Analysis of xx-top500-089-base.sdk
Contents
Original Sudoku
level: medium
position: ....2.8..5.......4.1.......2.8.4.......3..1.........7....7...3.6..1.....4.......2 initial
Autosolve
position: ...42.81.582.173.4.148..2..278.41..394.37.12.1.32..47.82.7.4631637182.4.4.1...782 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D4: 6,9 => CTR => D4: 5 * PRF # D4: 5 => SOL * PRF # D9: 6,9 => SOL * DIS # D9: 5 => CTR => D9: 6,9 * DIS # I3: 5,7 => CTR => I3: 6,9 * DIS # H3: 6,9 => CTR => H3: 5 * DIS # H4: 5 => CTR => H4: 6,9 * DIS # F6: 5,6 => CTR => F6: 8,9 * PRF # I6: 5,6 => SOL * DIS # H4: 5,9 => CTR => H4: 6 * PRF # I6: 5,9 => SOL * DIS # D4: 6 => CTR => D4: 5,9 * DIS # E9: 5,9 => CTR => E9: 3,6 * DIS # F9: 5,9 => CTR => F9: 3,6 * DIS # E9: 5,9 => CTR => E9: 3,6 * DIS # F9: 5,9 => CTR => F9: 3,6 * DIS # E3: 5,9 => CTR => E3: 3,6 * DIS # I3: 5,9 => CTR => I3: 6,7 * PRF # I6: 5,9 => SOL * CNT 19 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D4: 6,9 => CTR => D4: 5 * PRF D4: 5 => SOL * STA D4: 5 * CNT 2 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....2.8..5.......4.1.......2.8.4.......3..1.........7....7...3.6..1.....4.......2 | initial |
| ...42.81.582.173.4.148..2..278.41..394.37.12.1.32..47.82.7.4631637182.4.4.1...782 | autosolve |
| 396425817582617394714839256278541963945376128163298475829754631637182549451963782 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A1: 3,7 B1: 6,9 C1: 6,9 A3: 3,7 F1: 3,5 D2: 6,9 I1: 5,7 H2: 6,9 C5: 5,6 B6: 5,6 G4: 5,9 C7: 5,9 B9: 5,9 E7: 5,9 G8: 5,9 I8: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 3.. / A1 = 3 => 13 pairs (_) / A3 = 3 => 0 pairs (X) E9,F9: 3.. / E9 = 3 => 16 pairs (_) / F9 = 3 => 14 pairs (_) A1,F1: 3.. / A1 = 3 => 13 pairs (_) / F1 = 3 => 0 pairs (X) E3,E9: 3.. / E3 = 3 => 14 pairs (_) / E9 = 3 => 16 pairs (_) C5,B6: 5.. / C5 = 5 => 0 pairs (*) / B6 = 5 => 0 pairs (X) C7,B9: 5.. / C7 = 5 => 0 pairs (X) / B9 = 5 => 0 pairs (_) G8,I8: 5.. / G8 = 5 => 15 pairs (_) / I8 = 5 => 0 pairs (X) F1,I1: 5.. / F1 = 5 => 13 pairs (_) / I1 = 5 => 0 pairs (X) C7,E7: 5.. / C7 = 5 => 0 pairs (X) / E7 = 5 => 0 pairs (_) B6,B9: 5.. / B6 = 5 => 0 pairs (X) / B9 = 5 => 0 pairs (_) C5,C7: 5.. / C5 = 5 => 0 pairs (*) / C7 = 5 => 0 pairs (X) D4,D9: 5.. / D4 = 5 => 0 pairs (*) / D9 = 5 => 0 pairs (X) G4,G8: 5.. / G4 = 5 => 0 pairs (X) / G8 = 5 => 15 pairs (_) H3,H4: 5.. / H3 = 5 => 15 pairs (_) / H4 = 5 => 0 pairs (X) B1,C1: 6.. / B1 = 6 => 0 pairs (X) / C1 = 6 => 0 pairs (_) C5,B6: 6.. / C5 = 6 => 0 pairs (X) / B6 = 6 => 0 pairs (_) D2,H2: 6.. / D2 = 6 => 18 pairs (_) / H2 = 6 => 0 pairs (X) D4,H4: 6.. / D4 = 6 => 0 pairs (X) / H4 = 6 => 18 pairs (_) B1,B6: 6.. / B1 = 6 => 0 pairs (X) / B6 = 6 => 0 pairs (_) C1,C5: 6.. / C1 = 6 => 0 pairs (*) / C5 = 6 => 0 pairs (X) A1,A3: 7.. / A1 = 7 => 0 pairs (X) / A3 = 7 => 13 pairs (_) I1,I3: 7.. / I1 = 7 => 13 pairs (_) / I3 = 7 => 0 pairs (X) A1,I1: 7.. / A1 = 7 => 0 pairs (X) / I1 = 7 => 13 pairs (_) A3,I3: 7.. / A3 = 7 => 13 pairs (_) / I3 = 7 => 0 pairs (X) F5,F6: 8.. / F5 = 8 => 18 pairs (_) / F6 = 8 => 17 pairs (_) I5,I6: 8.. / I5 = 8 => 17 pairs (_) / I6 = 8 => 18 pairs (_) F5,I5: 8.. / F5 = 8 => 18 pairs (_) / I5 = 8 => 17 pairs (_) F6,I6: 8.. / F6 = 8 => 17 pairs (_) / I6 = 8 => 18 pairs (_) B1,C1: 9.. / B1 = 9 => 0 pairs (*) / C1 = 9 => 0 pairs (X) C7,B9: 9.. / C7 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) G8,I8: 9.. / G8 = 9 => 0 pairs (X) / I8 = 9 => 15 pairs (_) D2,H2: 9.. / D2 = 9 => 0 pairs (X) / H2 = 9 => 18 pairs (_) C7,E7: 9.. / C7 = 9 => 0 pairs (*) / E7 = 9 => 0 pairs (X) B1,B9: 9.. / B1 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) C1,C7: 9.. / C1 = 9 => 0 pairs (X) / C7 = 9 => 0 pairs (_) G4,G8: 9.. / G4 = 9 => 15 pairs (_) / G8 = 9 => 0 pairs (X) * DURATION: 0:01:00.481788 START: 05:49:16.657215 END: 05:50:17.139003 2017-05-04 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B1,B6,B9,C1,C5,C7,D2,E7,F1,G4,G8,H2,I1,I8) * ...42.81.582.173.4.148..2..278.41..394.37.12.1.32..47.82.7.4631637182.4.4.1...782 * PAIR F1: 3,5 BLK 2 E3: 3,5,6,9 # reduction candidate for 3,5 E3: 3,5 # 18 pairs F3: 3,5,6,9 # reduction candidate for 3,5 F3: 3,5 # 20 pairs * PAIR F1: 3,5 COL F F9: 3,5,6,9 # reduction candidate for 3,5 F9: 3,5 # 20 pairs F9: 6,9 # 17 pairs * PAIR D2: 6,9 BLK 2 E3: 6,9,3,5 # reduction candidate for 6,9 E3: 6,9 # 20 pairs F3: 6,9,3,5 # reduction candidate for 6,9 F3: 6,9 # 18 pairs * PAIR D2: 6,9 COL D D4: 6,9,5 # reduction candidate for 6,9 D4: 6,9 => CTR * .6942.81.582.173.4.1485.2..278.41.53946375128153268479825794631637182.4.4915..782 D4: 5 => SOLVED * 396425817582617394714839256278541963945376128163298475829754631637182549451963782 D9: 6,9,5 # reduction candidate for 6,9 D9: 6,9 => SOLVED * 396425817582617394714839256278541963945376128163298475829754631637182549451963782 D9: 5 => CTR * .6942.81.582.173.4.1485.2..278.41.53946375128153268479825794631637182.4.4915..782 * PAIR I1: 5,7 BLK 3 I3: 5,7,6,9 # reduction candidate for 5,7 I3: 5,7 => CTR * ...42.81.582917364.148..29.27864195394.37.12.15329.47.82.7.46316371825494.15..782 I3: 6,9 # 15 pairs * PAIR H2: 6,9 BLK 3 H3: 6,9,5 # reduction candidate for 6,9 H3: 6,9 => CTR * ...42.81.582.173.4.148..2..27864195394.37.12.15329.47.82.7.46316371825494.15..782 H3: 5 # 15 pairs I3: 6,9,5,7 # reduction candidate for 6,9 I3: 6,9 # 15 pairs * PAIR H2: 6,9 COL H H4: 6,9,5 # reduction candidate for 6,9 H4: 5 => CTR * ...42.81.582917364.148..29.27864195394.37.12.15329.47.82.7.46316371825494.15..782 H4: 6,9 # 15 pairs * PAIR C5: 5,6 ROW 5 F5: 5,6,8 # reduction candidate for 5,6 F5: 5,6 # 17 pairs I5: 5,6,8 # reduction candidate for 5,6 I5: 5,6 # 18 pairs * PAIR B6: 5,6 ROW 6 E6: 5,6,9 # reduction candidate for 5,6 E6: 5,6 # 19 pairs F6: 5,6,8,9 # reduction candidate for 5,6 F6: 5,6 => CTR * .9642.81.582.173.4.148..2..2785419.394.37812.1.329.478829754631637182.4.451...782 F6: 8,9 # 17 pairs I6: 5,6,8,9 # reduction candidate for 5,6 I6: 5,6 => SOLVED * 396425817582617394714839256278541963945376128163298475829754631637182549451963782 I6: 8,9 # 17 pairs * PAIR G4: 5,9 BLK 6 H4: 5,9,6 # reduction candidate for 5,9 H4: 5,9 => CTR * ...42.81.582917364.148..2..278641..394.37.12.15329.47.82.7.4631637182.4.4.15..782 H4: 6 # 18 pairs I6: 5,9,6,8 # reduction candidate for 5,9 I6: 5,9 => SOLVED * 396425817582617394714839256278541963945376128163298475829754631637182549451963782 I6: 6,8 # 18 pairs * PAIR G4: 5,9 ROW 4 D4: 5,9,6 # reduction candidate for 5,9 D4: 6 => CTR * ...42.81.582917364.148..2..278641..394.37.12.15329.47.82.7.4631637182.4.4.15..782 D4: 5,9 # 18 pairs * PAIR B9: 5,9 ROW 9 D9: 5,9,6 # reduction candidate for 5,9 D9: 5,9 # 19 pairs E9: 5,9,3,6 # reduction candidate for 5,9 E9: 5,9 => CTR * 369425817582.173.47148362..2785419639463781251532694788257946316371825494.1..3782 E9: 3,6 # 17 pairs F9: 5,9,3,6 # reduction candidate for 5,9 F9: 5,9 => CTR * ...42.81.582917364.148..2..2785419.394.37.12.1.32..47.82.7.4631637182.4.4.163.782 F9: 3,6 # 17 pairs * PAIR E7: 5,9 BLK 8 D9: 5,9,6 # reduction candidate for 5,9 D9: 5,9 # 19 pairs E9: 5,9,3,6 # reduction candidate for 5,9 E9: 5,9 => CTR * 369425817582.173.47148362..2785419639463781251532694788257946316371825494.1..3782 E9: 3,6 # 17 pairs F9: 5,9,3,6 # reduction candidate for 5,9 F9: 5,9 => CTR * ...42.81.582917364.148..2..2785419.394.37.12.1.32..47.82.7.4631637182.4.4.163.782 F9: 3,6 # 17 pairs * PAIR E7: 5,9 COL E E3: 5,9,3,6 # reduction candidate for 5,9 E3: 5,9 => CTR * .6942.81.582617394.1485.2..278.41.6394637.12.15326.47.825794631637182.4.491.3.782 E3: 3,6 # 18 pairs E6: 5,9,6 # reduction candidate for 5,9 E6: 5,9 # 20 pairs * PAIR I8: 5,9 COL I I3: 5,9,6,7 # reduction candidate for 5,9 I3: 5,9 => CTR * 3..425817582.173.47148..2..278641..394.37812.1.3259478825794631637182.4.4915..782 I3: 6,7 # 18 pairs I6: 5,9,6,8 # reduction candidate for 5,9 I6: 5,9 => SOLVED * 396425817582617394714839256278541963945376128163298475829754631637182549451963782 I6: 6,8 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-089-base-pr-000.dot * REASONING * DIS # D4: 6,9 => CTR => D4: 5 * PRF # D4: 5 => SOL * PRF # D9: 6,9 => SOL * DIS # D9: 5 => CTR => D9: 6,9 * DIS # I3: 5,7 => CTR => I3: 6,9 * DIS # H3: 6,9 => CTR => H3: 5 * DIS # H4: 5 => CTR => H4: 6,9 * DIS # F6: 5,6 => CTR => F6: 8,9 * PRF # I6: 5,6 => SOL * DIS # H4: 5,9 => CTR => H4: 6 * PRF # I6: 5,9 => SOL * DIS # D4: 6 => CTR => D4: 5,9 * DIS # E9: 5,9 => CTR => E9: 3,6 * DIS # F9: 5,9 => CTR => F9: 3,6 * DIS # E9: 5,9 => CTR => E9: 3,6 * DIS # F9: 5,9 => CTR => F9: 3,6 * DIS # E3: 5,9 => CTR => E3: 3,6 * DIS # I3: 5,9 => CTR => I3: 6,7 * PRF # I6: 5,9 => SOL * CNT 19 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B1,B6,B9,C1,C5,C7,D2,E7,F1,G4,G8,H2,I1,I8) * ...42.81.582.173.4.148..2..278.41..394.37.12.1.32..47.82.7.4631637182.4.4.1...782 * PAIR F1: 3,5 BLK 2 E3: 3,5,6,9 # reduction candidate for 3,5 E3: 3,5 # 18 pairs F3: 3,5,6,9 # reduction candidate for 3,5 F3: 3,5 # 20 pairs * PAIR F1: 3,5 COL F F9: 3,5,6,9 # reduction candidate for 3,5 F9: 3,5 # 20 pairs F9: 6,9 # 17 pairs * PAIR D2: 6,9 BLK 2 E3: 6,9,3,5 # reduction candidate for 6,9 E3: 6,9 # 20 pairs F3: 6,9,3,5 # reduction candidate for 6,9 F3: 6,9 # 18 pairs * PAIR D2: 6,9 COL D D4: 6,9,5 # reduction candidate for 6,9 D4: 6,9 => CTR * .6942.81.582.173.4.1485.2..278.41.53946375128153268479825794631637182.4.4915..782 D4: 5 => SOLVED * 396425817582617394714839256278541963945376128163298475829754631637182549451963782 * DURATION: 0:00:07.001277 START: 05:51:01.108626 END: 05:51:08.109903 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-089-base-pr-001.dot * REASONING * DIS # D4: 6,9 => CTR => D4: 5 * PRF D4: 5 => SOL * STA D4: 5 * CNT 2 HDP CHAINS / 7 HYP OPENED
Header Info
Top 500 Minimum 17 089 solution: 396425817582617394714839256278541963945376128163298475829754631637182549451963782 info: 1565 FNBTWXY S8.f 3431 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 396425817582617394714839256278541963945376128163298475829754631637182549451963782 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: 3,5 => UNS * INC # F3: 3,5 => UNS * INC # F9: 3,5 => UNS * INC # F9: 6,9 => UNS * INC # E3: 6,9 => UNS * INC # F3: 6,9 => UNS * DIS # D4: 6,9 => CTR => D4: 5 * PRF # D4: 5 => SOL * PRF # D9: 6,9 => SOL * DIS # D9: 5 => CTR => D9: 6,9 * DIS # I3: 5,7 => CTR => I3: 6,9 * INC # I3: 6,9 => UNS * DIS # H3: 6,9 => CTR => H3: 5 * INC # H3: 5 => UNS * INC # I3: 6,9 => UNS * INC # H4: 6,9 => UNS * DIS # H4: 5 => CTR => H4: 6,9 * INC # F5: 5,6 => UNS * INC # I5: 5,6 => UNS * INC # E6: 5,6 => UNS * DIS # F6: 5,6 => CTR => F6: 8,9 * INC # F6: 8,9 => UNS * PRF # I6: 5,6 => SOL * INC # I6: 8,9 => UNS * DIS # H4: 5,9 => CTR => H4: 6 * INC # H4: 6 => UNS * PRF # I6: 5,9 => SOL * INC # I6: 6,8 => UNS * INC # D4: 5,9 => UNS * DIS # D4: 6 => CTR => D4: 5,9 * INC # D9: 5,9 => UNS * DIS # E9: 5,9 => CTR => E9: 3,6 * INC # E9: 3,6 => UNS * DIS # F9: 5,9 => CTR => F9: 3,6 * INC # F9: 3,6 => UNS * INC # D9: 5,9 => UNS * DIS # E9: 5,9 => CTR => E9: 3,6 * INC # E9: 3,6 => UNS * DIS # F9: 5,9 => CTR => F9: 3,6 * INC # F9: 3,6 => UNS * DIS # E3: 5,9 => CTR => E3: 3,6 * INC # E3: 3,6 => UNS * INC # E6: 5,9 => UNS * DIS # I3: 5,9 => CTR => I3: 6,7 * INC # I3: 6,7 => UNS * PRF # I6: 5,9 => SOL * INC # I6: 6,8 => UNS * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E3: 3,5 => UNS * INC # F3: 3,5 => UNS * INC # F9: 3,5 => UNS * INC # F9: 6,9 => UNS * INC # E3: 6,9 => UNS * INC # F3: 6,9 => UNS * DIS # D4: 6,9 => CTR => D4: 5 * PRF D4: 5 => SOL * STA D4: 5 * CNT 8 HDP CHAINS / 7 HYP OPENED