,B7,C1,E3,F3,G3,I3,I5) * 6..281539195...6828329...1..8....3217...128..21...8...4.8.2.1.5.218....33..1..2.8 * PAIR E3: 5,6 COL E E8: 5,6,4,7,9 # reduction candidate for 5,6 E8: 5,6 # 11 pairs E9: 5,6,4,7,9 # reduction candidate for 5,6 E9: 5,6 # 11 pairs * PAIR F3: 5,6 COL F F8: 5,6,4,7,9 # reduction candidate for 5,6 F8: 5,6 # 11 pairs F9: 5,6,4,7,9 # reduction candidate for 5,6 F9: 5,6 # 11 pairs * PAIR G3: 4,7 COL G G6: 4,7,9 # reduction candidate for 4,7 G6: 4,7 => CTR * 647281539195.3.6828329...1.98.5..32175..1289.21..98.5.4.83291.55218..9.33.91..2.8 * RESTART * PAIR RESTART * PAIR I3: 4,7 COL I I6: 4,7,6 # reduction candidate for 4,7 I6: 4,7 => CTR * 6..281539195.3.6828329...1.58....3217.93128562135689..4687231959218....33571..2.8 I6: 6 => SOLVED * 647281539195437682832965417584796321769312854213548976478623195921854763356179248 * DURATION: 0:00:07.816034 START: 18:31:55.119191 END: 18:32:02.935225 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-462-base-pr-001.dot * REASONING * DIS # G6: 4,7 => CTR => G6: 9 * DIS G6: 9 # I6: 4,7 => CTR => I6: 6 * PRF G6: 9 + I6: 6 => SOL * STA G6: 9 + I6: 6 * CNT 3 HDP CHAINS / 6 HYP OPENED
Header Info
Top 500 Minimum 17 462 solution: 647281539195437682832965417584796321769312854213548976478623195921854763356179248 info: 95545 FNBXYK S8.f 8079 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 647281539195437682832965417584796321769312854213548976478623195921854763356179248 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 # E8: 5,6 => UNS * INC # E9: 5,6 => UNS * INC # F8: 5,6 => UNS * INC # F9: 5,6 => UNS * DIS # G6: 4,7 => CTR => G6: 9 * INC # G6: 9 => UNS * INC # G8: 4,7 => UNS * INC # I6: 4,7 => UNS * INC # I6: 6 => UNS * INC # I6: 4,6 => UNS * INC # I6: 7 => UNS * INC # B5: 4,6 => UNS * DIS # C5: 4,6 => CTR => C5: 3,9 * INC # C5: 3,9 => UNS * DIS # D5: 4,6 => CTR => D5: 3,5 * INC # D5: 3,5 => UNS * DIS # B9: 6,7 => CTR => B9: 5 * INC # B9: 5 => UNS * INC # C9: 6,7 => UNS * INC # D7: 6,7 => UNS * DIS # F7: 6,7 => CTR => F7: 3,9 * INC # F7: 3,9 => UNS * DIS # H7: 6,7 => CTR => H7: 9 * INC # H7: 9 => UNS * PRF # E8: 5,9 => SOL * INC # E8: 4,6,7 => UNS * INC # F8: 5,9 => UNS * CNT 27 HDP CHAINS / 27 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E8: 5,6 => UNS * INC # E9: 5,6 => UNS * INC # F8: 5,6 => UNS * INC # F9: 5,6 => UNS * DIS # G6: 4,7 => CTR => G6: 9 * DIS G6: 9 # I6: 4,7 => CTR => I6: 6 * PRF G6: 9 + I6: 6 => SOL * STA G6: 9 + I6: 6 * CNT 7 HDP CHAINS / 6 HYP OPENED