Analysis of xx-top95-010-base.sdk
Contents
Original Sudoku
level: medium
position: .923.........8.1...........1.7.4...........658.........6.5.2...4.....7.....9..... initial
Autosolve
position: .92351.......8.1.....42....1.7.4...........658.629.....6.5.2...4.....7.....9.4... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 6,7 => CTR => A2: 3,5 * PRF # A3: 6,7 => SOL * DIS # I1: 6,7 => CTR => I1: 4,8 * DIS # B9: 1,8 => CTR => B9: 2,3,7 * PRF # B9: 2,3,7 => SOL * PRF # F2: 6,7 => SOL * DIS # A2: 6,7 => CTR => A2: 3,5 * DIS # I2: 6,7 => CTR => I2: 2,3,9 * PRF # I1: 6,8 => SOL * DIS # G9: 6,8 => CTR => G9: 2,3,5 * PRF # F4: 6,8 => SOL * DIS # F4: 3,5 => CTR => F4: 6,8 * DIS # E7: 1,3 => CTR => E7: 7 * DIS # E8: 1,3 => CTR => E8: 6 * DIS # F4: 3,5 => CTR => F4: 6,8 * PRF # F4: 6,8 => SOL * DIS # B6: 4 => CTR => B6: 3,5 * DIS # G5: 3,4 => CTR => G5: 2,8 * DIS # B6: 5 => CTR => B6: 3,4 * PRF # D5: 1,8 => SOL * DIS # D5: 7 => CTR => D5: 1,8 * PRF # F4: 3,8 => SOL * DIS # F5: 3,8 => CTR => F5: 7 * PRF # F5: 7 => SOL * CNT 24 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 6,7 => CTR => A2: 3,5 * PRF A2: 3,5 # A3: 6,7 => SOL * STA A2: 3,5 + A3: 6,7 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .923.........8.1...........1.7.4...........658.........6.5.2...4.....7.....9..... | initial |
| .92351.......8.1.....42....1.7.4...........658.629.....6.5.2...4.....7.....9.4... | autosolve |
| 792351648543786129681429537157648293924137865836295471368572914419863752275914386 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A1: 6,7 B3: 1,8 C3: 1,8 D2: 6,7 G1: 6,8 D4: 6,8 E5: 1,3 F6: 3,5 G6: 3,4 H6: 1,7 I6: 1,7 D8: 1,8 F8: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B3,C3: 1.. / B3 = 1 => 0 pairs (X) / C3 = 1 => 11 pairs (_) D5,E5: 1.. / D5 = 1 => 0 pairs (*) / E5 = 1 => 0 pairs (X) H6,I6: 1.. / H6 = 1 => 11 pairs (_) / I6 = 1 => 12 pairs (_) D5,D8: 1.. / D5 = 1 => 0 pairs (*) / D8 = 1 => 0 pairs (X) H2,I2: 2.. / H2 = 2 => 13 pairs (_) / I2 = 2 => 13 pairs (_) A5,A9: 2.. / A5 = 2 => 0 pairs (X) / A9 = 2 => 18 pairs (_) B2,C2: 4.. / B2 = 4 => 0 pairs (*) / C2 = 4 => 0 pairs (X) H1,I1: 4.. / H1 = 4 => 13 pairs (_) / I1 = 4 => 14 pairs (_) G5,G6: 4.. / G5 = 4 => 0 pairs (X) / G6 = 4 => 13 pairs (_) H7,I7: 4.. / H7 = 4 => 14 pairs (_) / I7 = 4 => 13 pairs (_) B6,G6: 4.. / B6 = 4 => 0 pairs (X) / G6 = 4 => 13 pairs (_) C2,C5: 4.. / C2 = 4 => 15 pairs (_) / C5 = 4 => 0 pairs (*) H1,H7: 4.. / H1 = 4 => 13 pairs (_) / H7 = 4 => 14 pairs (_) I1,I7: 4.. / I1 = 4 => 14 pairs (_) / I7 = 4 => 13 pairs (_) B4,B6: 5.. / B4 = 5 => 13 pairs (_) / B6 = 5 => 0 pairs (X) F4,F6: 5.. / F4 = 5 => 0 pairs (X) / F6 = 5 => 13 pairs (_) B4,F4: 5.. / B4 = 5 => 13 pairs (_) / F4 = 5 => 0 pairs (X) B6,F6: 5.. / B6 = 5 => 0 pairs (X) / F6 = 5 => 13 pairs (_) C8,H8: 5.. / C8 = 5 => 15 pairs (_) / H8 = 5 => 13 pairs (_) G3,G9: 5.. / G3 = 5 => 13 pairs (_) / G9 = 5 => 15 pairs (_) D4,F4: 6.. / D4 = 6 => 0 pairs (*) / F4 = 6 => 0 pairs (X) E8,E9: 6.. / E8 = 6 => 13 pairs (_) / E9 = 6 => 0 pairs (X) E8,I8: 6.. / E8 = 6 => 13 pairs (_) / I8 = 6 => 0 pairs (X) D2,D4: 6.. / D2 = 6 => 0 pairs (X) / D4 = 6 => 0 pairs (_) D5,F5: 7.. / D5 = 7 => 0 pairs (X) / F5 = 7 => 0 pairs (_) H6,I6: 7.. / H6 = 7 => 12 pairs (_) / I6 = 7 => 11 pairs (_) E7,E9: 7.. / E7 = 7 => 14 pairs (_) / E9 = 7 => 0 pairs (X) A7,E7: 7.. / A7 = 7 => 0 pairs (X) / E7 = 7 => 14 pairs (_) B2,B9: 7.. / B2 = 7 => 0 pairs (X) / B9 = 7 => 0 pairs (_) D2,D5: 7.. / D2 = 7 => 0 pairs (*) / D5 = 7 => 0 pairs (X) B3,C3: 8.. / B3 = 8 => 11 pairs (_) / C3 = 8 => 0 pairs (X) D8,F8: 8.. / D8 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) B3,B9: 8.. / B3 = 8 => 11 pairs (_) / B9 = 8 => 0 pairs (X) F2,F3: 9.. / F2 = 9 => 14 pairs (_) / F3 = 9 => 0 pairs (*) A5,C5: 9.. / A5 = 9 => 19 pairs (_) / C5 = 9 => 18 pairs (_) A5,A7: 9.. / A5 = 9 => 19 pairs (_) / A7 = 9 => 18 pairs (_) * DURATION: 0:01:04.296412 START: 23:02:02.045038 END: 23:03:06.341450 2017-05-03 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,C3,D2,D4,D8,E5,F6,F8,G1,G6,H6,I6) * .92351.......8.1.....42....1.7.4...........658.629.....6.5.2...4.....7.....9.4... * PAIR A1: 6,7 BLK 1 A2: 6,7,3,5 # reduction candidate for 6,7 A2: 6,7 => CTR * .92351.......891..58142....1.764.......1378658.62954..36.5729..419863752275914... A2: 3,5 # 14 pairs A3: 6,7,3,5 # reduction candidate for 6,7 A3: 6,7 => SOLVED * 792351648543786129681429537157648293924137865836295471368572914419863752275914386 A3: 3,5 # 14 pairs * PAIR A1: 6,7 ROW 1 I1: 6,7,4,8 # reduction candidate for 6,7 I1: 6,7 => CTR * .9235184....78.1...8142....1.764.......817.658.629.....6.572.1441...87...7.9.4... I1: 4,8 # 14 pairs * PAIR B3: 1,8 COL B B9: 1,8,2,3,7 # reduction candidate for 1,8 B9: 1,8 => CTR * .92351....746891.....427...1.7846......7138658.62954...6.5.2...4..1.87.....9.4... B9: 2,3,7 => SOLVED * 792351648543786129681429537157648293924137865836295471368572914419863752275914386 * PAIR C3: 1,8 COL C C7: 1,8,3,9 # reduction candidate for 1,8 C7: 1,8 # 15 pairs C9: 1,8,3,5 # reduction candidate for 1,8 C9: 1,8 # 15 pairs * PAIR D2: 6,7 BLK 2 F2: 6,7,9 # reduction candidate for 6,7 F2: 6,7 => SOLVED * 792351648543786129681429537157648293924137865836295471368572914419863752275914386 F2: 9 # 14 pairs F3: 6,7,9 # reduction candidate for 6,7 F3: 6,7 # 14 pairs * PAIR D2: 6,7 ROW 2 A2: 6,7,3,5 # reduction candidate for 6,7 A2: 6,7 => CTR * .92351.......891..58142....1.764.......1378658.62954..36.5729..419863752275914... A2: 3,5 # 14 pairs I2: 6,7,2,3,9 # reduction candidate for 6,7 I2: 6,7 => CTR * .923516..5.3.8912..8142....1.764.......1378658.62954..36.5729..419863752275914... I2: 2,3,9 # 13 pairs * PAIR G1: 6,8 BLK 3 I1: 6,8,4,7 # reduction candidate for 6,8 I1: 6,8 => SOLVED * 792351648543786129681429537157648293924137865836295471368572914419863752275914386 I1: 4,7 # 14 pairs * PAIR G1: 6,8 COL G G9: 6,8,2,3,5 # reduction candidate for 6,8 G9: 6,8 => CTR * .92351......78.1...8142.5..1.764.......817.658.629.....6.572...41...87...7.9.4... G9: 2,3,5 # 13 pairs * PAIR D4: 6,8 BLK 5 F4: 6,8,3,5 # reduction candidate for 6,8 F4: 6,8 => SOLVED * 792351648543786129681429537157648293924137865836295471368572914419863752275914386 F4: 3,5 => CTR * .92351......78.1...8142....1.764.......817.658.629.....6.572...41...87...7.9.4... * PAIR E5: 1,3 COL E E7: 1,3,7 # reduction candidate for 1,3 E7: 1,3 => CTR * 6923518...746891.....427...1.7846...9.3....658.629....76.5.2...4.....7.....974... E7: 7 # 14 pairs E8: 1,3,6 # reduction candidate for 1,3 E8: 1,3 => CTR * .92351....746891.....427...1.7846...2.97138658.62954..96.5723..4251387967.3964... E8: 6 # 13 pairs E9: 1,3,6,7 # reduction candidate for 1,3 E9: 1,3 # 15 pairs * PAIR F6: 3,5 BLK 5 F4: 3,5,6,8 # reduction candidate for 3,5 F4: 3,5 => CTR * .92351......78.1...8142....1.764.......817.658.629.....6.572...41...87...7.9.4... F4: 6,8 => SOLVED * 792351648543786129681429537157648293924137865836295471368572914419863752275914386 * PAIR F6: 3,5 ROW 6 B6: 3,5,4 # reduction candidate for 3,5 B6: 4 => CTR * .92351.....478.1.....42....157643......8174658462953...6.5.2...4..1.87...7.9.4... B6: 3,5 # 13 pairs * PAIR G6: 3,4 BLK 6 G5: 3,4,2,8 # reduction candidate for 3,4 G5: 3,4 => CTR * .92351......78.1...8142....1.764.......817.658.629.....6.572...41...87...7.9.4... G5: 2,8 # 15 pairs * PAIR G6: 3,4 ROW 6 B6: 3,4,5 # reduction candidate for 3,4 B6: 5 => CTR * .92351......78.1.....42....1.7645......817.658562934...6.5.2...4..1.87...7.9.4... B6: 3,4 # 13 pairs * PAIR D8: 1,8 COL D D5: 1,8,7 # reduction candidate for 1,8 D5: 1,8 => SOLVED * 792351648543786129681429537157648293924137865836295471368572914419863752275914386 D5: 7 => CTR * 7923516...4.68.1..6..42....157846......7138658362954...6.5.2...42.1.87.....9.4... * PAIR F8: 3,8 COL F F4: 3,8,5,6 # reduction candidate for 3,8 F4: 3,8 => SOLVED * 792351648543786129681429537157648293924137865836295471368572914419863752275914386 F4: 5,6 # 14 pairs F5: 3,8,7 # reduction candidate for 3,8 F5: 3,8 => CTR * 7923516...4.68.1..6..42....157846......7138658362954...6.5.2...42.1.87.....9.4... F5: 7 => SOLVED * 792351648543786129681429537157648293924137865836295471368572914419863752275914386 * INCONCLUSIVE * SAVE PR GRAPH xx-top95-010-base-pr-000.dot * REASONING * DIS # A2: 6,7 => CTR => A2: 3,5 * PRF # A3: 6,7 => SOL * DIS # I1: 6,7 => CTR => I1: 4,8 * DIS # B9: 1,8 => CTR => B9: 2,3,7 * PRF # B9: 2,3,7 => SOL * PRF # F2: 6,7 => SOL * DIS # A2: 6,7 => CTR => A2: 3,5 * DIS # I2: 6,7 => CTR => I2: 2,3,9 * PRF # I1: 6,8 => SOL * DIS # G9: 6,8 => CTR => G9: 2,3,5 * PRF # F4: 6,8 => SOL * DIS # F4: 3,5 => CTR => F4: 6,8 * DIS # E7: 1,3 => CTR => E7: 7 * DIS # E8: 1,3 => CTR => E8: 6 * DIS # F4: 3,5 => CTR => F4: 6,8 * PRF # F4: 6,8 => SOL * DIS # B6: 4 => CTR => B6: 3,5 * DIS # G5: 3,4 => CTR => G5: 2,8 * DIS # B6: 5 => CTR => B6: 3,4 * PRF # D5: 1,8 => SOL * DIS # D5: 7 => CTR => D5: 1,8 * PRF # F4: 3,8 => SOL * DIS # F5: 3,8 => CTR => F5: 7 * PRF # F5: 7 => SOL * CNT 24 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,C3,D2,D4,D8,E5,F6,F8,G1,G6,H6,I6) * .92351.......8.1.....42....1.7.4...........658.629.....6.5.2...4.....7.....9.4... * PAIR A1: 6,7 BLK 1 A2: 6,7,3,5 # reduction candidate for 6,7 A2: 6,7 => CTR * .92351.......891..58142....1.764.......1378658.62954..36.5729..419863752275914... A3: 6,7,3,5 # reduction candidate for 6,7 A3: 6,7 => SOLVED * 792351648543786129681429537157648293924137865836295471368572914419863752275914386 * DURATION: 0:00:04.085078 START: 23:03:52.670610 END: 23:03:56.755688 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-010-base-pr-001.dot * REASONING * DIS # A2: 6,7 => CTR => A2: 3,5 * PRF A2: 3,5 # A3: 6,7 => SOL * STA A2: 3,5 + A3: 6,7 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
Top 95 Sudokus 010 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 792351648543786129681429537157648293924137865836295471368572914419863752275914386 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 # A2: 6,7 => CTR => A2: 3,5 * INC # A2: 3,5 => UNS * PRF # A3: 6,7 => SOL * INC # A3: 3,5 => UNS * DIS # I1: 6,7 => CTR => I1: 4,8 * INC # I1: 4,8 => UNS * DIS # B9: 1,8 => CTR => B9: 2,3,7 * PRF # B9: 2,3,7 => SOL * INC # C7: 1,8 => UNS * INC # C9: 1,8 => UNS * PRF # F2: 6,7 => SOL * INC # F2: 9 => UNS * INC # F3: 6,7 => UNS * DIS # A2: 6,7 => CTR => A2: 3,5 * INC # A2: 3,5 => UNS * DIS # I2: 6,7 => CTR => I2: 2,3,9 * INC # I2: 2,3,9 => UNS * PRF # I1: 6,8 => SOL * INC # I1: 4,7 => UNS * DIS # G9: 6,8 => CTR => G9: 2,3,5 * INC # G9: 2,3,5 => UNS * PRF # F4: 6,8 => SOL * DIS # F4: 3,5 => CTR => F4: 6,8 * DIS # E7: 1,3 => CTR => E7: 7 * INC # E7: 7 => UNS * DIS # E8: 1,3 => CTR => E8: 6 * INC # E8: 6 => UNS * INC # E9: 1,3 => UNS * DIS # F4: 3,5 => CTR => F4: 6,8 * PRF # F4: 6,8 => SOL * INC # B6: 3,5 => UNS * DIS # B6: 4 => CTR => B6: 3,5 * DIS # G5: 3,4 => CTR => G5: 2,8 * INC # G5: 2,8 => UNS * INC # B6: 3,4 => UNS * DIS # B6: 5 => CTR => B6: 3,4 * PRF # D5: 1,8 => SOL * DIS # D5: 7 => CTR => D5: 1,8 * PRF # F4: 3,8 => SOL * INC # F4: 5,6 => UNS * DIS # F5: 3,8 => CTR => F5: 7 * PRF # F5: 7 => SOL * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 6,7 => CTR => A2: 3,5 * PRF A2: 3,5 # A3: 6,7 => SOL * STA A2: 3,5 + A3: 6,7 * CNT 2 HDP CHAINS / 2 HYP OPENED