Analysis of xx-top95-068-base.sdk
Contents
Original Sudoku
level: medium
position: .4..5..67...1...4....2.....1..8..3........2...6...........4..5.3.....8..2........ initial
Autosolve
position: .42.5.167...1...42...2.4.3812.8..394......2.6.6..2.7.5....4265.3.46..82.2.6...47. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 8,9 => CTR => A2: 5,6,7 * DIS # B2: 8,9 => CTR => B2: 3,7 * DIS # F1: 3 => CTR => F1: 8,9 * DIS # A5: 8,9 => CTR => A5: 4,5,7 * DIS # A7: 8,9 => CTR => A7: 7 * PRF # F1: 3,9 => SOL * DIS # F1: 8 => CTR => F1: 3,9 * DIS # D5: 3,9 => CTR => D5: 4,5,7 * DIS # D6: 3,9 => CTR => D6: 4 * DIS # D9: 3,9 => CTR => D9: 5 * DIS # A3: 5,9 => CTR => A3: 6,7 * DIS # A5: 5,7 => CTR => A5: 4,8,9 * DIS # F4: 6 => CTR => F4: 5,7 * DIS # F4: 6,7 => CTR => F4: 5 * DIS # E2: 6,7 => CTR => E2: 8,9 * DIS # I7: 1,9 => CTR => I7: 3 * DIS # B8: 1,9 => CTR => B8: 5,7 * DIS # F8: 1,9 => CTR => F8: 5,7 * CNT 18 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 8,9 => CTR => A2: 5,6,7 * DIS A2: 5,6,7 # B2: 8,9 => CTR => B2: 3,7 * PRF A2: 5,6,7 + B2: 3,7 # C2: 3,5,7 => SOL * STA A2: 5,6,7 + B2: 3,7 + C2: 3,5,7 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .4..5..67...1...4....2.....1..8..3........2...6...........4..5.3.....8..2........ | initial |
| .42.5.167...1...42...2.4.3812.8..394......2.6.6..2.7.5....4265.3.46..82.2.6...47. | autosolve |
| 842359167573186942619274538127865394435791286968423715781942653354617829296538471 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) A1: 8,9 D1: 3,9 G2: 5,9 G3: 5,9 C4: 5,7 E4: 6,7 H5: 1,8 H6: 1,8 I8: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B3,C3: 1.. / B3 = 1 => 11 pairs (_) / C3 = 1 => 10 pairs (_) H5,H6: 1.. / H5 = 1 => 9 pairs (_) / H6 = 1 => 8 pairs (_) F6,H6: 1.. / F6 = 1 => 9 pairs (_) / H6 = 1 => 8 pairs (_) C3,C7: 1.. / C3 = 1 => 10 pairs (_) / C7 = 1 => 11 pairs (_) B2,C2: 3.. / B2 = 3 => 9 pairs (_) / C2 = 3 => 0 pairs (*) D1,F1: 3.. / D1 = 3 => 17 pairs (_) / F1 = 3 => 0 pairs (X) I7,I9: 3.. / I7 = 3 => 12 pairs (_) / I9 = 3 => 0 pairs (X) D7,I7: 3.. / D7 = 3 => 0 pairs (X) / I7 = 3 => 12 pairs (_) B2,B5: 3.. / B2 = 3 => 9 pairs (_) / B5 = 3 => 0 pairs (*) E5,E9: 3.. / E5 = 3 => 11 pairs (_) / E9 = 3 => 0 pairs (*) A5,A6: 4.. / A5 = 4 => 13 pairs (_) / A6 = 4 => 0 pairs (X) D5,D6: 4.. / D5 = 4 => 0 pairs (X) / D6 = 4 => 13 pairs (_) A5,D5: 4.. / A5 = 4 => 13 pairs (_) / D5 = 4 => 0 pairs (X) A6,D6: 4.. / A6 = 4 => 0 pairs (X) / D6 = 4 => 13 pairs (_) G2,G3: 5.. / G2 = 5 => 14 pairs (_) / G3 = 5 => 7 pairs (_) B8,B9: 5.. / B8 = 5 => 13 pairs (_) / B9 = 5 => 0 pairs (X) C4,F4: 5.. / C4 = 5 => 0 pairs (X) / F4 = 5 => 13 pairs (_) B8,F8: 5.. / B8 = 5 => 13 pairs (_) / F8 = 5 => 0 pairs (X) D5,D9: 5.. / D5 = 5 => 0 pairs (X) / D9 = 5 => 13 pairs (_) A2,A3: 6.. / A2 = 6 => 0 pairs (X) / A3 = 6 => 10 pairs (_) E4,F4: 6.. / E4 = 6 => 13 pairs (_) / F4 = 6 => 0 pairs (X) A3,E3: 6.. / A3 = 6 => 10 pairs (_) / E3 = 6 => 0 pairs (X) F2,F4: 6.. / F2 = 6 => 13 pairs (_) / F4 = 6 => 0 pairs (X) D5,D7: 7.. / D5 = 7 => 13 pairs (_) / D7 = 7 => 0 pairs (X) H5,H6: 8.. / H5 = 8 => 8 pairs (_) / H6 = 8 => 9 pairs (_) E9,F9: 8.. / E9 = 8 => 0 pairs (X) / F9 = 8 => 0 pairs (_) A1,F1: 8.. / A1 = 8 => 0 pairs (*) / F1 = 8 => 0 pairs (X) E2,E9: 8.. / E2 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) G2,G3: 9.. / G2 = 9 => 7 pairs (_) / G3 = 9 => 14 pairs (_) * DURATION: 0:00:53.422274 START: 00:23:49.218871 END: 00:24:42.641145 2017-05-04 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C4,D1,E4,G2,G3,H5,H6,I8) * .42.5.167...1...42...2.4.3812.8..394......2.6.6..2.7.5....4265.3.46..82.2.6...47. * PAIR A1: 8,9 BLK 1 A2: 8,9,5,6,7 # reduction candidate for 8,9 A2: 8,9 => CTR * .42.5.167...1...426..2.4.3812.8..3945..4..2.646..2.7.57...4265.3.46..82.2.65..47. A2: 5,6,7 # 9 pairs B2: 8,9,3,7 # reduction candidate for 8,9 B2: 8,9 => CTR * 842359167.9318.542.1.2.493812.8..394.3.59.2.6.6942.7.5.81.426533.46..82.256938471 B2: 3,7 # 10 pairs C2: 8,9,3,5,7 # reduction candidate for 8,9 C2: 8,9 # 11 pairs * PAIR A1: 8,9 ROW 1 F1: 8,9,3 # reduction candidate for 8,9 F1: 3 => CTR * 842953167.371869426..274.3812.8..3944...3.2169634217857..34265.3546.782.2.65.8473 F1: 8,9 # 17 pairs * PAIR A1: 8,9 COL A A5: 8,9,4,5,7 # reduction candidate for 8,9 A5: 8,9 => CTR * .42.5.167...1...42...2.4.3812.8..394...4..2.646..2.7.5...7426533746.582.256...47. A5: 4,5,7 # 9 pairs A6: 8,9,4 # reduction candidate for 8,9 A6: 8,9 # 13 pairs A7: 8,9,7 # reduction candidate for 8,9 A7: 8,9 => CTR * .42.5.167...1...42...2.4.3812.8..394...4..2.646..2.7.5...7426533746.582.256...47. A7: 7 # 13 pairs * PAIR D1: 3,9 BLK 2 F1: 3,9,8 # reduction candidate for 3,9 F1: 3,9 => SOLVED * 842359167573186942619274538127865394435791286968423715781942653354617829296538471 F1: 8 => CTR * 942358167.3.1...42...2.4.3812.8..3944...31286863429715781942653354617829296583471 * PAIR D1: 3,9 COL D D5: 3,9,4,5,7 # reduction candidate for 3,9 D5: 3,9 => CTR * .42.5.167...1...42...2.4.3812.8..3944.....2.6.6.42.7.5...7426533746.582.256...47. D5: 4,5,7 # 9 pairs D6: 3,9,4 # reduction candidate for 3,9 D6: 3,9 => CTR * .42.5.167...1...42...2.4.3812.8..394...4..2.646..2.7.5...7426533746.582.256...47. D6: 4 # 13 pairs D7: 3,9,7 # reduction candidate for 3,9 D7: 3,9 # 13 pairs D9: 3,9,5 # reduction candidate for 3,9 D9: 3,9 => CTR * .42.5.167...1...42...2.4.381258..3944.75..2.6.6.42.7.5...7426533746.582.256...47. D9: 5 # 13 pairs * PAIR G2: 5,9 ROW 2 A2: 5,9,6,7,8 # reduction candidate for 5,9 A2: 5,9 # 11 pairs C2: 5,9,3,7,8 # reduction candidate for 5,9 C2: 5,9 # 12 pairs * PAIR G3: 5,9 ROW 3 A3: 5,9,6,7 # reduction candidate for 5,9 A3: 5,9 => CTR * .42.5.1676..1.7.42..7264.381258763947.....2.6.6..2.7.5...7426533746.582.256...47. A3: 6,7 # 10 pairs C3: 5,9,1,7 # reduction candidate for 5,9 C3: 5,9 # 19 pairs * PAIR C4: 5,7 BLK 4 A5: 5,7,4,8,9 # reduction candidate for 5,7 A5: 5,7 => CTR * .42.5.167...1...42...2.4.3812.8..394...4..2.646..2.7.5...7426533746.582.256...47. A5: 4,8,9 # 13 pairs C5: 5,7,3,8,9 # reduction candidate for 5,7 C5: 5,7 # 13 pairs * PAIR C4: 5,7 ROW 4 F4: 5,7,6 # reduction candidate for 5,7 F4: 6 => CTR * .42.5.167...1.7.427..2645381258763944.75..2.6.6.42.7.5...7426533746.582.256...47. F4: 5,7 # 13 pairs * PAIR C4: 5,7 COL C C2: 5,7,3,8,9 # reduction candidate for 5,7 C2: 5,7 # 13 pairs C3: 5,7,1,9 # reduction candidate for 5,7 C3: 5,7 # 12 pairs * PAIR E4: 6,7 BLK 5 F4: 6,7,5 # reduction candidate for 6,7 F4: 6,7 => CTR * .42.5.167...1...42...2.4.381258..3944.75..2.6.6.42.7.5...7426533746.582.256...47. F4: 5 # 13 pairs * PAIR E4: 6,7 COL E E2: 6,7,8,9 # reduction candidate for 6,7 E2: 6,7 => CTR * 942358167.3.1..9426..29453812.8..3944...31286863429715781942653354617829296583471 E2: 8,9 # 15 pairs E3: 6,7,9 # reduction candidate for 6,7 E3: 6,7 # 15 pairs * PAIR I8: 1,9 BLK 9 I7: 1,9,3 # reduction candidate for 1,9 I7: 1,9 => CTR * 842953167.391.6542...2.4.381278653944.573.2.69634217857.834265.3546..82.2.65..473 I7: 3 # 12 pairs I9: 1,9,3 # reduction candidate for 1,9 I9: 1,9 # 12 pairs * PAIR I8: 1,9 ROW 8 B8: 1,9,5,7 # reduction candidate for 1,9 B8: 1,9 => CTR * .42.5.167...1...42...2.4.381258..394...5..2.6.6.42.7.5...7426533.46.582.256...47. B8: 5,7 # 10 pairs E8: 1,9,7 # reduction candidate for 1,9 E8: 1,9 # 12 pairs F8: 1,9,5,7 # reduction candidate for 1,9 F8: 1,9 => CTR * .42.5.167...1.7.42...2.4.3812786.394......2.6.6..2.7.5....4265.35467.82.2.6...47. F8: 5,7 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-068-base-pr-000.dot * REASONING * DIS # A2: 8,9 => CTR => A2: 5,6,7 * DIS # B2: 8,9 => CTR => B2: 3,7 * DIS # F1: 3 => CTR => F1: 8,9 * DIS # A5: 8,9 => CTR => A5: 4,5,7 * DIS # A7: 8,9 => CTR => A7: 7 * PRF # F1: 3,9 => SOL * DIS # F1: 8 => CTR => F1: 3,9 * DIS # D5: 3,9 => CTR => D5: 4,5,7 * DIS # D6: 3,9 => CTR => D6: 4 * DIS # D9: 3,9 => CTR => D9: 5 * DIS # A3: 5,9 => CTR => A3: 6,7 * DIS # A5: 5,7 => CTR => A5: 4,8,9 * DIS # F4: 6 => CTR => F4: 5,7 * DIS # F4: 6,7 => CTR => F4: 5 * DIS # E2: 6,7 => CTR => E2: 8,9 * DIS # I7: 1,9 => CTR => I7: 3 * DIS # B8: 1,9 => CTR => B8: 5,7 * DIS # F8: 1,9 => CTR => F8: 5,7 * CNT 18 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C4,D1,E4,G2,G3,H5,H6,I8) * .42.5.167...1...42...2.4.3812.8..394......2.6.6..2.7.5....4265.3.46..82.2.6...47. * PAIR A1: 8,9 BLK 1 A2: 8,9,5,6,7 # reduction candidate for 8,9 A2: 8,9 => CTR * .42.5.167...1...426..2.4.3812.8..3945..4..2.646..2.7.57...4265.3.46..82.2.65..47. B2: 8,9,3,7 # reduction candidate for 8,9 B2: 8,9 => CTR * 842359167.9318.542.1.2.493812.8..394.3.59.2.6.6942.7.5.81.426533.46..82.256938471 C2: 8,9,3,5,7 # reduction candidate for 8,9 C2: 8,9 # 11 pairs * RESTART * PAIR A1: 8,9 BLK 1 C2: 8,9,3,5,7 # reduction candidate for 8,9 C2: 3,5,7 => SOLVED * 842359167573186942619274538127865394435791286968423715781942653354617829296538471 * DURATION: 0:00:06.645261 START: 00:25:27.234545 END: 00:25:33.879806 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-068-base-pr-001.dot * REASONING * DIS # A2: 8,9 => CTR => A2: 5,6,7 * DIS A2: 5,6,7 # B2: 8,9 => CTR => B2: 3,7 * PRF A2: 5,6,7 + B2: 3,7 # C2: 3,5,7 => SOL * STA A2: 5,6,7 + B2: 3,7 + C2: 3,5,7 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
Top 95 Sudokus 068 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 842359167573186942619274538127865394435791286968423715781942653354617829296538471 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: 8,9 => CTR => A2: 5,6,7 * INC # A2: 5,6,7 => UNS * DIS # B2: 8,9 => CTR => B2: 3,7 * INC # B2: 3,7 => UNS * INC # C2: 8,9 => UNS * INC # F1: 8,9 => UNS * DIS # F1: 3 => CTR => F1: 8,9 * DIS # A5: 8,9 => CTR => A5: 4,5,7 * INC # A5: 4,5,7 => UNS * INC # A6: 8,9 => UNS * DIS # A7: 8,9 => CTR => A7: 7 * INC # A7: 7 => UNS * PRF # F1: 3,9 => SOL * DIS # F1: 8 => CTR => F1: 3,9 * DIS # D5: 3,9 => CTR => D5: 4,5,7 * INC # D5: 4,5,7 => UNS * DIS # D6: 3,9 => CTR => D6: 4 * INC # D6: 4 => UNS * INC # D7: 3,9 => UNS * DIS # D9: 3,9 => CTR => D9: 5 * INC # D9: 5 => UNS * INC # A2: 5,9 => UNS * INC # C2: 5,9 => UNS * DIS # A3: 5,9 => CTR => A3: 6,7 * INC # A3: 6,7 => UNS * INC # C3: 5,9 => UNS * DIS # A5: 5,7 => CTR => A5: 4,8,9 * INC # A5: 4,8,9 => UNS * INC # C5: 5,7 => UNS * INC # F4: 5,7 => UNS * DIS # F4: 6 => CTR => F4: 5,7 * INC # C2: 5,7 => UNS * INC # C3: 5,7 => UNS * DIS # F4: 6,7 => CTR => F4: 5 * INC # F4: 5 => UNS * DIS # E2: 6,7 => CTR => E2: 8,9 * INC # E2: 8,9 => UNS * INC # E3: 6,7 => UNS * DIS # I7: 1,9 => CTR => I7: 3 * INC # I7: 3 => UNS * INC # I9: 1,9 => UNS * DIS # B8: 1,9 => CTR => B8: 5,7 * INC # B8: 5,7 => UNS * INC # E8: 1,9 => UNS * DIS # F8: 1,9 => CTR => F8: 5,7 * INC # F8: 5,7 => UNS * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 8,9 => CTR => A2: 5,6,7 * DIS A2: 5,6,7 # B2: 8,9 => CTR => B2: 3,7 * INC A2: 5,6,7 + B2: 3,7 # C2: 8,9 => UNS * INC A2: 5,6,7 + B2: 3,7 # C2: 8,9 => UNS * PRF A2: 5,6,7 + B2: 3,7 # C2: 3,5,7 => SOL * STA A2: 5,6,7 + B2: 3,7 + C2: 3,5,7 * CNT 5 HDP CHAINS / 5 HYP OPENED