Analysis of xx-top500-421-base.sdk
Contents
Original Sudoku
level: medium
position: 38......2...1...........4....7..65......8..1.....2.......5..73.24.......8........ initial
Autosolve
position: 38......2..21..8.....2.84...27..6589.3..8.21...8.2.34....5427382438.....875....24 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I3: 1 => CTR => I3: 3,5 * DIS # E2: 3,5 => CTR => E2: 6,7,9 * PRF # E9: 1,3 => SOL * DIS # F5: 7,9 => CTR => F5: 4,5 * DIS # F6: 7,9 => CTR => F6: 1,5 * DIS # D1: 7,9 => CTR => D1: 4,6 * DIS # I3: 1,5 => CTR => I3: 3 * CNT 7 HDP CHAINS / 15 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I3: 1 => CTR => I3: 3,5 * PRF I3: 3,5 # E9: 1,3 => SOL * STA I3: 3,5 + E9: 1,3 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 38......2...1...........4....7..65......8..1.....2.......5..73.24.......8........ | initial |
| 38......2..21..8.....2.84...27..6589.3..8.21...8.2.34....5427382438.....875....24 | autosolve |
| 389654172462173895751298463127436589634985217598721346916542738243867951875319624 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) I2: 3,5 A4: 1,4 D4: 3,4 E4: 1,3 D6: 7,9 I5: 6,7 I6: 6,7 I8: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,I3: 1.. / G1 = 1 => 11 pairs (_) / I3 = 1 => 0 pairs (X) E4,F6: 1.. / E4 = 1 => 0 pairs (X) / F6 = 1 => 0 pairs (_) C1,G1: 1.. / C1 = 1 => 0 pairs (X) / G1 = 1 => 11 pairs (_) A4,E4: 1.. / A4 = 1 => 0 pairs (*) / E4 = 1 => 0 pairs (X) I3,I8: 1.. / I3 = 1 => 0 pairs (X) / I8 = 1 => 11 pairs (_) I2,I3: 3.. / I2 = 3 => 0 pairs (X) / I3 = 3 => 10 pairs (_) D4,E4: 3.. / D4 = 3 => 0 pairs (X) / E4 = 3 => 0 pairs (_) E3,I3: 3.. / E3 = 3 => 0 pairs (X) / I3 = 3 => 10 pairs (_) D4,D9: 3.. / D4 = 3 => 0 pairs (X) / D9 = 3 => 0 pairs (_) F2,F9: 3.. / F2 = 3 => 0 pairs (*) / F9 = 3 => 0 pairs (X) C1,A2: 4.. / C1 = 4 => 0 pairs (X) / A2 = 4 => 0 pairs (_) A2,F2: 4.. / A2 = 4 => 0 pairs (*) / F2 = 4 => 0 pairs (X) A4,D4: 4.. / A4 = 4 => 0 pairs (X) / D4 = 4 => 0 pairs (_) C1,C5: 4.. / C1 = 4 => 0 pairs (X) / C5 = 4 => 0 pairs (_) F5,F6: 5.. / F5 = 5 => 8 pairs (_) / F6 = 5 => 0 pairs (X) H8,I8: 5.. / H8 = 5 => 11 pairs (_) / I8 = 5 => 0 pairs (X) E1,H1: 5.. / E1 = 5 => 8 pairs (_) / H1 = 5 => 0 pairs (X) A5,F5: 5.. / A5 = 5 => 0 pairs (X) / F5 = 5 => 8 pairs (_) I5,I6: 6.. / I5 = 6 => 9 pairs (_) / I6 = 6 => 7 pairs (_) D1,D9: 6.. / D1 = 6 => 12 pairs (_) / D9 = 6 => 0 pairs (X) A2,A3: 7.. / A2 = 7 => 0 pairs (X) / A3 = 7 => 8 pairs (_) I5,I6: 7.. / I5 = 7 => 7 pairs (_) / I6 = 7 => 9 pairs (_) E8,F8: 7.. / E8 = 7 => 10 pairs (_) / F8 = 7 => 11 pairs (_) * DURATION: 0:00:37.097644 START: 17:12:23.736898 END: 17:13:00.834542 2017-05-04 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,D4,D6,E4,I2,I5,I6,I8) * 38......2..21..8.....2.84...27..6589.3..8.21...8.2.34....5427382438.....875....24 * PAIR I2: 3,5 BLK 3 I3: 3,5,1 # reduction candidate for 3,5 I3: 1 => CTR * 381.....24.21..8.3...2384.1.27316589.3..8.21...8.2.34....5427382438....5875..3124 I3: 3,5 # 11 pairs * PAIR I2: 3,5 ROW 2 E2: 3,5,6,7,9 # reduction candidate for 3,5 E2: 3,5 => CTR * 381.....24.21..8.....2.84...27316589.3..8.21...8.2.34....5427382438.1..5875..3124 E2: 6,7,9 # 8 pairs * PAIR E4: 1,3 COL E E9: 1,3,6,9 # reduction candidate for 1,3 E9: 1,3 => SOLVED * 389654172462173895751298463127436589634985217598721346916542738243867951875319624 E9: 6,9 # 9 pairs * PAIR D6: 7,9 BLK 5 D5: 7,9,4 # reduction candidate for 7,9 D5: 7,9 # 13 pairs F5: 7,9,4,5 # reduction candidate for 7,9 F5: 7,9 => CTR * 384...1.2..21.48.....2.84..42731658953.48.21...8.2534....5427382438....1875....24 F5: 4,5 # 9 pairs F6: 7,9,1,5 # reduction candidate for 7,9 F6: 7,9 => CTR * 384...1.2..21.48.....2.84..427316589.3.485217..8.2.346...5427382438....1875....24 F6: 1,5 # 9 pairs * PAIR D6: 7,9 COL D D1: 7,9,4,6 # reduction candidate for 7,9 D1: 7,9 => CTR * 384...1.2..21.48.....2.84..427316589.3.48.21...8.2.34....5427382438..6.18756...24 D1: 4,6 # 9 pairs * PAIR I8: 1,5 COL I I3: 1,5,3 # reduction candidate for 1,5 I3: 1,5 => CTR * 381.....24.21..8.3...2384...27316589.3..8.21...8.2.34....5427382438.....875..3124 I3: 3 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-421-base-pr-000.dot * REASONING * DIS # I3: 1 => CTR => I3: 3,5 * DIS # E2: 3,5 => CTR => E2: 6,7,9 * PRF # E9: 1,3 => SOL * DIS # F5: 7,9 => CTR => F5: 4,5 * DIS # F6: 7,9 => CTR => F6: 1,5 * DIS # D1: 7,9 => CTR => D1: 4,6 * DIS # I3: 1,5 => CTR => I3: 3 * CNT 7 HDP CHAINS / 15 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,D4,D6,E4,I2,I5,I6,I8) * 38......2..21..8.....2.84...27..6589.3..8.21...8.2.34....5427382438.....875....24 * PAIR I2: 3,5 BLK 3 I3: 3,5,1 # reduction candidate for 3,5 I3: 1 => CTR * 381.....24.21..8.3...2384.1.27316589.3..8.21...8.2.34....5427382438....5875..3124 * PAIR E4: 1,3 COL E E9: 1,3,6,9 # reduction candidate for 1,3 E9: 1,3 => SOLVED * 389654172462173895751298463127436589634985217598721346916542738243867951875319624 * DURATION: 0:00:04.205780 START: 17:13:13.678362 END: 17:13:17.884142 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-421-base-pr-001.dot * REASONING * DIS # I3: 1 => CTR => I3: 3,5 * PRF I3: 3,5 # E9: 1,3 => SOL * STA I3: 3,5 + E9: 1,3 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 421 solution: 389654172462173895751298463127436589634985217598721346916542738243867951875319624 info: 95113 FNBXYK S8.f 48374 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 389654172462173895751298463127436589634985217598721346916542738243867951875319624 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 # I3: 3,5 => UNS * DIS # I3: 1 => CTR => I3: 3,5 * DIS # E2: 3,5 => CTR => E2: 6,7,9 * INC # E2: 6,7,9 => UNS * PRF # E9: 1,3 => SOL * INC # E9: 6,9 => UNS * INC # D5: 7,9 => UNS * DIS # F5: 7,9 => CTR => F5: 4,5 * INC # F5: 4,5 => UNS * DIS # F6: 7,9 => CTR => F6: 1,5 * INC # F6: 1,5 => UNS * DIS # D1: 7,9 => CTR => D1: 4,6 * INC # D1: 4,6 => UNS * DIS # I3: 1,5 => CTR => I3: 3 * INC # I3: 3 => UNS * CNT 15 HDP CHAINS / 15 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # I3: 3,5 => UNS * DIS # I3: 1 => CTR => I3: 3,5 * PRF I3: 3,5 # E9: 1,3 => SOL * STA I3: 3,5 + E9: 1,3 * CNT 3 HDP CHAINS / 3 HYP OPENED