Analysis of xx-top500-078-base.sdk
Contents
Original Sudoku
level: medium
position: ...6...72.51...............6..7.9....3....1...............1.58....23....7.....4.. initial
Autosolve
position: 3..651.72.51.7.634.673...1561.7.9358.3....1.757.1.32...26.175831.523.7..7.3...421 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C1: 4,9 => SOL * DIS # C1: 8 => CTR => C1: 4,9 * PRF # E3: 8,9 => SOL * DIS # E3: 4 => CTR => E3: 8,9 * DIS # A2: 2 => CTR => A2: 8,9 * DIS # D9: 8,9 => CTR => D9: 5 * DIS # F3: 2,8 => CTR => F3: 4 * PRF # F3: 4 => SOL * PRF # A2: 2,8 => SOL * DIS # A2: 9 => CTR => A2: 2,8 * DIS # C1: 8,9 => CTR => C1: 4 * PRF # C1: 4 => SOL * DIS # A3: 8,9 => CTR => A3: 2 * PRF # E3: 8,9 => SOL * DIS # E3: 4 => CTR => E3: 8,9 * DIS # C5: 2,4 => CTR => C5: 8,9 * PRF # C5: 8,9 => SOL * PRF # E5: 2,4 => SOL * DIS # E5: 6,8 => CTR => E5: 2,4 * DIS # H6: 6,9 => CTR => H6: 4 * PRF # A5: 4,9 => SOL * DIS # A5: 8 => CTR => A5: 4,9 * DIS # D9: 8,9 => CTR => D9: 5 * DIS # F3: 2 => CTR => F3: 4,8 * DIS # H6: 6,9 => CTR => H6: 4 * CNT 25 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C1: 4,9 => SOL * STA C1: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...6...72.51...............6..7.9....3....1...............1.58....23....7.....4.. | initial |
| 3..651.72.51.7.634.673...1561.7.9358.3....1.757.1.32...26.175831.523.7..7.3...421 | autosolve |
| 394651872851972634267384915612749358439825167578163249926417583145238796783596421 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) B1: 4,9 D2: 8,9 F2: 2,8 G1: 8,9 G3: 8,9 C4: 2,4 E4: 2,4 F5: 5,6 I6: 6,9 A7: 4,9 B8: 4,8 B9: 8,9 D7: 4,9 F8: 4,8 F9: 5,6 H8: 6,9 I8: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 2.. / A2 = 2 => 0 pairs (X) / A3 = 2 => 18 pairs (_) F2,F3: 2.. / F2 = 2 => 18 pairs (_) / F3 = 2 => 0 pairs (X) C4,C5: 2.. / C4 = 2 => 0 pairs (*) / C5 = 2 => 0 pairs (X) E4,E5: 2.. / E4 = 2 => 0 pairs (X) / E5 = 2 => 0 pairs (_) A2,F2: 2.. / A2 = 2 => 0 pairs (X) / F2 = 2 => 18 pairs (_) A3,F3: 2.. / A3 = 2 => 18 pairs (_) / F3 = 2 => 0 pairs (X) C4,E4: 2.. / C4 = 2 => 0 pairs (*) / E4 = 2 => 0 pairs (X) C5,E5: 2.. / C5 = 2 => 0 pairs (X) / E5 = 2 => 0 pairs (_) B1,C1: 4.. / B1 = 4 => 0 pairs (X) / C1 = 4 => 0 pairs (_) E3,F3: 4.. / E3 = 4 => 0 pairs (X) / F3 = 4 => 0 pairs (_) H5,H6: 4.. / H5 = 4 => 0 pairs (X) / H6 = 4 => 20 pairs (_) A7,B8: 4.. / A7 = 4 => 0 pairs (X) / B8 = 4 => 0 pairs (_) D7,F8: 4.. / D7 = 4 => 0 pairs (*) / F8 = 4 => 0 pairs (X) C4,E4: 4.. / C4 = 4 => 0 pairs (X) / E4 = 4 => 0 pairs (_) A7,D7: 4.. / A7 = 4 => 0 pairs (X) / D7 = 4 => 0 pairs (_) B8,F8: 4.. / B8 = 4 => 0 pairs (*) / F8 = 4 => 0 pairs (X) A5,A7: 4.. / A5 = 4 => 0 pairs (*) / A7 = 4 => 0 pairs (X) B1,B8: 4.. / B1 = 4 => 0 pairs (X) / B8 = 4 => 0 pairs (_) D5,D7: 4.. / D5 = 4 => 0 pairs (X) / D7 = 4 => 0 pairs (_) F3,F8: 4.. / F3 = 4 => 0 pairs (*) / F8 = 4 => 0 pairs (X) D5,F5: 5.. / D5 = 5 => 0 pairs (X) / F5 = 5 => 17 pairs (_) D9,F9: 5.. / D9 = 5 => 17 pairs (_) / F9 = 5 => 0 pairs (X) D5,D9: 5.. / D5 = 5 => 0 pairs (X) / D9 = 5 => 17 pairs (_) F5,F9: 5.. / F5 = 5 => 17 pairs (_) / F9 = 5 => 0 pairs (X) E9,F9: 6.. / E9 = 6 => 0 pairs (X) / F9 = 6 => 17 pairs (_) H8,I8: 6.. / H8 = 6 => 17 pairs (_) / I8 = 6 => 17 pairs (_) F5,F9: 6.. / F5 = 6 => 0 pairs (X) / F9 = 6 => 17 pairs (_) I6,I8: 6.. / I6 = 6 => 17 pairs (_) / I8 = 6 => 17 pairs (_) G1,G3: 8.. / G1 = 8 => 0 pairs (*) / G3 = 8 => 0 pairs (X) B8,B9: 8.. / B8 = 8 => 0 pairs (X) / B9 = 8 => 0 pairs (_) C1,G1: 8.. / C1 = 8 => 0 pairs (X) / G1 = 8 => 0 pairs (_) C6,E6: 8.. / C6 = 8 => 0 pairs (*) / E6 = 8 => 0 pairs (X) B8,F8: 8.. / B8 = 8 => 0 pairs (X) / F8 = 8 => 0 pairs (_) D2,E3: 9.. / D2 = 9 => 0 pairs (*) / E3 = 9 => 0 pairs (X) G1,G3: 9.. / G1 = 9 => 0 pairs (X) / G3 = 9 => 0 pairs (_) A7,B9: 9.. / A7 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) H8,I8: 9.. / H8 = 9 => 17 pairs (_) / I8 = 9 => 17 pairs (_) A2,D2: 9.. / A2 = 9 => 0 pairs (X) / D2 = 9 => 0 pairs (_) A7,D7: 9.. / A7 = 9 => 0 pairs (*) / D7 = 9 => 0 pairs (X) B1,B9: 9.. / B1 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) E3,E9: 9.. / E3 = 9 => 0 pairs (X) / E9 = 9 => 0 pairs (_) I6,I8: 9.. / I6 = 9 => 17 pairs (_) / I8 = 9 => 17 pairs (_) * DURATION: 0:01:21.881490 START: 05:24:15.341452 END: 05:25:37.222942 2017-05-04 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B1,B8,B9,C4,D2,D7,E4,F2,F5,F8,F9,G1,G3,H8,I6,I8) * 3..651.72.51.7.634.673...1561.7.9358.3....1.757.1.32...26.175831.523.7..7.3...421 * PAIR B1: 4,9 BLK 1 C1: 4,9,8 # reduction candidate for 4,9 C1: 4,9 => SOLVED * 394651872851972634267384915612749358439825167578163249926417583145238796783596421 C1: 8 => CTR * 348651972.51.7.634.673..81561.7.935883....1.757.1832..4269175831852347..7938..421 * PAIR D2: 8,9 BLK 2 E3: 8,9,4 # reduction candidate for 8,9 E3: 8,9 => SOLVED * 394651872851972634267384915612749358439825167578163249926417583145238796783596421 E3: 4 => CTR * 3..651.72.5197.634.6734..15614729358.324..1.757.1.32...26.175831.523.7..7.3...421 * PAIR D2: 8,9 ROW 2 A2: 8,9,2 # reduction candidate for 8,9 A2: 2 => CTR * 3..651.72251978634.67342.15614729358.324..1.757.1.32...26.175831.523.7..7.3...421 A2: 8,9 # 18 pairs * PAIR D2: 8,9 COL D D9: 8,9,5 # reduction candidate for 8,9 D9: 8,9 => CTR * 394651872.51872634.673...1561.7.9358.3.5.61.757.1.32...264175831452387..783965421 D9: 5 # 17 pairs * PAIR F2: 2,8 BLK 2 F3: 2,8,4 # reduction candidate for 2,8 F3: 2,8 => CTR * 3..651.72.51.7.634.6734..15614729358.324.51.757.1.324.4269175831852347..793586421 F3: 4 => SOLVED * 394651872851972634267384915612749358439825167578163249926417583145238796783596421 * PAIR F2: 2,8 ROW 2 A2: 2,8,9 # reduction candidate for 2,8 A2: 2,8 => SOLVED * 394651872851972634267384915612749358439825167578163249926417583145238796783596421 A2: 9 => CTR * 3..651.7295187263426739481561.7.935883....1.757.1832..426.175831.523.7..7.3...421 * PAIR G1: 8,9 ROW 1 C1: 8,9,4 # reduction candidate for 8,9 C1: 8,9 => CTR * 34.651.72.51.7.634.673...1561.7.9358.3....1.757.1.32..4269175831852347..793...421 C1: 4 => SOLVED * 394651872851972634267384915612749358439825167578163249926417583145238796783596421 * PAIR G3: 8,9 ROW 3 A3: 8,9,2 # reduction candidate for 8,9 A3: 8,9 => CTR * 3..651.72251978634.67342.15614729358.324..1.757.1.32...26.175831.523.7..7.3...421 A3: 2 # 18 pairs E3: 8,9,4 # reduction candidate for 8,9 E3: 8,9 => SOLVED * 394651872851972634267384915612749358439825167578163249926417583145238796783596421 E3: 4 => CTR * 3..651.72.5197.634.6734..15614729358.324..1.757.1.32...26.175831.523.7..7.3...421 * PAIR C4: 2,4 BLK 4 C5: 2,4,8,9 # reduction candidate for 2,4 C5: 2,4 => CTR * 34.651.72.51.7.634.673...1561.7.9358.3....1.757.1.32..4269175831852347..793...421 C5: 8,9 => SOLVED * 394651872851972634267384915612749358439825167578163249926417583145238796783596421 * PAIR E4: 2,4 BLK 5 E5: 2,4,6,8 # reduction candidate for 2,4 E5: 2,4 => SOLVED * 394651872851972634267384915612749358439825167578163249926417583145238796783596421 E5: 6,8 => CTR * 3..651.72.51.7.634.673...15614729358.32...1.757.1.32..4269175831852347..793...421 * PAIR I6: 6,9 BLK 6 H5: 6,9,4 # reduction candidate for 6,9 H5: 6,9 # 20 pairs H6: 6,9,4 # reduction candidate for 6,9 H6: 6,9 => CTR * 3..651.72.51.7.634.673...1561.7.9358.3....14757.1.32..4269175831852347..793...421 H6: 4 # 20 pairs * PAIR A7: 4,9 COL A A5: 4,9,8 # reduction candidate for 4,9 A5: 4,9 => SOLVED * 394651872851972634267384915612749358439825167578163249926417583145238796783596421 A5: 8 => CTR * 3..651.72.51.7.634.673...1561.7.935883....1.757.1832..4269175831852347..7938..421 * PAIR B9: 8,9 ROW 9 D9: 8,9,5 # reduction candidate for 8,9 D9: 8,9 => CTR * 394651872.51872634.673...1561.7.9358.3.5.61.757.1.32...264175831452387..783965421 D9: 5 # 17 pairs E9: 8,9,6 # reduction candidate for 8,9 E9: 8,9 # 17 pairs * PAIR F8: 4,8 COL F F3: 4,8,2 # reduction candidate for 4,8 F3: 2 => CTR * 3..651.72.51.7.634.67342.15614729358.324.51.757.1.324.4269175831852347..793586421 F3: 4,8 # 18 pairs * PAIR H8: 6,9 COL H H5: 6,9,4 # reduction candidate for 6,9 H5: 6,9 # 20 pairs H6: 6,9,4 # reduction candidate for 6,9 H6: 6,9 => CTR * 3..651.72.51.7.634.673...1561.7.9358.3....14757.1.32..4269175831852347..793...421 H6: 4 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-078-base-pr-000.dot * REASONING * PRF # C1: 4,9 => SOL * DIS # C1: 8 => CTR => C1: 4,9 * PRF # E3: 8,9 => SOL * DIS # E3: 4 => CTR => E3: 8,9 * DIS # A2: 2 => CTR => A2: 8,9 * DIS # D9: 8,9 => CTR => D9: 5 * DIS # F3: 2,8 => CTR => F3: 4 * PRF # F3: 4 => SOL * PRF # A2: 2,8 => SOL * DIS # A2: 9 => CTR => A2: 2,8 * DIS # C1: 8,9 => CTR => C1: 4 * PRF # C1: 4 => SOL * DIS # A3: 8,9 => CTR => A3: 2 * PRF # E3: 8,9 => SOL * DIS # E3: 4 => CTR => E3: 8,9 * DIS # C5: 2,4 => CTR => C5: 8,9 * PRF # C5: 8,9 => SOL * PRF # E5: 2,4 => SOL * DIS # E5: 6,8 => CTR => E5: 2,4 * DIS # H6: 6,9 => CTR => H6: 4 * PRF # A5: 4,9 => SOL * DIS # A5: 8 => CTR => A5: 4,9 * DIS # D9: 8,9 => CTR => D9: 5 * DIS # F3: 2 => CTR => F3: 4,8 * DIS # H6: 6,9 => CTR => H6: 4 * CNT 25 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B1,B8,B9,C4,D2,D7,E4,F2,F5,F8,F9,G1,G3,H8,I6,I8) * 3..651.72.51.7.634.673...1561.7.9358.3....1.757.1.32...26.175831.523.7..7.3...421 * PAIR B1: 4,9 BLK 1 C1: 4,9,8 # reduction candidate for 4,9 C1: 4,9 => SOLVED * 394651872851972634267384915612749358439825167578163249926417583145238796783596421 * DURATION: 0:00:02.275347 START: 05:26:18.025137 END: 05:26:20.300484 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-078-base-pr-001.dot * REASONING * PRF # C1: 4,9 => SOL * STA C1: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 078 solution: 394651872851972634267384915612749358439825167578163249926417583145238796783596421 info: 1505 FNBHWY S8.f 10482 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 394651872851972634267384915612749358439825167578163249926417583145238796783596421 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:
* PRF # C1: 4,9 => SOL * DIS # C1: 8 => CTR => C1: 4,9 * PRF # E3: 8,9 => SOL * DIS # E3: 4 => CTR => E3: 8,9 * INC # A2: 8,9 => UNS * DIS # A2: 2 => CTR => A2: 8,9 * DIS # D9: 8,9 => CTR => D9: 5 * INC # D9: 5 => UNS * DIS # F3: 2,8 => CTR => F3: 4 * PRF # F3: 4 => SOL * PRF # A2: 2,8 => SOL * DIS # A2: 9 => CTR => A2: 2,8 * DIS # C1: 8,9 => CTR => C1: 4 * PRF # C1: 4 => SOL * DIS # A3: 8,9 => CTR => A3: 2 * INC # A3: 2 => UNS * PRF # E3: 8,9 => SOL * DIS # E3: 4 => CTR => E3: 8,9 * DIS # C5: 2,4 => CTR => C5: 8,9 * PRF # C5: 8,9 => SOL * PRF # E5: 2,4 => SOL * DIS # E5: 6,8 => CTR => E5: 2,4 * INC # H5: 6,9 => UNS * DIS # H6: 6,9 => CTR => H6: 4 * INC # H6: 4 => UNS * PRF # A5: 4,9 => SOL * DIS # A5: 8 => CTR => A5: 4,9 * DIS # D9: 8,9 => CTR => D9: 5 * INC # D9: 5 => UNS * INC # E9: 8,9 => UNS * INC # F3: 4,8 => UNS * DIS # F3: 2 => CTR => F3: 4,8 * INC # H5: 6,9 => UNS * DIS # H6: 6,9 => CTR => H6: 4 * INC # H6: 4 => UNS * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C1: 4,9 => SOL * STA C1: 4,9 * CNT 1 HDP CHAINS / 1 HYP OPENED