Analysis of xx-top500-387-base.sdk
Contents
Original Sudoku
level: medium
position: ..2.1.....7....3...6....8.....3..5..4......1....6.7...1......2.3..8.......9...... initial
Autosolve
position: 842.13....71...3.2.632..8.1.983215.443....21.2156479..1......2.3..8..1....91..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D2: 5,9 => CTR => D2: 4 * DIS # E3: 5,9 => CTR => E3: 7 * DIS # H3: 5,9 => CTR => H3: 4,7 * PRF # G9: 6,7 => SOL * DIS # D2: 5,9 => CTR => D2: 4 * DIS # D7: 5,9 => CTR => D7: 4,7 * DIS # I7: 6,7 => CTR => I7: 3,5,8,9 * PRF # G9: 6,7 => SOL * CNT 8 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 # D2: 5,9 => CTR => D2: 4 * PRF D2: 4 # G9: 6,7 => SOL * STA D2: 4 + G9: 6,7 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..2.1.....7....3...6....8.....3..5..4......1....6.7...1......2.3..8.......9...... | initial |
| 842.13....71...3.2.632..8.1.983215.443....21.2156479..1......2.3..8..1....91..... | autosolve |
| 842513769971486352563279841698321574437958216215647938186795423354862197729134685 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A2: 5,9 A3: 5,9 E2: 6,8 F2: 6,8 G1: 6,7 A4: 6,7 C5: 6,7 D5: 5,9 H4: 6,7 I5: 6,7 H6: 3,8 I6: 3,8 B7: 5,8 B8: 2,5 A9: 6,7 H9: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B8,B9: 2.. / B8 = 2 => 17 pairs (_) / B9 = 2 => 17 pairs (_) F8,F9: 2.. / F8 = 2 => 17 pairs (_) / F9 = 2 => 17 pairs (_) B8,F8: 2.. / B8 = 2 => 17 pairs (_) / F8 = 2 => 17 pairs (_) B9,F9: 2.. / B9 = 2 => 17 pairs (_) / F9 = 2 => 17 pairs (_) H6,I6: 3.. / H6 = 3 => 13 pairs (_) / I6 = 3 => 13 pairs (_) E7,E9: 3.. / E7 = 3 => 16 pairs (_) / E9 = 3 => 14 pairs (_) E7,I7: 3.. / E7 = 3 => 16 pairs (_) / I7 = 3 => 14 pairs (_) H6,H9: 3.. / H6 = 3 => 13 pairs (_) / H9 = 3 => 13 pairs (_) D2,F3: 4.. / D2 = 4 => 23 pairs (_) / F3 = 4 => 0 pairs (X) H2,H3: 4.. / H2 = 4 => 0 pairs (X) / H3 = 4 => 23 pairs (_) C7,C8: 4.. / C7 = 4 => 19 pairs (_) / C8 = 4 => 17 pairs (_) G7,G9: 4.. / G7 = 4 => 0 pairs (*) / G9 = 4 => 0 pairs (X) D2,H2: 4.. / D2 = 4 => 23 pairs (_) / H2 = 4 => 0 pairs (X) F3,H3: 4.. / F3 = 4 => 0 pairs (X) / H3 = 4 => 23 pairs (_) C8,F8: 4.. / C8 = 4 => 17 pairs (_) / F8 = 4 => 19 pairs (_) F9,G9: 4.. / F9 = 4 => 0 pairs (*) / G9 = 4 => 0 pairs (X) D2,D7: 4.. / D2 = 4 => 23 pairs (_) / D7 = 4 => 0 pairs (X) A2,A3: 5.. / A2 = 5 => 23 pairs (_) / A3 = 5 => 23 pairs (_) E2,F2: 6.. / E2 = 6 => 15 pairs (_) / F2 = 6 => 15 pairs (_) A4,C5: 6.. / A4 = 6 => 21 pairs (_) / C5 = 6 => 14 pairs (_) H4,I5: 6.. / H4 = 6 => 14 pairs (_) / I5 = 6 => 21 pairs (_) A4,H4: 6.. / A4 = 6 => 21 pairs (_) / H4 = 6 => 14 pairs (_) C5,I5: 6.. / C5 = 6 => 14 pairs (_) / I5 = 6 => 21 pairs (_) A4,A9: 6.. / A4 = 6 => 21 pairs (_) / A9 = 6 => 14 pairs (_) D1,E3: 7.. / D1 = 7 => 0 pairs (X) / E3 = 7 => 23 pairs (_) A4,C5: 7.. / A4 = 7 => 14 pairs (_) / C5 = 7 => 21 pairs (_) H4,I5: 7.. / H4 = 7 => 21 pairs (_) / I5 = 7 => 14 pairs (_) E3,H3: 7.. / E3 = 7 => 23 pairs (_) / H3 = 7 => 0 pairs (X) A4,H4: 7.. / A4 = 7 => 14 pairs (_) / H4 = 7 => 21 pairs (_) C5,I5: 7.. / C5 = 7 => 21 pairs (_) / I5 = 7 => 14 pairs (_) A4,A9: 7.. / A4 = 7 => 14 pairs (_) / A9 = 7 => 21 pairs (_) D1,D7: 7.. / D1 = 7 => 0 pairs (X) / D7 = 7 => 23 pairs (_) E2,F2: 8.. / E2 = 8 => 15 pairs (_) / F2 = 8 => 15 pairs (_) E5,F5: 8.. / E5 = 8 => 15 pairs (_) / F5 = 8 => 15 pairs (_) H6,I6: 8.. / H6 = 8 => 13 pairs (_) / I6 = 8 => 13 pairs (_) B7,B9: 8.. / B7 = 8 => 16 pairs (_) / B9 = 8 => 12 pairs (_) B7,I7: 8.. / B7 = 8 => 16 pairs (_) / I7 = 8 => 12 pairs (_) E2,E5: 8.. / E2 = 8 => 15 pairs (_) / E5 = 8 => 15 pairs (_) F2,F5: 8.. / F2 = 8 => 15 pairs (_) / F5 = 8 => 15 pairs (_) H6,H9: 8.. / H6 = 8 => 13 pairs (_) / H9 = 8 => 13 pairs (_) A2,A3: 9.. / A2 = 9 => 23 pairs (_) / A3 = 9 => 23 pairs (_) * DURATION: 0:01:34.149805 START: 16:04:25.714690 END: 16:05:59.864495 2017-05-04 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A4,A9,B7,B8,C5,D5,E2,F2,G1,H4,H6,H9,I5,I6) * 842.13....71...3.2.632..8.1.983215.443....21.2156479..1......2.3..8..1....91..... * PAIR A2: 5,9 ROW 2 D2: 5,9,4 # reduction candidate for 5,9 D2: 5,9 => CTR * 8427136...71...342.632.4871798321564436...2172156479..1.74...2.3.48..1....91..4.. D2: 4 # 23 pairs H2: 5,9,4 # reduction candidate for 5,9 H2: 5,9 # 23 pairs * PAIR A3: 5,9 ROW 3 E3: 5,9,7 # reduction candidate for 5,9 E3: 5,9 => CTR * 8427136...71...342.632.4871798321564436...2172156479..1..4..72.3..8..1..6.91..... E3: 7 # 23 pairs F3: 5,9,4 # reduction candidate for 5,9 F3: 5,9 # 23 pairs H3: 5,9,4,7 # reduction candidate for 5,9 H3: 5,9 => CTR * 842.13....71...342.632748.1.983215.443....21.2156479..1......2.3..8..1....91..... H3: 4,7 # 17 pairs * PAIR G1: 6,7 BLK 3 H1: 6,7,5,9 # reduction candidate for 6,7 H1: 6,7 # 26 pairs I1: 6,7,5,9 # reduction candidate for 6,7 I1: 6,7 # 27 pairs * PAIR G1: 6,7 COL G G7: 6,7,4 # reduction candidate for 6,7 G7: 6,7 # 17 pairs G9: 6,7,4 # reduction candidate for 6,7 G9: 6,7 => SOLVED * 842513769971486352563279841698321574437958216215647938186795423354862197729134685 G9: 4 # 17 pairs * PAIR C5: 6,7 COL C C7: 6,7,4 # reduction candidate for 6,7 C7: 6,7 # 17 pairs C8: 6,7,4 # reduction candidate for 6,7 C8: 6,7 # 19 pairs * PAIR D5: 5,9 BLK 5 E5: 5,9,8 # reduction candidate for 5,9 E5: 5,9 # 15 pairs F5: 5,9,8 # reduction candidate for 5,9 F5: 5,9 # 15 pairs * PAIR D5: 5,9 COL D D1: 5,9,7 # reduction candidate for 5,9 D1: 5,9 # 23 pairs D2: 5,9,4 # reduction candidate for 5,9 D2: 5,9 => CTR * 8427136...71...342.632.4871798321564436...2172156479..1.74...2.3.48..1....91..4.. D2: 4 # 23 pairs D7: 5,9,4,7 # reduction candidate for 5,9 D7: 5,9 => CTR * 8427136...714..3.2.632..8.1.983215.443....21.2156479..1......2.3..8..1....91..... D7: 4,7 # 18 pairs * PAIR H4: 6,7 COL H H1: 6,7,5,9 # reduction candidate for 6,7 H1: 6,7 # 26 pairs H8: 6,7,5,9 # reduction candidate for 6,7 H8: 6,7 # 27 pairs * PAIR I5: 6,7 COL I I1: 6,7,5,9 # reduction candidate for 6,7 I1: 6,7 # 27 pairs I7: 6,7,3,5,8,9 # reduction candidate for 6,7 I7: 6,7 => CTR * 842.13....71...3.2.632..8.1.983215.443....21.2156479..18..3..2.3..8..1....91..... I7: 3,5,8,9 # 16 pairs I8: 6,7,5,9 # reduction candidate for 6,7 I8: 6,7 # 19 pairs I9: 6,7,3,5,8 # reduction candidate for 6,7 I9: 6,7 # 25 pairs * PAIR I6: 3,8 COL I I7: 3,8,5,6,7,9 # reduction candidate for 3,8 I7: 3,8 # 17 pairs I9: 3,8,5,6,7 # reduction candidate for 3,8 I9: 3,8 # 17 pairs * PAIR B7: 5,8 BLK 7 B9: 5,8,2 # reduction candidate for 5,8 B9: 5,8 # 17 pairs B9: 2 # 17 pairs * PAIR B7: 5,8 ROW 7 I7: 5,8,3,6,7,9 # reduction candidate for 5,8 I7: 5,8 # 17 pairs I7: 3,6,7,9 # 16 pairs * PAIR B8: 2,5 BLK 7 B9: 2,5,8 # reduction candidate for 2,5 B9: 2,5 # 16 pairs B9: 8 # 12 pairs * PAIR B8: 2,5 ROW 8 F8: 2,5,4,6,9 # reduction candidate for 2,5 F8: 2,5 # 19 pairs F8: 4,6,9 # 17 pairs * PAIR A9: 6,7 BLK 7 C7: 6,7,4 # reduction candidate for 6,7 C7: 6,7 # 17 pairs C8: 6,7,4 # reduction candidate for 6,7 C8: 6,7 # 19 pairs * PAIR A9: 6,7 ROW 9 E9: 6,7,3,5 # reduction candidate for 6,7 E9: 6,7 # 19 pairs G9: 6,7,4 # reduction candidate for 6,7 G9: 6,7 => SOLVED * 842513769971486352563279841698321574437958216215647938186795423354862197729134685 G9: 4 # 17 pairs I9: 6,7,3,5,8 # reduction candidate for 6,7 I9: 6,7 # 25 pairs * PAIR H9: 3,8 BLK 9 I7: 3,8,5,6,7,9 # reduction candidate for 3,8 I7: 3,8 # 17 pairs I9: 3,8,5,6,7 # reduction candidate for 3,8 I9: 3,8 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-387-base-pr-000.dot * REASONING * DIS # D2: 5,9 => CTR => D2: 4 * DIS # E3: 5,9 => CTR => E3: 7 * DIS # H3: 5,9 => CTR => H3: 4,7 * PRF # G9: 6,7 => SOL * DIS # D2: 5,9 => CTR => D2: 4 * DIS # D7: 5,9 => CTR => D7: 4,7 * DIS # I7: 6,7 => CTR => I7: 3,5,8,9 * PRF # G9: 6,7 => SOL * CNT 8 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A4,A9,B7,B8,C5,D5,E2,F2,G1,H4,H6,H9,I5,I6) * 842.13....71...3.2.632..8.1.983215.443....21.2156479..1......2.3..8..1....91..... * PAIR A2: 5,9 ROW 2 D2: 5,9,4 # reduction candidate for 5,9 D2: 5,9 => CTR * 8427136...71...342.632.4871798321564436...2172156479..1.74...2.3.48..1....91..4.. * RESTART * PAIR RESTART * PAIR G1: 6,7 BLK 3 H1: 6,7,5,9 # reduction candidate for 6,7 H1: 6,7 # 26 pairs I1: 6,7,5,9 # reduction candidate for 6,7 I1: 6,7 # 27 pairs * PAIR G1: 6,7 COL G G9: 6,7,4 # reduction candidate for 6,7 G9: 6,7 => SOLVED * 842513769971486352563279841698321574437958216215647938186795423354862197729134685 * DURATION: 0:00:07.229020 START: 16:06:58.115694 END: 16:07:05.344714 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-387-base-pr-001.dot * REASONING * DIS # D2: 5,9 => CTR => D2: 4 * PRF D2: 4 # G9: 6,7 => SOL * STA D2: 4 + G9: 6,7 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 387 solution: 842513769971486352563279841698321574437958216215647938186795423354862197729134685 info: 35128 FNBTHXYK S8.f 44644 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 842513769971486352563279841698321574437958216215647938186795423354862197729134685 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:
* DIS # D2: 5,9 => CTR => D2: 4 * INC # D2: 4 => UNS * INC # H2: 5,9 => UNS * DIS # E3: 5,9 => CTR => E3: 7 * INC # E3: 7 => UNS * INC # F3: 5,9 => UNS * DIS # H3: 5,9 => CTR => H3: 4,7 * INC # H3: 4,7 => UNS * INC # H1: 6,7 => UNS * INC # I1: 6,7 => UNS * INC # G7: 6,7 => UNS * PRF # G9: 6,7 => SOL * INC # G9: 4 => UNS * INC # C7: 6,7 => UNS * INC # C8: 6,7 => UNS * INC # E5: 5,9 => UNS * INC # F5: 5,9 => UNS * INC # D1: 5,9 => UNS * DIS # D2: 5,9 => CTR => D2: 4 * INC # D2: 4 => UNS * DIS # D7: 5,9 => CTR => D7: 4,7 * INC # D7: 4,7 => UNS * INC # H1: 6,7 => UNS * INC # H8: 6,7 => UNS * INC # I1: 6,7 => UNS * DIS # I7: 6,7 => CTR => I7: 3,5,8,9 * INC # I7: 3,5,8,9 => UNS * INC # I8: 6,7 => UNS * INC # I9: 6,7 => UNS * INC # I7: 3,8 => UNS * INC # I9: 3,8 => UNS * INC # B9: 5,8 => UNS * INC # B9: 2 => UNS * INC # I7: 5,8 => UNS * INC # I7: 3,6,7,9 => UNS * INC # B9: 2,5 => UNS * INC # B9: 8 => UNS * INC # F8: 2,5 => UNS * INC # F8: 4,6,9 => UNS * INC # C7: 6,7 => UNS * INC # C8: 6,7 => UNS * INC # E9: 6,7 => UNS * PRF # G9: 6,7 => SOL * INC # G9: 4 => UNS * INC # I9: 6,7 => UNS * INC # I7: 3,8 => UNS * INC # I9: 3,8 => UNS * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D2: 5,9 => CTR => D2: 4 * INC D2: 4 # H1: 6,7 => UNS * INC D2: 4 # I1: 6,7 => UNS * PRF D2: 4 # G9: 6,7 => SOL * STA D2: 4 + G9: 6,7 * CNT 4 HDP CHAINS / 4 HYP OPENED