Analysis of xx-top500-480-base.sdk
Contents
Original Sudoku
level: medium
position: .5.6...7..38...............4......2.....31......5.8.........1.39..7.........4.8.. initial
Autosolve
position: .5.6...7..38...............4..9...2....431......528.........1.39..7.........4.8.7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 1,2 => CTR => A2: 6,7 * PRF # I1: 1,2 => SOL * DIS # A9: 1,2 => CTR => A9: 3,5,6 * DIS # D3: 1,2 => CTR => D3: 3,8 * DIS # A2: 1,2 => CTR => A2: 6,7 * DIS # I2: 1,2 => CTR => I2: 4,5,6,9 * PRF # D9: 1,2 => SOL * DIS # D9: 3 => CTR => D9: 1,2 * DIS # I4: 5 => CTR => I4: 1,8 * DIS # B8: 4,6 => CTR => B8: 1,8 * DIS # C4: 1 => CTR => C4: 3,5 * DIS # G3: 3,5 => CTR => G3: 2,4,6,9 * DIS # B7: 2,8 => CTR => B7: 4,6,7 * DIS # D3: 2,8 => CTR => D3: 1,3 * PRF # D3: 1,3 => SOL * CNT 15 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 1,2 => CTR => A2: 6,7 * PRF A2: 6,7 # I1: 1,2 => SOL * STA A2: 6,7 + I1: 1,2 * CNT 2 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5.6...7..38...............4......2.....31......5.8.........1.39..7.........4.8.. | initial |
| .5.6...7..38...............4..9...2....431......528.........1.39..7.........4.8.7 | autosolve |
| 159684372738295614246317985413976528825431769697528431574862193981753246362149857 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) A1: 1,2 D2: 1,2 B4: 1,8 E4: 6,7 F4: 6,7 G4: 3,5 D7: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E8,D9: 1.. / E8 = 1 => 0 pairs (X) / D9 = 1 => 0 pairs (_) G8,I8: 2.. / G8 = 2 => 7 pairs (_) / I8 = 2 => 7 pairs (_) F1,G1: 3.. / F1 = 3 => 0 pairs (X) / G1 = 3 => 0 pairs (_) C4,G4: 3.. / C4 = 3 => 0 pairs (*) / G4 = 3 => 0 pairs (X) C8,F8: 3.. / C8 = 3 => 0 pairs (X) / F8 = 3 => 0 pairs (_) A6,A9: 3.. / A6 = 3 => 0 pairs (X) / A9 = 3 => 0 pairs (_) D3,D9: 3.. / D3 = 3 => 0 pairs (*) / D9 = 3 => 0 pairs (X) H3,H6: 3.. / H3 = 3 => 0 pairs (X) / H6 = 3 => 0 pairs (_) E4,F4: 6.. / E4 = 6 => 5 pairs (_) / F4 = 6 => 6 pairs (_) E4,F4: 7.. / E4 = 7 => 6 pairs (_) / F4 = 7 => 5 pairs (_) G5,G6: 7.. / G5 = 7 => 7 pairs (_) / G6 = 7 => 7 pairs (_) E1,I1: 8.. / E1 = 8 => 0 pairs (*) / I1 = 8 => 0 pairs (X) B4,I4: 8.. / B4 = 8 => 0 pairs (X) / I4 = 8 => 0 pairs (_) B8,E8: 8.. / B8 = 8 => 0 pairs (*) / E8 = 8 => 0 pairs (X) A5,A7: 8.. / A5 = 8 => 0 pairs (*) / A7 = 8 => 0 pairs (X) D3,D7: 8.. / D3 = 8 => 0 pairs (X) / D7 = 8 => 0 pairs (_) H3,H5: 8.. / H3 = 8 => 0 pairs (*) / H5 = 8 => 0 pairs (X) H7,H9: 9.. / H7 = 9 => 8 pairs (_) / H9 = 9 => 7 pairs (_) F9,H9: 9.. / F9 = 9 => 8 pairs (_) / H9 = 9 => 7 pairs (_) * DURATION: 0:00:30.930698 START: 19:04:11.683347 END: 19:04:42.614045 2017-05-04 * CP COUNT: (19) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B4,D2,D7,E4,F4,G4) * .5.6...7..38...............4..9...2....431......528.........1.39..7.........4.8.7 * PAIR A1: 1,2 BLK 1 C1: 1,2,4,9 # reduction candidate for 1,2 C1: 1,2 # 14 pairs A2: 1,2,6,7 # reduction candidate for 1,2 A2: 1,2 => CTR * .5.6...7..38...............4..9...2....431.8....528...8..2..1.39..78.......14.8.7 A2: 6,7 # 8 pairs A3: 1,2,6,7 # reduction candidate for 1,2 A3: 1,2 # 10 pairs B3: 1,2,4,6,7,9 # reduction candidate for 1,2 B3: 1,2 # 13 pairs C3: 1,2,4,6,7,9 # reduction candidate for 1,2 C3: 1,2 # 13 pairs * PAIR A1: 1,2 ROW 1 I1: 1,2,4,8,9 # reduction candidate for 1,2 I1: 1,2 => SOLVED * 159684372738295614246317985413976528825431769697528431574862193981753246362149857 I1: 4,8,9 # 7 pairs * PAIR A1: 1,2 COL A A9: 1,2,3,5,6 # reduction candidate for 1,2 A9: 1,2 => CTR * .5.6...7..38.............3.4..9..32....431.8.3..528...8..2..1.39..78........4.8.7 A9: 3,5,6 # 7 pairs * PAIR D2: 1,2 BLK 2 D3: 1,2,3,8 # reduction candidate for 1,2 D3: 1,2 => CTR * .5.6...7..38...............41.9...288..431...3..528......8..1.398371.......34.8.7 D3: 3,8 # 8 pairs * PAIR D2: 1,2 ROW 2 A2: 1,2,6,7 # reduction candidate for 1,2 A2: 1,2 => CTR * .5.6...7..38...............4..9...2....431.8....528...8..2..1.39..78.......14.8.7 A2: 6,7 # 8 pairs I2: 1,2,4,5,6,9 # reduction candidate for 1,2 I2: 1,2 => CTR * .5.6...7..38...............4..9...2....431.8....528...8..2..1.39..78.......14.8.7 I2: 4,5,6,9 # 7 pairs * PAIR D2: 1,2 COL D D9: 1,2,3 # reduction candidate for 1,2 D9: 1,2 => SOLVED * 159684372738295614246317985413976528825431769697528431574862193981753246362149857 D9: 3 => CTR * .5.6...7..38.............3.4159..3288..431...3..528.........1.398371.......34.8.7 * PAIR B4: 1,8 ROW 4 I4: 1,8,5 # reduction candidate for 1,8 I4: 5 => CTR * .5.6...7..38...............4819..325...431......528...8..2..1.39..78.......14.8.7 I4: 1,8 # 9 pairs * PAIR B4: 1,8 COL B B8: 1,8,4,6 # reduction candidate for 1,8 B8: 4,6 => CTR * .5.6...7..38...............4..9...2....431......528.........1.39..78.......14.8.7 B8: 1,8 # 9 pairs * PAIR G4: 3,5 ROW 4 C4: 3,5,1 # reduction candidate for 3,5 C4: 1 => CTR * .5.6.3.7..38.............3.4819..325...431.8....528...8..2..1.39.378........4.8.7 C4: 3,5 # 9 pairs * PAIR G4: 3,5 COL G G3: 3,5,2,4,6,9 # reduction candidate for 3,5 G3: 3,5 => CTR * .5.6.3.7..38............53.4..9..32....431.8.3..528...8..2..1.39.371.......34.8.7 G3: 2,4,6,9 # 7 pairs * PAIR D7: 2,8 ROW 7 A7: 2,8,5,6,7 # reduction candidate for 2,8 A7: 2,8 # 8 pairs B7: 2,8,4,6,7 # reduction candidate for 2,8 B7: 2,8 => CTR * .5.68..7..38....1..4.31..8.4139..5288.5431.69.9.52843152.8..1.398.7.....3...4.8.7 B7: 4,6,7 # 7 pairs * PAIR D7: 2,8 COL D D3: 2,8,1,3 # reduction candidate for 2,8 D3: 2,8 => CTR * .5.6...7..381............3.4..9..32....431.8.3..528.1.8..2..1.39.371.......34.8.7 D3: 1,3 => SOLVED * 159684372738295614246317985413976528825431769697528431574862193981753246362149857 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-480-base-pr-000.dot * REASONING * DIS # A2: 1,2 => CTR => A2: 6,7 * PRF # I1: 1,2 => SOL * DIS # A9: 1,2 => CTR => A9: 3,5,6 * DIS # D3: 1,2 => CTR => D3: 3,8 * DIS # A2: 1,2 => CTR => A2: 6,7 * DIS # I2: 1,2 => CTR => I2: 4,5,6,9 * PRF # D9: 1,2 => SOL * DIS # D9: 3 => CTR => D9: 1,2 * DIS # I4: 5 => CTR => I4: 1,8 * DIS # B8: 4,6 => CTR => B8: 1,8 * DIS # C4: 1 => CTR => C4: 3,5 * DIS # G3: 3,5 => CTR => G3: 2,4,6,9 * DIS # B7: 2,8 => CTR => B7: 4,6,7 * DIS # D3: 2,8 => CTR => D3: 1,3 * PRF # D3: 1,3 => SOL * CNT 15 HDP CHAINS / 31 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B4,D2,D7,E4,F4,G4) * .5.6...7..38...............4..9...2....431......528.........1.39..7.........4.8.7 * PAIR A1: 1,2 BLK 1 C1: 1,2,4,9 # reduction candidate for 1,2 C1: 1,2 # 14 pairs A2: 1,2,6,7 # reduction candidate for 1,2 A2: 1,2 => CTR * .5.6...7..38...............4..9...2....431.8....528...8..2..1.39..78.......14.8.7 A3: 1,2,6,7 # reduction candidate for 1,2 A3: 1,2 # 10 pairs B3: 1,2,4,6,7,9 # reduction candidate for 1,2 B3: 1,2 # 13 pairs C3: 1,2,4,6,7,9 # reduction candidate for 1,2 C3: 1,2 # 13 pairs * PAIR A1: 1,2 ROW 1 I1: 1,2,4,8,9 # reduction candidate for 1,2 I1: 1,2 => SOLVED * 159684372738295614246317985413976528825431769697528431574862193981753246362149857 * DURATION: 0:00:05.894230 START: 19:05:03.796821 END: 19:05:09.691051 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-480-base-pr-001.dot * REASONING * DIS # A2: 1,2 => CTR => A2: 6,7 * PRF A2: 6,7 # I1: 1,2 => SOL * STA A2: 6,7 + I1: 1,2 * CNT 2 HDP CHAINS / 6 HYP OPENED
Header Info
Top 500 Minimum 17 480 solution: 159684372738295614246317985413976528825431769697528431574862193981753246362149857 info: 95780 FNBHWYK S8.f 20311 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 159684372738295614246317985413976528825431769697528431574862193981753246362149857 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 # C1: 1,2 => UNS * DIS # A2: 1,2 => CTR => A2: 6,7 * INC # A2: 6,7 => UNS * INC # A3: 1,2 => UNS * INC # B3: 1,2 => UNS * INC # C3: 1,2 => UNS * PRF # I1: 1,2 => SOL * INC # I1: 4,8,9 => UNS * DIS # A9: 1,2 => CTR => A9: 3,5,6 * INC # A9: 3,5,6 => UNS * DIS # D3: 1,2 => CTR => D3: 3,8 * INC # D3: 3,8 => UNS * DIS # A2: 1,2 => CTR => A2: 6,7 * INC # A2: 6,7 => UNS * DIS # I2: 1,2 => CTR => I2: 4,5,6,9 * INC # I2: 4,5,6,9 => UNS * PRF # D9: 1,2 => SOL * DIS # D9: 3 => CTR => D9: 1,2 * INC # I4: 1,8 => UNS * DIS # I4: 5 => CTR => I4: 1,8 * INC # B8: 1,8 => UNS * DIS # B8: 4,6 => CTR => B8: 1,8 * INC # C4: 3,5 => UNS * DIS # C4: 1 => CTR => C4: 3,5 * DIS # G3: 3,5 => CTR => G3: 2,4,6,9 * INC # G3: 2,4,6,9 => UNS * INC # A7: 2,8 => UNS * DIS # B7: 2,8 => CTR => B7: 4,6,7 * INC # B7: 4,6,7 => UNS * DIS # D3: 2,8 => CTR => D3: 1,3 * PRF # D3: 1,3 => SOL * CNT 31 HDP CHAINS / 31 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 1,2 => UNS * DIS # A2: 1,2 => CTR => A2: 6,7 * INC A2: 6,7 # A3: 1,2 => UNS * INC A2: 6,7 # B3: 1,2 => UNS * INC A2: 6,7 # C3: 1,2 => UNS * PRF A2: 6,7 # I1: 1,2 => SOL * STA A2: 6,7 + I1: 1,2 * CNT 6 HDP CHAINS / 6 HYP OPENED