Analysis of xx-top500-071-base.sdk
Contents
Original Sudoku
level: medium
position: .5..4.3..2......7.............6.2.8..31.........7.....6..2...........4.3....1.5.. initial
Autosolve
position: 15..4.3..2.4..3.7.3.9.2..4.495632.8.7314..2568..7519346432.5.1.51....4.39..31456. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 8 => CTR => B3: 6,7 * DIS # B3: 6,8 => CTR => B3: 7 * PRF # B3: 7 => SOL * DIS # E2: 6,8 => CTR => E2: 9 * PRF # E2: 9 => SOL * PRF # G2: 6,8 => SOL * PRF # E2: 8,9 => SOL * DIS # E2: 6 => CTR => E2: 8,9 * DIS # I1: 8,9 => CTR => I1: 2 * PRF # I1: 2 => SOL * PRF # F3: 6,7 => SOL * DIS # F3: 8 => CTR => F3: 6,7 * PRF # I2: 1,5 => SOL * PRF # I3: 8 => SOL * PRF # I1: 2,9 => SOL * DIS # I1: 8 => CTR => I1: 2,9 * PRF # E2: 8,9 => SOL * DIS # E2: 6 => CTR => E2: 8,9 * DIS # E7: 8,9 => CTR => E7: 7 * PRF # E7: 7 => SOL * DIS # E8: 8,9 => CTR => E8: 6,7 * PRF # F8: 8,9 => SOL * DIS # F8: 6 => CTR => F8: 8,9 * DIS # C9: 2,7 => CTR => C9: 8 * DIS # I9: 8 => CTR => I9: 2,7 * DIS # E7: 8,9 => CTR => E7: 7 * PRF # E7: 7 => SOL * DIS # E8: 8,9 => CTR => E8: 6,7 * PRF # F8: 8,9 => SOL * DIS # F8: 6 => CTR => F8: 8,9 * DIS # I7: 7,8 => CTR => I7: 9 * PRF # I7: 9 => SOL * PRF # I9: 7,8 => SOL * DIS # I9: 2 => CTR => I9: 7,8 * PRF # E7: 7,8 => SOL * DIS # E7: 9 => CTR => E7: 7,8 * CNT 36 HDP CHAINS / 45 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 8 => CTR => B3: 6,7 * DIS B3: 6,7 # I1: 8,9 => CTR => I1: 2 * PRF B3: 6,7 + I1: 2 => SOL * STA B3: 6,7 + I1: 2 * CNT 3 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5..4.3..2......7.............6.2.8..31.........7.....6..2...........4.3....1.5.. | initial |
| 15..4.3..2.4..3.7.3.9.2..4.495632.8.7314..2568..7519346432.5.1.51....4.39..31456. | autosolve |
| 156847392284193675379526148495632781731489256862751934643275819517968423928314567 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C1: 6,7 B2: 6,8 D1: 8,9 F1: 6,7 D2: 1,5 D3: 1,5 H1: 2,9 B6: 2,6 C6: 2,6 E5: 8,9 F5: 8,9 G4: 1,7 I4: 1,7 B9: 2,7 D8: 8,9 G7: 7,8 H8: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,D3: 1.. / D2 = 1 => 0 pairs (*) / D3 = 1 => 0 pairs (X) G4,I4: 1.. / G4 = 1 => 0 pairs (X) / I4 = 1 => 21 pairs (_) H1,I1: 2.. / H1 = 2 => 0 pairs (X) / I1 = 2 => 0 pairs (_) B6,C6: 2.. / B6 = 2 => 0 pairs (X) / C6 = 2 => 0 pairs (_) H8,I9: 2.. / H8 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) C8,H8: 2.. / C8 = 2 => 0 pairs (X) / H8 = 2 => 0 pairs (_) B6,B9: 2.. / B6 = 2 => 0 pairs (X) / B9 = 2 => 0 pairs (_) H1,H8: 2.. / H1 = 2 => 0 pairs (X) / H8 = 2 => 0 pairs (_) I1,I9: 2.. / I1 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) D2,D3: 5.. / D2 = 5 => 16 pairs (_) / D3 = 5 => 0 pairs (*) I2,I3: 5.. / I2 = 5 => 0 pairs (*) / I3 = 5 => 0 pairs (X) D2,I2: 5.. / D2 = 5 => 16 pairs (_) / I2 = 5 => 0 pairs (*) D3,I3: 5.. / D3 = 5 => 0 pairs (*) / I3 = 5 => 0 pairs (X) G2,G3: 6.. / G2 = 6 => 0 pairs (*) / G3 = 6 => 0 pairs (X) B6,C6: 6.. / B6 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) E8,F8: 6.. / E8 = 6 => 0 pairs (*) / F8 = 6 => 0 pairs (X) C1,F1: 6.. / C1 = 6 => 0 pairs (*) / F1 = 6 => 0 pairs (X) C1,C6: 6.. / C1 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) E2,E8: 6.. / E2 = 6 => 0 pairs (X) / E8 = 6 => 0 pairs (_) C1,B3: 7.. / C1 = 7 => 0 pairs (X) / B3 = 7 => 0 pairs (_) F1,F3: 7.. / F1 = 7 => 0 pairs (*) / F3 = 7 => 0 pairs (X) G4,I4: 7.. / G4 = 7 => 21 pairs (_) / I4 = 7 => 0 pairs (X) E7,E8: 7.. / E7 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) C1,F1: 7.. / C1 = 7 => 0 pairs (X) / F1 = 7 => 0 pairs (_) B3,F3: 7.. / B3 = 7 => 0 pairs (*) / F3 = 7 => 0 pairs (X) C8,E8: 7.. / C8 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) B3,B9: 7.. / B3 = 7 => 0 pairs (*) / B9 = 7 => 0 pairs (X) G4,G7: 7.. / G4 = 7 => 21 pairs (_) / G7 = 7 => 0 pairs (X) B2,B3: 8.. / B2 = 8 => 19 pairs (_) / B3 = 8 => 0 pairs (X) E5,F5: 8.. / E5 = 8 => 20 pairs (_) / F5 = 8 => 0 pairs (X) C8,C9: 8.. / C8 = 8 => 0 pairs (X) / C9 = 8 => 20 pairs (_) D1,I1: 8.. / D1 = 8 => 0 pairs (*) / I1 = 8 => 0 pairs (X) C9,I9: 8.. / C9 = 8 => 20 pairs (_) / I9 = 8 => 0 pairs (X) D1,D8: 8.. / D1 = 8 => 0 pairs (*) / D8 = 8 => 0 pairs (X) D1,E2: 9.. / D1 = 9 => 0 pairs (X) / E2 = 9 => 0 pairs (_) E5,F5: 9.. / E5 = 9 => 0 pairs (X) / F5 = 9 => 20 pairs (_) I7,H8: 9.. / I7 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) E2,I2: 9.. / E2 = 9 => 0 pairs (*) / I2 = 9 => 0 pairs (X) E7,I7: 9.. / E7 = 9 => 0 pairs (X) / I7 = 9 => 0 pairs (_) D1,D8: 9.. / D1 = 9 => 0 pairs (X) / D8 = 9 => 0 pairs (_) F5,F8: 9.. / F5 = 9 => 20 pairs (_) / F8 = 9 => 0 pairs (X) H1,H8: 9.. / H1 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) * DURATION: 0:01:32.678191 START: 05:06:38.529858 END: 05:08:11.208049 2017-05-04 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B6,B9,C1,C6,D1,D2,D3,D8,E5,F1,F5,G4,G7,H1,H8,I4) * 15..4.3..2.4..3.7.3.9.2..4.495632.8.7314..2568..7519346432.5.1.51....4.39..31456. * PAIR C1: 6,7 BLK 1 B3: 6,7,8 # reduction candidate for 6,7 B3: 8 => CTR * 157.463..264..3.7.389.2764.495632.8.7314..2568267519346432.5.1.51....4.39..31456. B3: 6,7 # 19 pairs * PAIR B2: 6,8 BLK 1 B3: 6,8,7 # reduction candidate for 6,8 B3: 6,8 => CTR * 157.463..2.4..3.7.3.9.27.4.495632.8.7314..2568.67519346432.5.1.51....4.39..31456. B3: 7 => SOLVED * 156847392284193675379526148495632781731489256862751934643275819517968423928314567 * PAIR B2: 6,8 ROW 2 E2: 6,8,9 # reduction candidate for 6,8 E2: 6,8 => CTR * 15.94.3282.4..3.793.9.2..45495632.817314..2568..75193464329581751287649397831456. E2: 9 => SOLVED * 156847392284193675379526148495632781731489256862751934643275819517968423928314567 G2: 6,8,1 # reduction candidate for 6,8 G2: 6,8 => SOLVED * 156847392284193675379526148495632781731489256862751934643275819517968423928314567 G2: 1 # 19 pairs * PAIR D1: 8,9 BLK 2 E2: 8,9,6 # reduction candidate for 8,9 E2: 8,9 => SOLVED * 156847392284193675379526148495632781731489256862751934643275819517968423928314567 E2: 6 => CTR * 15.94.328284.631793.912864549563278173148925686275193464329581751.87.4.39..31456. * PAIR D1: 8,9 ROW 1 I1: 8,9,2 # reduction candidate for 8,9 I1: 8,9 => CTR * 15..4.32.2.4..3.7.3.9.2..4.495632.8.7314..2568..7519346432.5.1.512.7649397831456. I1: 2 => SOLVED * 156847392284193675379526148495632781731489256862751934643275819517968423928314567 * PAIR F1: 6,7 BLK 2 F3: 6,7,8 # reduction candidate for 6,7 F3: 6,7 => SOLVED * 156847392284193675379526148495632781731489256862751934643275819517968423928314567 F3: 8 => CTR * 15..473..2.4.63.79379.28645495632.81731489256862751934643295.1.51.8..4.39..31456. * PAIR D2: 1,5 ROW 2 I2: 1,5,8,9 # reduction candidate for 1,5 I2: 1,5 => SOLVED * 156847392284193675379526148495632781731489256862751934643275819517968423928314567 I2: 8,9 # 19 pairs * PAIR D3: 1,5 ROW 3 I3: 1,5,8 # reduction candidate for 1,5 I3: 8 => SOLVED * 156847392284193675379526148495632781731489256862751934643275819517968423928314567 I3: 1,5 # 19 pairs * PAIR H1: 2,9 BLK 3 I1: 2,9,8 # reduction candidate for 2,9 I1: 2,9 => SOLVED * 156847392284193675379526148495632781731489256862751934643275819517968423928314567 I1: 8 => CTR * 15..4.3282.4..3.793.9.2..45495632.817314..2568..75193464329581751287649397831456. * PAIR E5: 8,9 COL E E2: 8,9,6 # reduction candidate for 8,9 E2: 8,9 => SOLVED * 156847392284193675379526148495632781731489256862751934643275819517968423928314567 E2: 6 => CTR * 15.94.328284.631793.912864549563278173148925686275193464329581751.87.4.39..31456. E7: 8,9,7 # reduction candidate for 8,9 E7: 8,9 => CTR * 156.473..284.6317937912864549563278173148925686275193464329581.51..764.39..31456. E7: 7 => SOLVED * 156847392284193675379526148495632781731489256862751934643275819517968423928314567 E8: 8,9,6,7 # reduction candidate for 8,9 E8: 8,9 => CTR * 15..4.3..2.4.63.793.9.2.645495632.817314..2568627519346432.5.1.51....4.39..31456. E8: 6,7 # 18 pairs * PAIR F5: 8,9 COL F F8: 8,9,6 # reduction candidate for 8,9 F8: 8,9 => SOLVED * 156847392284193675379526148495632781731489256862751934643275819517968423928314567 F8: 6 => CTR * 156.473..284.6317937912864549563278173148925686275193464329581.51...64.39..31456. * PAIR B9: 2,7 BLK 7 C8: 2,7,8 # reduction candidate for 2,7 C8: 2,7 # 20 pairs C9: 2,7,8 # reduction candidate for 2,7 C9: 2,7 => CTR * 15..4.3..2.4..3.7.3.9.2..4.495632.8.7314..2568..7519346432.5.1.5189764239..314568 C9: 8 # 20 pairs * PAIR B9: 2,7 ROW 9 I9: 2,7,8 # reduction candidate for 2,7 I9: 8 => CTR * 15.84.3922.4.93.7.3.9.2..4.495632.8.7314892568..751934643275.1.51....4239..314568 I9: 2,7 # 20 pairs * PAIR D8: 8,9 BLK 8 E7: 8,9,7 # reduction candidate for 8,9 E7: 8,9 => CTR * 156.473..284.6317937912864549563278173148925686275193464329581.51..764.39..31456. E7: 7 => SOLVED * 156847392284193675379526148495632781731489256862751934643275819517968423928314567 E8: 8,9,6,7 # reduction candidate for 8,9 E8: 8,9 => CTR * 15..4.3..2.4.63.793.9.2.645495632.817314..2568627519346432.5.1.51....4.39..31456. E8: 6,7 # 18 pairs F8: 8,9,6 # reduction candidate for 8,9 F8: 8,9 => SOLVED * 156847392284193675379526148495632781731489256862751934643275819517968423928314567 F8: 6 => CTR * 156.473..284.6317937912864549563278173148925686275193464329581.51...64.39..31456. * PAIR G7: 7,8 BLK 9 I7: 7,8,9 # reduction candidate for 7,8 I7: 7,8 => CTR * 15..4.3..2.4..3.7.3.9.2..4.495632.8.7314..2568..751934643295.1.51.8764939.8314562 I7: 9 => SOLVED * 156847392284193675379526148495632781731489256862751934643275819517968423928314567 I9: 7,8,2 # reduction candidate for 7,8 I9: 7,8 => SOLVED * 156847392284193675379526148495632781731489256862751934643275819517968423928314567 I9: 2 => CTR * 15..4.32.2.4..3.7.3.9.2..4.495632.8.7314..2568267519346432.5.1.512.76493978314562 * PAIR G7: 7,8 ROW 7 E7: 7,8,9 # reduction candidate for 7,8 E7: 7,8 => SOLVED * 156847392284193675379526148495632781731489256862751934643275819517968423928314567 E7: 9 => CTR * 15..4.3..2.4..3.7.3.9.2..4.495632.8.7314..2568..751934643295.1.51.8764939.8314562 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-071-base-pr-000.dot * REASONING * DIS # B3: 8 => CTR => B3: 6,7 * DIS # B3: 6,8 => CTR => B3: 7 * PRF # B3: 7 => SOL * DIS # E2: 6,8 => CTR => E2: 9 * PRF # E2: 9 => SOL * PRF # G2: 6,8 => SOL * PRF # E2: 8,9 => SOL * DIS # E2: 6 => CTR => E2: 8,9 * DIS # I1: 8,9 => CTR => I1: 2 * PRF # I1: 2 => SOL * PRF # F3: 6,7 => SOL * DIS # F3: 8 => CTR => F3: 6,7 * PRF # I2: 1,5 => SOL * PRF # I3: 8 => SOL * PRF # I1: 2,9 => SOL * DIS # I1: 8 => CTR => I1: 2,9 * PRF # E2: 8,9 => SOL * DIS # E2: 6 => CTR => E2: 8,9 * DIS # E7: 8,9 => CTR => E7: 7 * PRF # E7: 7 => SOL * DIS # E8: 8,9 => CTR => E8: 6,7 * PRF # F8: 8,9 => SOL * DIS # F8: 6 => CTR => F8: 8,9 * DIS # C9: 2,7 => CTR => C9: 8 * DIS # I9: 8 => CTR => I9: 2,7 * DIS # E7: 8,9 => CTR => E7: 7 * PRF # E7: 7 => SOL * DIS # E8: 8,9 => CTR => E8: 6,7 * PRF # F8: 8,9 => SOL * DIS # F8: 6 => CTR => F8: 8,9 * DIS # I7: 7,8 => CTR => I7: 9 * PRF # I7: 9 => SOL * PRF # I9: 7,8 => SOL * DIS # I9: 2 => CTR => I9: 7,8 * PRF # E7: 7,8 => SOL * DIS # E7: 9 => CTR => E7: 7,8 * CNT 36 HDP CHAINS / 45 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B6,B9,C1,C6,D1,D2,D3,D8,E5,F1,F5,G4,G7,H1,H8,I4) * 15..4.3..2.4..3.7.3.9.2..4.495632.8.7314..2568..7519346432.5.1.51....4.39..31456. * PAIR C1: 6,7 BLK 1 B3: 6,7,8 # reduction candidate for 6,7 B3: 8 => CTR * 157.463..264..3.7.389.2764.495632.8.7314..2568267519346432.5.1.51....4.39..31456. * PAIR D1: 8,9 ROW 1 I1: 8,9,2 # reduction candidate for 8,9 I1: 8,9 => CTR * 15..4.32.284..3.7.3.9.2..4.495632.8.7314..2568..7519346432.5.1.512.7649397831456. I1: 2 => SOLVED * 156847392284193675379526148495632781731489256862751934643275819517968423928314567 * DURATION: 0:00:06.304868 START: 05:09:18.036926 END: 05:09:24.341794 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-071-base-pr-001.dot * REASONING * DIS # B3: 8 => CTR => B3: 6,7 * DIS B3: 6,7 # I1: 8,9 => CTR => I1: 2 * PRF B3: 6,7 + I1: 2 => SOL * STA B3: 6,7 + I1: 2 * CNT 3 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 071 solution: 156847392284193675379526148495632781731489256862751934643275819517968423928314567 info: 1460 FNBTHWY S8.f 20013 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 156847392284193675379526148495632781731489256862751934643275819517968423928314567 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 # B3: 6,7 => UNS * DIS # B3: 8 => CTR => B3: 6,7 * DIS # B3: 6,8 => CTR => B3: 7 * PRF # B3: 7 => SOL * DIS # E2: 6,8 => CTR => E2: 9 * PRF # E2: 9 => SOL * PRF # G2: 6,8 => SOL * INC # G2: 1 => UNS * PRF # E2: 8,9 => SOL * DIS # E2: 6 => CTR => E2: 8,9 * DIS # I1: 8,9 => CTR => I1: 2 * PRF # I1: 2 => SOL * PRF # F3: 6,7 => SOL * DIS # F3: 8 => CTR => F3: 6,7 * PRF # I2: 1,5 => SOL * INC # I2: 8,9 => UNS * INC # I3: 1,5 => UNS * PRF # I3: 8 => SOL * PRF # I1: 2,9 => SOL * DIS # I1: 8 => CTR => I1: 2,9 * PRF # E2: 8,9 => SOL * DIS # E2: 6 => CTR => E2: 8,9 * DIS # E7: 8,9 => CTR => E7: 7 * PRF # E7: 7 => SOL * DIS # E8: 8,9 => CTR => E8: 6,7 * INC # E8: 6,7 => UNS * PRF # F8: 8,9 => SOL * DIS # F8: 6 => CTR => F8: 8,9 * INC # C8: 2,7 => UNS * DIS # C9: 2,7 => CTR => C9: 8 * INC # C9: 8 => UNS * INC # I9: 2,7 => UNS * DIS # I9: 8 => CTR => I9: 2,7 * DIS # E7: 8,9 => CTR => E7: 7 * PRF # E7: 7 => SOL * DIS # E8: 8,9 => CTR => E8: 6,7 * INC # E8: 6,7 => UNS * PRF # F8: 8,9 => SOL * DIS # F8: 6 => CTR => F8: 8,9 * DIS # I7: 7,8 => CTR => I7: 9 * PRF # I7: 9 => SOL * PRF # I9: 7,8 => SOL * DIS # I9: 2 => CTR => I9: 7,8 * PRF # E7: 7,8 => SOL * DIS # E7: 9 => CTR => E7: 7,8 * CNT 45 HDP CHAINS / 45 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B3: 6,7 => UNS * DIS # B3: 8 => CTR => B3: 6,7 * DIS B3: 6,7 # I1: 8,9 => CTR => I1: 2 * PRF B3: 6,7 + I1: 2 => SOL * STA B3: 6,7 + I1: 2 * CNT 4 HDP CHAINS / 3 HYP OPENED