Analysis of xx-top500-255-base.sdk
Contents
Original Sudoku
level: medium
position: .4.1.....5......2.....4.......5..1.48.7............6.......7.83..2.6.....1....... initial
Autosolve
position: .4.15....531.7842..7..4..159235861748674.1.5.15472.6.8496217583.82.65.41.158.4... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G3: 3 => CTR => G3: 8,9 * PRF # D3: 6,9 => SOL * DIS # D3: 3 => CTR => D3: 6,9 * PRF # H1: 6,9 => SOL * DIS # H1: 3 => CTR => H1: 6,9 * DIS # I1: 6,9 => CTR => I1: 7 * DIS # I9: 6,9 => CTR => I9: 2,7 * PRF # G5: 2 => SOL * PRF # F3: 3,9 => SOL * PRF # G5: 2,9 => SOL * DIS # G5: 3 => CTR => G5: 2,9 * PRF # I9: 2,9 => SOL * PRF # G5: 2 => SOL * DIS # H1: 6 => CTR => H1: 3,9 * PRF # D3: 6 => SOL * PRF # G9: 7,9 => SOL * DIS # G1: 7,9 => CTR => G1: 3,8 * DIS # I9: 6,9 => CTR => I9: 2,7 * PRF # H1: 6,9 => SOL * DIS # H1: 3 => CTR => H1: 6,9 * CNT 20 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G3: 3 => CTR => G3: 8,9 * PRF G3: 8,9 # H1: 6,9 => SOL * STA G3: 8,9 + H1: 6,9 * CNT 2 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .4.1.....5......2.....4.......5..1.48.7............6.......7.83..2.6.....1....... | initial |
| .4.15....531.7842..7..4..159235861748674.1.5.15472.6.8496217583.82.65.41.158.4... | autosolve |
| 648152397531978426279643815923586174867431259154729638496217583782365941315894762 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A1: 2,6 C1: 8,9 A3: 2,6 C3: 8,9 D2: 6,9 I2: 6,9 E5: 3,9 F6: 3,9 I5: 2,9 H6: 3,9 A8: 3,7 A9: 3,7 D8: 3,9 E9: 3,9 G8: 7,9 H9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 2.. / A1 = 2 => 18 pairs (_) / A3 = 2 => 0 pairs (*) F1,F3: 2.. / F1 = 2 => 0 pairs (*) / F3 = 2 => 0 pairs (X) G5,I5: 2.. / G5 = 2 => 0 pairs (*) / I5 = 2 => 0 pairs (X) G9,I9: 2.. / G9 = 2 => 16 pairs (_) / I9 = 2 => 0 pairs (*) A1,F1: 2.. / A1 = 2 => 18 pairs (_) / F1 = 2 => 0 pairs (*) A3,F3: 2.. / A3 = 2 => 0 pairs (*) / F3 = 2 => 0 pairs (X) G5,G9: 2.. / G5 = 2 => 0 pairs (*) / G9 = 2 => 0 pairs (X) I5,I9: 2.. / I5 = 2 => 16 pairs (_) / I9 = 2 => 0 pairs (*) E5,F6: 3.. / E5 = 3 => 0 pairs (*) / F6 = 3 => 0 pairs (X) G5,H6: 3.. / G5 = 3 => 0 pairs (X) / H6 = 3 => 0 pairs (_) A8,A9: 3.. / A8 = 3 => 0 pairs (X) / A9 = 3 => 0 pairs (_) D8,E9: 3.. / D8 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) E5,G5: 3.. / E5 = 3 => 0 pairs (*) / G5 = 3 => 0 pairs (X) F6,H6: 3.. / F6 = 3 => 0 pairs (X) / H6 = 3 => 0 pairs (_) A8,D8: 3.. / A8 = 3 => 0 pairs (X) / D8 = 3 => 0 pairs (_) A9,E9: 3.. / A9 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) D3,D8: 3.. / D3 = 3 => 0 pairs (X) / D8 = 3 => 0 pairs (_) E5,E9: 3.. / E5 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) H1,H6: 3.. / H1 = 3 => 0 pairs (X) / H6 = 3 => 0 pairs (_) A1,A3: 6.. / A1 = 6 => 0 pairs (*) / A3 = 6 => 0 pairs (X) D2,D3: 6.. / D2 = 6 => 18 pairs (_) / D3 = 6 => 0 pairs (*) H9,I9: 6.. / H9 = 6 => 16 pairs (_) / I9 = 6 => 0 pairs (X) D2,I2: 6.. / D2 = 6 => 18 pairs (_) / I2 = 6 => 0 pairs (*) A3,D3: 6.. / A3 = 6 => 18 pairs (_) / D3 = 6 => 0 pairs (*) H1,H9: 6.. / H1 = 6 => 0 pairs (X) / H9 = 6 => 16 pairs (_) G1,I1: 7.. / G1 = 7 => 0 pairs (X) / I1 = 7 => 16 pairs (_) A8,A9: 7.. / A8 = 7 => 0 pairs (*) / A9 = 7 => 0 pairs (X) A8,G8: 7.. / A8 = 7 => 0 pairs (*) / G8 = 7 => 0 pairs (X) I1,I9: 7.. / I1 = 7 => 16 pairs (_) / I9 = 7 => 0 pairs (X) C1,C3: 8.. / C1 = 8 => 17 pairs (_) / C3 = 8 => 17 pairs (_) G1,G3: 8.. / G1 = 8 => 17 pairs (_) / G3 = 8 => 17 pairs (_) C1,G1: 8.. / C1 = 8 => 17 pairs (_) / G1 = 8 => 17 pairs (_) C3,G3: 8.. / C3 = 8 => 17 pairs (_) / G3 = 8 => 17 pairs (_) C1,C3: 9.. / C1 = 9 => 17 pairs (_) / C3 = 9 => 17 pairs (_) E5,F6: 9.. / E5 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) D8,E9: 9.. / D8 = 9 => 0 pairs (X) / E9 = 9 => 0 pairs (_) D2,I2: 9.. / D2 = 9 => 0 pairs (*) / I2 = 9 => 0 pairs (X) F6,H6: 9.. / F6 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) D8,G8: 9.. / D8 = 9 => 0 pairs (X) / G8 = 9 => 0 pairs (_) E5,E9: 9.. / E5 = 9 => 0 pairs (X) / E9 = 9 => 0 pairs (_) * DURATION: 0:01:18.249977 START: 11:29:47.271120 END: 11:31:05.521097 2017-05-04 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A8,A9,C1,C3,D2,D8,E5,E9,F6,G8,H6,H9,I2,I5) * .4.15....531.7842..7..4..159235861748674.1.5.15472.6.8496217583.82.65.41.158.4... * PAIR C1: 8,9 ROW 1 G1: 8,9,3,7 # reduction candidate for 8,9 G1: 8,9 # 19 pairs G1: 3,7 # 18 pairs * PAIR C3: 8,9 ROW 3 G3: 8,9,3 # reduction candidate for 8,9 G3: 3 => CTR * .4.15.8.7531.7842..78.4.315923586174867431.5.154729638496217583.82365941315894762 G3: 8,9 # 20 pairs * PAIR D2: 6,9 BLK 2 D3: 6,9,3 # reduction candidate for 6,9 D3: 6,9 => SOLVED * 648152397531978426279643815923586174867431259154729638496217583782365941315894762 D3: 3 => CTR * .4.15....53167842967.3428159235861748674.1.52154723698496217583382965741.158.4... * PAIR I2: 6,9 BLK 3 H1: 6,9,3 # reduction candidate for 6,9 H1: 6,9 => SOLVED * 648152397531978426279643815923586174867431259154729638496217583782365941315894762 H1: 3 => CTR * .4.15..3753197842..7..4..159235861748674.1352154723698496217583.82.65.41.15834269 I1: 6,9,7 # reduction candidate for 6,9 I1: 6,9 => CTR * .4.15.7..531.7842..7..4.8159235861748674.1352154723698496217583782365941315894... I1: 7 # 16 pairs * PAIR I2: 6,9 COL I I9: 6,9,2,7 # reduction candidate for 6,9 I9: 6,9 => CTR * .4.15...7531.7842..7.34..15923586174867491352154723698496217583382965741715834269 I9: 2,7 # 19 pairs * PAIR E5: 3,9 ROW 5 G5: 3,9,2 # reduction candidate for 3,9 G5: 2 => SOLVED * 648152397531978426279643815923586174867431259154729638496217583782365941315894762 G5: 3,9 # 16 pairs * PAIR F6: 3,9 COL F F1: 3,9,2 # reduction candidate for 3,9 F1: 3,9 # 18 pairs F3: 3,9,2 # reduction candidate for 3,9 F3: 3,9 => SOLVED * 648152397531978426279643815923586174867431259154729638496217583782365941315894762 F3: 2 # 18 pairs * PAIR I5: 2,9 BLK 6 G5: 2,9,3 # reduction candidate for 2,9 G5: 2,9 => SOLVED * 648152397531978426279643815923586174867431259154729638496217583782365941315894762 G5: 3 => CTR * .4.15..3753197842..7..4..159235861748674.1352154723698496217583.82.65.41.15834269 * PAIR I5: 2,9 COL I I9: 2,9,6,7 # reduction candidate for 2,9 I9: 2,9 => SOLVED * 648152397531978426279643815923586174867431259154729638496217583782365941315894762 I9: 6,7 # 19 pairs * PAIR H6: 3,9 BLK 6 G5: 3,9,2 # reduction candidate for 3,9 G5: 2 => SOLVED * 648152397531978426279643815923586174867431259154729638496217583782365941315894762 G5: 3,9 # 16 pairs * PAIR H6: 3,9 COL H H1: 3,9,6 # reduction candidate for 3,9 H1: 6 => CTR * .4.15..6.53167842967..42.159235861748674.1.5215472.638496217583.82.65.41.158.4296 H1: 3,9 # 16 pairs * PAIR D8: 3,9 COL D D3: 3,9,6 # reduction candidate for 3,9 D3: 6 => SOLVED * 648152397531978426279643815923586174867431259154729638496217583782365941315894762 D3: 3,9 # 18 pairs * PAIR G8: 7,9 BLK 9 G9: 7,9,2 # reduction candidate for 7,9 G9: 7,9 => SOLVED * 648152397531978426279643815923586174867431259154729638496217583782365941315894762 G9: 2 # 16 pairs I9: 7,9,2,6 # reduction candidate for 7,9 I9: 7,9 # 17 pairs * PAIR G8: 7,9 COL G G1: 7,9,3,8 # reduction candidate for 7,9 G1: 7,9 => CTR * .481597..531.7842..79.4.8159235861748674.1352154723698496217583.82.65.41.15834269 G1: 3,8 # 17 pairs * PAIR H9: 6,9 BLK 9 I9: 6,9,2,7 # reduction candidate for 6,9 I9: 6,9 => CTR * .4.15...7531.7842..7.34..15923586174867491352154723698496217583382965741715834269 I9: 2,7 # 19 pairs * PAIR H9: 6,9 COL H H1: 6,9,3 # reduction candidate for 6,9 H1: 6,9 => SOLVED * 648152397531978426279643815923586174867431259154729638496217583782365941315894762 H1: 3 => CTR * .4.15..3753197842..7..4..159235861748674.1352154723698496217583.82.65.41.15834269 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-255-base-pr-000.dot * REASONING * DIS # G3: 3 => CTR => G3: 8,9 * PRF # D3: 6,9 => SOL * DIS # D3: 3 => CTR => D3: 6,9 * PRF # H1: 6,9 => SOL * DIS # H1: 3 => CTR => H1: 6,9 * DIS # I1: 6,9 => CTR => I1: 7 * DIS # I9: 6,9 => CTR => I9: 2,7 * PRF # G5: 2 => SOL * PRF # F3: 3,9 => SOL * PRF # G5: 2,9 => SOL * DIS # G5: 3 => CTR => G5: 2,9 * PRF # I9: 2,9 => SOL * PRF # G5: 2 => SOL * DIS # H1: 6 => CTR => H1: 3,9 * PRF # D3: 6 => SOL * PRF # G9: 7,9 => SOL * DIS # G1: 7,9 => CTR => G1: 3,8 * DIS # I9: 6,9 => CTR => I9: 2,7 * PRF # H1: 6,9 => SOL * DIS # H1: 3 => CTR => H1: 6,9 * CNT 20 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A8,A9,C1,C3,D2,D8,E5,E9,F6,G8,H6,H9,I2,I5) * .4.15....531.7842..7..4..159235861748674.1.5.15472.6.8496217583.82.65.41.158.4... * PAIR C1: 8,9 ROW 1 G1: 8,9,3,7 # reduction candidate for 8,9 G1: 8,9 # 19 pairs G1: 3,7 # 18 pairs * PAIR C3: 8,9 ROW 3 G3: 8,9,3 # reduction candidate for 8,9 G3: 3 => CTR * .4.15.8.7531.7842..78.4.315923586174867431.5.154729638496217583.82365941315894762 * PAIR RESTART * PAIR I2: 6,9 BLK 3 H1: 6,9,3 # reduction candidate for 6,9 H1: 6,9 => SOLVED * 648152397531978426279643815923586174867431259154729638496217583782365941315894762 * DURATION: 0:00:06.725410 START: 11:31:48.916471 END: 11:31:55.641881 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-255-base-pr-001.dot * REASONING * DIS # G3: 3 => CTR => G3: 8,9 * PRF G3: 8,9 # H1: 6,9 => SOL * STA G3: 8,9 + H1: 6,9 * CNT 2 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 255 solution: 648152397531978426279643815923586174867431259154729638496217583782365941315894762 info: 2077 FNBWXY S8.f 46430 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 648152397531978426279643815923586174867431259154729638496217583782365941315894762 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 # G1: 8,9 => UNS * INC # G1: 3,7 => UNS * INC # G3: 8,9 => UNS * DIS # G3: 3 => CTR => G3: 8,9 * PRF # D3: 6,9 => SOL * DIS # D3: 3 => CTR => D3: 6,9 * PRF # H1: 6,9 => SOL * DIS # H1: 3 => CTR => H1: 6,9 * DIS # I1: 6,9 => CTR => I1: 7 * INC # I1: 7 => UNS * DIS # I9: 6,9 => CTR => I9: 2,7 * INC # I9: 2,7 => UNS * INC # G5: 3,9 => UNS * PRF # G5: 2 => SOL * INC # F1: 3,9 => UNS * PRF # F3: 3,9 => SOL * INC # F3: 2 => UNS * PRF # G5: 2,9 => SOL * DIS # G5: 3 => CTR => G5: 2,9 * PRF # I9: 2,9 => SOL * INC # I9: 6,7 => UNS * INC # G5: 3,9 => UNS * PRF # G5: 2 => SOL * INC # H1: 3,9 => UNS * DIS # H1: 6 => CTR => H1: 3,9 * INC # D3: 3,9 => UNS * PRF # D3: 6 => SOL * PRF # G9: 7,9 => SOL * INC # G9: 2 => UNS * INC # I9: 7,9 => UNS * DIS # G1: 7,9 => CTR => G1: 3,8 * INC # G1: 3,8 => UNS * DIS # I9: 6,9 => CTR => I9: 2,7 * INC # I9: 2,7 => UNS * PRF # H1: 6,9 => SOL * DIS # H1: 3 => CTR => H1: 6,9 * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G1: 8,9 => UNS * INC # G1: 3,7 => UNS * INC # G3: 8,9 => UNS * DIS # G3: 3 => CTR => G3: 8,9 * PRF G3: 8,9 # H1: 6,9 => SOL * STA G3: 8,9 + H1: 6,9 * CNT 5 HDP CHAINS / 5 HYP OPENED