Analysis of xx-top500-235-base.sdk
Contents
Original Sudoku
level: medium
position: 6.....1.....5.3......7......2.1.........2.6....7.....334..8..........27........5. initial
Autosolve
position: 67...21352..5.37.653.76...2.231765.9.5.32.617167.5..23345287961.16.3527.7.26..35. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 8,9 => CTR => C2: 1,4 * DIS # H2: 4 => CTR => H2: 8,9 * DIS # D1: 4,9 => CTR => D1: 8 * DIS # C1: 8 => CTR => C1: 4,9 * DIS # H3: 4,8 => CTR => H3: 9 * DIS # A5: 9 => CTR => A5: 4,8 * DIS # A5: 8,9 => CTR => A5: 4 * PRF # A5: 4 => SOL * DIS # C2: 8,9 => CTR => C2: 1,4 * PRF # F6: 4,8 => SOL * DIS # A5: 9 => CTR => A5: 4,8 * DIS # H3: 4,8 => CTR => H3: 9 * PRF # F6: 4,8 => SOL * DIS # A5: 8,9 => CTR => A5: 4 * PRF # A5: 4 => SOL * DIS # D1: 4,9 => CTR => D1: 8 * CNT 16 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 8,9 => CTR => C2: 1,4 * DIS C2: 1,4 # H2: 4 => CTR => H2: 8,9 * DIS C2: 1,4 + H2: 8,9 # D1: 4,9 => CTR => D1: 8 * DIS C2: 1,4 + H2: 8,9 + D1: 8 # H3: 4,8 => CTR => H3: 9 * PRF C2: 1,4 + H2: 8,9 + D1: 8 + H3: 9 => SOL * STA C2: 1,4 + H2: 8,9 + D1: 8 + H3: 9 * CNT 5 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6.....1.....5.3......7......2.1.........2.6....7.....334..8..........27........5. | initial |
| 67...21352..5.37.653.76...2.231765.9.5.32.617167.5..23345287961.16.3527.7.26..35. | autosolve |
| 674892135291543786538761492823176549459328617167954823345287961916435278782619354 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) B2: 8,9 E1: 4,9 G3: 4,8 A4: 4,8 C5: 8,9 F5: 4,8 H4: 4,8 G6: 4,8 A8: 8,9 B9: 8,9 D8: 4,9 I8: 4,8 I9: 4,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 1.. / C2 = 1 => 17 pairs (_) / C3 = 1 => 14 pairs (_) E2,F3: 1.. / E2 = 1 => 14 pairs (_) / F3 = 1 => 17 pairs (_) E9,F9: 1.. / E9 = 1 => 17 pairs (_) / F9 = 1 => 14 pairs (_) C2,E2: 1.. / C2 = 1 => 17 pairs (_) / E2 = 1 => 14 pairs (_) C3,F3: 1.. / C3 = 1 => 14 pairs (_) / F3 = 1 => 17 pairs (_) E2,E9: 1.. / E2 = 1 => 14 pairs (_) / E9 = 1 => 17 pairs (_) F3,F9: 1.. / F3 = 1 => 17 pairs (_) / F9 = 1 => 14 pairs (_) A4,A5: 4.. / A4 = 4 => 0 pairs (X) / A5 = 4 => 0 pairs (_) H4,G6: 4.. / H4 = 4 => 0 pairs (*) / G6 = 4 => 0 pairs (X) I8,I9: 4.. / I8 = 4 => 0 pairs (X) / I9 = 4 => 15 pairs (_) A4,H4: 4.. / A4 = 4 => 0 pairs (X) / H4 = 4 => 0 pairs (_) A5,F5: 4.. / A5 = 4 => 0 pairs (*) / F5 = 4 => 0 pairs (X) D8,I8: 4.. / D8 = 4 => 15 pairs (_) / I8 = 4 => 0 pairs (X) G3,G6: 4.. / G3 = 4 => 0 pairs (*) / G6 = 4 => 0 pairs (X) D1,F3: 8.. / D1 = 8 => 15 pairs (_) / F3 = 8 => 0 pairs (X) H4,G6: 8.. / H4 = 8 => 0 pairs (X) / G6 = 8 => 0 pairs (_) A8,B9: 8.. / A8 = 8 => 0 pairs (X) / B9 = 8 => 15 pairs (_) I8,I9: 8.. / I8 = 8 => 15 pairs (_) / I9 = 8 => 0 pairs (X) C1,D1: 8.. / C1 = 8 => 0 pairs (X) / D1 = 8 => 15 pairs (_) A4,H4: 8.. / A4 = 8 => 0 pairs (*) / H4 = 8 => 0 pairs (X) A8,I8: 8.. / A8 = 8 => 0 pairs (X) / I8 = 8 => 15 pairs (_) B9,I9: 8.. / B9 = 8 => 15 pairs (_) / I9 = 8 => 0 pairs (X) B2,B9: 8.. / B2 = 8 => 0 pairs (X) / B9 = 8 => 15 pairs (_) D1,D6: 8.. / D1 = 8 => 15 pairs (_) / D6 = 8 => 0 pairs (X) G3,G6: 8.. / G3 = 8 => 0 pairs (X) / G6 = 8 => 0 pairs (_) H2,H3: 9.. / H2 = 9 => 0 pairs (X) / H3 = 9 => 14 pairs (_) A5,C5: 9.. / A5 = 9 => 0 pairs (X) / C5 = 9 => 15 pairs (_) D6,F6: 9.. / D6 = 9 => 0 pairs (*) / F6 = 9 => 0 pairs (X) A8,B9: 9.. / A8 = 9 => 15 pairs (_) / B9 = 9 => 0 pairs (X) A8,D8: 9.. / A8 = 9 => 15 pairs (_) / D8 = 9 => 0 pairs (X) A5,A8: 9.. / A5 = 9 => 0 pairs (X) / A8 = 9 => 15 pairs (_) B2,B9: 9.. / B2 = 9 => 15 pairs (_) / B9 = 9 => 0 pairs (X) * DURATION: 0:00:55.617899 START: 10:51:29.150857 END: 10:52:24.768756 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B2,B9,C5,D8,E1,F5,G3,G6,H4,I8,I9) * 67...21352..5.37.653.76...2.231765.9.5.32.617167.5..23345287961.16.3527.7.26..35. * PAIR B2: 8,9 BLK 1 C1: 8,9,4 # reduction candidate for 8,9 C1: 8,9 # 17 pairs C2: 8,9,1,4 # reduction candidate for 8,9 C2: 8,9 => CTR * 67...21352..513746531764892423176589.5.32861716745..23345287961.16.3527.7.26..35. C2: 1,4 # 14 pairs C3: 8,9,1,4 # reduction candidate for 8,9 C3: 8,9 # 16 pairs * PAIR B2: 8,9 ROW 2 H2: 8,9,4 # reduction candidate for 8,9 H2: 4 => CTR * 67.84213529.5.374653.76.892423176589.5.324617167.58423345287961.16.3527.7.26.935. H2: 8,9 # 16 pairs * PAIR E1: 4,9 BLK 2 D1: 4,9,8 # reduction candidate for 4,9 D1: 4,9 => CTR * 678..213529.5.378653.76849282317654945.32.617167.5..23345287961.16.3527.7.26..35. D1: 8 # 15 pairs E2: 4,9,1 # reduction candidate for 4,9 E2: 4,9 # 17 pairs F3: 4,9,1,8 # reduction candidate for 4,9 F3: 4,9 # 18 pairs * PAIR E1: 4,9 ROW 1 C1: 4,9,8 # reduction candidate for 4,9 C1: 8 => CTR * 678..213529.5.378653.76849282317654945.32.617167.5..23345287961.16.3527.7.26..35. C1: 4,9 # 15 pairs * PAIR E1: 4,9 COL E E9: 4,9,1 # reduction candidate for 4,9 E9: 1 # 17 pairs E9: 4,9 # 14 pairs * PAIR G3: 4,8 BLK 3 H2: 4,8,9 # reduction candidate for 4,8 H2: 4,8 # 14 pairs H3: 4,8,9 # reduction candidate for 4,8 H3: 4,8 => CTR * 67..9213528.5.3796539761..2.231765.9958324617167.5..23345287961.16.3527.7926..358 H3: 9 # 14 pairs * PAIR G3: 4,8 ROW 3 C3: 4,8,1,9 # reduction candidate for 4,8 C3: 4,8 # 19 pairs F3: 4,8,1,9 # reduction candidate for 4,8 F3: 4,8 # 18 pairs * PAIR A4: 4,8 BLK 4 A5: 4,8,9 # reduction candidate for 4,8 A5: 9 => CTR * 67...21352..5.37.653.76...2423176589958324617167.5.423345287961816935274792641358 A5: 4,8 # 15 pairs * PAIR C5: 8,9 BLK 4 A5: 8,9,4 # reduction candidate for 8,9 A5: 8,9 => CTR * 67.8.213529851374653.76.8.2423176589.5.3246171679584233452879619164352787826..354 A5: 4 => SOLVED * 674892135291543786538761492823176549459328617167954823345287961916435278782619354 * PAIR C5: 8,9 COL C C1: 8,9,4 # reduction candidate for 8,9 C1: 8,9 # 17 pairs C2: 8,9,1,4 # reduction candidate for 8,9 C2: 8,9 => CTR * 67...21352..513746531764892423176589.5.32861716745..23345287961.16.3527.7.26..35. C2: 1,4 # 14 pairs C3: 8,9,1,4 # reduction candidate for 8,9 C3: 8,9 # 16 pairs * PAIR F5: 4,8 BLK 5 D6: 4,8,9 # reduction candidate for 4,8 D6: 4,8 # 15 pairs F6: 4,8,9 # reduction candidate for 4,8 F6: 4,8 => SOLVED * 674892135291543786538761492823176549459328617167954823345287961916435278782619354 F6: 9 # 15 pairs * PAIR F5: 4,8 ROW 5 A5: 4,8,9 # reduction candidate for 4,8 A5: 9 => CTR * 67...21352..5.37.653.76...2423176589958324617167.5.423345287961816935274792641358 A5: 4,8 # 15 pairs * PAIR F5: 4,8 COL F F3: 4,8,1,9 # reduction candidate for 4,8 F3: 4,8 # 18 pairs F3: 1,9 # 17 pairs * PAIR H4: 4,8 COL H H2: 4,8,9 # reduction candidate for 4,8 H2: 4,8 # 14 pairs H3: 4,8,9 # reduction candidate for 4,8 H3: 4,8 => CTR * 67..9213528.5.3796539761..2.231765.9958324617167.5..23345287961.16.3527.7926..358 H3: 9 # 14 pairs * PAIR G6: 4,8 ROW 6 D6: 4,8,9 # reduction candidate for 4,8 D6: 4,8 # 15 pairs F6: 4,8,9 # reduction candidate for 4,8 F6: 4,8 => SOLVED * 674892135291543786538761492823176549459328617167954823345287961916435278782619354 F6: 9 # 15 pairs * PAIR A8: 8,9 COL A A5: 8,9,4 # reduction candidate for 8,9 A5: 8,9 => CTR * 67.8.213529851374653.76.8.2423176589.5.3246171679584233452879619164352787826..354 A5: 4 => SOLVED * 674892135291543786538761492823176549459328617167954823345287961916435278782619354 * PAIR D8: 4,9 BLK 8 E9: 4,9,1 # reduction candidate for 4,9 E9: 4,9 # 14 pairs F9: 4,9,1 # reduction candidate for 4,9 F9: 4,9 # 17 pairs * PAIR D8: 4,9 COL D D1: 4,9,8 # reduction candidate for 4,9 D1: 4,9 => CTR * 678..213529.5.378653.76849282317654945.32.617167.5..23345287961.16.3527.7.26..35. D1: 8 # 15 pairs D6: 4,9,8 # reduction candidate for 4,9 D6: 4,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-235-base-pr-000.dot * REASONING * DIS # C2: 8,9 => CTR => C2: 1,4 * DIS # H2: 4 => CTR => H2: 8,9 * DIS # D1: 4,9 => CTR => D1: 8 * DIS # C1: 8 => CTR => C1: 4,9 * DIS # H3: 4,8 => CTR => H3: 9 * DIS # A5: 9 => CTR => A5: 4,8 * DIS # A5: 8,9 => CTR => A5: 4 * PRF # A5: 4 => SOL * DIS # C2: 8,9 => CTR => C2: 1,4 * PRF # F6: 4,8 => SOL * DIS # A5: 9 => CTR => A5: 4,8 * DIS # H3: 4,8 => CTR => H3: 9 * PRF # F6: 4,8 => SOL * DIS # A5: 8,9 => CTR => A5: 4 * PRF # A5: 4 => SOL * DIS # D1: 4,9 => CTR => D1: 8 * CNT 16 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B2,B9,C5,D8,E1,F5,G3,G6,H4,I8,I9) * 67...21352..5.37.653.76...2.231765.9.5.32.617167.5..23345287961.16.3527.7.26..35. * PAIR B2: 8,9 BLK 1 C1: 8,9,4 # reduction candidate for 8,9 C1: 8,9 # 17 pairs C2: 8,9,1,4 # reduction candidate for 8,9 C2: 8,9 => CTR * 67...21352..513746531764892423176589.5.32861716745..23345287961.16.3527.7.26..35. C3: 8,9,1,4 # reduction candidate for 8,9 C3: 8,9 # 16 pairs * PAIR B2: 8,9 ROW 2 H2: 8,9,4 # reduction candidate for 8,9 H2: 4 => CTR * 67...213528.59374653.761892423176589.58324617167.5842334528796181693527.7.26..35. * PAIR RESTART * PAIR B2: 8,9 BLK 1 C1: 8,9,4 # reduction candidate for 8,9 C1: 8,9 # 18 pairs C3: 8,9,1 # reduction candidate for 8,9 C3: 8,9 # 16 pairs * PAIR E1: 4,9 BLK 2 D1: 4,9,8 # reduction candidate for 4,9 D1: 4,9 => CTR * 678..213529451378653176849282317654945.32.617167.5..23345287961.16.3527.7.26..35. * PAIR G3: 4,8 BLK 3 H3: 4,8,9 # reduction candidate for 4,8 H3: 4,8 => CTR * 67.8.21352..5.379653.76...2.231765.9.5.32.617167.5..23345287961.16.3527.792614358 H3: 9 => SOLVED * 674892135291543786538761492823176549459328617167954823345287961916435278782619354 * DURATION: 0:00:12.613780 START: 10:53:10.711873 END: 10:53:23.325653 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-235-base-pr-001.dot * REASONING * DIS # C2: 8,9 => CTR => C2: 1,4 * DIS C2: 1,4 # H2: 4 => CTR => H2: 8,9 * DIS C2: 1,4 + H2: 8,9 # D1: 4,9 => CTR => D1: 8 * DIS C2: 1,4 + H2: 8,9 + D1: 8 # H3: 4,8 => CTR => H3: 9 * PRF C2: 1,4 + H2: 8,9 + D1: 8 + H3: 9 => SOL * STA C2: 1,4 + H2: 8,9 + D1: 8 + H3: 9 * CNT 5 HDP CHAINS / 9 HYP OPENED
Header Info
Top 500 Minimum 17 235 solution: 674892135291543786538761492823176549459328617167954823345287961916435278782619354 info: 2068 FNBWXY S8.f 34170 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 674892135291543786538761492823176549459328617167954823345287961916435278782619354 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 # C1: 8,9 => UNS * DIS # C2: 8,9 => CTR => C2: 1,4 * INC # C2: 1,4 => UNS * INC # C3: 8,9 => UNS * INC # H2: 8,9 => UNS * DIS # H2: 4 => CTR => H2: 8,9 * DIS # D1: 4,9 => CTR => D1: 8 * INC # D1: 8 => UNS * INC # E2: 4,9 => UNS * INC # F3: 4,9 => UNS * INC # C1: 4,9 => UNS * DIS # C1: 8 => CTR => C1: 4,9 * INC # E9: 4,9 => UNS * INC # E9: 1 => UNS * INC # H2: 4,8 => UNS * DIS # H3: 4,8 => CTR => H3: 9 * INC # H3: 9 => UNS * INC # C3: 4,8 => UNS * INC # F3: 4,8 => UNS * INC # A5: 4,8 => UNS * DIS # A5: 9 => CTR => A5: 4,8 * DIS # A5: 8,9 => CTR => A5: 4 * PRF # A5: 4 => SOL * INC # C1: 8,9 => UNS * DIS # C2: 8,9 => CTR => C2: 1,4 * INC # C2: 1,4 => UNS * INC # C3: 8,9 => UNS * INC # D6: 4,8 => UNS * PRF # F6: 4,8 => SOL * INC # F6: 9 => UNS * INC # A5: 4,8 => UNS * DIS # A5: 9 => CTR => A5: 4,8 * INC # F3: 4,8 => UNS * INC # F3: 1,9 => UNS * INC # H2: 4,8 => UNS * DIS # H3: 4,8 => CTR => H3: 9 * INC # H3: 9 => UNS * INC # D6: 4,8 => UNS * PRF # F6: 4,8 => SOL * INC # F6: 9 => UNS * DIS # A5: 8,9 => CTR => A5: 4 * PRF # A5: 4 => SOL * INC # E9: 4,9 => UNS * INC # F9: 4,9 => UNS * DIS # D1: 4,9 => CTR => D1: 8 * INC # D1: 8 => UNS * INC # D6: 4,9 => UNS * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 8,9 => UNS * DIS # C2: 8,9 => CTR => C2: 1,4 * INC C2: 1,4 # C3: 8,9 => UNS * INC C2: 1,4 # H2: 8,9 => UNS * DIS C2: 1,4 # H2: 4 => CTR => H2: 8,9 * INC C2: 1,4 + H2: 8,9 # C1: 8,9 => UNS * INC C2: 1,4 + H2: 8,9 # C3: 8,9 => UNS * DIS C2: 1,4 + H2: 8,9 # D1: 4,9 => CTR => D1: 8 * DIS C2: 1,4 + H2: 8,9 + D1: 8 # H3: 4,8 => CTR => H3: 9 * PRF C2: 1,4 + H2: 8,9 + D1: 8 + H3: 9 => SOL * STA C2: 1,4 + H2: 8,9 + D1: 8 + H3: 9 * CNT 10 HDP CHAINS / 9 HYP OPENED