Analysis of xx-top500-217-base.sdk
Contents
Original Sudoku
level: medium
position: .5.....8......3......4.....3.42.........7..9.6.............64.3....1.2...7.5..... initial
Autosolve
position: .5.....8......3......4.....3.42.........7..9.6.7...........64.3....1.2...7.5..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I2: 4,6 => CTR => I2: 1,2,5,7,9 * DIS # B8: 3 => CTR => B8: 4,6 * DIS # C1: 3,6 => CTR => C1: 1,2,9 * DIS # C3: 3,6 => CTR => C3: 1,2,8,9 * DIS # G3: 3,6 => CTR => G3: 1,5,7,9 * DIS # B8: 3,6 => CTR => B8: 4 * DIS # I1: 2,4 => CTR => I1: 1,6,7,9 * DIS # I2: 2,4 => CTR => I2: 1,5,6,7,9 * DIS # A2: 2,4 => CTR => A2: 1,7,8,9 * DIS # H6: 2,4 => CTR => H6: 3 * DIS # C3: 2,3 => CTR => C3: 1,6,8,9 * DIS # H6: 4 => CTR => H6: 2,3 * DIS # H6: 2 => CTR => H6: 3,4 * CNT 13 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I2: 4,6 => CTR => I2: 1,2,5,7,9 * DIS I2: 1,2,5,7,9 # B8: 3 => CTR => B8: 4,6 * PRF I2: 1,2,5,7,9 + B8: 4,6 # A2: 8,9 => SOL * STA I2: 1,2,5,7,9 + B8: 4,6 + A2: 8,9 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5.....8......3......4.....3.42.........7..9.6.............64.3....1.2...7.5..... | initial |
| .5.....8......3......4.....3.42.........7..9.6.7...........64.3....1.2...7.5..... | autosolve |
| 451692387862753149739481526384269751125378694697145832518926473943817265276534918 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) B2: 4,6 B3: 3,6 H2: 2,4 H3: 2,3 E6: 3,4 E9: 3,4 H9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E7,F9: 2.. / E7 = 2 => 9 pairs (_) / F9 = 2 => 8 pairs (_) D8,E9: 3.. / D8 = 3 => 0 pairs (X) / E9 = 3 => 17 pairs (_) C1,G1: 3.. / C1 = 3 => 0 pairs (X) / G1 = 3 => 17 pairs (_) D5,G5: 3.. / D5 = 3 => 17 pairs (_) / G5 = 3 => 0 pairs (X) C9,E9: 3.. / C9 = 3 => 0 pairs (X) / E9 = 3 => 17 pairs (_) B3,B8: 3.. / B3 = 3 => 17 pairs (_) / B8 = 3 => 0 pairs (X) E6,E9: 3.. / E6 = 3 => 0 pairs (X) / E9 = 3 => 17 pairs (_) H3,H6: 3.. / H3 = 3 => 0 pairs (X) / H6 = 3 => 17 pairs (_) A1,I1: 4.. / A1 = 4 => 17 pairs (_) / I1 = 4 => 0 pairs (X) F5,I5: 4.. / F5 = 4 => 0 pairs (X) / I5 = 4 => 17 pairs (_) B2,B8: 4.. / B2 = 4 => 0 pairs (X) / B8 = 4 => 17 pairs (_) E6,E9: 4.. / E6 = 4 => 17 pairs (_) / E9 = 4 => 0 pairs (X) H2,H6: 4.. / H2 = 4 => 17 pairs (_) / H6 = 4 => 0 pairs (X) A5,C5: 5.. / A5 = 5 => 7 pairs (_) / C5 = 5 => 7 pairs (_) E4,D5: 6.. / E4 = 6 => 8 pairs (_) / D5 = 6 => 0 pairs (X) D7,H7: 7.. / D7 = 7 => 8 pairs (_) / H7 = 7 => 9 pairs (_) B4,B6: 9.. / B4 = 9 => 7 pairs (_) / B6 = 9 => 8 pairs (_) * DURATION: 0:00:25.358043 START: 10:13:14.221572 END: 10:13:39.579615 2017-05-04 * CP COUNT: (17) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,E6,E9,H2,H3,H9) * .5.....8......3......4.....3.42.........7..9.6.7...........64.3....1.2...7.5..... * PAIR B2: 4,6 ROW 2 I2: 4,6,1,2,5,7,9 # reduction candidate for 4,6 I2: 4,6 => CTR * .5.....8......3.2....4...3.3.42.........7..9.6.7....4......64.3.3..1.2...7.5..... I2: 1,2,5,7,9 # 7 pairs * PAIR B2: 4,6 COL B B8: 4,6,3 # reduction candidate for 4,6 B8: 3 => CTR * .5.....8..4...3.2..6.4...3.3.42.........7..9.6.7....4......64.3.3..1.2...7.5..... B8: 4,6 # 17 pairs * PAIR B3: 3,6 BLK 1 C1: 3,6,1,2,9 # reduction candidate for 3,6 C1: 3,6 => CTR * .5.....8..4...3.2....4...3.3.42.........7..9.6.7....4......64.3.3..1.2...7.5..... C1: 1,2,9 # 17 pairs C3: 3,6,1,2,8,9 # reduction candidate for 3,6 C3: 3,6 => CTR * .5....38..4...3.2....4.....3.42.........7..9.6.7...........64.3....1.2...7.5..... C3: 1,2,8,9 # 7 pairs * PAIR B3: 3,6 ROW 3 G3: 3,6,1,5,7,9 # reduction candidate for 3,6 G3: 3,6 => CTR * 45...238..6...3.4..3.4..62.3.426.......37..9.6.7.4..3......64.3.43.1.2...76534.1. G3: 1,5,7,9 # 7 pairs * PAIR B3: 3,6 COL B B8: 3,6,4 # reduction candidate for 3,6 B8: 3,6 => CTR * .5.....8..4...3.2....4...3.3.42.........7..9.6.7....4......64.3.3..1.2...7.5..... B8: 4 # 17 pairs * PAIR H2: 2,4 BLK 3 I1: 2,4,1,6,7,9 # reduction candidate for 2,4 I1: 2,4 => CTR * .53....8..4...3.2..6.4...3.3.42.........7..9.6.7.4.........64.3.3..1.2...7.53.... I1: 1,6,7,9 # 17 pairs I2: 2,4,1,5,6,7,9 # reduction candidate for 2,4 I2: 2,4 => CTR * 45.....8..6...3....3.4.....3.42.........7..9.6.7...........64.3....1.2...7.5..... I2: 1,5,6,7,9 # 7 pairs * PAIR H2: 2,4 ROW 2 A2: 2,4,1,7,8,9 # reduction candidate for 2,4 A2: 2,4 => CTR * .5...238.26...3.4..3.4...2.3.42........37..946.7.4..32....264.3.43.1.2...7.534... A2: 1,7,8,9 # 7 pairs * PAIR H2: 2,4 COL H H6: 2,4,3 # reduction candidate for 2,4 H6: 2,4 => CTR * .53....8..4...3.2..6.4...3.3.42.........7..9.6.7.4.........64.3.3..1.2...7.53.... H6: 3 # 17 pairs * PAIR H3: 2,3 ROW 3 C3: 2,3,1,6,8,9 # reduction candidate for 2,3 C3: 2,3 => CTR * .5.....8..4...3.2..624...3.3.42.........7..9.6.7.4.........64.3.3..1.2...7.53.... C3: 1,6,8,9 # 7 pairs * PAIR H3: 2,3 COL H H6: 2,3,4 # reduction candidate for 2,3 H6: 4 => CTR * .5.....8......3......4...3.3.42.........7..9.6.7....4......64.3.3..1.2...7.5..... H6: 2,3 # 17 pairs * PAIR E6: 3,4 ROW 6 H6: 3,4,2 # reduction candidate for 3,4 H6: 2 => CTR * .5.....8......3.4....4...3.3.42.........7..9.6.7....2......64.3....1.2...7.5..... H6: 3,4 # 8 pairs * PAIR H9: 1,6 BLK 9 G9: 1,6,8,9 # reduction candidate for 1,6 G9: 1,6 # 13 pairs I9: 1,6,8,9 # reduction candidate for 1,6 I9: 1,6 # 13 pairs * PAIR H9: 1,6 ROW 9 C9: 1,6,2,3,8,9 # reduction candidate for 1,6 C9: 1,6 # 17 pairs C9: 2,3,8,9 # 8 pairs * PAIR H9: 1,6 COL H H4: 1,6,5,7 # reduction candidate for 1,6 H4: 5,7 # 12 pairs H4: 1,6 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-217-base-pr-000.dot * REASONING * DIS # I2: 4,6 => CTR => I2: 1,2,5,7,9 * DIS # B8: 3 => CTR => B8: 4,6 * DIS # C1: 3,6 => CTR => C1: 1,2,9 * DIS # C3: 3,6 => CTR => C3: 1,2,8,9 * DIS # G3: 3,6 => CTR => G3: 1,5,7,9 * DIS # B8: 3,6 => CTR => B8: 4 * DIS # I1: 2,4 => CTR => I1: 1,6,7,9 * DIS # I2: 2,4 => CTR => I2: 1,5,6,7,9 * DIS # A2: 2,4 => CTR => A2: 1,7,8,9 * DIS # H6: 2,4 => CTR => H6: 3 * DIS # C3: 2,3 => CTR => C3: 1,6,8,9 * DIS # H6: 4 => CTR => H6: 2,3 * DIS # H6: 2 => CTR => H6: 3,4 * CNT 13 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,E6,E9,H2,H3,H9) * .5.....8......3......4.....3.42.........7..9.6.7...........64.3....1.2...7.5..... * PAIR B2: 4,6 ROW 2 I2: 4,6,1,2,5,7,9 # reduction candidate for 4,6 I2: 4,6 => CTR * .5.....8......3.2....4...3.3.42.........7..9.6.7....4......64.3.3..1.2...7.5..... * PAIR B2: 4,6 COL B B8: 4,6,3 # reduction candidate for 4,6 B8: 3 => CTR * .5.....8..4...3.2..6.4...3.3.42.........7..9.6.7....4......64.3.3..1.2...7.5..... * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A5,A7,A8,B7,C3,C5,D2,D7,E2,E3,F3,F5,G6,G9,I2,I4,I9) * 451692387.62..3.4..3.4...263.426.75..2.37.6946.7.45.32....26473.43.1.265276534.1. * PAIR C3: 8,9 BLK 1 A2: 8,9,7 # reduction candidate for 8,9 A2: 8,9 => SOLVED * 451692387862753149739481526384269751125378694697145832518926473943817265276534918 * DURATION: 0:00:06.235572 START: 10:14:03.862070 END: 10:14:10.097642 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-217-base-pr-001.dot * REASONING * DIS # I2: 4,6 => CTR => I2: 1,2,5,7,9 * DIS I2: 1,2,5,7,9 # B8: 3 => CTR => B8: 4,6 * PRF I2: 1,2,5,7,9 + B8: 4,6 # A2: 8,9 => SOL * STA I2: 1,2,5,7,9 + B8: 4,6 + A2: 8,9 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 217 solution: 451692387862753149739481526384269751125378694697145832518926473943817265276534918 info: 1949 FNBHXY S8.f 19701 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 451692387862753149739481526384269751125378694697145832518926473943817265276534918 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 # I2: 4,6 => CTR => I2: 1,2,5,7,9 * INC # I2: 1,2,5,7,9 => UNS * INC # B8: 4,6 => UNS * DIS # B8: 3 => CTR => B8: 4,6 * DIS # C1: 3,6 => CTR => C1: 1,2,9 * INC # C1: 1,2,9 => UNS * DIS # C3: 3,6 => CTR => C3: 1,2,8,9 * INC # C3: 1,2,8,9 => UNS * DIS # G3: 3,6 => CTR => G3: 1,5,7,9 * INC # G3: 1,5,7,9 => UNS * DIS # B8: 3,6 => CTR => B8: 4 * INC # B8: 4 => UNS * DIS # I1: 2,4 => CTR => I1: 1,6,7,9 * INC # I1: 1,6,7,9 => UNS * DIS # I2: 2,4 => CTR => I2: 1,5,6,7,9 * INC # I2: 1,5,6,7,9 => UNS * DIS # A2: 2,4 => CTR => A2: 1,7,8,9 * INC # A2: 1,7,8,9 => UNS * DIS # H6: 2,4 => CTR => H6: 3 * INC # H6: 3 => UNS * DIS # C3: 2,3 => CTR => C3: 1,6,8,9 * INC # C3: 1,6,8,9 => UNS * INC # H6: 2,3 => UNS * DIS # H6: 4 => CTR => H6: 2,3 * INC # H6: 3,4 => UNS * DIS # H6: 2 => CTR => H6: 3,4 * INC # G9: 1,6 => UNS * INC # I9: 1,6 => UNS * INC # C9: 1,6 => UNS * INC # C9: 2,3,8,9 => UNS * INC # H4: 1,6 => UNS * INC # H4: 5,7 => UNS * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # I2: 4,6 => CTR => I2: 1,2,5,7,9 * INC I2: 1,2,5,7,9 # B8: 4,6 => UNS * DIS I2: 1,2,5,7,9 # B8: 3 => CTR => B8: 4,6 * PRF I2: 1,2,5,7,9 + B8: 4,6 # A2: 8,9 => SOL * STA I2: 1,2,5,7,9 + B8: 4,6 + A2: 8,9 * CNT 4 HDP CHAINS / 4 HYP OPENED