Analysis of xx-top500-474-base.sdk
Contents
Original Sudoku
level: medium
position: .......524...6...........1..7.2.....6.....4.....1.8....18..........3.7..5.2...... initial
Autosolve
position: .......524...6...........14.7.2.6...6.....4.....1.8...718......9...3.7..532...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H6: 2,3 => CTR => H6: 6,7,9 * DIS # A3: 8 => CTR => A3: 2,3 * DIS # I8: 5,8 => CTR => I8: 1 * PRF # I8: 1 => SOL * DIS # H5: 7,9 => CTR => H5: 2,8 * CNT 5 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H6: 2,3 => CTR => H6: 6,7,9 * PRF H6: 6,7,9 # G6: 5,9 => SOL * STA H6: 6,7,9 + G6: 5,9 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......524...6...........1..7.2.....6.....4.....1.8....18..........3.7..5.2...... | initial |
| .......524...6...........14.7.2.6...6.....4.....1.8...718......9...3.7..532...... | autosolve |
| 167489352425361879389725614874256193651973428293148567718694235946532781532817946 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) A6: 2,3 B8: 4,6 C8: 4,6 D8: 5,8 H8: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,F2: 1.. / C2 = 1 => 0 pairs (X) / F2 = 1 => 0 pairs (_) C5,I5: 1.. / C5 = 1 => 0 pairs (*) / I5 = 1 => 0 pairs (X) F8,I8: 1.. / F8 = 1 => 0 pairs (X) / I8 = 1 => 0 pairs (_) A1,A4: 1.. / A1 = 1 => 0 pairs (*) / A4 = 1 => 0 pairs (X) E1,E9: 1.. / E1 = 1 => 0 pairs (X) / E9 = 1 => 0 pairs (_) G4,G9: 1.. / G4 = 1 => 0 pairs (*) / G9 = 1 => 0 pairs (X) B2,F2: 2.. / B2 = 2 => 0 pairs (*) / F2 = 2 => 0 pairs (X) B5,H5: 2.. / B5 = 2 => 0 pairs (X) / H5 = 2 => 0 pairs (_) F8,H8: 2.. / F8 = 2 => 0 pairs (*) / H8 = 2 => 0 pairs (X) A3,A6: 2.. / A3 = 2 => 0 pairs (X) / A6 = 2 => 0 pairs (_) E3,E7: 2.. / E3 = 2 => 0 pairs (*) / E7 = 2 => 0 pairs (X) G6,G7: 2.. / G6 = 2 => 0 pairs (X) / G7 = 2 => 0 pairs (_) D5,F5: 3.. / D5 = 3 => 5 pairs (_) / F5 = 3 => 5 pairs (_) D1,F1: 4.. / D1 = 4 => 5 pairs (_) / F1 = 4 => 7 pairs (_) E4,E6: 4.. / E4 = 4 => 5 pairs (_) / E6 = 4 => 6 pairs (_) B8,C8: 4.. / B8 = 4 => 3 pairs (_) / C8 = 4 => 6 pairs (_) H7,H9: 4.. / H7 = 4 => 5 pairs (_) / H9 = 4 => 5 pairs (_) C4,E4: 4.. / C4 = 4 => 6 pairs (_) / E4 = 4 => 5 pairs (_) B6,B8: 4.. / B6 = 4 => 6 pairs (_) / B8 = 4 => 3 pairs (_) G1,G3: 6.. / G1 = 6 => 6 pairs (_) / G3 = 6 => 5 pairs (_) H6,I6: 6.. / H6 = 6 => 5 pairs (_) / I6 = 6 => 7 pairs (_) B8,C8: 6.. / B8 = 6 => 6 pairs (_) / C8 = 6 => 3 pairs (_) D7,D9: 6.. / D7 = 6 => 5 pairs (_) / D9 = 6 => 5 pairs (_) C1,C3: 7.. / C1 = 7 => 5 pairs (_) / C3 = 7 => 5 pairs (_) H2,I2: 7.. / H2 = 7 => 5 pairs (_) / I2 = 7 => 5 pairs (_) A4,B5: 8.. / A4 = 8 => 0 pairs (*) / B5 = 8 => 0 pairs (X) * DURATION: 0:00:37.508409 START: 18:52:26.383906 END: 18:53:03.892315 2017-05-04 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B8,C8,D8,H8) * .......524...6...........14.7.2.6...6.....4.....1.8...718......9...3.7..532...... * PAIR A6: 2,3 ROW 6 G6: 2,3,5,9 # reduction candidate for 2,3 G6: 2,3 # 6 pairs H6: 2,3,6,7,9 # reduction candidate for 2,3 H6: 2,3 => CTR * 1......5242..61..........14.7.2461..681...4272..178.36718...2..9...3.7.1532.1.... H6: 6,7,9 # 5 pairs * PAIR A6: 2,3 COL A A3: 2,3,8 # reduction candidate for 2,3 A3: 8 => CTR * 1..4...5242..61.7985..2..14375246198681.5.4272..1785637186942359..532781532.17946 A3: 2,3 # 8 pairs * PAIR D8: 5,8 ROW 8 I8: 5,8,1 # reduction candidate for 5,8 I8: 5,8 => CTR * ....1..524.1.6...........1417.2.6...6.....4.....1.8...718......9...3172.532...... I8: 1 => SOLVED * 167489352425361879389725614874256193651973428293148567718694235946532781532817946 * PAIR D8: 5,8 COL D D2: 5,8,3,9 # reduction candidate for 5,8 D2: 5,8 # 6 pairs D3: 5,8,3,7,9 # reduction candidate for 5,8 D3: 5,8 # 9 pairs * PAIR H8: 2,8 COL H H5: 2,8,7,9 # reduction candidate for 2,8 H5: 7,9 => CTR * .......524...62...2......1487.2.6...621...4.83..1.8...718.2....9...3.72.532...... H5: 2,8 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-474-base-pr-000.dot * REASONING * DIS # H6: 2,3 => CTR => H6: 6,7,9 * DIS # A3: 8 => CTR => A3: 2,3 * DIS # I8: 5,8 => CTR => I8: 1 * PRF # I8: 1 => SOL * DIS # H5: 7,9 => CTR => H5: 2,8 * CNT 5 HDP CHAINS / 11 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B8,C8,D8,H8) * .......524...6...........14.7.2.6...6.....4.....1.8...718......9...3.7..532...... * PAIR A6: 2,3 ROW 6 G6: 2,3,5,9 # reduction candidate for 2,3 G6: 2,3 # 6 pairs H6: 2,3,6,7,9 # reduction candidate for 2,3 H6: 2,3 => CTR * 1......5242..61..........14.7.2461..681...4272..178.36718...2..9...3.7.1532.1.... * RESTART * PAIR A6: 2,3 ROW 6 G6: 2,3,5,9 # reduction candidate for 2,3 G6: 5,9 => SOLVED * 167489352425361879389725614874256193651973428293148567718694235946532781532817946 * DURATION: 0:00:04.673812 START: 18:53:12.779372 END: 18:53:17.453184 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-474-base-pr-001.dot * REASONING * DIS # H6: 2,3 => CTR => H6: 6,7,9 * PRF H6: 6,7,9 # G6: 5,9 => SOL * STA H6: 6,7,9 + G6: 5,9 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 474 solution: 167489352425361879389725614874256193651973428293148567718694235946532781532817946 info: 95689 FNBHWYK S8.f 454 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 167489352425361879389725614874256193651973428293148567718694235946532781532817946 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 # G6: 2,3 => UNS * DIS # H6: 2,3 => CTR => H6: 6,7,9 * INC # H6: 6,7,9 => UNS * INC # A3: 2,3 => UNS * DIS # A3: 8 => CTR => A3: 2,3 * DIS # I8: 5,8 => CTR => I8: 1 * PRF # I8: 1 => SOL * INC # D2: 5,8 => UNS * INC # D3: 5,8 => UNS * INC # H5: 2,8 => UNS * DIS # H5: 7,9 => CTR => H5: 2,8 * CNT 11 HDP CHAINS / 11 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G6: 2,3 => UNS * DIS # H6: 2,3 => CTR => H6: 6,7,9 * INC H6: 6,7,9 # G6: 2,3 => UNS * PRF H6: 6,7,9 # G6: 5,9 => SOL * STA H6: 6,7,9 + G6: 5,9 * CNT 4 HDP CHAINS / 4 HYP OPENED