Analysis of xx-top500-381-base.sdk
Contents
Original Sudoku
level: medium
position: ...9...329.18............4..3...2...6.....1......4.....2..8.......7..6..7........ initial
Autosolve
position: 5..914832941823...283...94143.1.2.8.6.23.81.481..4.2.312.48.3..3.47.16287.823.41. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E3: 7 => SOL * DIS # I4: 5,7 => CTR => I4: 6,9 * CNT 2 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:
* PRF # E3: 7 => SOL * STA E3: 7 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...9...329.18............4..3...2...6.....1......4.....2..8.......7..6..7........ | initial |
| 5..914832941823...283...94143.1.2.8.6.23.81.481..4.2.312.48.3..3.47.16287.823.41. | autosolve |
| 576914832941823756283675941437162589652398174819547263125486397394751628768239415 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) B1: 6,7 C1: 6,7 D3: 5,6 F3: 5,7 G2: 5,7 D6: 5,6 G4: 5,7 B8: 5,9 E8: 5,9 I9: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B8,E8: 5.. / B8 = 5 => 15 pairs (_) / E8 = 5 => 17 pairs (_) D3,D6: 5.. / D3 = 5 => 10 pairs (_) / D6 = 5 => 13 pairs (_) G2,G4: 5.. / G2 = 5 => 12 pairs (_) / G4 = 5 => 12 pairs (_) B1,C1: 6.. / B1 = 6 => 16 pairs (_) / C1 = 6 => 11 pairs (_) D3,E3: 6.. / D3 = 6 => 13 pairs (_) / E3 = 6 => 10 pairs (_) H2,I2: 6.. / H2 = 6 => 10 pairs (_) / I2 = 6 => 13 pairs (_) E4,D6: 6.. / E4 = 6 => 13 pairs (_) / D6 = 6 => 10 pairs (_) I4,H6: 6.. / I4 = 6 => 10 pairs (_) / H6 = 6 => 13 pairs (_) C7,B9: 6.. / C7 = 6 => 16 pairs (_) / B9 = 6 => 11 pairs (_) F7,F9: 6.. / F7 = 6 => 11 pairs (_) / F9 = 6 => 16 pairs (_) E4,I4: 6.. / E4 = 6 => 13 pairs (_) / I4 = 6 => 10 pairs (_) D6,H6: 6.. / D6 = 6 => 10 pairs (_) / H6 = 6 => 13 pairs (_) C7,F7: 6.. / C7 = 6 => 16 pairs (_) / F7 = 6 => 11 pairs (_) B9,F9: 6.. / B9 = 6 => 11 pairs (_) / F9 = 6 => 16 pairs (_) B1,B9: 6.. / B1 = 6 => 16 pairs (_) / B9 = 6 => 11 pairs (_) C1,C7: 6.. / C1 = 6 => 11 pairs (_) / C7 = 6 => 16 pairs (_) D3,D6: 6.. / D3 = 6 => 13 pairs (_) / D6 = 6 => 10 pairs (_) E3,E4: 6.. / E3 = 6 => 10 pairs (_) / E4 = 6 => 13 pairs (_) H2,H6: 6.. / H2 = 6 => 10 pairs (_) / H6 = 6 => 13 pairs (_) I2,I4: 6.. / I2 = 6 => 13 pairs (_) / I4 = 6 => 10 pairs (_) B1,C1: 7.. / B1 = 7 => 11 pairs (_) / C1 = 7 => 16 pairs (_) E3,F3: 7.. / E3 = 7 => 0 pairs (*) / F3 = 7 => 0 pairs (X) H7,I7: 7.. / H7 = 7 => 16 pairs (_) / I7 = 7 => 12 pairs (_) B1,B5: 7.. / B1 = 7 => 11 pairs (_) / B5 = 7 => 16 pairs (_) F3,F6: 7.. / F3 = 7 => 11 pairs (_) / F6 = 7 => 0 pairs (*) G2,G4: 7.. / G2 = 7 => 12 pairs (_) / G4 = 7 => 12 pairs (_) B8,E8: 9.. / B8 = 9 => 17 pairs (_) / E8 = 9 => 15 pairs (_) * DURATION: 0:00:45.601564 START: 15:53:28.224748 END: 15:54:13.826312 2017-05-04 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B8,C1,D3,D6,E8,F3,G2,G4,I9) * 5..914832941823...283...94143.1.2.8.6.23.81.481..4.2.312.48.3..3.47.16287.823.41. * PAIR D3: 5,6 BLK 2 E3: 5,6,7 # reduction candidate for 5,6 E3: 7 => SOLVED * 576914832941823756283675941437162589652398174819547263125486397394751628768239415 E3: 5,6 # 11 pairs * PAIR F3: 5,7 BLK 2 E3: 5,7,6 # reduction candidate for 5,7 E3: 5,7 # 13 pairs E3: 6 # 10 pairs * PAIR F3: 5,7 COL F F6: 5,7,9 # reduction candidate for 5,7 F6: 5,7 # 17 pairs F6: 9 # 15 pairs * PAIR G2: 5,7 BLK 3 H2: 5,7,6 # reduction candidate for 5,7 H2: 5,7 # 13 pairs I2: 5,7,6 # reduction candidate for 5,7 I2: 5,7 # 10 pairs * PAIR D6: 5,6 BLK 5 E4: 5,6,7,9 # reduction candidate for 5,6 E4: 5,6 # 13 pairs E4: 7,9 # 11 pairs * PAIR D6: 5,6 ROW 6 H6: 5,6,7,9 # reduction candidate for 5,6 H6: 5,6 # 13 pairs H6: 7,9 # 11 pairs * PAIR G4: 5,7 BLK 6 I4: 5,7,6,9 # reduction candidate for 5,7 I4: 5,7 => CTR * 5..914832941823..62836..941439162.8.6523.81948175492631254863..3.47.16287.823.41. I4: 6,9 # 11 pairs H5: 5,7,9 # reduction candidate for 5,7 H5: 5,7 # 13 pairs H6: 5,7,6,9 # reduction candidate for 5,7 H6: 5,7 # 14 pairs * PAIR G4: 5,7 ROW 4 C4: 5,7,9 # reduction candidate for 5,7 C4: 5,7 # 13 pairs E4: 5,7,6,9 # reduction candidate for 5,7 E4: 5,7 # 14 pairs * PAIR B8: 5,9 BLK 7 C7: 5,9,6 # reduction candidate for 5,9 C7: 5,9 # 11 pairs B9: 5,9,6 # reduction candidate for 5,9 B9: 5,9 # 16 pairs * PAIR B8: 5,9 COL B B5: 5,9,7 # reduction candidate for 5,9 B5: 7 # 16 pairs B5: 5,9 # 11 pairs * PAIR E8: 5,9 BLK 8 F7: 5,9,6 # reduction candidate for 5,9 F7: 5,9 # 16 pairs F9: 5,9,6 # reduction candidate for 5,9 F9: 5,9 # 11 pairs * PAIR E8: 5,9 COL E E4: 5,9,6,7 # reduction candidate for 5,9 E4: 5,9 # 13 pairs E5: 5,9,7 # reduction candidate for 5,9 E5: 5,9 # 13 pairs * PAIR I9: 5,9 BLK 9 H7: 5,9,7 # reduction candidate for 5,9 H7: 5,9 # 12 pairs I7: 5,9,7 # reduction candidate for 5,9 I7: 5,9 # 16 pairs * PAIR I9: 5,9 ROW 9 B9: 5,9,6 # reduction candidate for 5,9 B9: 5,9 # 16 pairs F9: 5,9,6 # reduction candidate for 5,9 F9: 5,9 # 11 pairs * PAIR I9: 5,9 COL I I4: 5,9,6,7 # reduction candidate for 5,9 I4: 5,9 # 15 pairs I4: 6,7 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-381-base-pr-000.dot * REASONING * PRF # E3: 7 => SOL * DIS # I4: 5,7 => CTR => I4: 6,9 * CNT 2 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B8,C1,D3,D6,E8,F3,G2,G4,I9) * 5..914832941823...283...94143.1.2.8.6.23.81.481..4.2.312.48.3..3.47.16287.823.41. * PAIR D3: 5,6 BLK 2 E3: 5,6,7 # reduction candidate for 5,6 E3: 7 => SOLVED * 576914832941823756283675941437162589652398174819547263125486397394751628768239415 * DURATION: 0:00:02.934968 START: 15:54:43.753397 END: 15:54:46.688365 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-381-base-pr-001.dot * REASONING * PRF # E3: 7 => SOL * STA E3: 7 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 381 solution: 576914832941823756283675941437162589652398174819547263125486397394751628768239415 info: 33306 FNBTYO S8.f 12538 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 576914832941823756283675941437162589652398174819547263125486397394751628768239415 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 # E3: 5,6 => UNS * PRF # E3: 7 => SOL * INC # E3: 5,7 => UNS * INC # E3: 6 => UNS * INC # F6: 5,7 => UNS * INC # F6: 9 => UNS * INC # H2: 5,7 => UNS * INC # I2: 5,7 => UNS * INC # E4: 5,6 => UNS * INC # E4: 7,9 => UNS * INC # H6: 5,6 => UNS * INC # H6: 7,9 => UNS * DIS # I4: 5,7 => CTR => I4: 6,9 * INC # I4: 6,9 => UNS * INC # H5: 5,7 => UNS * INC # H6: 5,7 => UNS * INC # C4: 5,7 => UNS * INC # E4: 5,7 => UNS * INC # C7: 5,9 => UNS * INC # B9: 5,9 => UNS * INC # B5: 5,9 => UNS * INC # B5: 7 => UNS * INC # F7: 5,9 => UNS * INC # F9: 5,9 => UNS * INC # E4: 5,9 => UNS * INC # E5: 5,9 => UNS * INC # H7: 5,9 => UNS * INC # I7: 5,9 => UNS * INC # B9: 5,9 => UNS * INC # F9: 5,9 => UNS * INC # I4: 5,9 => UNS * INC # I4: 6,7 => UNS * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E3: 5,6 => UNS * PRF # E3: 7 => SOL * STA E3: 7 * CNT 2 HDP CHAINS / 2 HYP OPENED