Analysis of xx-top500-465-base.sdk
Contents
Original Sudoku
level: medium
position: 1...6..7.7.2......4..8.....3....4....6.....9....2...........4.2.5..9..........6.. initial
Autosolve
position: 1.5.6..7.7.2......4.68.....3....4....6.....9....2...........4.2.5..9..........6.9 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F3: 3,9 => CTR => F3: 1,2,5,7 * PRF # C7: 1,7 => SOL * DIS # B9: 1,7 => CTR => B9: 2,4 * PRF # B4: 1,7 => SOL * DIS # B4: 2 => CTR => B4: 1,7 * DIS # B6: 1,7 => CTR => B6: 4 * PRF # B6: 4 => SOL * DIS # A8: 2,8 => CTR => A8: 6 * PRF # A8: 6 => SOL * DIS # E9: 2,8 => CTR => E9: 1,3,4,5,7 * PRF # E9: 1,3,4,5,7 => SOL * DIS # F9: 2,8 => CTR => F9: 1,3,5,7 * PRF # A5: 2,8 => SOL * DIS # A5: 5 => CTR => A5: 2,8 * CNT 14 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F3: 3,9 => CTR => F3: 1,2,5,7 * PRF F3: 1,2,5,7 # C7: 1,7 => SOL * STA F3: 1,2,5,7 + C7: 1,7 * CNT 2 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1...6..7.7.2......4..8.....3....4....6.....9....2...........4.2.5..9..........6.. | initial |
| 1.5.6..7.7.2......4.68.....3....4....6.....9....2...........4.2.5..9..........6.9 | autosolve |
| 195463278782915346436827915319654827267138594548279163971586432654392781823741659 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) B3: 3,9 D4: 6,9 F6: 6,9 B7: 1,7 A9: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B4,A5: 2.. / B4 = 2 => 0 pairs (X) / A5 = 2 => 0 pairs (_) F1,G1: 2.. / F1 = 2 => 0 pairs (X) / G1 = 2 => 0 pairs (_) A5,G5: 2.. / A5 = 2 => 0 pairs (*) / G5 = 2 => 0 pairs (X) A8,F8: 2.. / A8 = 2 => 0 pairs (X) / F8 = 2 => 0 pairs (_) B4,B9: 2.. / B4 = 2 => 0 pairs (X) / B9 = 2 => 0 pairs (_) E3,E9: 2.. / E3 = 2 => 0 pairs (*) / E9 = 2 => 0 pairs (X) H3,H4: 2.. / H3 = 2 => 0 pairs (X) / H4 = 2 => 0 pairs (_) D1,I1: 4.. / D1 = 4 => 0 pairs (*) / I1 = 4 => 0 pairs (X) C5,I5: 4.. / C5 = 4 => 0 pairs (X) / I5 = 4 => 0 pairs (_) C8,D8: 4.. / C8 = 4 => 0 pairs (*) / D8 = 4 => 0 pairs (X) B6,B9: 4.. / B6 = 4 => 0 pairs (*) / B9 = 4 => 0 pairs (X) E2,E9: 4.. / E2 = 4 => 0 pairs (X) / E9 = 4 => 0 pairs (_) H2,H6: 4.. / H2 = 4 => 0 pairs (*) / H6 = 4 => 0 pairs (X) A5,A6: 5.. / A5 = 5 => 0 pairs (X) / A6 = 5 => 0 pairs (_) H7,H9: 5.. / H7 = 5 => 5 pairs (_) / H9 = 5 => 5 pairs (_) H2,I2: 6.. / H2 = 6 => 0 pairs (X) / I2 = 6 => 5 pairs (_) D4,F6: 6.. / D4 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) A7,A8: 6.. / A7 = 6 => 0 pairs (X) / A8 = 6 => 0 pairs (_) E3,F3: 7.. / E3 = 7 => 0 pairs (X) / F3 = 7 => 5 pairs (_) G8,I8: 7.. / G8 = 7 => 5 pairs (_) / I8 = 7 => 5 pairs (_) B1,B2: 8.. / B1 = 8 => 7 pairs (_) / B2 = 8 => 6 pairs (_) D4,F6: 9.. / D4 = 9 => 4 pairs (_) / F6 = 9 => 0 pairs (*) A7,C7: 9.. / A7 = 9 => 0 pairs (*) / C7 = 9 => 0 pairs (X) C4,D4: 9.. / C4 = 9 => 0 pairs (*) / D4 = 9 => 0 pairs (X) A6,A7: 9.. / A6 = 9 => 0 pairs (X) / A7 = 9 => 0 pairs (_) * DURATION: 0:00:44.210884 START: 18:36:36.809938 END: 18:37:21.020822 2017-05-04 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B3,B7,D4,F6) * 1.5.6..7.7.2......4.68.....3....4....6.....9....2...........4.2.5..9..........6.9 * PAIR B3: 3,9 BLK 1 B1: 3,9,8 # reduction candidate for 3,9 B1: 3,9 # 6 pairs B2: 3,9,8 # reduction candidate for 3,9 B2: 3,9 # 7 pairs * PAIR B3: 3,9 ROW 3 F3: 3,9,1,2,5,7 # reduction candidate for 3,9 F3: 3,9 => CTR * 1.5.62.747.2.4....4.687..2.32...4...564...29.9..2.6.4.6.9...4.225..9....84..2.6.9 F3: 1,2,5,7 # 5 pairs G3: 3,9,1,2,5 # reduction candidate for 3,9 G3: 3,9 # 8 pairs * PAIR B7: 1,7 BLK 7 C7: 1,7,3,8,9 # reduction candidate for 1,7 C7: 1,7 => SOLVED * 195463278782915346436827915319654827267138594548279163971586432654392781823741659 C7: 3,8,9 # 5 pairs B9: 1,7,2,4 # reduction candidate for 1,7 B9: 1,7 => CTR * 1.5.62.7.7.2....464.68...2.32...4....6....294.4.2...........4.225..9....8.....6.9 B9: 2,4 # 6 pairs C9: 1,7,3,4,8 # reduction candidate for 1,7 C9: 1,7 # 7 pairs * PAIR B7: 1,7 ROW 7 D7: 1,7,3,5,6 # reduction candidate for 1,7 D7: 1,7 # 6 pairs E7: 1,7,3,5,8 # reduction candidate for 1,7 E7: 1,7 # 6 pairs F7: 1,7,3,5,6,8 # reduction candidate for 1,7 F7: 1,7 # 6 pairs * PAIR B7: 1,7 COL B B4: 1,7,2 # reduction candidate for 1,7 B4: 1,7 => SOLVED * 195463278782915346436827915319654827267138594548279163971586432654392781823741659 B4: 2 => CTR * 1.5.62.7.7.2.4....4.68...2.32...4...56....29.9..2.6.4.6.9...4.225.69....84..2.6.9 B6: 1,7,4 # reduction candidate for 1,7 B6: 1,7 => CTR * 1.5.62.747.2.4....4.68...2.32.6.4...564...29.9..2...4.......4.225.496...84..2.6.9 B6: 4 => SOLVED * 195463278782915346436827915319654827267138594548279163971586432654392781823741659 * PAIR A9: 2,8 BLK 7 A8: 2,8,6 # reduction candidate for 2,8 A8: 2,8 => CTR * 1.5462.7.7.2....464.68...2.32.9.4.6.56....29494.2.6...6.9...4.225469....8.3.2.6.9 A8: 6 => SOLVED * 195463278782915346436827915319654827267138594548279163971586432654392781823741659 * PAIR A9: 2,8 ROW 9 E9: 2,8,1,3,4,5,7 # reduction candidate for 2,8 E9: 2,8 => CTR * 1.5.62.747.2.4....4.68...2.32.6.4...564...29.9..2...4.......4.225.496...84..2.6.9 E9: 1,3,4,5,7 => SOLVED * 195463278782915346436827915319654827267138594548279163971586432654392781823741659 F9: 2,8,1,3,5,7 # reduction candidate for 2,8 F9: 2,8 => CTR * 1.5.6..7.7.2......4.6827...32...4....6....29....2...........4.2.5..9..........6.9 F9: 1,3,5,7 # 5 pairs * PAIR A9: 2,8 COL A A5: 2,8,5 # reduction candidate for 2,8 A5: 2,8 => SOLVED * 195463278782915346436827915319654827267138594548279163971586432654392781823741659 A5: 5 => CTR * 1.5.62.7.7.2.4....4.68...2.32...4...56....29.9..2.6.4.6.9...4.225.69....84..2.6.9 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-465-base-pr-000.dot * REASONING * DIS # F3: 3,9 => CTR => F3: 1,2,5,7 * PRF # C7: 1,7 => SOL * DIS # B9: 1,7 => CTR => B9: 2,4 * PRF # B4: 1,7 => SOL * DIS # B4: 2 => CTR => B4: 1,7 * DIS # B6: 1,7 => CTR => B6: 4 * PRF # B6: 4 => SOL * DIS # A8: 2,8 => CTR => A8: 6 * PRF # A8: 6 => SOL * DIS # E9: 2,8 => CTR => E9: 1,3,4,5,7 * PRF # E9: 1,3,4,5,7 => SOL * DIS # F9: 2,8 => CTR => F9: 1,3,5,7 * PRF # A5: 2,8 => SOL * DIS # A5: 5 => CTR => A5: 2,8 * CNT 14 HDP CHAINS / 25 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B3,B7,D4,F6) * 1.5.6..7.7.2......4.68.....3....4....6.....9....2...........4.2.5..9..........6.9 * PAIR B3: 3,9 BLK 1 B1: 3,9,8 # reduction candidate for 3,9 B1: 3,9 # 6 pairs B2: 3,9,8 # reduction candidate for 3,9 B2: 3,9 # 7 pairs * PAIR B3: 3,9 ROW 3 F3: 3,9,1,2,5,7 # reduction candidate for 3,9 F3: 3,9 => CTR * 1.5.62.747.2.4....4.687..2.32...4...564...29.9..2.6.4.6.9...4.225..9....84..2.6.9 G3: 3,9,1,2,5 # reduction candidate for 3,9 G3: 3,9 # 8 pairs * RESTART * PAIR B3: 3,9 ROW 3 G3: 3,9,1,2,5 # reduction candidate for 3,9 G3: 3,9 # 8 pairs G3: 1,2,5 # 6 pairs * PAIR RESTART * PAIR B3: 3,9 BLK 1 B1: 3,9,8 # reduction candidate for 3,9 B1: 3,9 # 6 pairs B2: 3,9,8 # reduction candidate for 3,9 B2: 3,9 # 7 pairs * PAIR B3: 3,9 ROW 3 G3: 3,9,1,2,5 # reduction candidate for 3,9 G3: 3,9 # 8 pairs G3: 1,2,5 # 6 pairs * PAIR B7: 1,7 BLK 7 C7: 1,7,3,8,9 # reduction candidate for 1,7 C7: 1,7 => SOLVED * 195463278782915346436827915319654827267138594548279163971586432654392781823741659 * DURATION: 0:00:09.400793 START: 18:37:44.021185 END: 18:37:53.421978 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-465-base-pr-001.dot * REASONING * DIS # F3: 3,9 => CTR => F3: 1,2,5,7 * PRF F3: 1,2,5,7 # C7: 1,7 => SOL * STA F3: 1,2,5,7 + C7: 1,7 * CNT 2 HDP CHAINS / 11 HYP OPENED
Header Info
Top 500 Minimum 17 465 solution: 195463278782915346436827915319654827267138594548279163971586432654392781823741659 info: 95552 FNBHWYK S8.f 25360 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 195463278782915346436827915319654827267138594548279163971586432654392781823741659 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 # B1: 3,9 => UNS * INC # B2: 3,9 => UNS * DIS # F3: 3,9 => CTR => F3: 1,2,5,7 * INC # F3: 1,2,5,7 => UNS * INC # G3: 3,9 => UNS * PRF # C7: 1,7 => SOL * INC # C7: 3,8,9 => UNS * DIS # B9: 1,7 => CTR => B9: 2,4 * INC # B9: 2,4 => UNS * INC # C9: 1,7 => UNS * INC # D7: 1,7 => UNS * INC # E7: 1,7 => UNS * INC # F7: 1,7 => UNS * PRF # B4: 1,7 => SOL * DIS # B4: 2 => CTR => B4: 1,7 * DIS # B6: 1,7 => CTR => B6: 4 * PRF # B6: 4 => SOL * DIS # A8: 2,8 => CTR => A8: 6 * PRF # A8: 6 => SOL * DIS # E9: 2,8 => CTR => E9: 1,3,4,5,7 * PRF # E9: 1,3,4,5,7 => SOL * DIS # F9: 2,8 => CTR => F9: 1,3,5,7 * INC # F9: 1,3,5,7 => UNS * PRF # A5: 2,8 => SOL * DIS # A5: 5 => CTR => A5: 2,8 * CNT 25 HDP CHAINS / 25 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 3,9 => UNS * INC # B2: 3,9 => UNS * DIS # F3: 3,9 => CTR => F3: 1,2,5,7 * INC F3: 1,2,5,7 # G3: 3,9 => UNS * INC F3: 1,2,5,7 # G3: 3,9 => UNS * INC F3: 1,2,5,7 # G3: 1,2,5 => UNS * INC F3: 1,2,5,7 # B1: 3,9 => UNS * INC F3: 1,2,5,7 # B2: 3,9 => UNS * INC F3: 1,2,5,7 # G3: 3,9 => UNS * INC F3: 1,2,5,7 # G3: 1,2,5 => UNS * PRF F3: 1,2,5,7 # C7: 1,7 => SOL * STA F3: 1,2,5,7 + C7: 1,7 * CNT 11 HDP CHAINS / 11 HYP OPENED