Analysis of xx-top500-328-base.sdk
Contents
Original Sudoku
level: medium
position: .4.5...6..17...............8......2.....13......4.7.........1.35..6.........8.7.. initial
Autosolve
position: .4.5...6..17...............8..9...2....813......427.........1.35..6.........8.7.6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D3: 2,3 => CTR => D3: 1,7 * DIS # A2: 2,3 => CTR => A2: 6,9 * DIS # G2: 2,3 => CTR => G2: 4,5,8,9 * PRF # D9: 2,3 => SOL * DIS # D9: 1 => CTR => D9: 2,3 * DIS # B8: 8,9 => CTR => B8: 3,7 * DIS # C4: 3,4 => CTR => C4: 1 * PRF # C4: 1 => SOL * DIS # B7: 2,7 => CTR => B7: 6,8,9 * DIS # D3: 2,7 => CTR => D3: 1,3 * PRF # D3: 1,3 => SOL * CNT 11 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D3: 2,3 => CTR => D3: 1,7 * DIS D3: 1,7 # A2: 2,3 => CTR => A2: 6,9 * DIS D3: 1,7 + A2: 6,9 # G2: 2,3 => CTR => G2: 4,5,8,9 * PRF D3: 1,7 + A2: 6,9 + G2: 4,5,8,9 # D9: 2,3 => SOL * STA D3: 1,7 + A2: 6,9 + G2: 4,5,8,9 + D9: 2,3 * CNT 4 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .4.5...6..17...............8......2.....13......4.7.........1.35..6.........8.7.. | initial |
| .4.5...6..17...............8..9...2....813......427.........1.35..6.........8.7.6 | autosolve |
| 348579261917268534265134879831956427724813695659427318486792153573641982192385746 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) D2: 2,3 B4: 3,7 E4: 5,6 F4: 5,6 G4: 3,4 D7: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,I1: 1.. / F1 = 1 => 0 pairs (X) / I1 = 1 => 0 pairs (_) C4,I4: 1.. / C4 = 1 => 0 pairs (*) / I4 = 1 => 0 pairs (X) C8,F8: 1.. / C8 = 1 => 0 pairs (X) / F8 = 1 => 0 pairs (_) A6,A9: 1.. / A6 = 1 => 0 pairs (X) / A9 = 1 => 0 pairs (_) D3,D9: 1.. / D3 = 1 => 0 pairs (*) / D9 = 1 => 0 pairs (X) H3,H6: 1.. / H3 = 1 => 0 pairs (X) / H6 = 1 => 0 pairs (_) G8,I8: 2.. / G8 = 2 => 6 pairs (_) / I8 = 2 => 6 pairs (_) E8,D9: 3.. / E8 = 3 => 0 pairs (X) / D9 = 3 => 0 pairs (_) B3,C3: 5.. / B3 = 5 => 6 pairs (_) / C3 = 5 => 6 pairs (_) G2,I2: 5.. / G2 = 5 => 6 pairs (_) / I2 = 5 => 8 pairs (_) E4,F4: 5.. / E4 = 5 => 4 pairs (_) / F4 = 5 => 4 pairs (_) H7,H9: 5.. / H7 = 5 => 5 pairs (_) / H9 = 5 => 6 pairs (_) F9,H9: 5.. / F9 = 5 => 5 pairs (_) / H9 = 5 => 6 pairs (_) E4,E7: 5.. / E4 = 5 => 4 pairs (_) / E7 = 5 => 4 pairs (_) E4,F4: 6.. / E4 = 6 => 4 pairs (_) / F4 = 6 => 4 pairs (_) G5,G6: 6.. / G5 = 6 => 6 pairs (_) / G6 = 6 => 6 pairs (_) E1,I1: 7.. / E1 = 7 => 0 pairs (*) / I1 = 7 => 0 pairs (X) B4,I4: 7.. / B4 = 7 => 0 pairs (X) / I4 = 7 => 0 pairs (_) B8,E8: 7.. / B8 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) A5,A7: 7.. / A5 = 7 => 0 pairs (*) / A7 = 7 => 0 pairs (X) D3,D7: 7.. / D3 = 7 => 0 pairs (X) / D7 = 7 => 0 pairs (_) H3,H5: 7.. / H3 = 7 => 0 pairs (*) / H5 = 7 => 0 pairs (X) * DURATION: 0:00:31.394652 START: 14:02:59.164332 END: 14:03:30.558984 2017-05-04 * CP COUNT: (22) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,D2,D7,E4,F4,G4) * .4.5...6..17...............8..9...2....813......427.........1.35..6.........8.7.6 * PAIR D2: 2,3 BLK 2 D3: 2,3,1,7 # reduction candidate for 2,3 D3: 2,3 => CTR * .4.5...6..17...............83.9..4277.4813.951..427......7..1.357.6........18.7.6 D3: 1,7 # 7 pairs * PAIR D2: 2,3 ROW 2 A2: 2,3,6,9 # reduction candidate for 2,3 A2: 2,3 => CTR * .4.5...6..17...............8..9...2....813.7....427...7..2..1.35..67.......38.7.6 A2: 6,9 # 7 pairs G2: 2,3,4,5,8,9 # reduction candidate for 2,3 G2: 2,3 => CTR * .4.5...6..17.....5.........8..9...2....813.7....427..87..2..1.35..67.......38.7.6 G2: 4,5,8,9 # 6 pairs * PAIR D2: 2,3 COL D D9: 2,3,1 # reduction candidate for 2,3 D9: 2,3 => SOLVED * 348579261917268534265134879831956427724813695659427318486792153573641982192385746 D9: 1 => CTR * .4.5...6..17...............8..9...2....813...1..427.........1.357163.......18.7.6 * PAIR B4: 3,7 COL B B8: 3,7,8,9 # reduction candidate for 3,7 B8: 8,9 => CTR * .4.5...6..17...............8..9...2....813......427.........1.35..67.......38.7.6 B8: 3,7 # 8 pairs * PAIR G4: 3,4 ROW 4 C4: 3,4,1 # reduction candidate for 3,4 C4: 3,4 => CTR * .4.5.1.6..17.............1.87.9...21...813.7....427...7..2..1.35.167........8.7.6 C4: 1 => SOLVED * 348579261917268534265134879831956427724813695659427318486792153573641982192385746 * PAIR G4: 3,4 COL G G2: 3,4,2,5,8,9 # reduction candidate for 3,4 G2: 3,4 # 9 pairs G3: 3,4,2,8,9 # reduction candidate for 3,4 G3: 3,4 # 7 pairs * PAIR D7: 2,7 ROW 7 A7: 2,7,4,6,9 # reduction candidate for 2,7 A7: 2,7 # 7 pairs B7: 2,7,6,8,9 # reduction candidate for 2,7 B7: 2,7 => CTR * .4.57..6..17...53..8513..7.8319..427724813.95...427.18...7..1.357.6.....1...8.7.6 B7: 6,8,9 # 6 pairs * PAIR D7: 2,7 COL D D3: 2,7,1,3 # reduction candidate for 2,7 D3: 2,7 => CTR * .4.5...6..173............1.8..9...21...813.7.1..427.3.7..2..1.35.163.......18.7.6 D3: 1,3 => SOLVED * 348579261917268534265134879831956427724813695659427318486792153573641982192385746 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-328-base-pr-000.dot * REASONING * DIS # D3: 2,3 => CTR => D3: 1,7 * DIS # A2: 2,3 => CTR => A2: 6,9 * DIS # G2: 2,3 => CTR => G2: 4,5,8,9 * PRF # D9: 2,3 => SOL * DIS # D9: 1 => CTR => D9: 2,3 * DIS # B8: 8,9 => CTR => B8: 3,7 * DIS # C4: 3,4 => CTR => C4: 1 * PRF # C4: 1 => SOL * DIS # B7: 2,7 => CTR => B7: 6,8,9 * DIS # D3: 2,7 => CTR => D3: 1,3 * PRF # D3: 1,3 => SOL * CNT 11 HDP CHAINS / 19 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,D2,D7,E4,F4,G4) * .4.5...6..17...............8..9...2....813......427.........1.35..6.........8.7.6 * PAIR D2: 2,3 BLK 2 D3: 2,3,1,7 # reduction candidate for 2,3 D3: 2,3 => CTR * .4.5...6..17...............83.9..4277.4813.951..427......7..1.357.6........18.7.6 * PAIR D2: 2,3 ROW 2 A2: 2,3,6,9 # reduction candidate for 2,3 A2: 2,3 => CTR * .4.5...6..17...............8..9...2....813.7....427...7..2..1.35..67.......38.7.6 G2: 2,3,4,5,8,9 # reduction candidate for 2,3 G2: 2,3 => CTR * .4.5...6..17.....5.........8..9...2....813.7....427..87..2..1.35..67.......38.7.6 * RESTART * PAIR D2: 2,3 COL D D9: 2,3,1 # reduction candidate for 2,3 D9: 2,3 => SOLVED * 348579261917268534265134879831956427724813695659427318486792153573641982192385746 * DURATION: 0:00:05.289574 START: 14:03:44.818565 END: 14:03:50.108139 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-328-base-pr-001.dot * REASONING * DIS # D3: 2,3 => CTR => D3: 1,7 * DIS D3: 1,7 # A2: 2,3 => CTR => A2: 6,9 * DIS D3: 1,7 + A2: 6,9 # G2: 2,3 => CTR => G2: 4,5,8,9 * PRF D3: 1,7 + A2: 6,9 + G2: 4,5,8,9 # D9: 2,3 => SOL * STA D3: 1,7 + A2: 6,9 + G2: 4,5,8,9 + D9: 2,3 * CNT 4 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 328 solution: 348579261917268534265134879831956427724813695659427318486792153573641982192385746 info: 2965 FNBHWY S8.f 19113 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 348579261917268534265134879831956427724813695659427318486792153573641982192385746 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 # D3: 2,3 => CTR => D3: 1,7 * INC # D3: 1,7 => UNS * DIS # A2: 2,3 => CTR => A2: 6,9 * INC # A2: 6,9 => UNS * DIS # G2: 2,3 => CTR => G2: 4,5,8,9 * INC # G2: 4,5,8,9 => UNS * PRF # D9: 2,3 => SOL * DIS # D9: 1 => CTR => D9: 2,3 * INC # B8: 3,7 => UNS * DIS # B8: 8,9 => CTR => B8: 3,7 * DIS # C4: 3,4 => CTR => C4: 1 * PRF # C4: 1 => SOL * INC # G2: 3,4 => UNS * INC # G3: 3,4 => UNS * INC # A7: 2,7 => UNS * DIS # B7: 2,7 => CTR => B7: 6,8,9 * INC # B7: 6,8,9 => UNS * DIS # D3: 2,7 => CTR => D3: 1,3 * PRF # D3: 1,3 => SOL * CNT 19 HDP CHAINS / 19 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D3: 2,3 => CTR => D3: 1,7 * DIS D3: 1,7 # A2: 2,3 => CTR => A2: 6,9 * DIS D3: 1,7 + A2: 6,9 # G2: 2,3 => CTR => G2: 4,5,8,9 * PRF D3: 1,7 + A2: 6,9 + G2: 4,5,8,9 # D9: 2,3 => SOL * STA D3: 1,7 + A2: 6,9 + G2: 4,5,8,9 + D9: 2,3 * CNT 4 HDP CHAINS / 4 HYP OPENED