Analysis of xx-top500-315-base.sdk
Contents
Original Sudoku
level: medium
position: ...9...5.3....6....8....7....74..1........2..6........8......63...7...8.....1.... initial
Autosolve
position: 71.98365.3...7681..861..73..3746.1981.83.72466..8.1375871....63.6.73..81..3618.27 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C6: 2,4 => SOL * DIS # C6: 9 => CTR => C6: 2,4 * DIS # I2: 2,4 => CTR => I2: 9 * PRF # I2: 9 => SOL * PRF # C8: 5,9 => SOL * DIS # C8: 2 => CTR => C8: 5,9 * DIS # A8: 5,9 => CTR => A8: 2,4 * DIS # A9: 5,9 => CTR => A9: 4 * DIS # I2: 2,4 => CTR => I2: 9 * PRF # I2: 9 => SOL * PRF # I2: 2,9 => SOL * DIS # I2: 4 => CTR => I2: 2,9 * PRF # A8: 2,5 => SOL * DIS # A8: 4,9 => CTR => A8: 2,5 * PRF # C6: 2,4 => SOL * DIS # C6: 9 => CTR => C6: 2,4 * DIS # C6: 2,9 => CTR => C6: 4 * PRF # C6: 4 => SOL * DIS # A8: 5,9 => CTR => A8: 2,4 * PRF # C8: 5,9 => SOL * DIS # C8: 2 => CTR => C8: 5,9 * DIS # A9: 5,9 => CTR => A9: 4 * DIS # G9: 4 => CTR => G9: 5,9 * CNT 23 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C6: 2,4 => SOL * STA C6: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...9...5.3....6....8....7....74..1........2..6........8......63...7...8.....1.... | initial |
| 71.98365.3...7681..861..73..3746.1981.83.72466..8.1375871....63.6.73..81..3618.27 | autosolve |
| 712983654345276819986145732537462198198357246624891375871529463269734581453618927 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) C1: 2,4 B2: 2,4 C2: 5,9 A3: 5,9 D2: 2,5 I1: 2,4 I3: 2,9 A4: 2,5 B5: 5,9 B6: 2,4 F4: 2,5 E5: 5,9 E6: 2,9 B9: 5,9 D7: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,B2: 2.. / C1 = 2 => 0 pairs (*) / B2 = 2 => 0 pairs (X) F4,E6: 2.. / F4 = 2 => 0 pairs (*) / E6 = 2 => 0 pairs (X) A8,C8: 2.. / A8 = 2 => 0 pairs (*) / C8 = 2 => 0 pairs (X) C1,I1: 2.. / C1 = 2 => 0 pairs (*) / I1 = 2 => 0 pairs (X) A4,F4: 2.. / A4 = 2 => 0 pairs (X) / F4 = 2 => 0 pairs (_) A4,A8: 2.. / A4 = 2 => 0 pairs (X) / A8 = 2 => 0 pairs (_) B2,B6: 2.. / B2 = 2 => 0 pairs (X) / B6 = 2 => 0 pairs (_) D2,D7: 2.. / D2 = 2 => 0 pairs (*) / D7 = 2 => 0 pairs (X) C1,B2: 4.. / C1 = 4 => 0 pairs (X) / B2 = 4 => 0 pairs (_) E3,F3: 4.. / E3 = 4 => 20 pairs (_) / F3 = 4 => 18 pairs (_) I1,I2: 4.. / I1 = 4 => 0 pairs (*) / I2 = 4 => 0 pairs (X) B6,C6: 4.. / B6 = 4 => 0 pairs (X) / C6 = 4 => 0 pairs (_) A8,A9: 4.. / A8 = 4 => 0 pairs (X) / A9 = 4 => 16 pairs (_) C1,I1: 4.. / C1 = 4 => 0 pairs (X) / I1 = 4 => 0 pairs (_) B2,I2: 4.. / B2 = 4 => 0 pairs (*) / I2 = 4 => 0 pairs (X) A9,G9: 4.. / A9 = 4 => 16 pairs (_) / G9 = 4 => 0 pairs (X) B2,B6: 4.. / B2 = 4 => 0 pairs (*) / B6 = 4 => 0 pairs (X) C1,C6: 4.. / C1 = 4 => 0 pairs (X) / C6 = 4 => 0 pairs (_) E3,E7: 4.. / E3 = 4 => 20 pairs (_) / E7 = 4 => 18 pairs (_) C2,A3: 5.. / C2 = 5 => 0 pairs (*) / A3 = 5 => 0 pairs (X) A4,B5: 5.. / A4 = 5 => 0 pairs (*) / B5 = 5 => 0 pairs (X) F4,E5: 5.. / F4 = 5 => 0 pairs (X) / E5 = 5 => 0 pairs (_) C2,D2: 5.. / C2 = 5 => 0 pairs (*) / D2 = 5 => 0 pairs (X) A4,F4: 5.. / A4 = 5 => 0 pairs (*) / F4 = 5 => 0 pairs (X) B5,E5: 5.. / B5 = 5 => 0 pairs (X) / E5 = 5 => 0 pairs (_) B5,B9: 5.. / B5 = 5 => 0 pairs (X) / B9 = 5 => 0 pairs (_) C2,C8: 5.. / C2 = 5 => 0 pairs (*) / C8 = 5 => 0 pairs (X) D2,D7: 5.. / D2 = 5 => 0 pairs (X) / D7 = 5 => 0 pairs (_) C2,A3: 9.. / C2 = 9 => 0 pairs (X) / A3 = 9 => 0 pairs (_) I2,I3: 9.. / I2 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) B5,C6: 9.. / B5 = 9 => 0 pairs (*) / C6 = 9 => 0 pairs (X) E5,E6: 9.. / E5 = 9 => 0 pairs (X) / E6 = 9 => 0 pairs (_) F7,F8: 9.. / F7 = 9 => 17 pairs (_) / F8 = 9 => 18 pairs (_) C2,I2: 9.. / C2 = 9 => 0 pairs (X) / I2 = 9 => 0 pairs (_) A3,I3: 9.. / A3 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) B5,E5: 9.. / B5 = 9 => 0 pairs (*) / E5 = 9 => 0 pairs (X) C6,E6: 9.. / C6 = 9 => 0 pairs (X) / E6 = 9 => 0 pairs (_) F7,G7: 9.. / F7 = 9 => 17 pairs (_) / G7 = 9 => 18 pairs (_) B5,B9: 9.. / B5 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) * DURATION: 0:01:23.547717 START: 13:45:31.329044 END: 13:46:54.876761 2017-05-04 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B2,B5,B6,B9,C1,C2,D2,D7,E5,E6,F4,I1,I3) * 71.98365.3...7681..861..73..3746.1981.83.72466..8.1375871....63.6.73..81..3618.27 * PAIR C1: 2,4 COL C C6: 2,4,9 # reduction candidate for 2,4 C6: 2,4 => SOLVED * 712983654345276819986145732537462198198357246624891375871529463269734581453618927 C6: 9 => CTR * 71498365232.5768145861..7392374651981583972466498.1375871....63.6.73..81..3618.27 * PAIR B2: 2,4 ROW 2 I2: 2,4,9 # reduction candidate for 2,4 I2: 2,4 => CTR * 71.98365.3.957681.5861..73923746.1981.83.72466..8.1375871....63.6.73..81..3618.27 I2: 9 => SOLVED * 712983654345276819986145732537462198198357246624891375871529463269734581453618927 * PAIR C2: 5,9 COL C C8: 5,9,2 # reduction candidate for 5,9 C8: 5,9 => SOLVED * 712983654345276819986145732537462198198357246624891375871529463269734581453618927 C8: 2 => CTR * 71.98365.3.52768199861..732.3746.1981.83.724662.8.1375871....63.6.73..81..3618.27 * PAIR A3: 5,9 COL A A8: 5,9,2,4 # reduction candidate for 5,9 A8: 5,9 => CTR * 71.98365.3...7681..861..73.237465198158397246649821375871....63.6273..81493618527 A8: 2,4 # 16 pairs A9: 5,9,4 # reduction candidate for 5,9 A9: 5,9 => CTR * 714983652325.7681..861..73..3746.1981.83.72466..8.1375871....6346273..81..3618427 A9: 4 # 16 pairs * PAIR D2: 2,5 BLK 2 E3: 2,5,4 # reduction candidate for 2,5 E3: 2,5 # 18 pairs F3: 2,5,4 # reduction candidate for 2,5 F3: 2,5 # 20 pairs * PAIR I1: 2,4 BLK 3 I2: 2,4,9 # reduction candidate for 2,4 I2: 2,4 => CTR * 71.98365.3.957681.5861..73923746.1981.83.72466..8.1375871....63.6.73..81..3618.27 I2: 9 => SOLVED * 712983654345276819986145732537462198198357246624891375871529463269734581453618927 * PAIR I3: 2,9 BLK 3 I2: 2,9,4 # reduction candidate for 2,9 I2: 2,9 => SOLVED * 712983654345276819986145732537462198198357246624891375871529463269734581453618927 I2: 4 => CTR * 71.98365.3.95768145861..73923746.1981.83.72466..8.1375871....63.6.73..81..3618.27 * PAIR A4: 2,5 COL A A8: 2,5,4,9 # reduction candidate for 2,5 A8: 2,5 => SOLVED * 712983654345276819986145732537462198198357246624891375871529463269734581453618927 A8: 4,9 => CTR * 71.98365.3...7681..861..73.237465198158397246649821375871....63.6273.581593618427 * PAIR B6: 2,4 BLK 4 C6: 2,4,9 # reduction candidate for 2,4 C6: 2,4 => SOLVED * 712983654345276819986145732537462198198357246624891375871529463269734581453618927 C6: 9 => CTR * 71498365232.5768145861..7392374651981583972466498.1375871....63.6.73..81..3618.27 * PAIR F4: 2,5 COL F F3: 2,5,4 # reduction candidate for 2,5 F3: 2,5 # 20 pairs F7: 2,5,4,9 # reduction candidate for 2,5 F7: 2,5 # 20 pairs * PAIR E6: 2,9 ROW 6 C6: 2,9,4 # reduction candidate for 2,9 C6: 2,9 => CTR * 71498365232.5768145861..7392374651981583972466498.1375871....63.6.73..81..3618.27 C6: 4 => SOLVED * 712983654345276819986145732537462198198357246624891375871529463269734581453618927 * PAIR B9: 5,9 BLK 7 A8: 5,9,2,4 # reduction candidate for 5,9 A8: 5,9 => CTR * 71.98365.3...7681..861..73.237465198158397246649821375871....63.6273..81493618527 A8: 2,4 # 16 pairs C8: 5,9,2 # reduction candidate for 5,9 C8: 5,9 => SOLVED * 712983654345276819986145732537462198198357246624891375871529463269734581453618927 C8: 2 => CTR * 71.98365.3.52768199861..732.3746.1981.83.724662.8.1375871....63.6.73..81..3618.27 A9: 5,9,4 # reduction candidate for 5,9 A9: 5,9 => CTR * 714983652325.7681..861..73..3746.1981.83.72466..8.1375871....6346273..81..3618427 A9: 4 # 16 pairs * PAIR B9: 5,9 ROW 9 G9: 5,9,4 # reduction candidate for 5,9 G9: 4 => CTR * 714983652325.7681..861..73..3746.1981.83.72466..8.1375871....6346273..81..3618427 G9: 5,9 # 16 pairs * PAIR D7: 2,5 BLK 8 E7: 2,5,4 # reduction candidate for 2,5 E7: 2,5 # 20 pairs F7: 2,5,4,9 # reduction candidate for 2,5 F7: 2,5 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-315-base-pr-000.dot * REASONING * PRF # C6: 2,4 => SOL * DIS # C6: 9 => CTR => C6: 2,4 * DIS # I2: 2,4 => CTR => I2: 9 * PRF # I2: 9 => SOL * PRF # C8: 5,9 => SOL * DIS # C8: 2 => CTR => C8: 5,9 * DIS # A8: 5,9 => CTR => A8: 2,4 * DIS # A9: 5,9 => CTR => A9: 4 * DIS # I2: 2,4 => CTR => I2: 9 * PRF # I2: 9 => SOL * PRF # I2: 2,9 => SOL * DIS # I2: 4 => CTR => I2: 2,9 * PRF # A8: 2,5 => SOL * DIS # A8: 4,9 => CTR => A8: 2,5 * PRF # C6: 2,4 => SOL * DIS # C6: 9 => CTR => C6: 2,4 * DIS # C6: 2,9 => CTR => C6: 4 * PRF # C6: 4 => SOL * DIS # A8: 5,9 => CTR => A8: 2,4 * PRF # C8: 5,9 => SOL * DIS # C8: 2 => CTR => C8: 5,9 * DIS # A9: 5,9 => CTR => A9: 4 * DIS # G9: 4 => CTR => G9: 5,9 * CNT 23 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B2,B5,B6,B9,C1,C2,D2,D7,E5,E6,F4,I1,I3) * 71.98365.3...7681..861..73..3746.1981.83.72466..8.1375871....63.6.73..81..3618.27 * PAIR C1: 2,4 COL C C6: 2,4,9 # reduction candidate for 2,4 C6: 2,4 => SOLVED * 712983654345276819986145732537462198198357246624891375871529463269734581453618927 * DURATION: 0:00:02.332948 START: 13:47:41.158792 END: 13:47:43.491740 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-315-base-pr-001.dot * REASONING * PRF # C6: 2,4 => SOL * STA C6: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 315 solution: 712983654345276819986145732537462198198357246624891375871529463269734581453618927 info: 2893 FNBTWXY S8.f 46549 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 712983654345276819986145732537462198198357246624891375871529463269734581453618927 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:
* PRF # C6: 2,4 => SOL * DIS # C6: 9 => CTR => C6: 2,4 * DIS # I2: 2,4 => CTR => I2: 9 * PRF # I2: 9 => SOL * PRF # C8: 5,9 => SOL * DIS # C8: 2 => CTR => C8: 5,9 * DIS # A8: 5,9 => CTR => A8: 2,4 * INC # A8: 2,4 => UNS * DIS # A9: 5,9 => CTR => A9: 4 * INC # A9: 4 => UNS * INC # E3: 2,5 => UNS * INC # F3: 2,5 => UNS * DIS # I2: 2,4 => CTR => I2: 9 * PRF # I2: 9 => SOL * PRF # I2: 2,9 => SOL * DIS # I2: 4 => CTR => I2: 2,9 * PRF # A8: 2,5 => SOL * DIS # A8: 4,9 => CTR => A8: 2,5 * PRF # C6: 2,4 => SOL * DIS # C6: 9 => CTR => C6: 2,4 * INC # F3: 2,5 => UNS * INC # F7: 2,5 => UNS * DIS # C6: 2,9 => CTR => C6: 4 * PRF # C6: 4 => SOL * DIS # A8: 5,9 => CTR => A8: 2,4 * INC # A8: 2,4 => UNS * PRF # C8: 5,9 => SOL * DIS # C8: 2 => CTR => C8: 5,9 * DIS # A9: 5,9 => CTR => A9: 4 * INC # A9: 4 => UNS * INC # G9: 5,9 => UNS * DIS # G9: 4 => CTR => G9: 5,9 * INC # E7: 2,5 => UNS * INC # F7: 2,5 => UNS * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C6: 2,4 => SOL * STA C6: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED