Analysis of xx-top500-434-base.sdk
Contents
Original Sudoku
level: medium
position: ......8.1...6........5........4...5..9.....4..2..7....3...1.7..5.....1..4.6...... initial
Autosolve
position: 657.4.8.1.4.6..5...3.5..4.61634.8.577951...48824.7561.38..1476557.8..1.441675..8. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E2: 2,9 => CTR => E2: 3,8 * DIS # H2: 2,9 => CTR => H2: 3,7 * DIS # E2: 2,9 => CTR => E2: 3,8 * DIS # E8: 2,9 => CTR => E8: 3,6 * PRF # D1: 2 => SOL * PRF # I9: 3,9 => SOL * DIS # E8: 2,9 => CTR => E8: 3,6 * DIS # F8: 2,9 => CTR => F8: 3,6 * DIS # E8: 2,9 => CTR => E8: 3,6 * DIS # F8: 2,9 => CTR => F8: 3,6 * DIS # D1: 3 => CTR => D1: 2,9 * PRF # I9: 3,9 => SOL * PRF # F9: 2 => SOL * CNT 13 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 # E2: 2,9 => CTR => E2: 3,8 * DIS E2: 3,8 # H2: 2,9 => CTR => H2: 3,7 * PRF E2: 3,8 + H2: 3,7 # H3: 2,9 => SOL * STA E2: 3,8 + H2: 3,7 + H3: 2,9 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......8.1...6........5........4...5..9.....4..2..7....3...1.7..5.....1..4.6...... | initial |
| 657.4.8.1.4.6..5...3.5..4.61634.8.577951...48824.7561.38..1476557.8..1.441675..8. | autosolve |
| 657249831948631572231587496163498257795126348824375619382914765579863124416752983 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A2: 2,9 C2: 1,8 A3: 2,9 C3: 1,8 F2: 1,7 F3: 1,7 E4: 2,9 D6: 3,9 G4: 2,9 G5: 2,3 I6: 3,9 C7: 2,9 C8: 2,9 D7: 2,9 G9: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 1.. / C2 = 1 => 15 pairs (_) / C3 = 1 => 12 pairs (_) F2,F3: 1.. / F2 = 1 => 12 pairs (_) / F3 = 1 => 15 pairs (_) C2,F2: 1.. / C2 = 1 => 15 pairs (_) / F2 = 1 => 12 pairs (_) C3,F3: 1.. / C3 = 1 => 12 pairs (_) / F3 = 1 => 15 pairs (_) A2,A3: 2.. / A2 = 2 => 18 pairs (_) / A3 = 2 => 18 pairs (_) G4,G5: 2.. / G4 = 2 => 20 pairs (_) / G5 = 2 => 0 pairs (X) C7,C8: 2.. / C7 = 2 => 0 pairs (*) / C8 = 2 => 0 pairs (X) H8,I9: 2.. / H8 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) E4,G4: 2.. / E4 = 2 => 0 pairs (X) / G4 = 2 => 20 pairs (_) C7,D7: 2.. / C7 = 2 => 0 pairs (*) / D7 = 2 => 0 pairs (X) F9,I9: 2.. / F9 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) D1,D7: 2.. / D1 = 2 => 0 pairs (*) / D7 = 2 => 0 pairs (X) I2,I9: 2.. / I2 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) G5,I6: 3.. / G5 = 3 => 20 pairs (_) / I6 = 3 => 0 pairs (X) D6,I6: 3.. / D6 = 3 => 20 pairs (_) / I6 = 3 => 0 pairs (X) D1,D6: 3.. / D1 = 3 => 0 pairs (X) / D6 = 3 => 20 pairs (_) G5,G9: 3.. / G5 = 3 => 20 pairs (_) / G9 = 3 => 0 pairs (X) E5,F5: 6.. / E5 = 6 => 16 pairs (_) / F5 = 6 => 19 pairs (_) E8,F8: 6.. / E8 = 6 => 19 pairs (_) / F8 = 6 => 16 pairs (_) E5,E8: 6.. / E5 = 6 => 16 pairs (_) / E8 = 6 => 19 pairs (_) F5,F8: 6.. / F5 = 6 => 19 pairs (_) / F8 = 6 => 16 pairs (_) F2,F3: 7.. / F2 = 7 => 15 pairs (_) / F3 = 7 => 12 pairs (_) H2,H3: 7.. / H2 = 7 => 12 pairs (_) / H3 = 7 => 15 pairs (_) F2,H2: 7.. / F2 = 7 => 15 pairs (_) / H2 = 7 => 12 pairs (_) F3,H3: 7.. / F3 = 7 => 12 pairs (_) / H3 = 7 => 15 pairs (_) C2,C3: 8.. / C2 = 8 => 12 pairs (_) / C3 = 8 => 15 pairs (_) E2,E3: 8.. / E2 = 8 => 15 pairs (_) / E3 = 8 => 12 pairs (_) C2,E2: 8.. / C2 = 8 => 12 pairs (_) / E2 = 8 => 15 pairs (_) C3,E3: 8.. / C3 = 8 => 15 pairs (_) / E3 = 8 => 12 pairs (_) A2,A3: 9.. / A2 = 9 => 18 pairs (_) / A3 = 9 => 18 pairs (_) E4,D6: 9.. / E4 = 9 => 20 pairs (_) / D6 = 9 => 0 pairs (X) G4,I6: 9.. / G4 = 9 => 0 pairs (X) / I6 = 9 => 20 pairs (_) C7,C8: 9.. / C7 = 9 => 16 pairs (_) / C8 = 9 => 0 pairs (*) E4,G4: 9.. / E4 = 9 => 20 pairs (_) / G4 = 9 => 0 pairs (X) D6,I6: 9.. / D6 = 9 => 0 pairs (X) / I6 = 9 => 20 pairs (_) C7,D7: 9.. / C7 = 9 => 16 pairs (_) / D7 = 9 => 0 pairs (*) G4,G9: 9.. / G4 = 9 => 0 pairs (X) / G9 = 9 => 20 pairs (_) * DURATION: 0:01:15.709411 START: 17:35:05.888015 END: 17:36:21.597426 2017-05-04 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,C2,C3,C7,C8,D6,D7,E4,F2,F3,G4,G5,G9,I6) * 657.4.8.1.4.6..5...3.5..4.61634.8.577951...48824.7561.38..1476557.8..1.441675..8. * PAIR A2: 2,9 ROW 2 E2: 2,9,3,8 # reduction candidate for 2,9 E2: 2,9 => CTR * 657.4.8.1.486.1573.315874.61634.8.577951..34882437561938..1476557.8361.441675.982 E2: 3,8 # 16 pairs H2: 2,9,3,7 # reduction candidate for 2,9 H2: 2,9 => CTR * 657.4.8.1.416875.3.385.14761634.8.577951..34882437561938..1476557.8361.441675.982 H2: 3,7 # 16 pairs I2: 2,9,3 # reduction candidate for 2,9 I2: 2,9 # 22 pairs * PAIR A3: 2,9 ROW 3 E3: 2,9,8 # reduction candidate for 2,9 E3: 2,9 # 15 pairs H3: 2,9,7 # reduction candidate for 2,9 H3: 2,9 # 12 pairs * PAIR E4: 2,9 COL E E2: 2,9,3,8 # reduction candidate for 2,9 E2: 2,9 => CTR * 657.4.8.1.486.1573.315874.61634.8.577951..34882437561938..1476557.8361.441675.982 E2: 3,8 # 16 pairs E3: 2,9,8 # reduction candidate for 2,9 E3: 2,9 # 15 pairs E8: 2,9,3,6 # reduction candidate for 2,9 E8: 2,9 => CTR * 657349821.4.6..5.3.3.5..4.61634.8.5779516..48824.7561.38..1476557.8.6134416753982 E8: 3,6 # 16 pairs * PAIR D6: 3,9 COL D D1: 3,9,2 # reduction candidate for 3,9 D1: 2 => SOLVED * 657249831948631572231587496163498257795126348824375619382914765579863124416752983 D1: 3,9 # 16 pairs * PAIR G5: 2,3 ROW 5 E5: 2,3,6 # reduction candidate for 2,3 E5: 2,3 # 19 pairs F5: 2,3,6 # reduction candidate for 2,3 F5: 2,3 # 16 pairs * PAIR I6: 3,9 COL I I2: 3,9,2 # reduction candidate for 3,9 I2: 3,9 # 18 pairs I9: 3,9,2 # reduction candidate for 3,9 I9: 3,9 => SOLVED * 657249831948631572231587496163498257795126348824375619382914765579863124416752983 I9: 2 # 18 pairs * PAIR C8: 2,9 ROW 8 E8: 2,9,3,6 # reduction candidate for 2,9 E8: 2,9 => CTR * 657349821.4.6..5.3.3.5..4.61634.8.5779516..48824.7561.38..1476557.8.6134416753982 E8: 3,6 # 16 pairs F8: 2,9,3,6 # reduction candidate for 2,9 F8: 2,9 => CTR * 65734.8.1.4.6..5.3.3.5..4.61634.8.577951.6.48824.7561.38..1476557.86.134416753982 F8: 3,6 # 16 pairs H8: 2,9,3 # reduction candidate for 2,9 H8: 2,9 # 22 pairs * PAIR D7: 2,9 BLK 8 E8: 2,9,3,6 # reduction candidate for 2,9 E8: 2,9 => CTR * 657349821.4.6..5.3.3.5..4.61634.8.5779516..48824.7561.38..1476557.8.6134416753982 E8: 3,6 # 16 pairs F8: 2,9,3,6 # reduction candidate for 2,9 F8: 2,9 => CTR * 65734.8.1.4.6..5.3.3.5..4.61634.8.577951.6.48824.7561.38..1476557.86.134416753982 F8: 3,6 # 16 pairs F9: 2,9,3 # reduction candidate for 2,9 F9: 2,9 # 22 pairs * PAIR D7: 2,9 COL D D1: 2,9,3 # reduction candidate for 2,9 D1: 3 => CTR * 65734.8.1.4.6..53993.5..4761634289577951..24882497561338921476557289.1.441675.382 D1: 2,9 # 20 pairs * PAIR G9: 3,9 BLK 9 H8: 3,9,2 # reduction candidate for 3,9 H8: 3,9 # 18 pairs I9: 3,9,2 # reduction candidate for 3,9 I9: 3,9 => SOLVED * 657249831948631572231587496163498257795126348824375619382914765579863124416752983 I9: 2 # 18 pairs * PAIR G9: 3,9 ROW 9 F9: 3,9,2 # reduction candidate for 3,9 F9: 2 => SOLVED * 657249831948631572231587496163498257795126348824375619382914765579863124416752983 F9: 3,9 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-434-base-pr-000.dot * REASONING * DIS # E2: 2,9 => CTR => E2: 3,8 * DIS # H2: 2,9 => CTR => H2: 3,7 * DIS # E2: 2,9 => CTR => E2: 3,8 * DIS # E8: 2,9 => CTR => E8: 3,6 * PRF # D1: 2 => SOL * PRF # I9: 3,9 => SOL * DIS # E8: 2,9 => CTR => E8: 3,6 * DIS # F8: 2,9 => CTR => F8: 3,6 * DIS # E8: 2,9 => CTR => E8: 3,6 * DIS # F8: 2,9 => CTR => F8: 3,6 * DIS # D1: 3 => CTR => D1: 2,9 * PRF # I9: 3,9 => SOL * PRF # F9: 2 => SOL * CNT 13 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,C2,C3,C7,C8,D6,D7,E4,F2,F3,G4,G5,G9,I6) * 657.4.8.1.4.6..5...3.5..4.61634.8.577951...48824.7561.38..1476557.8..1.441675..8. * PAIR A2: 2,9 ROW 2 E2: 2,9,3,8 # reduction candidate for 2,9 E2: 2,9 => CTR * 657.4.8.1.486.1573.315874.61634.8.577951..34882437561938..1476557.8361.441675.982 H2: 2,9,3,7 # reduction candidate for 2,9 H2: 2,9 => CTR * 657.4.8.1.416875.3.385.14761634.8.577951..34882437561938..1476557.8361.441675.982 * RESTART * PAIR RESTART * PAIR A3: 2,9 ROW 3 E3: 2,9,8 # reduction candidate for 2,9 E3: 2,9 # 19 pairs H3: 2,9,7 # reduction candidate for 2,9 H3: 2,9 => SOLVED * 657249831948631572231587496163498257795126348824375619382914765579863124416752983 * DURATION: 0:00:06.458833 START: 17:37:01.933241 END: 17:37:08.392074 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-434-base-pr-001.dot * REASONING * DIS # E2: 2,9 => CTR => E2: 3,8 * DIS E2: 3,8 # H2: 2,9 => CTR => H2: 3,7 * PRF E2: 3,8 + H2: 3,7 # H3: 2,9 => SOL * STA E2: 3,8 + H2: 3,7 + H3: 2,9 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 434 solution: 657249831948631572231587496163498257795126348824375619382914765579863124416752983 info: 95230 FNBTHWXK S8.f 1619 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 657249831948631572231587496163498257795126348824375619382914765579863124416752983 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 # E2: 2,9 => CTR => E2: 3,8 * INC # E2: 3,8 => UNS * DIS # H2: 2,9 => CTR => H2: 3,7 * INC # H2: 3,7 => UNS * INC # I2: 2,9 => UNS * INC # E3: 2,9 => UNS * INC # H3: 2,9 => UNS * DIS # E2: 2,9 => CTR => E2: 3,8 * INC # E2: 3,8 => UNS * INC # E3: 2,9 => UNS * DIS # E8: 2,9 => CTR => E8: 3,6 * INC # E8: 3,6 => UNS * INC # D1: 3,9 => UNS * PRF # D1: 2 => SOL * INC # E5: 2,3 => UNS * INC # F5: 2,3 => UNS * INC # I2: 3,9 => UNS * PRF # I9: 3,9 => SOL * INC # I9: 2 => UNS * DIS # E8: 2,9 => CTR => E8: 3,6 * INC # E8: 3,6 => UNS * DIS # F8: 2,9 => CTR => F8: 3,6 * INC # F8: 3,6 => UNS * INC # H8: 2,9 => UNS * DIS # E8: 2,9 => CTR => E8: 3,6 * INC # E8: 3,6 => UNS * DIS # F8: 2,9 => CTR => F8: 3,6 * INC # F8: 3,6 => UNS * INC # F9: 2,9 => UNS * INC # D1: 2,9 => UNS * DIS # D1: 3 => CTR => D1: 2,9 * INC # H8: 3,9 => UNS * PRF # I9: 3,9 => SOL * INC # I9: 2 => UNS * INC # F9: 3,9 => UNS * PRF # F9: 2 => SOL * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E2: 2,9 => CTR => E2: 3,8 * DIS E2: 3,8 # H2: 2,9 => CTR => H2: 3,7 * INC E2: 3,8 + H2: 3,7 # E3: 2,9 => UNS * PRF E2: 3,8 + H2: 3,7 # H3: 2,9 => SOL * STA E2: 3,8 + H2: 3,7 + H3: 2,9 * CNT 4 HDP CHAINS / 4 HYP OPENED