Analysis of xx-top500-498-base.sdk
Contents
Original Sudoku
level: medium
position: 27..........8..6...35......6...32...4.....1......7...5.......37...1............2. initial
Autosolve
position: 276.........8..6..835......6...32...4.....1......71..5.......37...1....6.......21 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A7: 1,9 => CTR => A7: 5 * DIS # F2: 5,7 => CTR => F2: 3 * PRF # F2: 3 => SOL * DIS # G1: 4,9 => CTR => G1: 3,5,8 * PRF # G3: 4,9 => SOL * PRF # C6: 3,9 => SOL * PRF # A8: 3,9 => SOL * DIS # C5: 2,3 => CTR => C5: 7 * PRF # C5: 7 => SOL * CNT 9 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A7: 1,9 => CTR => A7: 5 * DIS A7: 5 # F2: 5,7 => CTR => F2: 3 * PRF A7: 5 + F2: 3 => SOL * STA A7: 5 + F2: 3 * CNT 3 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 27..........8..6...35......6...32...4.....1......7...5.......37...1............2. | initial |
| 276.........8..6..835......6...32...4.....1......71..5.......37...1....6.......21 | autosolve |
| 276914358194853672835726914651432789427598163983671245518269437342187596769345821 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A2: 1,9 E2: 2,5 H2: 5,7 I2: 2,3 I3: 4,9 B4: 1,5 C4: 1,7 B5: 2,5 A6: 3,9 D6: 4,6 I5: 2,3 G6: 2,3 H6: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,E3: 1.. / E1 = 1 => 13 pairs (_) / E3 = 1 => 13 pairs (_) H1,H3: 1.. / H1 = 1 => 13 pairs (_) / H3 = 1 => 13 pairs (_) B4,C4: 1.. / B4 = 1 => 0 pairs (X) / C4 = 1 => 0 pairs (_) E1,H1: 1.. / E1 = 1 => 13 pairs (_) / H1 = 1 => 13 pairs (_) E3,H3: 1.. / E3 = 1 => 13 pairs (_) / H3 = 1 => 13 pairs (_) A2,A7: 1.. / A2 = 1 => 15 pairs (_) / A7 = 1 => 0 pairs (X) I2,G3: 2.. / I2 = 2 => 0 pairs (*) / G3 = 2 => 0 pairs (X) I5,G6: 2.. / I5 = 2 => 0 pairs (X) / G6 = 2 => 0 pairs (_) E2,I2: 2.. / E2 = 2 => 0 pairs (X) / I2 = 2 => 0 pairs (_) D3,D7: 2.. / D3 = 2 => 0 pairs (X) / D7 = 2 => 13 pairs (_) G3,G6: 2.. / G3 = 2 => 0 pairs (X) / G6 = 2 => 0 pairs (_) I2,I5: 2.. / I2 = 2 => 0 pairs (*) / I5 = 2 => 0 pairs (X) G1,I2: 3.. / G1 = 3 => 0 pairs (*) / I2 = 3 => 0 pairs (X) I5,G6: 3.. / I5 = 3 => 0 pairs (*) / G6 = 3 => 0 pairs (X) F2,I2: 3.. / F2 = 3 => 0 pairs (*) / I2 = 3 => 0 pairs (X) C5,I5: 3.. / C5 = 3 => 0 pairs (X) / I5 = 3 => 0 pairs (_) D1,D9: 3.. / D1 = 3 => 0 pairs (X) / D9 = 3 => 0 pairs (_) G1,G6: 3.. / G1 = 3 => 0 pairs (*) / G6 = 3 => 0 pairs (X) I2,I5: 3.. / I2 = 3 => 0 pairs (X) / I5 = 3 => 0 pairs (_) B2,C2: 4.. / B2 = 4 => 14 pairs (_) / C2 = 4 => 14 pairs (_) D4,D6: 4.. / D4 = 4 => 0 pairs (*) / D6 = 4 => 0 pairs (X) D6,H6: 4.. / D6 = 4 => 13 pairs (_) / H6 = 4 => 0 pairs (*) B4,B5: 5.. / B4 = 5 => 0 pairs (*) / B5 = 5 => 0 pairs (X) B4,D4: 5.. / B4 = 5 => 0 pairs (*) / D4 = 5 => 0 pairs (X) H5,H6: 6.. / H5 = 6 => 0 pairs (*) / H6 = 6 => 0 pairs (X) B7,B9: 6.. / B7 = 6 => 13 pairs (_) / B9 = 6 => 13 pairs (_) D6,H6: 6.. / D6 = 6 => 0 pairs (*) / H6 = 6 => 0 pairs (X) C4,C5: 7.. / C4 = 7 => 0 pairs (X) / C5 = 7 => 0 pairs (_) A8,A9: 7.. / A8 = 7 => 13 pairs (_) / A9 = 7 => 0 pairs (*) F2,H2: 7.. / F2 = 7 => 0 pairs (X) / H2 = 7 => 0 pairs (_) C5,H5: 7.. / C5 = 7 => 0 pairs (*) / H5 = 7 => 0 pairs (X) A8,F8: 7.. / A8 = 7 => 13 pairs (_) / F8 = 7 => 0 pairs (*) D3,D9: 7.. / D3 = 7 => 0 pairs (*) / D9 = 7 => 0 pairs (X) G3,G4: 7.. / G3 = 7 => 0 pairs (X) / G4 = 7 => 0 pairs (_) B6,C6: 8.. / B6 = 8 => 13 pairs (_) / C6 = 8 => 14 pairs (_) E5,F5: 8.. / E5 = 8 => 13 pairs (_) / F5 = 8 => 13 pairs (_) I1,I4: 8.. / I1 = 8 => 14 pairs (_) / I4 = 8 => 16 pairs (_) * DURATION: 0:01:08.628011 START: 19:43:16.792239 END: 19:44:25.420250 2017-05-04 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,B4,B5,C4,D6,E2,G6,H2,H6,I2,I3,I5) * 276.........8..6..835......6...32...4.....1......71..5.......37...1....6.......21 * PAIR A2: 1,9 BLK 1 B2: 1,9,4 # reduction candidate for 1,9 B2: 1,9 # 14 pairs C2: 1,9,4 # reduction candidate for 1,9 C2: 1,9 # 14 pairs * PAIR A2: 1,9 COL A A7: 1,9,5 # reduction candidate for 1,9 A7: 1,9 => CTR * 276...358...853672835726.1.6.1.3278.427...1.33...712.5..2....37..31....6...3...21 A7: 5 # 14 pairs * PAIR E2: 2,5 COL E E7: 2,5,4,6,8,9 # reduction candidate for 2,5 E7: 2,5 # 14 pairs E8: 2,5,4,8,9 # reduction candidate for 2,5 E8: 2,5 # 14 pairs * PAIR H2: 5,7 ROW 2 F2: 5,7,3 # reduction candidate for 5,7 F2: 5,7 => CTR * 276.........8..6.3835...2..6...327..4.....1......71..5.......37...1....6.......21 F2: 3 => SOLVED * 276914358194853672835726914651432789427598163983671245518269437342187596769345821 * PAIR I3: 4,9 BLK 3 G1: 4,9,3,5,8 # reduction candidate for 4,9 G1: 4,9 => CTR * 276.........8..6.3835...2..6...327..4.....1......71..5.......37...1....6.......21 G1: 3,5,8 # 13 pairs H1: 4,9,1,5,8 # reduction candidate for 4,9 H1: 4,9 # 17 pairs I1: 4,9,8 # reduction candidate for 4,9 I1: 4,9 # 16 pairs G3: 4,9,2,7 # reduction candidate for 4,9 G3: 4,9 => SOLVED * 276914358194853672835726914651432789427598163983671245518269437342187596769345821 G3: 2,7 # 14 pairs H3: 4,9,1,7 # reduction candidate for 4,9 H3: 4,9 # 18 pairs * PAIR I3: 4,9 ROW 3 E3: 4,9,1,2,6 # reduction candidate for 4,9 E3: 4,9 # 16 pairs F3: 4,9,6,7 # reduction candidate for 4,9 F3: 4,9 # 16 pairs * PAIR I3: 4,9 COL I I4: 4,9,8 # reduction candidate for 4,9 I4: 8 # 16 pairs I4: 4,9 # 14 pairs * PAIR A6: 3,9 BLK 4 C6: 3,9,2,8 # reduction candidate for 3,9 C6: 3,9 => SOLVED * 276914358194853672835726914651432789427598163983671245518269437342187596769345821 C6: 2,8 # 14 pairs * PAIR A6: 3,9 COL A A8: 3,9,5,7 # reduction candidate for 3,9 A8: 3,9 => SOLVED * 276914358194853672835726914651432789427598163983671245518269437342187596769345821 A8: 5,7 # 14 pairs A9: 3,9,5,7 # reduction candidate for 3,9 A9: 3,9 # 15 pairs * PAIR I5: 2,3 ROW 5 C5: 2,3,7 # reduction candidate for 2,3 C5: 2,3 => CTR * 276.........8.7653835......6.7.32...4.....17.....71.65.......37...1....6.......21 C5: 7 => SOLVED * 276914358194853672835726914651432789427598163983671245518269437342187596769345821 * PAIR G6: 2,3 ROW 6 C6: 2,3,8,9 # reduction candidate for 2,3 C6: 2,3 # 17 pairs C6: 8,9 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-498-base-pr-000.dot * REASONING * DIS # A7: 1,9 => CTR => A7: 5 * DIS # F2: 5,7 => CTR => F2: 3 * PRF # F2: 3 => SOL * DIS # G1: 4,9 => CTR => G1: 3,5,8 * PRF # G3: 4,9 => SOL * PRF # C6: 3,9 => SOL * PRF # A8: 3,9 => SOL * DIS # C5: 2,3 => CTR => C5: 7 * PRF # C5: 7 => SOL * CNT 9 HDP CHAINS / 28 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,B4,B5,C4,D6,E2,G6,H2,H6,I2,I3,I5) * 276.........8..6..835......6...32...4.....1......71..5.......37...1....6.......21 * PAIR A2: 1,9 BLK 1 B2: 1,9,4 # reduction candidate for 1,9 B2: 1,9 # 14 pairs C2: 1,9,4 # reduction candidate for 1,9 C2: 1,9 # 14 pairs * PAIR A2: 1,9 COL A A7: 1,9,5 # reduction candidate for 1,9 A7: 1,9 => CTR * 276...358...853672835726.1.6.1.3278.427...1.33...712.5..2....37..31....6...3...21 * PAIR RESTART * PAIR E2: 2,5 COL E E8: 2,5,4,8,9 # reduction candidate for 2,5 E8: 2,5 # 15 pairs E8: 4,8,9 # 14 pairs * PAIR H2: 5,7 ROW 2 F2: 5,7,3 # reduction candidate for 5,7 F2: 5,7 => CTR * 276......1..8..6.3835...2..6...327..4.....1......71..55......37...1....6.......21 F2: 3 => SOLVED * 276914358194853672835726914651432789427598163983671245518269437342187596769345821 * DURATION: 0:00:08.803165 START: 19:44:54.192456 END: 19:45:02.995621 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-498-base-pr-001.dot * REASONING * DIS # A7: 1,9 => CTR => A7: 5 * DIS A7: 5 # F2: 5,7 => CTR => F2: 3 * PRF A7: 5 + F2: 3 => SOL * STA A7: 5 + F2: 3 * CNT 3 HDP CHAINS / 6 HYP OPENED
Header Info
Top 500 Minimum 17 498 solution: 276914358194853672835726914651432789427598163983671245518269437342187596769345821 info: 96638 FNBTHXYK S8.f 28515 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 276914358194853672835726914651432789427598163983671245518269437342187596769345821 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 # B2: 1,9 => UNS * INC # C2: 1,9 => UNS * DIS # A7: 1,9 => CTR => A7: 5 * INC # A7: 5 => UNS * INC # E7: 2,5 => UNS * INC # E8: 2,5 => UNS * DIS # F2: 5,7 => CTR => F2: 3 * PRF # F2: 3 => SOL * DIS # G1: 4,9 => CTR => G1: 3,5,8 * INC # G1: 3,5,8 => UNS * INC # H1: 4,9 => UNS * INC # I1: 4,9 => UNS * PRF # G3: 4,9 => SOL * INC # G3: 2,7 => UNS * INC # H3: 4,9 => UNS * INC # E3: 4,9 => UNS * INC # F3: 4,9 => UNS * INC # I4: 4,9 => UNS * INC # I4: 8 => UNS * PRF # C6: 3,9 => SOL * INC # C6: 2,8 => UNS * PRF # A8: 3,9 => SOL * INC # A8: 5,7 => UNS * INC # A9: 3,9 => UNS * DIS # C5: 2,3 => CTR => C5: 7 * PRF # C5: 7 => SOL * INC # C6: 2,3 => UNS * INC # C6: 8,9 => UNS * CNT 28 HDP CHAINS / 28 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 1,9 => UNS * INC # C2: 1,9 => UNS * DIS # A7: 1,9 => CTR => A7: 5 * INC A7: 5 # E8: 2,5 => UNS * INC A7: 5 # E8: 4,8,9 => UNS * DIS A7: 5 # F2: 5,7 => CTR => F2: 3 * PRF A7: 5 + F2: 3 => SOL * STA A7: 5 + F2: 3 * CNT 7 HDP CHAINS / 6 HYP OPENED