Analysis of xx-top500-403-base.sdk
Contents
Original Sudoku
level: medium
position: 35...2....1.....8.....9.7..4...6.......8...1..3.......6.....2..7.......4...1..... initial
Autosolve
position: 358712...917....82264.987.148..61...57.8...1.13....8..6.1...2.87...8.1.48..1..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D2: 3,5 => CTR => D2: 4,6 * DIS # D7: 3,5 => CTR => D7: 4,9 * DIS # D8: 3,5 => CTR => D8: 2,6,9 * DIS # I5: 6,9 => CTR => I5: 3 * PRF # I5: 3 => SOL * PRF # I6: 6,9 => SOL * DIS # I6: 5 => CTR => I6: 6,9 * DIS # I9: 6,9 => CTR => I9: 3,5,7 * DIS # D2: 3,5 => CTR => D2: 4,6 * DIS # H4: 3,5 => CTR => H4: 2,7,9 * DIS # H9: 3,5 => CTR => H9: 6,7,9 * DIS # D4: 2,9 => CTR => D4: 3,5 * DIS # F7: 4,9 => CTR => F7: 3,5,7 * DIS # D8: 3,5 => CTR => D8: 2,6,9 * DIS # E9: 3,5 => CTR => E9: 2,4,7 * DIS # F9: 3,5 => CTR => F9: 4,6,7,9 * DIS # H9: 3,5 => CTR => H9: 6,7,9 * CNT 17 HDP CHAINS / 55 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D2: 3,5 => CTR => D2: 4,6 * DIS D2: 4,6 # D7: 3,5 => CTR => D7: 4,9 * DIS D2: 4,6 + D7: 4,9 # D8: 3,5 => CTR => D8: 2,6,9 * DIS D2: 4,6 + D7: 4,9 + D8: 2,6,9 # D4: 2,9 => CTR => D4: 3,5 * DIS D2: 4,6 + D7: 4,9 + D8: 2,6,9 + D4: 3,5 # I5: 6,9 => CTR => I5: 3 * PRF D2: 4,6 + D7: 4,9 + D8: 2,6,9 + D4: 3,5 + I5: 3 => SOL * STA D2: 4,6 + D7: 4,9 + D8: 2,6,9 + D4: 3,5 + I5: 3 * CNT 6 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 35...2....1.....8.....9.7..4...6.......8...1..3.......6.....2..7.......4...1..... | initial |
| 358712...917....82264.987.148..61...57.8...1.13....8..6.1...2.87...8.1.48..1..... | autosolve |
| 358712649917634582264598731482361975576829413139457826641973258793285164825146397 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) D3: 3,5 I1: 6,9 G2: 3,5 H3: 3,5 C4: 2,9 B7: 4,9 B8: 2,9 C8: 3,5 C9: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H4,H6: 2.. / H4 = 2 => 15 pairs (_) / H6 = 2 => 12 pairs (_) B8,B9: 2.. / B8 = 2 => 12 pairs (_) / B9 = 2 => 10 pairs (_) D8,E9: 2.. / D8 = 2 => 10 pairs (_) / E9 = 2 => 12 pairs (_) C5,E5: 2.. / C5 = 2 => 12 pairs (_) / E5 = 2 => 11 pairs (_) B8,D8: 2.. / B8 = 2 => 12 pairs (_) / D8 = 2 => 10 pairs (_) B9,E9: 2.. / B9 = 2 => 10 pairs (_) / E9 = 2 => 12 pairs (_) G2,H3: 3.. / G2 = 3 => 0 pairs (X) / H3 = 3 => 0 pairs (_) C8,C9: 3.. / C8 = 3 => 0 pairs (*) / C9 = 3 => 0 pairs (X) D3,H3: 3.. / D3 = 3 => 0 pairs (X) / H3 = 3 => 0 pairs (_) G1,H1: 4.. / G1 = 4 => 18 pairs (_) / H1 = 4 => 12 pairs (_) G5,H6: 4.. / G5 = 4 => 12 pairs (_) / H6 = 4 => 18 pairs (_) B7,B9: 4.. / B7 = 4 => 9 pairs (_) / B9 = 4 => 10 pairs (_) G1,G5: 4.. / G1 = 4 => 18 pairs (_) / G5 = 4 => 12 pairs (_) H1,H6: 4.. / H1 = 4 => 12 pairs (_) / H6 = 4 => 18 pairs (_) G2,H3: 5.. / G2 = 5 => 0 pairs (*) / H3 = 5 => 0 pairs (X) C8,C9: 5.. / C8 = 5 => 0 pairs (X) / C9 = 5 => 0 pairs (_) D3,H3: 5.. / D3 = 5 => 0 pairs (*) / H3 = 5 => 0 pairs (X) D2,F2: 6.. / D2 = 6 => 9 pairs (_) / F2 = 6 => 12 pairs (_) C5,C6: 6.. / C5 = 6 => 12 pairs (_) / C6 = 6 => 11 pairs (_) D2,D8: 6.. / D2 = 6 => 9 pairs (_) / D8 = 6 => 12 pairs (_) E6,F6: 7.. / E6 = 7 => 9 pairs (_) / F6 = 7 => 9 pairs (_) H4,I4: 7.. / H4 = 7 => 17 pairs (_) / I4 = 7 => 9 pairs (_) I4,I9: 7.. / I4 = 7 => 9 pairs (_) / I9 = 7 => 17 pairs (_) * DURATION: 0:00:36.735771 START: 16:37:57.335318 END: 16:38:34.071089 2017-05-04 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,B8,C4,C8,C9,D3,G2,H3,I1) * 358712...917....82264.987.148..61...57.8...1.13....8..6.1...2.87...8.1.48..1..... * PAIR D3: 3,5 BLK 2 D2: 3,5,4,6 # reduction candidate for 3,5 D2: 3,5 => CTR * 358712.4.917.46.82264.987.1489261...57283.416136...8296.1...2.872.68.1.48..12.... D2: 4,6 # 10 pairs E2: 3,5,4 # reduction candidate for 3,5 E2: 3,5 # 12 pairs F2: 3,5,4,6 # reduction candidate for 3,5 F2: 3,5 # 11 pairs * PAIR D3: 3,5 COL D D4: 3,5,2,9 # reduction candidate for 3,5 D4: 3,5 # 12 pairs D7: 3,5,4,9 # reduction candidate for 3,5 D7: 3,5 => CTR * 358712...917....82264.987.148..61...57.8...1.13....8..6.1...2.87...8.1.48..1..... D7: 4,9 # 10 pairs D8: 3,5,2,6,9 # reduction candidate for 3,5 D8: 3,5 => CTR * 358712.4.9176...82264.987.1489261...5728..416136...8296.1...2.872..8.1.48..12.... D8: 2,6,9 # 9 pairs * PAIR I1: 6,9 BLK 3 G1: 6,9,4 # reduction candidate for 6,9 G1: 6,9 # 12 pairs H1: 6,9,4 # reduction candidate for 6,9 H1: 6,9 # 18 pairs * PAIR I1: 6,9 COL I I5: 6,9,3 # reduction candidate for 6,9 I5: 6,9 => CTR * 358712649917...382264398751482561973579823416136...8256.1.3.2.87.5.8.1.48.31..5.7 I5: 3 => SOLVED * 358712649917634582264598731482361975576829413139457826641973258793285164825146397 I6: 6,9,5 # reduction candidate for 6,9 I6: 6,9 => SOLVED * 358712649917634582264598731482361975576829413139457826641973258793285164825146397 I6: 5 => CTR * 358712...917...3822643987514825619..57.823416136...8256.1.352787.528.1348.31..5.. I9: 6,9,3,5,7 # reduction candidate for 6,9 I9: 6,9 => CTR * 358712...917....82264.987.148..61..757.8...1313....8.56.1...2.87...8.1.48..1..... I9: 3,5,7 # 9 pairs * PAIR G2: 3,5 ROW 2 D2: 3,5,4,6 # reduction candidate for 3,5 D2: 3,5 => CTR * 358712.4.917.46.82264.987.1489261...57283.416136...8296.1...2.872.68.1.48..12.... D2: 4,6 # 10 pairs E2: 3,5,4 # reduction candidate for 3,5 E2: 3,5 # 12 pairs F2: 3,5,4,6 # reduction candidate for 3,5 F2: 3,5 # 11 pairs * PAIR G2: 3,5 COL G G4: 3,5,9 # reduction candidate for 3,5 G4: 3,5 # 11 pairs G9: 3,5,6,9 # reduction candidate for 3,5 G9: 3,5 # 17 pairs * PAIR H3: 3,5 COL H H4: 3,5,2,7,9 # reduction candidate for 3,5 H4: 3,5 => CTR * 3587126499176...82264.987.1482.619.757.82.41.13.4..82.6419..27879.28.16482.1.6.9. H4: 2,7,9 # 9 pairs H7: 3,5,7,9 # reduction candidate for 3,5 H7: 3,5 # 11 pairs H8: 3,5,6,9 # reduction candidate for 3,5 H8: 3,5 # 12 pairs H9: 3,5,6,7,9 # reduction candidate for 3,5 H9: 3,5 => CTR * 358712...917....82264.987.148..61...57.8...1.13....8..6.1...2.87...8.1.48..1..... H9: 6,7,9 # 9 pairs * PAIR C4: 2,9 BLK 4 C5: 2,9,6 # reduction candidate for 2,9 C5: 2,9 # 11 pairs C6: 2,9,6 # reduction candidate for 2,9 C6: 2,9 # 12 pairs * PAIR C4: 2,9 ROW 4 D4: 2,9,3,5 # reduction candidate for 2,9 D4: 2,9 => CTR * 358712...917....82264.987.148..61...57.8...1.13....8..6.1...2.87...8.1.48..1..... D4: 3,5 # 12 pairs H4: 2,9,3,5,7 # reduction candidate for 2,9 H4: 2,9 # 15 pairs * PAIR B7: 4,9 BLK 7 B9: 4,9,2 # reduction candidate for 4,9 B9: 4,9 # 12 pairs B9: 2 # 10 pairs * PAIR B7: 4,9 ROW 7 D7: 4,9,3,5 # reduction candidate for 4,9 D7: 4,9 # 10 pairs F7: 4,9,3,5,7 # reduction candidate for 4,9 F7: 4,9 => CTR * 358712...917....82264.987.148..61...57.8...1.13....8..6.1...2.87...8.1.48..1..... F7: 3,5,7 # 9 pairs * PAIR B8: 2,9 BLK 7 B9: 2,9,4 # reduction candidate for 2,9 B9: 4 # 10 pairs B9: 2,9 # 9 pairs * PAIR B8: 2,9 ROW 8 D8: 2,9,3,5,6 # reduction candidate for 2,9 D8: 3,5,6 # 12 pairs D8: 2,9 # 10 pairs * PAIR C8: 3,5 ROW 8 D8: 3,5,2,6,9 # reduction candidate for 3,5 D8: 3,5 => CTR * 358712.4.9176...82264.987.1489261...5728..416136...8296.1...2.872..8.1.48..12.... D8: 2,6,9 # 9 pairs F8: 3,5,6,9 # reduction candidate for 3,5 F8: 3,5 # 11 pairs H8: 3,5,6,9 # reduction candidate for 3,5 H8: 3,5 # 12 pairs * PAIR C9: 3,5 ROW 9 E9: 3,5,2,4,7 # reduction candidate for 3,5 E9: 3,5 => CTR * 358712.4.91764..82264.987.148..61...57.8..41.13.4..8..641...2.879.2861.482.1.4... E9: 2,4,7 # 9 pairs F9: 3,5,4,6,7,9 # reduction candidate for 3,5 F9: 3,5 => CTR * 358712...917....82264.987.148..61...57.8...1.13....8..6.1...2.87...8.1.48..1..... F9: 4,6,7,9 # 9 pairs G9: 3,5,6,9 # reduction candidate for 3,5 G9: 3,5 # 17 pairs H9: 3,5,6,7,9 # reduction candidate for 3,5 H9: 3,5 => CTR * 358712...917....82264.987.148..61...57.8...1.13....8..6.1...2.87...8.1.48..1..... H9: 6,7,9 # 9 pairs I9: 3,5,6,7,9 # reduction candidate for 3,5 I9: 3,5 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-403-base-pr-000.dot * REASONING * DIS # D2: 3,5 => CTR => D2: 4,6 * DIS # D7: 3,5 => CTR => D7: 4,9 * DIS # D8: 3,5 => CTR => D8: 2,6,9 * DIS # I5: 6,9 => CTR => I5: 3 * PRF # I5: 3 => SOL * PRF # I6: 6,9 => SOL * DIS # I6: 5 => CTR => I6: 6,9 * DIS # I9: 6,9 => CTR => I9: 3,5,7 * DIS # D2: 3,5 => CTR => D2: 4,6 * DIS # H4: 3,5 => CTR => H4: 2,7,9 * DIS # H9: 3,5 => CTR => H9: 6,7,9 * DIS # D4: 2,9 => CTR => D4: 3,5 * DIS # F7: 4,9 => CTR => F7: 3,5,7 * DIS # D8: 3,5 => CTR => D8: 2,6,9 * DIS # E9: 3,5 => CTR => E9: 2,4,7 * DIS # F9: 3,5 => CTR => F9: 4,6,7,9 * DIS # H9: 3,5 => CTR => H9: 6,7,9 * CNT 17 HDP CHAINS / 55 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,B8,C4,C8,C9,D3,G2,H3,I1) * 358712...917....82264.987.148..61...57.8...1.13....8..6.1...2.87...8.1.48..1..... * PAIR D3: 3,5 BLK 2 D2: 3,5,4,6 # reduction candidate for 3,5 D2: 3,5 => CTR * 358712.4.917.46.82264.987.1489261...57283.416136...8296.1...2.872.68.1.48..12.... E2: 3,5,4 # reduction candidate for 3,5 E2: 3,5 # 12 pairs F2: 3,5,4,6 # reduction candidate for 3,5 F2: 3,5 # 11 pairs * PAIR D3: 3,5 COL D D4: 3,5,2,9 # reduction candidate for 3,5 D4: 3,5 # 12 pairs D7: 3,5,4,9 # reduction candidate for 3,5 D7: 3,5 => CTR * 358712...917....82264.987.148..61...57.8...1.13....8..6.1...2.87...8.1.48..1..... D8: 3,5,2,6,9 # reduction candidate for 3,5 D8: 3,5 => CTR * 358712.4.9176...82264.987.1489261...5728..416136...8296.1...2.872..8.1.48..12.... * RESTART * PAIR D3: 3,5 COL D D4: 3,5,2,9 # reduction candidate for 3,5 D4: 2,9 => CTR * 358712...917...38226439875148..61..357.8...1.13.5..8..6.1...2.87.5.8.1.48.31..... * PAIR RESTART * PAIR D3: 3,5 BLK 2 E2: 3,5,4 # reduction candidate for 3,5 E2: 3,5 # 14 pairs F2: 3,5,4,6 # reduction candidate for 3,5 F2: 3,5 # 16 pairs * PAIR I1: 6,9 BLK 3 G1: 6,9,4 # reduction candidate for 6,9 G1: 6,9 # 15 pairs H1: 6,9,4 # reduction candidate for 6,9 H1: 6,9 # 18 pairs * PAIR I1: 6,9 COL I I5: 6,9,3 # reduction candidate for 6,9 I5: 6,9 => CTR * 358712649917...382264398751482561973579823416136...8256.1.3.2.87.5.8.1.48.31..5.7 I5: 3 => SOLVED * 358712649917634582264598731482361975576829413139457826641973258793285164825146397 * DURATION: 0:00:12.534549 START: 16:39:18.172517 END: 16:39:30.707066 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-403-base-pr-001.dot * REASONING * DIS # D2: 3,5 => CTR => D2: 4,6 * DIS D2: 4,6 # D7: 3,5 => CTR => D7: 4,9 * DIS D2: 4,6 + D7: 4,9 # D8: 3,5 => CTR => D8: 2,6,9 * DIS D2: 4,6 + D7: 4,9 + D8: 2,6,9 # D4: 2,9 => CTR => D4: 3,5 * DIS D2: 4,6 + D7: 4,9 + D8: 2,6,9 + D4: 3,5 # I5: 6,9 => CTR => I5: 3 * PRF D2: 4,6 + D7: 4,9 + D8: 2,6,9 + D4: 3,5 + I5: 3 => SOL * STA D2: 4,6 + D7: 4,9 + D8: 2,6,9 + D4: 3,5 + I5: 3 * CNT 6 HDP CHAINS / 13 HYP OPENED
Header Info
Top 500 Minimum 17 403 solution: 358712649917634582264598731482361975576829413139457826641973258793285164825146397 info: 90611 FNBTXY S8.f 30038 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 358712649917634582264598731482361975576829413139457826641973258793285164825146397 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: 3,5 => CTR => D2: 4,6 * INC # D2: 4,6 => UNS * INC # E2: 3,5 => UNS * INC # F2: 3,5 => UNS * INC # D4: 3,5 => UNS * DIS # D7: 3,5 => CTR => D7: 4,9 * INC # D7: 4,9 => UNS * DIS # D8: 3,5 => CTR => D8: 2,6,9 * INC # D8: 2,6,9 => UNS * INC # G1: 6,9 => UNS * INC # H1: 6,9 => UNS * DIS # I5: 6,9 => CTR => I5: 3 * PRF # I5: 3 => SOL * PRF # I6: 6,9 => SOL * DIS # I6: 5 => CTR => I6: 6,9 * DIS # I9: 6,9 => CTR => I9: 3,5,7 * INC # I9: 3,5,7 => UNS * DIS # D2: 3,5 => CTR => D2: 4,6 * INC # D2: 4,6 => UNS * INC # E2: 3,5 => UNS * INC # F2: 3,5 => UNS * INC # G4: 3,5 => UNS * INC # G9: 3,5 => UNS * DIS # H4: 3,5 => CTR => H4: 2,7,9 * INC # H4: 2,7,9 => UNS * INC # H7: 3,5 => UNS * INC # H8: 3,5 => UNS * DIS # H9: 3,5 => CTR => H9: 6,7,9 * INC # H9: 6,7,9 => UNS * INC # C5: 2,9 => UNS * INC # C6: 2,9 => UNS * DIS # D4: 2,9 => CTR => D4: 3,5 * INC # D4: 3,5 => UNS * INC # H4: 2,9 => UNS * INC # B9: 4,9 => UNS * INC # B9: 2 => UNS * INC # D7: 4,9 => UNS * DIS # F7: 4,9 => CTR => F7: 3,5,7 * INC # F7: 3,5,7 => UNS * INC # B9: 2,9 => UNS * INC # B9: 4 => UNS * INC # D8: 2,9 => UNS * INC # D8: 3,5,6 => UNS * DIS # D8: 3,5 => CTR => D8: 2,6,9 * INC # D8: 2,6,9 => UNS * INC # F8: 3,5 => UNS * INC # H8: 3,5 => UNS * DIS # E9: 3,5 => CTR => E9: 2,4,7 * INC # E9: 2,4,7 => UNS * DIS # F9: 3,5 => CTR => F9: 4,6,7,9 * INC # F9: 4,6,7,9 => UNS * INC # G9: 3,5 => UNS * DIS # H9: 3,5 => CTR => H9: 6,7,9 * INC # H9: 6,7,9 => UNS * INC # I9: 3,5 => UNS * CNT 55 HDP CHAINS / 55 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D2: 3,5 => CTR => D2: 4,6 * INC D2: 4,6 # E2: 3,5 => UNS * INC D2: 4,6 # F2: 3,5 => UNS * INC D2: 4,6 # D4: 3,5 => UNS * DIS D2: 4,6 # D7: 3,5 => CTR => D7: 4,9 * DIS D2: 4,6 + D7: 4,9 # D8: 3,5 => CTR => D8: 2,6,9 * INC D2: 4,6 + D7: 4,9 + D8: 2,6,9 # D4: 3,5 => UNS * DIS D2: 4,6 + D7: 4,9 + D8: 2,6,9 # D4: 2,9 => CTR => D4: 3,5 * INC D2: 4,6 + D7: 4,9 + D8: 2,6,9 + D4: 3,5 # E2: 3,5 => UNS * INC D2: 4,6 + D7: 4,9 + D8: 2,6,9 + D4: 3,5 # F2: 3,5 => UNS * INC D2: 4,6 + D7: 4,9 + D8: 2,6,9 + D4: 3,5 # G1: 6,9 => UNS * INC D2: 4,6 + D7: 4,9 + D8: 2,6,9 + D4: 3,5 # H1: 6,9 => UNS * DIS D2: 4,6 + D7: 4,9 + D8: 2,6,9 + D4: 3,5 # I5: 6,9 => CTR => I5: 3 * PRF D2: 4,6 + D7: 4,9 + D8: 2,6,9 + D4: 3,5 + I5: 3 => SOL * STA D2: 4,6 + D7: 4,9 + D8: 2,6,9 + D4: 3,5 + I5: 3 * CNT 14 HDP CHAINS / 13 HYP OPENED