Analysis of xx-top500-473-base.sdk
Contents
Original Sudoku
level: medium
position: ...8.1....7....4...6.......8.......2....6.7..3.........5....69.1..2........3...8. initial
Autosolve
position: .3.8.19...7.6..4...6.......8.......2....6.7..3........752...6931832965..6..3..281 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 4,5 => CTR => A3: 2,9 * DIS # E1: 4,5 => CTR => E1: 2,7 * DIS # C5: 4,5 => CTR => C5: 9 * PRF # C5: 9 => SOL * PRF # G3: 1,8 => SOL * DIS # G3: 3 => CTR => G3: 1,8 * DIS # I3: 5,8 => CTR => I3: 7 * DIS # I6: 5,8 => CTR => I6: 4,6,9 * DIS # C5: 4,5 => CTR => C5: 9 * PRF # C5: 9 => SOL * DIS # A3: 4,5 => CTR => A3: 2,9 * DIS # H4: 1,3 => CTR => H4: 4,5,6 * DIS # H5: 1,3 => CTR => H5: 4 * PRF # H5: 4 => SOL * DIS # G3: 1,3 => CTR => G3: 8 * PRF # G3: 8 => SOL * DIS # E6: 2,4,5,7 => CTR => E6: 1,8 * PRF # G3: 1,8 => SOL * DIS # G3: 3 => CTR => G3: 1,8 * DIS # B5: 4,9 => CTR => B5: 1,2 * PRF # B6: 4,9 => SOL * DIS # C5: 5 => CTR => C5: 4,9 * PRF # E7: 1,4 => SOL * DIS # E7: 8 => CTR => E7: 1,4 * DIS # D4: 1,4 => CTR => D4: 5,7,9 * DIS # D6: 1,4 => CTR => D6: 5,7,9 * DIS # E7: 4,8 => CTR => E7: 1 * PRF # E7: 1 => SOL * DIS # F5: 4,8 => CTR => F5: 2,3,9 * PRF # F5: 2,3,9 => SOL * DIS # F6: 4,8 => CTR => F6: 2,5,7,9 * DIS # E3: 5,7 => CTR => E3: 2,3,4 * DIS # E4: 5,7 => CTR => E4: 1,3,4 * DIS # E6: 5,7 => CTR => E6: 1,2,4,8 * DIS # F6: 5,7 => CTR => F6: 2,4,8,9 * CNT 35 HDP CHAINS / 61 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 4,5 => CTR => A3: 2,9 * DIS A3: 2,9 # A1: 2 => CTR => A1: 4,5 * DIS A3: 2,9 + A1: 4,5 # C5: 4,5 => CTR => C5: 9 * PRF A3: 2,9 + A1: 4,5 + C5: 9 => SOL * STA A3: 2,9 + A1: 4,5 + C5: 9 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...8.1....7....4...6.......8.......2....6.7..3.........5....69.1..2........3...8. | initial |
| .3.8.19...7.6..4...6.......8.......2....6.7..3........752...6931832965..6..3..281 | autosolve |
| 435871926278639415961524837817945362529163748346782159752418693183296574694357281 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C1: 4,5 C2: 1,8 C3: 1,8 I2: 5,8 C4: 6,7 A5: 4,5 C6: 6,7 G4: 1,3 G6: 1,8 B9: 4,9 C9: 4,9 D7: 1,4 F7: 4,8 E9: 5,7 F9: 5,7 H8: 4,7 I8: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 1.. / C2 = 1 => 0 pairs (X) / C3 = 1 => 20 pairs (_) D7,E7: 1.. / D7 = 1 => 0 pairs (X) / E7 = 1 => 0 pairs (_) C2,H2: 1.. / C2 = 1 => 0 pairs (X) / H2 = 1 => 20 pairs (_) B5,B6: 2.. / B5 = 2 => 17 pairs (_) / B6 = 2 => 0 pairs (X) B5,F5: 2.. / B5 = 2 => 17 pairs (_) / F5 = 2 => 0 pairs (X) F5,H5: 3.. / F5 = 3 => 0 pairs (*) / H5 = 3 => 0 pairs (X) G3,G4: 3.. / G3 = 3 => 0 pairs (X) / G4 = 3 => 0 pairs (_) B9,C9: 4.. / B9 = 4 => 0 pairs (X) / C9 = 4 => 0 pairs (_) H8,I8: 4.. / H8 = 4 => 0 pairs (X) / I8 = 4 => 16 pairs (_) A5,C5: 5.. / A5 = 5 => 19 pairs (_) / C5 = 5 => 0 pairs (X) E9,F9: 5.. / E9 = 5 => 16 pairs (_) / F9 = 5 => 0 pairs (X) C1,C5: 5.. / C1 = 5 => 19 pairs (_) / C5 = 5 => 0 pairs (X) H1,I1: 6.. / H1 = 6 => 0 pairs (X) / I1 = 6 => 17 pairs (_) C4,C6: 6.. / C4 = 6 => 15 pairs (_) / C6 = 6 => 15 pairs (_) C4,H4: 6.. / C4 = 6 => 15 pairs (_) / H4 = 6 => 15 pairs (_) I1,I6: 6.. / I1 = 6 => 17 pairs (_) / I6 = 6 => 0 pairs (X) C4,C6: 7.. / C4 = 7 => 15 pairs (_) / C6 = 7 => 15 pairs (_) E9,F9: 7.. / E9 = 7 => 0 pairs (X) / F9 = 7 => 16 pairs (_) H8,I8: 7.. / H8 = 7 => 16 pairs (_) / I8 = 7 => 0 pairs (X) C2,C3: 8.. / C2 = 8 => 20 pairs (_) / C3 = 8 => 0 pairs (X) E7,F7: 8.. / E7 = 8 => 0 pairs (X) / F7 = 8 => 0 pairs (_) C2,I2: 8.. / C2 = 8 => 20 pairs (_) / I2 = 8 => 0 pairs (X) F5,I5: 8.. / F5 = 8 => 0 pairs (X) / I5 = 8 => 0 pairs (_) E6,E7: 8.. / E6 = 8 => 0 pairs (*) / E7 = 8 => 0 pairs (X) G3,G6: 8.. / G3 = 8 => 0 pairs (*) / G6 = 8 => 0 pairs (X) A2,A3: 9.. / A2 = 9 => 17 pairs (_) / A3 = 9 => 18 pairs (_) I5,I6: 9.. / I5 = 9 => 0 pairs (X) / I6 = 9 => 0 pairs (_) B9,C9: 9.. / B9 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) A2,F2: 9.. / A2 = 9 => 17 pairs (_) / F2 = 9 => 18 pairs (_) C5,C9: 9.. / C5 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) * DURATION: 0:00:51.315025 START: 18:50:12.239436 END: 18:51:03.554461 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B9,C1,C2,C3,C4,C6,C9,D7,E9,F7,F9,G4,G6,H8,I2,I8) * .3.8.19...7.6..4...6.......8.......2....6.7..3........752...6931832965..6..3..281 * PAIR C1: 4,5 BLK 1 A1: 4,5,2 # reduction candidate for 4,5 A1: 4,5 # 22 pairs A3: 4,5,2,9 # reduction candidate for 4,5 A3: 4,5 => CTR * 23.8.19..97.6..4...6.......8.......2....6873.3.....8..7521846931832965..6..3..281 A3: 2,9 # 18 pairs * PAIR C1: 4,5 ROW 1 E1: 4,5,2,7 # reduction candidate for 4,5 E1: 4,5 => CTR * 23.8.19...7.6..4...6....3..8.....1.2.2.16873.3.....8..752.846931832965..6..3..281 E1: 2,7 # 18 pairs * PAIR C1: 4,5 COL C C5: 4,5,9 # reduction candidate for 4,5 C5: 4,5 => CTR * .3.8.19...7.6..4...6.......8.......2....687393.....8..752.846931832965..6493..281 C5: 9 => SOLVED * 435871926278639415961524837817945362529163748346782159752418693183296574694357281 * PAIR C3: 1,8 ROW 3 G3: 1,8,3 # reduction candidate for 1,8 G3: 1,8 => SOLVED * 435871926278639415961524837817945362529163748346782159752418693183296574694357281 G3: 3 => CTR * .3.8.19...7.6..4...6....3..8.....1.2....6873.3...128..7521846931832965..6..3..281 * PAIR I2: 5,8 BLK 3 I3: 5,8,7 # reduction candidate for 5,8 I3: 5,8 => CTR * .3.8.19...7.6..4...6....3..8.....1.2.2.16873.3.....8..752.846931832965..6..3..281 I3: 7 # 16 pairs * PAIR I2: 5,8 COL I I6: 5,8,4,6,9 # reduction candidate for 5,8 I6: 5,8 => CTR * .3.8719.6.7.6..4...6....3.78.....1.2.2.1687393........752.846931832965746493..281 I6: 4,6,9 # 17 pairs * PAIR A5: 4,5 BLK 4 C5: 4,5,9 # reduction candidate for 4,5 C5: 4,5 => CTR * .3.8.19...7.6..4...6.......8.......2....687393.....8..752.846931832965..6493..281 C5: 9 => SOLVED * 435871926278639415961524837817945362529163748346782159752418693183296574694357281 * PAIR A5: 4,5 COL A A1: 4,5,2 # reduction candidate for 4,5 A1: 4,5 # 22 pairs A3: 4,5,2,9 # reduction candidate for 4,5 A3: 4,5 => CTR * 23.8.19..97.6..4...6.......8.......2....6873.3.....8..7521846931832965..6..3..281 A3: 2,9 # 18 pairs * PAIR G4: 1,3 BLK 6 H4: 1,3,4,5,6 # reduction candidate for 1,3 H4: 1,3 => CTR * .3.8.19...7.6..4...6.......8.6.....2....6.7..3.7......752...6931832965..6..3..281 H4: 4,5,6 # 17 pairs H5: 1,3,4 # reduction candidate for 1,3 H5: 1,3 => CTR * .3.8.19...7.6..4...6....3..8.....1.2.2.16873.3.....8..752.846931832965..6..3..281 H5: 4 => SOLVED * 435871926278639415961524837817945362529163748346782159752418693183296574694357281 * PAIR G4: 1,3 ROW 4 E4: 1,3,4,5,7 # reduction candidate for 1,3 E4: 1,3 # 21 pairs E4: 4,5,7 # 20 pairs * PAIR G4: 1,3 COL G G3: 1,3,8 # reduction candidate for 1,3 G3: 1,3 => CTR * .3.8.19...7.6..4...6.......8.......2....6873.3.....8..7521846931832965..6..3..281 G3: 8 => SOLVED * 435871926278639415961524837817945362529163748346782159752418693183296574694357281 * PAIR G6: 1,8 ROW 6 E6: 1,8,2,4,5,7 # reduction candidate for 1,8 E6: 2,4,5,7 => CTR * .3.8.19...7.6..4...6.......8...1.3.2....637.83....81.97521846931832965.46..3..281 E6: 1,8 # 18 pairs * PAIR G6: 1,8 COL G G3: 1,8,3 # reduction candidate for 1,8 G3: 1,8 => SOLVED * 435871926278639415961524837817945362529163748346782159752418693183296574694357281 G3: 3 => CTR * .3.8.19...7.6..4...6....3..8.....1.2....6873.3...128..7521846931832965..6..3..281 * PAIR B9: 4,9 COL B B4: 4,9,1 # reduction candidate for 4,9 B4: 4,9 # 20 pairs B5: 4,9,1,2 # reduction candidate for 4,9 B5: 4,9 => CTR * .3.8.19...7.6..4...6.......8.......2....6273832....1..752...6931832965..6..3..281 B5: 1,2 # 18 pairs B6: 4,9,1,2 # reduction candidate for 4,9 B6: 4,9 => SOLVED * 435871926278639415961524837817945362529163748346782159752418693183296574694357281 B6: 1,2 # 18 pairs * PAIR C9: 4,9 COL C C5: 4,9,5 # reduction candidate for 4,9 C5: 5 => CTR * .348.19...7.6..4...6.......8.......24.5.687393.....8..752.846931832965..6493..281 C5: 4,9 # 19 pairs * PAIR D7: 1,4 BLK 8 E7: 1,4,8 # reduction candidate for 1,4 E7: 1,4 => SOLVED * 435871926278639415961524837817945362529163748346782159752418693183296574694357281 E7: 8 => CTR * .3.8.19...7.6..4...6.......8.......2....6.7.83....81.97521846931832965.46..3..281 * PAIR D7: 1,4 COL D D4: 1,4,5,7,9 # reduction candidate for 1,4 D4: 1,4 => CTR * .3.8.19.6.7.6..4...6.......89......2...96.7.83.....1.9752...6931832965746493..281 D4: 5,7,9 # 17 pairs D5: 1,4,9 # reduction candidate for 1,4 D5: 1,4 # 18 pairs D6: 1,4,5,7,9 # reduction candidate for 1,4 D6: 1,4 => CTR * .3.8.19.6.7.6..4...6.......89......2...96.7.83.....1.97521..6931832965746493..281 D6: 5,7,9 # 17 pairs * PAIR F7: 4,8 BLK 8 E7: 4,8,1 # reduction candidate for 4,8 E7: 4,8 => CTR * .3.8.19...7.6..4...6.......8.......2....6.7.83.....1.97521..6931832965.46..3..281 E7: 1 => SOLVED * 435871926278639415961524837817945362529163748346782159752418693183296574694357281 * PAIR F7: 4,8 COL F F5: 4,8,2,3,9 # reduction candidate for 4,8 F5: 4,8 => CTR * .3.8.19...7.6..4...6....3..8.....1.2.2.16.73.31....8..7524..6931832965..6..3..281 F5: 2,3,9 => SOLVED * 435871926278639415961524837817945362529163748346782159752418693183296574694357281 F6: 4,8,2,5,7,9 # reduction candidate for 4,8 F6: 4,8 => CTR * .3.871926.7863.415.61...8378...1.3.25...637483...281.9752.846931832965746..3..281 F6: 2,5,7,9 # 17 pairs * PAIR E9: 5,7 COL E E1: 5,7,2,4 # reduction candidate for 5,7 E1: 5,7 # 19 pairs E3: 5,7,2,3,4 # reduction candidate for 5,7 E3: 5,7 => CTR * .3.8.19...7.6..4...6....3..8.....1.2.2.16873.3.....8..752.846931832965..6..3..281 E3: 2,3,4 # 17 pairs E4: 5,7,1,3,4 # reduction candidate for 5,7 E4: 5,7 => CTR * .3.8.19...7.6..4...6.......8.......2....6873.3...128..7521846931832965..6..3..281 E4: 1,3,4 # 17 pairs E6: 5,7,1,2,4,8 # reduction candidate for 5,7 E6: 5,7 => CTR * .3.8.19...7.6..4...6.......8...1.3.2....637.83........752.846931832965..6..3..281 E6: 1,2,4,8 # 17 pairs * PAIR F9: 5,7 COL F F3: 5,7,2,3,4,9 # reduction candidate for 5,7 F3: 5,7 # 18 pairs F4: 5,7,3,4,9 # reduction candidate for 5,7 F4: 5,7 # 18 pairs F6: 5,7,2,4,8,9 # reduction candidate for 5,7 F6: 5,7 => CTR * .3.8.19...7.6..4...6....3..8.....1.2....6.73.3.....8..752...6931832965..6..3..281 F6: 2,4,8,9 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-473-base-pr-000.dot * REASONING * DIS # A3: 4,5 => CTR => A3: 2,9 * DIS # E1: 4,5 => CTR => E1: 2,7 * DIS # C5: 4,5 => CTR => C5: 9 * PRF # C5: 9 => SOL * PRF # G3: 1,8 => SOL * DIS # G3: 3 => CTR => G3: 1,8 * DIS # I3: 5,8 => CTR => I3: 7 * DIS # I6: 5,8 => CTR => I6: 4,6,9 * DIS # C5: 4,5 => CTR => C5: 9 * PRF # C5: 9 => SOL * DIS # A3: 4,5 => CTR => A3: 2,9 * DIS # H4: 1,3 => CTR => H4: 4,5,6 * DIS # H5: 1,3 => CTR => H5: 4 * PRF # H5: 4 => SOL * DIS # G3: 1,3 => CTR => G3: 8 * PRF # G3: 8 => SOL * DIS # E6: 2,4,5,7 => CTR => E6: 1,8 * PRF # G3: 1,8 => SOL * DIS # G3: 3 => CTR => G3: 1,8 * DIS # B5: 4,9 => CTR => B5: 1,2 * PRF # B6: 4,9 => SOL * DIS # C5: 5 => CTR => C5: 4,9 * PRF # E7: 1,4 => SOL * DIS # E7: 8 => CTR => E7: 1,4 * DIS # D4: 1,4 => CTR => D4: 5,7,9 * DIS # D6: 1,4 => CTR => D6: 5,7,9 * DIS # E7: 4,8 => CTR => E7: 1 * PRF # E7: 1 => SOL * DIS # F5: 4,8 => CTR => F5: 2,3,9 * PRF # F5: 2,3,9 => SOL * DIS # F6: 4,8 => CTR => F6: 2,5,7,9 * DIS # E3: 5,7 => CTR => E3: 2,3,4 * DIS # E4: 5,7 => CTR => E4: 1,3,4 * DIS # E6: 5,7 => CTR => E6: 1,2,4,8 * DIS # F6: 5,7 => CTR => F6: 2,4,8,9 * CNT 35 HDP CHAINS / 61 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B9,C1,C2,C3,C4,C6,C9,D7,E9,F7,F9,G4,G6,H8,I2,I8) * .3.8.19...7.6..4...6.......8.......2....6.7..3........752...6931832965..6..3..281 * PAIR C1: 4,5 BLK 1 A1: 4,5,2 # reduction candidate for 4,5 A1: 4,5 # 22 pairs A3: 4,5,2,9 # reduction candidate for 4,5 A3: 4,5 => CTR * 23.8.19..97.6..4...6.......8.......2....6873.3.....8..7521846931832965..6..3..281 * RESTART * PAIR C1: 4,5 BLK 1 A1: 4,5,2 # reduction candidate for 4,5 A1: 2 => CTR * 2348.19..57.6.94.8968......8.......24.5.687393.....8..752.846931832965..6493..281 * PAIR C1: 4,5 COL C C5: 4,5,9 # reduction candidate for 4,5 C5: 4,5 => CTR * .3.8.19...7.6..4...6.......8.......2....687393.....8..752.846931832965..6493..281 C5: 9 => SOLVED * 435871926278639415961524837817945362529163748346782159752418693183296574694357281 * DURATION: 0:00:07.635299 START: 18:52:02.275475 END: 18:52:09.910774 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-473-base-pr-001.dot * REASONING * DIS # A3: 4,5 => CTR => A3: 2,9 * DIS A3: 2,9 # A1: 2 => CTR => A1: 4,5 * DIS A3: 2,9 + A1: 4,5 # C5: 4,5 => CTR => C5: 9 * PRF A3: 2,9 + A1: 4,5 + C5: 9 => SOL * STA A3: 2,9 + A1: 4,5 + C5: 9 * CNT 4 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 473 solution: 435871926278639415961524837817945362529163748346782159752418693183296574694357281 info: 95683 FNBTHXYK S8.f 44995 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 435871926278639415961524837817945362529163748346782159752418693183296574694357281 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 # A1: 4,5 => UNS * DIS # A3: 4,5 => CTR => A3: 2,9 * INC # A3: 2,9 => UNS * DIS # E1: 4,5 => CTR => E1: 2,7 * INC # E1: 2,7 => UNS * DIS # C5: 4,5 => CTR => C5: 9 * PRF # C5: 9 => SOL * PRF # G3: 1,8 => SOL * DIS # G3: 3 => CTR => G3: 1,8 * DIS # I3: 5,8 => CTR => I3: 7 * INC # I3: 7 => UNS * DIS # I6: 5,8 => CTR => I6: 4,6,9 * INC # I6: 4,6,9 => UNS * DIS # C5: 4,5 => CTR => C5: 9 * PRF # C5: 9 => SOL * INC # A1: 4,5 => UNS * DIS # A3: 4,5 => CTR => A3: 2,9 * INC # A3: 2,9 => UNS * DIS # H4: 1,3 => CTR => H4: 4,5,6 * INC # H4: 4,5,6 => UNS * DIS # H5: 1,3 => CTR => H5: 4 * PRF # H5: 4 => SOL * INC # E4: 1,3 => UNS * INC # E4: 4,5,7 => UNS * DIS # G3: 1,3 => CTR => G3: 8 * PRF # G3: 8 => SOL * INC # E6: 1,8 => UNS * DIS # E6: 2,4,5,7 => CTR => E6: 1,8 * PRF # G3: 1,8 => SOL * DIS # G3: 3 => CTR => G3: 1,8 * INC # B4: 4,9 => UNS * DIS # B5: 4,9 => CTR => B5: 1,2 * INC # B5: 1,2 => UNS * PRF # B6: 4,9 => SOL * INC # B6: 1,2 => UNS * INC # C5: 4,9 => UNS * DIS # C5: 5 => CTR => C5: 4,9 * PRF # E7: 1,4 => SOL * DIS # E7: 8 => CTR => E7: 1,4 * DIS # D4: 1,4 => CTR => D4: 5,7,9 * INC # D4: 5,7,9 => UNS * INC # D5: 1,4 => UNS * DIS # D6: 1,4 => CTR => D6: 5,7,9 * INC # D6: 5,7,9 => UNS * DIS # E7: 4,8 => CTR => E7: 1 * PRF # E7: 1 => SOL * DIS # F5: 4,8 => CTR => F5: 2,3,9 * PRF # F5: 2,3,9 => SOL * DIS # F6: 4,8 => CTR => F6: 2,5,7,9 * INC # F6: 2,5,7,9 => UNS * INC # E1: 5,7 => UNS * DIS # E3: 5,7 => CTR => E3: 2,3,4 * INC # E3: 2,3,4 => UNS * DIS # E4: 5,7 => CTR => E4: 1,3,4 * INC # E4: 1,3,4 => UNS * DIS # E6: 5,7 => CTR => E6: 1,2,4,8 * INC # E6: 1,2,4,8 => UNS * INC # F3: 5,7 => UNS * INC # F4: 5,7 => UNS * DIS # F6: 5,7 => CTR => F6: 2,4,8,9 * INC # F6: 2,4,8,9 => UNS * CNT 61 HDP CHAINS / 61 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 4,5 => UNS * DIS # A3: 4,5 => CTR => A3: 2,9 * INC A3: 2,9 # A1: 4,5 => UNS * DIS A3: 2,9 # A1: 2 => CTR => A1: 4,5 * DIS A3: 2,9 + A1: 4,5 # C5: 4,5 => CTR => C5: 9 * PRF A3: 2,9 + A1: 4,5 + C5: 9 => SOL * STA A3: 2,9 + A1: 4,5 + C5: 9 * CNT 6 HDP CHAINS / 5 HYP OPENED