Analysis of xx-top500-468-base.sdk
Contents
Original Sudoku
level: medium
position: 67.3.....4......8........19..1...7.....6..2..5...8.....9..1.......5..4........... initial
Autosolve
position: 6783915..4192..387......619..1...7.8...6..2.15..18.9...9..1.8..1..5..4........1.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A4: 2,3 => CTR => A4: 9 * PRF # A4: 9 => SOL * PRF # A7: 2,3 => SOL * DIS # A7: 7 => CTR => A7: 2,3 * DIS # A9: 2,3 => CTR => A9: 7,8 * DIS # D3: 4,7 => CTR => D3: 8 * DIS # F4: 4,9 => CTR => F4: 2,3,5 * PRF # D9: 4,9 => SOL * DIS # D9: 7,8 => CTR => D9: 4,9 * DIS # F7: 4,7 => CTR => F7: 2,3,6 * DIS # D9: 4,7 => CTR => D9: 8,9 * PRF # C7: 4,7 => SOL * DIS # D3: 4,7 => CTR => D3: 8 * CNT 13 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A4: 2,3 => CTR => A4: 9 * PRF A4: 9 => SOL * STA A4: 9 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 67.3.....4......8........19..1...7.....6..2..5...8.....9..1.......5..4........... | initial |
| 6783915..4192..387......619..1...7.8...6..2.15..18.9...9..1.8..1..5..4........1.. | autosolve |
| 678391524419265387325874619961432758783659241542187963294716835137528496856943172 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A3: 2,3 E2: 5,6 F2: 5,6 E3: 4,7 H1: 2,4 I1: 2,4 D4: 4,9 D7: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,I1: 2.. / H1 = 2 => 7 pairs (_) / I1 = 2 => 10 pairs (_) H1,I1: 4.. / H1 = 4 => 10 pairs (_) / I1 = 4 => 7 pairs (_) I1,I6: 4.. / I1 = 4 => 7 pairs (_) / I6 = 4 => 10 pairs (_) B3,C3: 5.. / B3 = 5 => 9 pairs (_) / C3 = 5 => 10 pairs (_) E2,F2: 5.. / E2 = 5 => 6 pairs (_) / F2 = 5 => 6 pairs (_) H4,H5: 5.. / H4 = 5 => 9 pairs (_) / H5 = 5 => 8 pairs (_) I7,I9: 5.. / I7 = 5 => 8 pairs (_) / I9 = 5 => 9 pairs (_) C7,I7: 5.. / C7 = 5 => 9 pairs (_) / I7 = 5 => 8 pairs (_) B3,B9: 5.. / B3 = 5 => 9 pairs (_) / B9 = 5 => 10 pairs (_) E2,F2: 6.. / E2 = 6 => 6 pairs (_) / F2 = 6 => 6 pairs (_) B4,H4: 6.. / B4 = 6 => 8 pairs (_) / H4 = 6 => 12 pairs (_) C6,F6: 7.. / C6 = 7 => 9 pairs (_) / F6 = 7 => 10 pairs (_) D3,F3: 8.. / D3 = 8 => 9 pairs (_) / F3 = 8 => 0 pairs (X) A5,B5: 8.. / A5 = 8 => 0 pairs (X) / B5 = 8 => 0 pairs (_) B8,F8: 8.. / B8 = 8 => 0 pairs (X) / F8 = 8 => 0 pairs (_) A5,A9: 8.. / A5 = 8 => 0 pairs (X) / A9 = 8 => 0 pairs (_) D3,D9: 8.. / D3 = 8 => 9 pairs (_) / D9 = 8 => 0 pairs (X) A4,A5: 9.. / A4 = 9 => 0 pairs (*) / A5 = 9 => 0 pairs (X) H8,H9: 9.. / H8 = 9 => 8 pairs (_) / H9 = 9 => 0 pairs (X) A5,F5: 9.. / A5 = 9 => 0 pairs (X) / F5 = 9 => 0 pairs (_) F8,H8: 9.. / F8 = 9 => 0 pairs (X) / H8 = 9 => 8 pairs (_) D4,D9: 9.. / D4 = 9 => 0 pairs (X) / D9 = 9 => 0 pairs (_) * DURATION: 0:00:30.163992 START: 18:42:02.959779 END: 18:42:33.123771 2017-05-04 * CP COUNT: (22) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,D4,D7,E2,E3,F2,H1,I1) * 6783915..4192..387......619..1...7.8...6..2.15..18.9...9..1.8..1..5..4........1.. * PAIR A3: 2,3 BLK 1 B3: 2,3,5 # reduction candidate for 2,3 B3: 2,3 # 10 pairs C3: 2,3,5 # reduction candidate for 2,3 C3: 2,3 # 9 pairs * PAIR A3: 2,3 COL A A4: 2,3,9 # reduction candidate for 2,3 A4: 2,3 => CTR * 6783915..4192..387...8..619..1...7.898.6..2.15..18.9..79.41.8..1..57849.8..9..1.. A4: 9 => SOLVED * 678391524419265387325874619961432758783659241542187963294716835137528496856943172 A7: 2,3,7 # reduction candidate for 2,3 A7: 2,3 => SOLVED * 678391524419265387325874619961432758783659241542187963294716835137528496856943172 A7: 7 => CTR * 6783915..4192..387......619..19..7.898.6..2.15..18.9..79.41.8..1..5.849.8..7.91.. A9: 2,3,7,8 # reduction candidate for 2,3 A9: 2,3 => CTR * 6783915..4192..387......619..1...7.88..6.92.15..18.9..79.41.8..1..5..4........1.. A9: 7,8 # 9 pairs * PAIR E3: 4,7 BLK 2 D3: 4,7,8 # reduction candidate for 4,7 D3: 4,7 => CTR * 6783915..4192..387.....8619..19..7.8...6..2.15..18.9...9..1.8..18.5..4.....8..1.. D3: 8 # 9 pairs F3: 4,7,8 # reduction candidate for 4,7 F3: 4,7 # 9 pairs * PAIR E3: 4,7 COL E E5: 4,7,3,5 # reduction candidate for 4,7 E5: 4,7 # 9 pairs E9: 4,7,2,3,6 # reduction candidate for 4,7 E9: 4,7 # 12 pairs * PAIR D4: 4,9 BLK 5 F4: 4,9,2,3,5 # reduction candidate for 4,9 F4: 4,9 => CTR * 6783915..4192..387......619..1...7.898.6..2.15..18.9..79.41.8..1..5.849.8.....17. F4: 2,3,5 # 8 pairs F5: 4,9,3,5,7 # reduction candidate for 4,9 F5: 4,9 # 9 pairs * PAIR D4: 4,9 COL D D9: 4,9,7,8 # reduction candidate for 4,9 D9: 4,9 => SOLVED * 678391524419265387325874619961432758783659241542187963294716835137528496856943172 D9: 7,8 => CTR * 6783915..4192..387...8..619..19..7.898.6..2.15..18.9..79.41.8..1..5.849.8..7.91.. * PAIR D7: 4,7 BLK 8 F7: 4,7,2,3,6 # reduction candidate for 4,7 F7: 4,7 => CTR * 6783915..4192..387...8476199.14..7.878.6.92.15..18.9...9.7148..1.75.849.8..9..17. F7: 2,3,6 # 8 pairs D9: 4,7,8,9 # reduction candidate for 4,7 D9: 4,7 => CTR * 6783915..4192..387...8..619..19..7.898.6..2.15..18.9..79.41.8..1..57849.8....91.. D9: 8,9 # 9 pairs E9: 4,7,2,3,6 # reduction candidate for 4,7 E9: 4,7 # 12 pairs F9: 4,7,2,3,6,8,9 # reduction candidate for 4,7 F9: 4,7 # 11 pairs * PAIR D7: 4,7 ROW 7 C7: 4,7,2,3,5,6 # reduction candidate for 4,7 C7: 4,7 => SOLVED * 678391524419265387325874619961432758783659241542187963294716835137528496856943172 C7: 2,3,5,6 # 8 pairs * PAIR D7: 4,7 COL D D3: 4,7,8 # reduction candidate for 4,7 D3: 4,7 => CTR * 6783915..4192..387.....8619..19..7.8...6..2.15..18.9...9..1.8..18.5..4.....8..1.. D3: 8 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-468-base-pr-000.dot * REASONING * DIS # A4: 2,3 => CTR => A4: 9 * PRF # A4: 9 => SOL * PRF # A7: 2,3 => SOL * DIS # A7: 7 => CTR => A7: 2,3 * DIS # A9: 2,3 => CTR => A9: 7,8 * DIS # D3: 4,7 => CTR => D3: 8 * DIS # F4: 4,9 => CTR => F4: 2,3,5 * PRF # D9: 4,9 => SOL * DIS # D9: 7,8 => CTR => D9: 4,9 * DIS # F7: 4,7 => CTR => F7: 2,3,6 * DIS # D9: 4,7 => CTR => D9: 8,9 * PRF # C7: 4,7 => SOL * DIS # D3: 4,7 => CTR => D3: 8 * CNT 13 HDP CHAINS / 28 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,D4,D7,E2,E3,F2,H1,I1) * 6783915..4192..387......619..1...7.8...6..2.15..18.9...9..1.8..1..5..4........1.. * PAIR A3: 2,3 BLK 1 B3: 2,3,5 # reduction candidate for 2,3 B3: 2,3 # 10 pairs C3: 2,3,5 # reduction candidate for 2,3 C3: 2,3 # 9 pairs * PAIR A3: 2,3 COL A A4: 2,3,9 # reduction candidate for 2,3 A4: 2,3 => CTR * 6783915..4192..387...8..619..1...7.898.6..2.15..18.9..79.41.8..1..57849.8..9..1.. A4: 9 => SOLVED * 678391524419265387325874619961432758783659241542187963294716835137528496856943172 * DURATION: 0:00:02.938172 START: 18:42:55.019868 END: 18:42:57.958040 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-468-base-pr-001.dot * REASONING * DIS # A4: 2,3 => CTR => A4: 9 * PRF A4: 9 => SOL * STA A4: 9 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 468 solution: 678391524419265387325874619961432758783659241542187963294716835137528496856943172 info: 95591 FNBHYK S8.f 43904 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 678391524419265387325874619961432758783659241542187963294716835137528496856943172 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 # B3: 2,3 => UNS * INC # C3: 2,3 => UNS * DIS # A4: 2,3 => CTR => A4: 9 * PRF # A4: 9 => SOL * PRF # A7: 2,3 => SOL * DIS # A7: 7 => CTR => A7: 2,3 * DIS # A9: 2,3 => CTR => A9: 7,8 * INC # A9: 7,8 => UNS * DIS # D3: 4,7 => CTR => D3: 8 * INC # D3: 8 => UNS * INC # F3: 4,7 => UNS * INC # E5: 4,7 => UNS * INC # E9: 4,7 => UNS * DIS # F4: 4,9 => CTR => F4: 2,3,5 * INC # F4: 2,3,5 => UNS * INC # F5: 4,9 => UNS * PRF # D9: 4,9 => SOL * DIS # D9: 7,8 => CTR => D9: 4,9 * DIS # F7: 4,7 => CTR => F7: 2,3,6 * INC # F7: 2,3,6 => UNS * DIS # D9: 4,7 => CTR => D9: 8,9 * INC # D9: 8,9 => UNS * INC # E9: 4,7 => UNS * INC # F9: 4,7 => UNS * PRF # C7: 4,7 => SOL * INC # C7: 2,3,5,6 => UNS * DIS # D3: 4,7 => CTR => D3: 8 * INC # D3: 8 => UNS * CNT 28 HDP CHAINS / 28 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B3: 2,3 => UNS * INC # C3: 2,3 => UNS * DIS # A4: 2,3 => CTR => A4: 9 * PRF A4: 9 => SOL * STA A4: 9 * CNT 4 HDP CHAINS / 3 HYP OPENED