Analysis of xx-top500-013-base.sdk
Contents
Original Sudoku
level: medium
position: 5...92...1.....6...............1..928..6............5..2.4..3...7.3.......9...... initial
Autosolve
position: 56.79214.1.25..6799.71..2.57568134928946257..2..9..85662.4.93.747.3..92.3.92..564 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E2: 4,8 => CTR => E2: 3 * PRF # F3: 4,8 => SOL * DIS # B2: 3 => CTR => B2: 4,8 * PRF # C8: 1,8 => SOL * DIS # F9: 7 => CTR => F9: 1,8 * PRF # E8: 5,8 => SOL * PRF # C7: 5,8 => SOL * DIS # C7: 1 => CTR => C7: 5,8 * DIS # F9: 7,8 => CTR => F9: 1 * PRF # F9: 1 => SOL * PRF # C7: 5 => SOL * PRF # C8: 1,8 => SOL * CNT 12 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E2: 4,8 => CTR => E2: 3 * PRF E2: 3 # F3: 4,8 => SOL * STA E2: 3 + F3: 4,8 * CNT 2 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5...92...1.....6...............1..928..6............5..2.4..3...7.3.......9...... | initial |
| 56.79214.1.25..6799.71..2.57568134928946257..2..9..85662.4.93.747.3..92.3.92..564 | autosolve |
| 568792143142538679937164285756813492894625731213947856625489317471356928389271564 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) C1: 3,8 F2: 4,8 I1: 3,8 H3: 3,8 B6: 1,3 C6: 1,3 E6: 4,7 F6: 4,7 H5: 1,3 I5: 1,3 B9: 1,8 E7: 5,8 E9: 7,8 H7: 1,8 I8: 1,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B6,C6: 1.. / B6 = 1 => 0 pairs (*) / C6 = 1 => 0 pairs (X) H5,I5: 1.. / H5 = 1 => 0 pairs (X) / I5 = 1 => 0 pairs (_) F8,F9: 1.. / F8 = 1 => 0 pairs (X) / F9 = 1 => 0 pairs (_) H7,I8: 1.. / H7 = 1 => 0 pairs (*) / I8 = 1 => 0 pairs (X) C7,H7: 1.. / C7 = 1 => 0 pairs (X) / H7 = 1 => 0 pairs (_) B9,F9: 1.. / B9 = 1 => 0 pairs (X) / F9 = 1 => 0 pairs (_) B6,B9: 1.. / B6 = 1 => 0 pairs (*) / B9 = 1 => 0 pairs (X) H5,H7: 1.. / H5 = 1 => 0 pairs (X) / H7 = 1 => 0 pairs (_) I5,I8: 1.. / I5 = 1 => 0 pairs (*) / I8 = 1 => 0 pairs (X) E2,E3: 3.. / E2 = 3 => 16 pairs (_) / E3 = 3 => 0 pairs (X) I1,H3: 3.. / I1 = 3 => 0 pairs (*) / H3 = 3 => 0 pairs (X) B6,C6: 3.. / B6 = 3 => 0 pairs (X) / C6 = 3 => 0 pairs (_) H5,I5: 3.. / H5 = 3 => 0 pairs (*) / I5 = 3 => 0 pairs (X) C1,I1: 3.. / C1 = 3 => 0 pairs (X) / I1 = 3 => 0 pairs (_) B2,E2: 3.. / B2 = 3 => 0 pairs (X) / E2 = 3 => 16 pairs (_) C1,C6: 3.. / C1 = 3 => 0 pairs (X) / C6 = 3 => 0 pairs (_) H3,H5: 3.. / H3 = 3 => 0 pairs (X) / H5 = 3 => 0 pairs (_) I1,I5: 3.. / I1 = 3 => 0 pairs (*) / I5 = 3 => 0 pairs (X) B2,B3: 4.. / B2 = 4 => 19 pairs (_) / B3 = 4 => 17 pairs (_) E6,F6: 4.. / E6 = 4 => 14 pairs (_) / F6 = 4 => 0 pairs (X) C7,C8: 5.. / C7 = 5 => 0 pairs (*) / C8 = 5 => 0 pairs (X) E7,E8: 5.. / E7 = 5 => 16 pairs (_) / E8 = 5 => 0 pairs (*) C7,E7: 5.. / C7 = 5 => 0 pairs (*) / E7 = 5 => 0 pairs (X) C8,E8: 5.. / C8 = 5 => 16 pairs (_) / E8 = 5 => 0 pairs (*) E3,F3: 6.. / E3 = 6 => 0 pairs (*) / F3 = 6 => 0 pairs (X) E8,F8: 6.. / E8 = 6 => 16 pairs (_) / F8 = 6 => 0 pairs (*) E3,E8: 6.. / E3 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) F3,F8: 6.. / F3 = 6 => 16 pairs (_) / F8 = 6 => 0 pairs (*) E6,F6: 7.. / E6 = 7 => 0 pairs (X) / F6 = 7 => 14 pairs (_) E9,F9: 7.. / E9 = 7 => 14 pairs (_) / F9 = 7 => 0 pairs (X) E6,E9: 7.. / E6 = 7 => 0 pairs (X) / E9 = 7 => 14 pairs (_) F6,F9: 7.. / F6 = 7 => 14 pairs (_) / F9 = 7 => 0 pairs (X) I1,H3: 8.. / I1 = 8 => 0 pairs (X) / H3 = 8 => 0 pairs (_) H7,I8: 8.. / H7 = 8 => 0 pairs (X) / I8 = 8 => 0 pairs (_) C1,I1: 8.. / C1 = 8 => 0 pairs (*) / I1 = 8 => 0 pairs (X) H3,H7: 8.. / H3 = 8 => 0 pairs (*) / H7 = 8 => 0 pairs (X) I1,I8: 8.. / I1 = 8 => 0 pairs (X) / I8 = 8 => 0 pairs (_) * DURATION: 0:01:07.141198 START: 03:02:08.782291 END: 03:03:15.923489 2017-05-04 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,B9,C1,C6,E6,E7,E9,F2,F6,H3,H5,H7,I1,I5,I8) * 56.79214.1.25..6799.71..2.57568134928946257..2..9..85662.4.93.747.3..92.3.92..564 * PAIR C1: 3,8 BLK 1 B2: 3,8,4 # reduction candidate for 3,8 B2: 3,8 # 17 pairs B3: 3,8,4 # reduction candidate for 3,8 B3: 3,8 # 19 pairs * PAIR F2: 4,8 BLK 2 E2: 4,8,3 # reduction candidate for 4,8 E2: 4,8 => CTR * 56.79214.1325..6799471362857568134928946257312139..85662.4.93174713..92.3.92..564 E2: 3 # 16 pairs E3: 4,8,3,6 # reduction candidate for 4,8 E3: 4,8 # 18 pairs F3: 4,8,6 # reduction candidate for 4,8 F3: 4,8 => SOLVED * 568792143142538679937164285756813492894625731213947856625489317471356928389271564 F3: 6 # 16 pairs * PAIR F2: 4,8 ROW 2 B2: 4,8,3 # reduction candidate for 4,8 B2: 3 => CTR * 56.79214.1325..6799471362857568134928946257312139..85662.4.93174713..92.3.92..564 B2: 4,8 # 16 pairs * PAIR H3: 3,8 ROW 3 B3: 3,8,4 # reduction candidate for 3,8 B3: 3,8 # 19 pairs E3: 3,8,4,6 # reduction candidate for 3,8 E3: 3,8 # 18 pairs * PAIR B9: 1,8 BLK 7 C7: 1,8,5 # reduction candidate for 1,8 C7: 1,8 # 16 pairs C8: 1,8,5 # reduction candidate for 1,8 C8: 1,8 => SOLVED * 568792143142538679937164285756813492894625731213947856625489317471356928389271564 C8: 5 # 16 pairs * PAIR B9: 1,8 ROW 9 F9: 1,8,7 # reduction candidate for 1,8 F9: 7 => CTR * 5687921431.25.86799.71.628575681349289462573123.9..85662.4.93.747.3.1928319287564 F9: 1,8 # 14 pairs * PAIR E7: 5,8 BLK 8 E8: 5,8,6 # reduction candidate for 5,8 E8: 5,8 => SOLVED * 568792143142538679937164285756813492894625731213947856625489317471356928389271564 E8: 6 # 16 pairs * PAIR E7: 5,8 ROW 7 C7: 5,8,1 # reduction candidate for 5,8 C7: 5,8 => SOLVED * 568792143142538679937164285756813492894625731213947856625489317471356928389271564 C7: 1 => CTR * 5687921431.25..6799.71..2.57568134928946257..2..9..8566214593874753..921389271564 * PAIR E9: 7,8 BLK 8 F9: 7,8,1 # reduction candidate for 7,8 F9: 7,8 => CTR * 5687921431.25..6799.71.628575681349289462573123.9..85662.4.93.747.3.19283192..564 F9: 1 => SOLVED * 568792143142538679937164285756813492894625731213947856625489317471356928389271564 * PAIR H7: 1,8 ROW 7 C7: 1,8,5 # reduction candidate for 1,8 C7: 5 => SOLVED * 568792143142538679937164285756813492894625731213947856625489317471356928389271564 C7: 1,8 # 16 pairs * PAIR I8: 1,8 ROW 8 C8: 1,8,5 # reduction candidate for 1,8 C8: 1,8 => SOLVED * 568792143142538679937164285756813492894625731213947856625489317471356928389271564 C8: 5 # 16 pairs F8: 1,8,6 # reduction candidate for 1,8 F8: 1,8 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-013-base-pr-000.dot * REASONING * DIS # E2: 4,8 => CTR => E2: 3 * PRF # F3: 4,8 => SOL * DIS # B2: 3 => CTR => B2: 4,8 * PRF # C8: 1,8 => SOL * DIS # F9: 7 => CTR => F9: 1,8 * PRF # E8: 5,8 => SOL * PRF # C7: 5,8 => SOL * DIS # C7: 1 => CTR => C7: 5,8 * DIS # F9: 7,8 => CTR => F9: 1 * PRF # F9: 1 => SOL * PRF # C7: 5 => SOL * PRF # C8: 1,8 => SOL * CNT 12 HDP CHAINS / 27 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,B9,C1,C6,E6,E7,E9,F2,F6,H3,H5,H7,I1,I5,I8) * 56.79214.1.25..6799.71..2.57568134928946257..2..9..85662.4.93.747.3..92.3.92..564 * PAIR C1: 3,8 BLK 1 B2: 3,8,4 # reduction candidate for 3,8 B2: 3,8 # 17 pairs B3: 3,8,4 # reduction candidate for 3,8 B3: 3,8 # 19 pairs * PAIR F2: 4,8 BLK 2 E2: 4,8,3 # reduction candidate for 4,8 E2: 4,8 => CTR * 56.79214.1325..6799471362857568134928946257312139..85662.4.93174713..92.3.92..564 E3: 4,8,6 # reduction candidate for 4,8 E3: 4,8 # 18 pairs F3: 4,8,6 # reduction candidate for 4,8 F3: 4,8 => SOLVED * 568792143142538679937164285756813492894625731213947856625489317471356928389271564 * DURATION: 0:00:06.028763 START: 03:03:45.648831 END: 03:03:51.677594 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-013-base-pr-001.dot * REASONING * DIS # E2: 4,8 => CTR => E2: 3 * PRF E2: 3 # F3: 4,8 => SOL * STA E2: 3 + F3: 4,8 * CNT 2 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 013 solution: 568792143142538679937164285756813492894625731213947856625489317471356928389271564 info: 1309 FNBWXY S8.f 32644 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 568792143142538679937164285756813492894625731213947856625489317471356928389271564 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 # B2: 3,8 => UNS * INC # B3: 3,8 => UNS * DIS # E2: 4,8 => CTR => E2: 3 * INC # E2: 3 => UNS * INC # E3: 4,8 => UNS * PRF # F3: 4,8 => SOL * INC # F3: 6 => UNS * INC # B2: 4,8 => UNS * DIS # B2: 3 => CTR => B2: 4,8 * INC # B3: 3,8 => UNS * INC # E3: 3,8 => UNS * INC # C7: 1,8 => UNS * PRF # C8: 1,8 => SOL * INC # C8: 5 => UNS * INC # F9: 1,8 => UNS * DIS # F9: 7 => CTR => F9: 1,8 * PRF # E8: 5,8 => SOL * INC # E8: 6 => UNS * PRF # C7: 5,8 => SOL * DIS # C7: 1 => CTR => C7: 5,8 * DIS # F9: 7,8 => CTR => F9: 1 * PRF # F9: 1 => SOL * INC # C7: 1,8 => UNS * PRF # C7: 5 => SOL * PRF # C8: 1,8 => SOL * INC # C8: 5 => UNS * INC # F8: 1,8 => UNS * CNT 27 HDP CHAINS / 27 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 3,8 => UNS * INC # B3: 3,8 => UNS * DIS # E2: 4,8 => CTR => E2: 3 * INC E2: 3 # E3: 4,8 => UNS * PRF E2: 3 # F3: 4,8 => SOL * STA E2: 3 + F3: 4,8 * CNT 5 HDP CHAINS / 5 HYP OPENED