Analysis of xx-top500-046-base.sdk
Contents
Original Sudoku
level: medium
position: .4..35...6.....1...........1..2.......8.....4.......3..35....7....64.2.....1..... initial
Autosolve
position: .41.35.266..4..1.33.2...4..1.32.456.5283...14.645...32435...671.1.6432..2.615734. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 8,9 => CTR => B2: 5,7 * DIS # B3: 8,9 => CTR => B3: 5 * PRF # D1: 8,9 => SOL * PRF # A8: 8,9 => SOL * DIS # A8: 7 => CTR => A8: 8,9 * PRF # B2: 7,9 => SOL * DIS # B2: 5,8 => CTR => B2: 7,9 * DIS # E4: 7,9 => CTR => E4: 8 * PRF # B2: 7,9 => SOL * DIS # B2: 5,8 => CTR => B2: 7,9 * DIS # E6: 7,9 => CTR => E6: 1,8 * DIS # G6: 7,9 => CTR => G6: 8 * PRF # A8: 7,9 => SOL * DIS # A8: 8 => CTR => A8: 7,9 * DIS # G6: 7,9 => CTR => G6: 8 * DIS # G1: 8 => CTR => G1: 7,9 * PRF # A8: 7,9 => SOL * DIS # A8: 8 => CTR => A8: 7,9 * PRF # A8: 8,9 => SOL * DIS # A8: 7 => CTR => A8: 8,9 * DIS # B2: 8,9 => CTR => B2: 5,7 * DIS # B3: 8,9 => CTR => B3: 5 * PRF # D1: 8,9 => SOL * DIS # I8: 8,9 => CTR => I8: 5 * PRF # I3: 8,9 => SOL * CNT 25 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 8,9 => CTR => B2: 5,7 * DIS B2: 5,7 # B3: 8,9 => CTR => B3: 5 * PRF B2: 5,7 + B3: 5 => SOL * STA B2: 5,7 + B3: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .4..35...6.....1...........1..2.......8.....4.......3..35....7....64.2.....1..... | initial |
| .41.35.266..4..1.33.2...4..1.32.456.5283...14.645...32435...671.1.6432..2.615734. | autosolve |
| 841935726679428153352761498193284567528376914764519832435892671917643285286157349 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A1: 8,9 C2: 7,9 E3: 1,6 F3: 1,6 B4: 7,9 A6: 7,9 F5: 6,9 G5: 7,9 C8: 7,9 B9: 8,9 D7: 8,9 I9: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E3,F3: 1.. / E3 = 1 => 19 pairs (_) / F3 = 1 => 11 pairs (_) E6,F6: 1.. / E6 = 1 => 11 pairs (_) / F6 = 1 => 19 pairs (_) E3,E6: 1.. / E3 = 1 => 19 pairs (_) / E6 = 1 => 11 pairs (_) F3,F6: 1.. / F3 = 1 => 11 pairs (_) / F6 = 1 => 19 pairs (_) E2,F2: 2.. / E2 = 2 => 14 pairs (_) / F2 = 2 => 14 pairs (_) E7,F7: 2.. / E7 = 2 => 14 pairs (_) / F7 = 2 => 14 pairs (_) E2,E7: 2.. / E2 = 2 => 14 pairs (_) / E7 = 2 => 14 pairs (_) F2,F7: 2.. / F2 = 2 => 14 pairs (_) / F7 = 2 => 14 pairs (_) B2,B3: 5.. / B2 = 5 => 0 pairs (X) / B3 = 5 => 14 pairs (_) H8,I8: 5.. / H8 = 5 => 0 pairs (X) / I8 = 5 => 13 pairs (_) B2,H2: 5.. / B2 = 5 => 0 pairs (X) / H2 = 5 => 14 pairs (_) I3,I8: 5.. / I3 = 5 => 0 pairs (X) / I8 = 5 => 13 pairs (_) E3,F3: 6.. / E3 = 6 => 11 pairs (_) / F3 = 6 => 19 pairs (_) E5,F5: 6.. / E5 = 6 => 19 pairs (_) / F5 = 6 => 11 pairs (_) E3,E5: 6.. / E3 = 6 => 11 pairs (_) / E5 = 6 => 19 pairs (_) F3,F5: 6.. / F3 = 6 => 19 pairs (_) / F5 = 6 => 11 pairs (_) B2,C2: 7.. / B2 = 7 => 0 pairs (*) / C2 = 7 => 0 pairs (X) D1,D3: 7.. / D1 = 7 => 16 pairs (_) / D3 = 7 => 0 pairs (*) G1,I3: 7.. / G1 = 7 => 0 pairs (*) / I3 = 7 => 0 pairs (X) B4,A6: 7.. / B4 = 7 => 0 pairs (X) / A6 = 7 => 0 pairs (_) A8,C8: 7.. / A8 = 7 => 0 pairs (X) / C8 = 7 => 0 pairs (_) D1,G1: 7.. / D1 = 7 => 16 pairs (_) / G1 = 7 => 0 pairs (*) D3,I3: 7.. / D3 = 7 => 0 pairs (*) / I3 = 7 => 0 pairs (X) E5,G5: 7.. / E5 = 7 => 13 pairs (_) / G5 = 7 => 19 pairs (_) A6,A8: 7.. / A6 = 7 => 0 pairs (*) / A8 = 7 => 0 pairs (X) B2,B4: 7.. / B2 = 7 => 0 pairs (*) / B4 = 7 => 0 pairs (X) C2,C8: 7.. / C2 = 7 => 0 pairs (X) / C8 = 7 => 0 pairs (_) I3,I4: 7.. / I3 = 7 => 16 pairs (_) / I4 = 7 => 0 pairs (*) I4,G6: 8.. / I4 = 8 => 0 pairs (X) / G6 = 8 => 21 pairs (_) A8,B9: 8.. / A8 = 8 => 0 pairs (X) / B9 = 8 => 0 pairs (_) E4,I4: 8.. / E4 = 8 => 21 pairs (_) / I4 = 8 => 0 pairs (X) B9,I9: 8.. / B9 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) A1,A8: 8.. / A1 = 8 => 0 pairs (*) / A8 = 8 => 0 pairs (X) G1,G6: 8.. / G1 = 8 => 0 pairs (X) / G6 = 8 => 21 pairs (_) B4,A6: 9.. / B4 = 9 => 0 pairs (*) / A6 = 9 => 0 pairs (X) B9,I9: 9.. / B9 = 9 => 0 pairs (X) / I9 = 9 => 0 pairs (_) C2,C8: 9.. / C2 = 9 => 0 pairs (*) / C8 = 9 => 0 pairs (X) * DURATION: 0:01:02.763167 START: 04:14:03.370072 END: 04:15:06.133239 2017-05-04 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B4,B9,C2,C8,D7,E3,F3,F5,G5,I9) * .41.35.266..4..1.33.2...4..1.32.456.5283...14.645...32435...671.1.6432..2.615734. * PAIR A1: 8,9 BLK 1 B2: 8,9,5,7 # reduction candidate for 8,9 B2: 8,9 => CTR * 841.35.266974..153352...49.1732.456.5283...149645...32435...671719643285286157349 B2: 5,7 # 13 pairs B3: 8,9,5 # reduction candidate for 8,9 B3: 8,9 => CTR * 841.35.266574..1.3392...4.71732945685283.69149645...32435...6717196432..286157349 B3: 5 # 14 pairs * PAIR A1: 8,9 ROW 1 D1: 8,9,7 # reduction candidate for 8,9 D1: 8,9 => SOLVED * 841935726679428153352761498193284567528376914764519832435892671917643285286157349 D1: 7 # 16 pairs G1: 8,9,7 # reduction candidate for 8,9 G1: 8,9 # 16 pairs * PAIR A1: 8,9 COL A A8: 8,9,7 # reduction candidate for 8,9 A8: 8,9 => SOLVED * 841935726679428153352761498193284567528376914764519832435892671917643285286157349 A8: 7 => CTR * 841.35.266..4..1.33.2...4..1.32.456.5283...149645..832435...6717196432..286157349 * PAIR C2: 7,9 BLK 1 B2: 7,9,5,8 # reduction candidate for 7,9 B2: 7,9 => SOLVED * 841935726679428153352761498193284567528376914764519832435892671917643285286157349 B2: 5,8 => CTR * 841.35.266574..1.3392...4.71732945685283.69149645...32435...6717196432..286157349 * PAIR B4: 7,9 ROW 4 E4: 7,9,8 # reduction candidate for 7,9 E4: 7,9 => CTR * 841.35.266..4..1.33.28..4.71.32.45685283...14.645...324359..671.1.643285286157349 E4: 8 # 21 pairs I4: 7,9,8 # reduction candidate for 7,9 I4: 7,9 # 21 pairs * PAIR B4: 7,9 COL B B2: 7,9,5,8 # reduction candidate for 7,9 B2: 7,9 => SOLVED * 841935726679428153352761498193284567528376914764519832435892671917643285286157349 B2: 5,8 => CTR * 841.35.266574..1.3392...4.71732945685283.69149645...32435...6717196432..286157349 * PAIR A6: 7,9 ROW 6 E6: 7,9,1,8 # reduction candidate for 7,9 E6: 7,9 => CTR * .41.35.266..4..1.33.2.164..1.32.456.528369714.64571832435...6717196432..286157349 E6: 1,8 # 13 pairs G6: 7,9,8 # reduction candidate for 7,9 G6: 7,9 => CTR * .41.358266..4..1.33.2...4.71.32.45685283...14.645...32435...6718176432.529615734. G6: 8 # 21 pairs * PAIR A6: 7,9 COL A A8: 7,9,8 # reduction candidate for 7,9 A8: 7,9 => SOLVED * 841935726679428153352761498193284567528376914764519832435892671917643285286157349 A8: 8 => CTR * .41.35.266..4..1.33.2...4..1.32.456.5283...147645...32435...6718176432..29615734. * PAIR F5: 6,9 BLK 5 E5: 6,9,7 # reduction candidate for 6,9 E5: 6,9 # 19 pairs E5: 7 # 13 pairs * PAIR G5: 7,9 BLK 6 I4: 7,9,8 # reduction candidate for 7,9 I4: 7,9 # 21 pairs G6: 7,9,8 # reduction candidate for 7,9 G6: 7,9 => CTR * .41.358266..4..1.33.2...4.71.32.45685283...14.645...32435...6718176432.529615734. G6: 8 # 21 pairs * PAIR G5: 7,9 ROW 5 E5: 7,9,6 # reduction candidate for 7,9 E5: 6 # 19 pairs E5: 7,9 # 11 pairs * PAIR G5: 7,9 COL G G1: 7,9,8 # reduction candidate for 7,9 G1: 8 => CTR * .417358266..4..1.33.2...4.71.32.45685283...14.645...32435...6718176432.529615734. G1: 7,9 # 21 pairs * PAIR C8: 7,9 BLK 7 A8: 7,9,8 # reduction candidate for 7,9 A8: 7,9 => SOLVED * 841935726679428153352761498193284567528376914764519832435892671917643285286157349 A8: 8 => CTR * .41.35.266..4..1.33.2...4..1.32.456.5283...147645...32435...6718176432..29615734. * PAIR B9: 8,9 BLK 7 A8: 8,9,7 # reduction candidate for 8,9 A8: 8,9 => SOLVED * 841935726679428153352761498193284567528376914764519832435892671917643285286157349 A8: 7 => CTR * 841.35.266..4..1.33.2...4..1.32.456.5283...149645..832435...6717196432..286157349 * PAIR B9: 8,9 COL B B2: 8,9,5,7 # reduction candidate for 8,9 B2: 8,9 => CTR * 841.35.266974..153352...49.1732.456.5283...149645...32435...671719643285286157349 B2: 5,7 # 13 pairs B3: 8,9,5 # reduction candidate for 8,9 B3: 8,9 => CTR * 841.35.266574..1.3392...4.71732945685283.69149645...32435...6717196432..286157349 B3: 5 # 14 pairs * PAIR D7: 8,9 BLK 8 E7: 8,9,2 # reduction candidate for 8,9 E7: 8,9 # 14 pairs F7: 8,9,2 # reduction candidate for 8,9 F7: 8,9 # 14 pairs * PAIR D7: 8,9 COL D D1: 8,9,7 # reduction candidate for 8,9 D1: 8,9 => SOLVED * 841935726679428153352761498193284567528376914764519832435892671917643285286157349 D1: 7 # 16 pairs D3: 8,9,7 # reduction candidate for 8,9 D3: 8,9 # 16 pairs * PAIR I9: 8,9 BLK 9 H8: 8,9,5 # reduction candidate for 8,9 H8: 8,9 # 13 pairs I8: 8,9,5 # reduction candidate for 8,9 I8: 8,9 => CTR * .41.35.266..4..1.33.2...4.51.32.45675283769147645..832435...671.1764325.2.615734. I8: 5 # 13 pairs * PAIR I9: 8,9 COL I I3: 8,9,5,7 # reduction candidate for 8,9 I3: 8,9 => SOLVED * 841935726679428153352761498193284567528376914764519832435892671917643285286157349 I3: 5,7 # 13 pairs I4: 8,9,7 # reduction candidate for 8,9 I4: 8,9 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-046-base-pr-000.dot * REASONING * DIS # B2: 8,9 => CTR => B2: 5,7 * DIS # B3: 8,9 => CTR => B3: 5 * PRF # D1: 8,9 => SOL * PRF # A8: 8,9 => SOL * DIS # A8: 7 => CTR => A8: 8,9 * PRF # B2: 7,9 => SOL * DIS # B2: 5,8 => CTR => B2: 7,9 * DIS # E4: 7,9 => CTR => E4: 8 * PRF # B2: 7,9 => SOL * DIS # B2: 5,8 => CTR => B2: 7,9 * DIS # E6: 7,9 => CTR => E6: 1,8 * DIS # G6: 7,9 => CTR => G6: 8 * PRF # A8: 7,9 => SOL * DIS # A8: 8 => CTR => A8: 7,9 * DIS # G6: 7,9 => CTR => G6: 8 * DIS # G1: 8 => CTR => G1: 7,9 * PRF # A8: 7,9 => SOL * DIS # A8: 8 => CTR => A8: 7,9 * PRF # A8: 8,9 => SOL * DIS # A8: 7 => CTR => A8: 8,9 * DIS # B2: 8,9 => CTR => B2: 5,7 * DIS # B3: 8,9 => CTR => B3: 5 * PRF # D1: 8,9 => SOL * DIS # I8: 8,9 => CTR => I8: 5 * PRF # I3: 8,9 => SOL * CNT 25 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B4,B9,C2,C8,D7,E3,F3,F5,G5,I9) * .41.35.266..4..1.33.2...4..1.32.456.5283...14.645...32435...671.1.6432..2.615734. * PAIR A1: 8,9 BLK 1 B2: 8,9,5,7 # reduction candidate for 8,9 B2: 8,9 => CTR * 841.35.266974..153352...49.1732.456.5283...149645...32435...671719643285286157349 B3: 8,9,5 # reduction candidate for 8,9 B3: 8,9 => CTR * 841.35.266574..1.3392...4.71732945685283.69149645...32435...6717196432..286157349 B3: 5 => SOLVED * 841935726679428153352761498193284567528376914764519832435892671917643285286157349 * DURATION: 0:00:02.818963 START: 04:15:54.962086 END: 04:15:57.781049 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-046-base-pr-001.dot * REASONING * DIS # B2: 8,9 => CTR => B2: 5,7 * DIS B2: 5,7 # B3: 8,9 => CTR => B3: 5 * PRF B2: 5,7 + B3: 5 => SOL * STA B2: 5,7 + B3: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 046 solution: 841935726679428153352761498193284567528376914764519832435892671917643285286157349 info: 1378 FNBTHWXY S8.f 18884 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 841935726679428153352761498193284567528376914764519832435892671917643285286157349 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 # B2: 8,9 => CTR => B2: 5,7 * INC # B2: 5,7 => UNS * DIS # B3: 8,9 => CTR => B3: 5 * INC # B3: 5 => UNS * PRF # D1: 8,9 => SOL * INC # D1: 7 => UNS * INC # G1: 8,9 => UNS * PRF # A8: 8,9 => SOL * DIS # A8: 7 => CTR => A8: 8,9 * PRF # B2: 7,9 => SOL * DIS # B2: 5,8 => CTR => B2: 7,9 * DIS # E4: 7,9 => CTR => E4: 8 * INC # E4: 8 => UNS * INC # I4: 7,9 => UNS * PRF # B2: 7,9 => SOL * DIS # B2: 5,8 => CTR => B2: 7,9 * DIS # E6: 7,9 => CTR => E6: 1,8 * INC # E6: 1,8 => UNS * DIS # G6: 7,9 => CTR => G6: 8 * INC # G6: 8 => UNS * PRF # A8: 7,9 => SOL * DIS # A8: 8 => CTR => A8: 7,9 * INC # E5: 6,9 => UNS * INC # E5: 7 => UNS * INC # I4: 7,9 => UNS * DIS # G6: 7,9 => CTR => G6: 8 * INC # G6: 8 => UNS * INC # E5: 7,9 => UNS * INC # E5: 6 => UNS * INC # G1: 7,9 => UNS * DIS # G1: 8 => CTR => G1: 7,9 * PRF # A8: 7,9 => SOL * DIS # A8: 8 => CTR => A8: 7,9 * PRF # A8: 8,9 => SOL * DIS # A8: 7 => CTR => A8: 8,9 * DIS # B2: 8,9 => CTR => B2: 5,7 * INC # B2: 5,7 => UNS * DIS # B3: 8,9 => CTR => B3: 5 * INC # B3: 5 => UNS * INC # E7: 8,9 => UNS * INC # F7: 8,9 => UNS * PRF # D1: 8,9 => SOL * INC # D1: 7 => UNS * INC # D3: 8,9 => UNS * INC # H8: 8,9 => UNS * DIS # I8: 8,9 => CTR => I8: 5 * INC # I8: 5 => UNS * PRF # I3: 8,9 => SOL * INC # I3: 5,7 => UNS * INC # I4: 8,9 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B2: 8,9 => CTR => B2: 5,7 * DIS B2: 5,7 # B3: 8,9 => CTR => B3: 5 * PRF B2: 5,7 + B3: 5 => SOL * STA B2: 5,7 + B3: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED