Analysis of xx-top500-239-base.sdk
Contents
Original Sudoku
level: medium
position: .3..5.9........48............7.3.1..8.42.....2.........5......7...4...2.1........ initial
Autosolve
position: .3..5.9........48.......2..5.7.3.1.28.42.....2.3.......5......7...4...2.1........ autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B9: 2,7 => CTR => B9: 4,8 * PRF # B9: 4,8 => SOL * DIS # I2: 1,6 => CTR => I2: 3,5 * DIS # I3: 1,6 => CTR => I3: 3,5 * DIS # C1: 1,6 => CTR => C1: 2,8 * PRF # D1: 1,6 => SOL * DIS # F1: 1,6 => CTR => F1: 2,4,7,8 * DIS # I8: 3,5,8,9 => CTR => I8: 1,6 * DIS # D4: 6,9 => CTR => D4: 8 * PRF # D4: 8 => SOL * DIS # F4: 6,9 => CTR => F4: 4,8 * PRF # H4: 6,9 => SOL * DIS # H4: 4 => CTR => H4: 6,9 * DIS # B9: 7,8 => CTR => B9: 2,4 * DIS # E8: 7,8 => CTR => E8: 1,6,9 * DIS # F8: 7,8 => CTR => F8: 1,3,5,6,9 * PRF # B3: 7,8 => SOL * DIS # B3: 4 => CTR => B3: 7,8 * CNT 18 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B9: 2,7 => CTR => B9: 4,8 * PRF B9: 4,8 => SOL * STA B9: 4,8 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3..5.9........48............7.3.1..8.42.....2.........5......7...4...2.1........ | initial |
| .3..5.9........48.......2..5.7.3.1.28.42.....2.3.......5......7...4...2.1........ | autosolve |
| 438152976621379485975648213597834162864215739213796854352981647789463521146527398 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) B2: 2,7 I1: 1,6 B4: 6,9 B8: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,B6: 1.. / B5 = 1 => 5 pairs (_) / B6 = 1 => 5 pairs (_) H7,I8: 1.. / H7 = 1 => 0 pairs (X) / I8 = 1 => 12 pairs (_) C1,F1: 2.. / C1 = 2 => 0 pairs (X) / F1 = 2 => 0 pairs (_) B2,B9: 2.. / B2 = 2 => 0 pairs (*) / B9 = 2 => 0 pairs (X) A7,A8: 3.. / A7 = 3 => 0 pairs (*) / A8 = 3 => 0 pairs (X) A7,B9: 4.. / A7 = 4 => 0 pairs (X) / B9 = 4 => 0 pairs (_) A1,F1: 4.. / A1 = 4 => 0 pairs (*) / F1 = 4 => 0 pairs (X) F4,H4: 4.. / F4 = 4 => 0 pairs (*) / H4 = 4 => 0 pairs (X) A7,H7: 4.. / A7 = 4 => 0 pairs (X) / H7 = 4 => 0 pairs (_) B3,B9: 4.. / B3 = 4 => 0 pairs (X) / B9 = 4 => 0 pairs (_) E3,E6: 4.. / E3 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) I6,I9: 4.. / I6 = 4 => 0 pairs (*) / I9 = 4 => 0 pairs (X) C2,C3: 5.. / C2 = 5 => 4 pairs (_) / C3 = 5 => 4 pairs (_) C2,I2: 5.. / C2 = 5 => 4 pairs (_) / I2 = 5 => 4 pairs (_) D6,D9: 5.. / D6 = 5 => 4 pairs (_) / D9 = 5 => 4 pairs (_) H1,H3: 7.. / H1 = 7 => 5 pairs (_) / H3 = 7 => 18 pairs (_) G5,G6: 7.. / G5 = 7 => 4 pairs (_) / G6 = 7 => 0 pairs (X) D4,F4: 8.. / D4 = 8 => 0 pairs (*) / F4 = 8 => 0 pairs (X) G6,I6: 8.. / G6 = 8 => 6 pairs (_) / I6 = 8 => 0 pairs (X) * DURATION: 0:00:26.495416 START: 10:59:08.808406 END: 10:59:35.303822 2017-05-04 * CP COUNT: (19) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B4,B8,I1) * .3..5.9........48.......2..5.7.3.1.28.42.....2.3.......5......7...4...2.1........ * PAIR B2: 2,7 ROW 2 E2: 2,7,1,6,9 # reduction candidate for 2,7 E2: 2,7 # 6 pairs F2: 2,7,1,3,6,9 # reduction candidate for 2,7 F2: 2,7 # 6 pairs * PAIR B2: 2,7 COL B B9: 2,7,4,8 # reduction candidate for 2,7 B9: 2,7 => CTR * .3..549...2....48..4....2..5.7.3.1428.42.....2.3.4...845......738.4...2.17......4 B9: 4,8 => SOLVED * 438152976621379485975648213597834162864215739213796854352981647789463521146527398 * PAIR I1: 1,6 BLK 3 H1: 1,6,7 # reduction candidate for 1,6 H1: 1,6 # 18 pairs I2: 1,6,3,5 # reduction candidate for 1,6 I2: 1,6 => CTR * 63..54971..5...486.41...2..5.7.3.1428.42.....2.3.4....45.....173..4...2.1.......4 I2: 3,5 # 5 pairs H3: 1,6,3,5,7 # reduction candidate for 1,6 H3: 1,6 # 9 pairs I3: 1,6,3,5 # reduction candidate for 1,6 I3: 1,6 => CTR * 632854971.7....48.94....2.65.7.3.1428.42.....2.3.4....45.....173..4...2.1.......4 I3: 3,5 # 5 pairs * PAIR I1: 1,6 ROW 1 C1: 1,6,2,8 # reduction candidate for 1,6 C1: 1,6 => CTR * 43.85297.......48.......2..5.7.381428.42.....2.3.......5......7...4...2.14....... C1: 2,8 # 9 pairs D1: 1,6,7,8 # reduction candidate for 1,6 D1: 1,6 => SOLVED * 438152976621379485975648213597834162864215739213796854352981647789463521146527398 D1: 7,8 # 5 pairs F1: 1,6,2,4,7,8 # reduction candidate for 1,6 F1: 1,6 => CTR * 43285.97..7....48.......2..5.7.3.1.28.42.....2.3.......5......7...4...2.1........ F1: 2,4,7,8 # 4 pairs * PAIR I1: 1,6 COL I I8: 1,6,3,5,8,9 # reduction candidate for 1,6 I8: 3,5,8,9 => CTR * .328549.1.7....48..48...2..5.7.381428.42.....2.3.4....45.....1738.4...2.12......4 I8: 1,6 # 11 pairs * PAIR B4: 6,9 BLK 4 B5: 6,9,1 # reduction candidate for 6,9 B5: 6,9 # 5 pairs B6: 6,9,1 # reduction candidate for 6,9 B6: 6,9 # 5 pairs * PAIR B4: 6,9 ROW 4 D4: 6,9,8 # reduction candidate for 6,9 D4: 6,9 => CTR * .328549...7....48..48...2..5.7.381428.42.....2.3.4....45......738.4...2.12......4 D4: 8 => SOLVED * 438152976621379485975648213597834162864215739213796854352981647789463521146527398 F4: 6,9,4,8 # reduction candidate for 6,9 F4: 6,9 => CTR * .3..549........48..4....2..5.783.1428.42.....2.3......45......73..4...2.1.......4 F4: 4,8 # 5 pairs H4: 6,9,4 # reduction candidate for 6,9 H4: 6,9 => SOLVED * 438152976621379485975648213597834162864215739213796854352981647789463521146527398 H4: 4 => CTR * .328549...7....48..48...2..5.7.381428.42.....2.3.4....45......738.4...2.12......4 * PAIR B8: 7,8 BLK 7 B9: 7,8,2,4 # reduction candidate for 7,8 B9: 7,8 => CTR * .3..5.9...2....48..4....2..5.7.3.1.28.42.....2.3.4....45......73..4...2.1.......4 B9: 2,4 # 5 pairs * PAIR B8: 7,8 ROW 8 E8: 7,8,1,6,9 # reduction candidate for 7,8 E8: 7,8 => CTR * 43..529...2....48..8....2..5.7.3.1.28.42.....2.3.......5.....47.7.48..2114.....98 E8: 1,6,9 # 4 pairs F8: 7,8,1,3,5,6,9 # reduction candidate for 7,8 F8: 7,8 => CTR * 43..529...2....48..8....2..5.7.3.1.28.42.....2.3.......5.....47.7.4.8.2114.....98 F8: 1,3,5,6,9 # 4 pairs * PAIR B8: 7,8 COL B B3: 7,8,4 # reduction candidate for 7,8 B3: 7,8 => SOLVED * 438152976621379485975648213597834162864215739213796854352981647789463521146527398 B3: 4 => CTR * .328549...7....48..48...2..5.7.381428.42.....2.3.4....45......738.4...2.12......4 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-239-base-pr-000.dot * REASONING * DIS # B9: 2,7 => CTR => B9: 4,8 * PRF # B9: 4,8 => SOL * DIS # I2: 1,6 => CTR => I2: 3,5 * DIS # I3: 1,6 => CTR => I3: 3,5 * DIS # C1: 1,6 => CTR => C1: 2,8 * PRF # D1: 1,6 => SOL * DIS # F1: 1,6 => CTR => F1: 2,4,7,8 * DIS # I8: 3,5,8,9 => CTR => I8: 1,6 * DIS # D4: 6,9 => CTR => D4: 8 * PRF # D4: 8 => SOL * DIS # F4: 6,9 => CTR => F4: 4,8 * PRF # H4: 6,9 => SOL * DIS # H4: 4 => CTR => H4: 6,9 * DIS # B9: 7,8 => CTR => B9: 2,4 * DIS # E8: 7,8 => CTR => E8: 1,6,9 * DIS # F8: 7,8 => CTR => F8: 1,3,5,6,9 * PRF # B3: 7,8 => SOL * DIS # B3: 4 => CTR => B3: 7,8 * CNT 18 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B4,B8,I1) * .3..5.9........48.......2..5.7.3.1.28.42.....2.3.......5......7...4...2.1........ * PAIR B2: 2,7 ROW 2 E2: 2,7,1,6,9 # reduction candidate for 2,7 E2: 2,7 # 6 pairs F2: 2,7,1,3,6,9 # reduction candidate for 2,7 F2: 2,7 # 6 pairs * PAIR B2: 2,7 COL B B9: 2,7,4,8 # reduction candidate for 2,7 B9: 2,7 => CTR * .3..549...2....48..4....2..5.7.3.1428.42.....2.3.4...845......738.4...2.17......4 B9: 4,8 => SOLVED * 438152976621379485975648213597834162864215739213796854352981647789463521146527398 * DURATION: 0:00:04.550412 START: 11:00:00.447836 END: 11:00:04.998248 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-239-base-pr-001.dot * REASONING * DIS # B9: 2,7 => CTR => B9: 4,8 * PRF B9: 4,8 => SOL * STA B9: 4,8 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 239 solution: 438152976621379485975648213597834162864215739213796854352981647789463521146527398 info: 2069 FNBWXY S8.f 17759 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 438152976621379485975648213597834162864215739213796854352981647789463521146527398 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 # E2: 2,7 => UNS * INC # F2: 2,7 => UNS * DIS # B9: 2,7 => CTR => B9: 4,8 * PRF # B9: 4,8 => SOL * INC # H1: 1,6 => UNS * DIS # I2: 1,6 => CTR => I2: 3,5 * INC # I2: 3,5 => UNS * INC # H3: 1,6 => UNS * DIS # I3: 1,6 => CTR => I3: 3,5 * INC # I3: 3,5 => UNS * DIS # C1: 1,6 => CTR => C1: 2,8 * INC # C1: 2,8 => UNS * PRF # D1: 1,6 => SOL * INC # D1: 7,8 => UNS * DIS # F1: 1,6 => CTR => F1: 2,4,7,8 * INC # F1: 2,4,7,8 => UNS * INC # I8: 1,6 => UNS * DIS # I8: 3,5,8,9 => CTR => I8: 1,6 * INC # B5: 6,9 => UNS * INC # B6: 6,9 => UNS * DIS # D4: 6,9 => CTR => D4: 8 * PRF # D4: 8 => SOL * DIS # F4: 6,9 => CTR => F4: 4,8 * INC # F4: 4,8 => UNS * PRF # H4: 6,9 => SOL * DIS # H4: 4 => CTR => H4: 6,9 * DIS # B9: 7,8 => CTR => B9: 2,4 * INC # B9: 2,4 => UNS * DIS # E8: 7,8 => CTR => E8: 1,6,9 * INC # E8: 1,6,9 => UNS * DIS # F8: 7,8 => CTR => F8: 1,3,5,6,9 * INC # F8: 1,3,5,6,9 => UNS * PRF # B3: 7,8 => SOL * DIS # B3: 4 => CTR => B3: 7,8 * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E2: 2,7 => UNS * INC # F2: 2,7 => UNS * DIS # B9: 2,7 => CTR => B9: 4,8 * PRF B9: 4,8 => SOL * STA B9: 4,8 * CNT 4 HDP CHAINS / 3 HYP OPENED