Analysis of xx-top500-405-base.sdk
Contents
Original Sudoku
level: medium
position: .4..5..67...9...4....2.....1..8..3........2...6...........4..5.3.....8..2........ initial
Autosolve
position: .42.5..67...9...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 # A5: 8,9 => CTR => A5: 4,5,7 * PRF # A6: 8,9 => SOL * DIS # A6: 4 => CTR => A6: 8,9 * DIS # A7: 8,9 => CTR => A7: 7 * PRF # A7: 7 => SOL * PRF # F1: 1,3 => SOL * DIS # F1: 8 => CTR => F1: 1,3 * DIS # D5: 1,3 => CTR => D5: 4,5,7 * DIS # D6: 1,3 => CTR => D6: 4 * PRF # D6: 4 => SOL * PRF # D7: 1,3 => SOL * DIS # D7: 7 => CTR => D7: 1,3 * DIS # D9: 1,3 => CTR => D9: 5 * PRF # D9: 5 => SOL * PRF # G3: 5 => SOL * PRF # G3: 1,5 => SOL * DIS # G3: 9 => CTR => G3: 1,5 * DIS # A5: 5,7 => CTR => A5: 4,8,9 * PRF # A5: 4,8,9 => SOL * PRF # C5: 5,7 => SOL * PRF # F4: 5,7 => SOL * DIS # F4: 6 => CTR => F4: 5,7 * DIS # F4: 6,7 => CTR => F4: 5 * PRF # F4: 5 => SOL * DIS # E2: 6,7 => CTR => E2: 1,8 * DIS # I7: 1,9 => CTR => I7: 3 * DIS # B8: 1,9 => CTR => B8: 5,7 * DIS # F8: 1,9 => CTR => F8: 5,7 * CNT 28 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A5: 8,9 => CTR => A5: 4,5,7 * PRF A5: 4,5,7 # A6: 8,9 => SOL * STA A5: 4,5,7 + A6: 8,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .4..5..67...9...4....2.....1..8..3........2...6...........4..5.3.....8..2........ | initial |
| .42.5..67...9...42...2.4.3812.8..394......2.6.6..2.7.5....4265.3.46..82.2.6...47. | autosolve |
| 842351967573986142691274538127865394435719286968423715789142653354697821216538479 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) A1: 8,9 D1: 1,3 G1: 1,9 G2: 1,5 C4: 5,7 E4: 6,7 H5: 1,8 H6: 1,8 I8: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H5,H6: 1.. / H5 = 1 => 9 pairs (_) / H6 = 1 => 9 pairs (_) B2,C2: 3.. / B2 = 3 => 9 pairs (_) / C2 = 3 => 0 pairs (*) D1,F1: 3.. / D1 = 3 => 0 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 => 0 pairs (*) / A6 = 4 => 0 pairs (X) D5,D6: 4.. / D5 = 4 => 0 pairs (X) / D6 = 4 => 0 pairs (_) A5,D5: 4.. / A5 = 4 => 0 pairs (*) / D5 = 4 => 0 pairs (X) A6,D6: 4.. / A6 = 4 => 0 pairs (X) / D6 = 4 => 0 pairs (_) G2,G3: 5.. / G2 = 5 => 9 pairs (_) / G3 = 5 => 0 pairs (*) B8,B9: 5.. / B8 = 5 => 0 pairs (*) / B9 = 5 => 0 pairs (X) C4,F4: 5.. / C4 = 5 => 0 pairs (X) / F4 = 5 => 0 pairs (_) B8,F8: 5.. / B8 = 5 => 0 pairs (*) / F8 = 5 => 0 pairs (X) D5,D9: 5.. / D5 = 5 => 0 pairs (X) / D9 = 5 => 0 pairs (_) A2,A3: 6.. / A2 = 6 => 0 pairs (X) / A3 = 6 => 10 pairs (_) E4,F4: 6.. / E4 = 6 => 0 pairs (*) / F4 = 6 => 0 pairs (X) A3,E3: 6.. / A3 = 6 => 10 pairs (_) / E3 = 6 => 0 pairs (X) F2,F4: 6.. / F2 = 6 => 0 pairs (*) / F4 = 6 => 0 pairs (X) D5,D7: 7.. / D5 = 7 => 0 pairs (*) / D7 = 7 => 0 pairs (X) H5,H6: 8.. / H5 = 8 => 9 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) G1,G3: 9.. / G1 = 9 => 0 pairs (*) / G3 = 9 => 0 pairs (X) A1,G1: 9.. / A1 = 9 => 0 pairs (X) / G1 = 9 => 0 pairs (_) * DURATION: 0:00:51.444056 START: 16:40:55.883508 END: 16:41:47.327564 2017-05-04 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C4,D1,E4,G1,G2,H5,H6,I8) * .42.5..67...9...42...2.4.3812.8..394......2.6.6..2.7.5....4265.3.46..82.2.6...47. * PAIR A1: 8,9 COL A A5: 8,9,4,5,7 # reduction candidate for 8,9 A5: 8,9 => CTR * .42.5..67...9...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 => SOLVED * 842351967573986142691274538127865394435719286968423715789142653354697821216538479 A6: 4 => CTR * .42.5..67...9...42...2.4.3812.8..394...4..2.646..2.7.5...7426533746.582.256...47. A7: 8,9,7 # reduction candidate for 8,9 A7: 8,9 => CTR * .42.5..67...9...42...2.4.3812.8..394...4..2.646..2.7.5...7426533746.582.256...47. A7: 7 => SOLVED * 842351967573986142691274538127865394435719286968423715789142653354697821216538479 * PAIR D1: 1,3 BLK 2 F1: 1,3,8 # reduction candidate for 1,3 F1: 1,3 => SOLVED * 842351967573986142691274538127865394435719286968423715789142653354697821216538479 F1: 8 => CTR * 942358167.3.9..542...2.493812.8..394....31286863429715789142653354697821216583479 * PAIR D1: 1,3 COL D D5: 1,3,4,5,7 # reduction candidate for 1,3 D5: 1,3 => CTR * .42.5..67...9...42...2.4.3812.8..3944.....2.6.6.42.7.5...7426533746.582.256...47. D5: 4,5,7 # 9 pairs D6: 1,3,4 # reduction candidate for 1,3 D6: 1,3 => CTR * .42.5..67...9...42...2.4.3812.8..394...4..2.646..2.7.5...7426533746.582.256...47. D6: 4 => SOLVED * 842351967573986142691274538127865394435719286968423715789142653354697821216538479 D7: 1,3,7 # reduction candidate for 1,3 D7: 1,3 => SOLVED * 842351967573986142691274538127865394435719286968423715789142653354697821216538479 D7: 7 => CTR * .42.5..67...9...42...2.4.381258..3944.75..2.6.6.42.7.5...7426533746.582.256...47. D9: 1,3,5 # reduction candidate for 1,3 D9: 1,3 => CTR * .42.5..67...9...42...2.4.381258..3944.75..2.6.6.42.7.5...7426533746.582.256...47. D9: 5 => SOLVED * 842351967573986142691274538127865394435719286968423715789142653354697821216538479 * PAIR G1: 1,9 BLK 3 G3: 1,9,5 # reduction candidate for 1,9 G3: 5 => SOLVED * 842351967573986142691274538127865394435719286968423715789142653354697821216538479 G3: 1,9 # 9 pairs * PAIR G2: 1,5 BLK 3 G3: 1,5,9 # reduction candidate for 1,5 G3: 1,5 => SOLVED * 842351967573986142691274538127865394435719286968423715789142653354697821216538479 G3: 9 => CTR * 942358167.3.9..542...2.493812.8..394....31286863429715789142653354697821216583479 * PAIR G2: 1,5 ROW 2 C2: 1,5,3,7,8 # reduction candidate for 1,5 C2: 1,5 # 12 pairs C2: 3,7,8 # 9 pairs * PAIR C4: 5,7 BLK 4 A5: 5,7,4,8,9 # reduction candidate for 5,7 A5: 5,7 => CTR * .42.5..67...9...42...2.4.3812.8..394...4..2.646..2.7.5...7426533746.582.256...47. A5: 4,8,9 => SOLVED * 842351967573986142691274538127865394435719286968423715789142653354697821216538479 C5: 5,7,3,8,9 # reduction candidate for 5,7 C5: 5,7 => SOLVED * 842351967573986142691274538127865394435719286968423715789142653354697821216538479 C5: 3,8,9 # 9 pairs * PAIR C4: 5,7 ROW 4 F4: 5,7,6 # reduction candidate for 5,7 F4: 5,7 => SOLVED * 842351967573986142691274538127865394435719286968423715789142653354697821216538479 F4: 6 => CTR * .42.5..67...9.7.427..2645381258763944.75..2.6.6.42.7.5...7426533746.582.256...47. * PAIR C4: 5,7 COL C C2: 5,7,1,3,8 # reduction candidate for 5,7 C2: 5,7 # 20 pairs C3: 5,7,1,9 # reduction candidate for 5,7 C3: 5,7 # 10 pairs * PAIR E4: 6,7 BLK 5 F4: 6,7,5 # reduction candidate for 6,7 F4: 6,7 => CTR * .42.5..67...9...42...2.4.381258..3944.75..2.6.6.42.7.5...7426533746.582.256...47. F4: 5 => SOLVED * 842351967573986142691274538127865394435719286968423715789142653354697821216538479 * PAIR E4: 6,7 COL E E2: 6,7,1,8 # reduction candidate for 6,7 E2: 6,7 => CTR * .42358167.319..5426.52149381278653945..4372.6.63.2.7.5....4265.3.469.8212.6.8.47. E2: 1,8 # 15 pairs E3: 6,7,1 # 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 * 842153967.319.6542...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..67...9...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..67...9.7.42...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-top500-405-base-pr-000.dot * REASONING * DIS # A5: 8,9 => CTR => A5: 4,5,7 * PRF # A6: 8,9 => SOL * DIS # A6: 4 => CTR => A6: 8,9 * DIS # A7: 8,9 => CTR => A7: 7 * PRF # A7: 7 => SOL * PRF # F1: 1,3 => SOL * DIS # F1: 8 => CTR => F1: 1,3 * DIS # D5: 1,3 => CTR => D5: 4,5,7 * DIS # D6: 1,3 => CTR => D6: 4 * PRF # D6: 4 => SOL * PRF # D7: 1,3 => SOL * DIS # D7: 7 => CTR => D7: 1,3 * DIS # D9: 1,3 => CTR => D9: 5 * PRF # D9: 5 => SOL * PRF # G3: 5 => SOL * PRF # G3: 1,5 => SOL * DIS # G3: 9 => CTR => G3: 1,5 * DIS # A5: 5,7 => CTR => A5: 4,8,9 * PRF # A5: 4,8,9 => SOL * PRF # C5: 5,7 => SOL * PRF # F4: 5,7 => SOL * DIS # F4: 6 => CTR => F4: 5,7 * DIS # F4: 6,7 => CTR => F4: 5 * PRF # F4: 5 => SOL * DIS # E2: 6,7 => CTR => E2: 1,8 * DIS # I7: 1,9 => CTR => I7: 3 * DIS # B8: 1,9 => CTR => B8: 5,7 * DIS # F8: 1,9 => CTR => F8: 5,7 * CNT 28 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C4,D1,E4,G1,G2,H5,H6,I8) * .42.5..67...9...42...2.4.3812.8..394......2.6.6..2.7.5....4265.3.46..82.2.6...47. * PAIR A1: 8,9 COL A A5: 8,9,4,5,7 # reduction candidate for 8,9 A5: 8,9 => CTR * .42.5..67...9...42...2.4.3812.8..394...4..2.646..2.7.5...7426533746.582.256...47. A6: 8,9,4 # reduction candidate for 8,9 A6: 8,9 => SOLVED * 842351967573986142691274538127865394435719286968423715789142653354697821216538479 * DURATION: 0:00:03.650949 START: 16:42:34.227099 END: 16:42:37.878048 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-405-base-pr-001.dot * REASONING * DIS # A5: 8,9 => CTR => A5: 4,5,7 * PRF A5: 4,5,7 # A6: 8,9 => SOL * STA A5: 4,5,7 + A6: 8,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 405 solution: 842351967573986142691274538127865394435719286968423715789142653354697821216538479 info: 94802 FNBXK S8.f 18902 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 842351967573986142691274538127865394435719286968423715789142653354697821216538479 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 # A5: 8,9 => CTR => A5: 4,5,7 * INC # A5: 4,5,7 => UNS * PRF # A6: 8,9 => SOL * DIS # A6: 4 => CTR => A6: 8,9 * DIS # A7: 8,9 => CTR => A7: 7 * PRF # A7: 7 => SOL * PRF # F1: 1,3 => SOL * DIS # F1: 8 => CTR => F1: 1,3 * DIS # D5: 1,3 => CTR => D5: 4,5,7 * INC # D5: 4,5,7 => UNS * DIS # D6: 1,3 => CTR => D6: 4 * PRF # D6: 4 => SOL * PRF # D7: 1,3 => SOL * DIS # D7: 7 => CTR => D7: 1,3 * DIS # D9: 1,3 => CTR => D9: 5 * PRF # D9: 5 => SOL * INC # G3: 1,9 => UNS * PRF # G3: 5 => SOL * PRF # G3: 1,5 => SOL * DIS # G3: 9 => CTR => G3: 1,5 * INC # C2: 1,5 => UNS * INC # C2: 3,7,8 => UNS * DIS # A5: 5,7 => CTR => A5: 4,8,9 * PRF # A5: 4,8,9 => SOL * PRF # C5: 5,7 => SOL * INC # C5: 3,8,9 => UNS * PRF # F4: 5,7 => SOL * DIS # F4: 6 => CTR => F4: 5,7 * INC # C2: 5,7 => UNS * INC # C3: 5,7 => UNS * DIS # F4: 6,7 => CTR => F4: 5 * PRF # F4: 5 => SOL * DIS # E2: 6,7 => CTR => E2: 1,8 * INC # E2: 1,8 => 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 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A5: 8,9 => CTR => A5: 4,5,7 * PRF A5: 4,5,7 # A6: 8,9 => SOL * STA A5: 4,5,7 + A6: 8,9 * CNT 2 HDP CHAINS / 2 HYP OPENED