Analysis of xx-top500-352-base.sdk
Contents
Original Sudoku
level: medium
position: .6....7......5.4.......1......6...1.4..7.....5.......8.2.3..6..1...8...........5. initial
Autosolve
position: 8614.37.5...857461754.6183..876.5.1441.7385.65.614..78925314687173586.4.648.7.153 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # G4: 2,3 => SOL * DIS # G4: 9 => CTR => G4: 2,3 * PRF # G6: 3,9 => SOL * DIS # G6: 2 => CTR => G6: 3,9 * DIS # G4: 2,9 => CTR => G4: 3 * PRF # G4: 3 => SOL * PRF # G6: 2,9 => SOL * DIS # G6: 3 => CTR => G6: 2,9 * DIS # G4: 2,9 => CTR => G4: 3 * PRF # G4: 3 => SOL * PRF # G6: 2,9 => SOL * DIS # G6: 3 => CTR => G6: 2,9 * DIS # G4: 2,9 => CTR => G4: 3 * PRF # G4: 3 => SOL * PRF # G6: 2,9 => SOL * DIS # G6: 3 => CTR => G6: 2,9 * CNT 16 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # G4: 2,3 => SOL * STA G4: 2,3 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6....7......5.4.......1......6...1.4..7.....5.......8.2.3..6..1...8...........5. | initial |
| 8614.37.5...857461754.6183..876.5.1441.7385.65.614..78925314687173586.4.648.7.153 | autosolve |
| 861423795392857461754961832287695314419738526536142978925314687173586249648279153 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) A2: 2,3 B2: 3,9 C2: 2,9 E1: 2,9 D3: 2,9 H1: 2,9 I3: 2,9 A4: 2,3 C5: 2,9 B6: 3,9 E4: 2,9 F6: 2,9 H5: 2,9 D9: 2,9 F9: 2,9 G8: 2,9 I8: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,C2: 2.. / A2 = 2 => 0 pairs (X) / C2 = 2 => 0 pairs (_) E1,D3: 2.. / E1 = 2 => 0 pairs (*) / D3 = 2 => 0 pairs (X) H1,I3: 2.. / H1 = 2 => 0 pairs (X) / I3 = 2 => 0 pairs (_) A4,C5: 2.. / A4 = 2 => 0 pairs (*) / C5 = 2 => 0 pairs (X) E4,F6: 2.. / E4 = 2 => 0 pairs (X) / F6 = 2 => 0 pairs (_) D9,F9: 2.. / D9 = 2 => 0 pairs (*) / F9 = 2 => 0 pairs (X) G8,I8: 2.. / G8 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) E1,H1: 2.. / E1 = 2 => 0 pairs (*) / H1 = 2 => 0 pairs (X) D3,I3: 2.. / D3 = 2 => 0 pairs (X) / I3 = 2 => 0 pairs (_) C5,H5: 2.. / C5 = 2 => 0 pairs (X) / H5 = 2 => 0 pairs (_) F6,G6: 2.. / F6 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) A2,A4: 2.. / A2 = 2 => 0 pairs (X) / A4 = 2 => 0 pairs (_) C2,C5: 2.. / C2 = 2 => 0 pairs (*) / C5 = 2 => 0 pairs (X) D3,D9: 2.. / D3 = 2 => 0 pairs (X) / D9 = 2 => 0 pairs (_) E1,E4: 2.. / E1 = 2 => 0 pairs (*) / E4 = 2 => 0 pairs (X) F6,F9: 2.. / F6 = 2 => 0 pairs (*) / F9 = 2 => 0 pairs (X) H1,H5: 2.. / H1 = 2 => 0 pairs (X) / H5 = 2 => 0 pairs (_) I3,I8: 2.. / I3 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) A2,B2: 3.. / A2 = 3 => 0 pairs (*) / B2 = 3 => 0 pairs (X) A4,B6: 3.. / A4 = 3 => 0 pairs (X) / B6 = 3 => 0 pairs (_) G4,G6: 3.. / G4 = 3 => 0 pairs (*) / G6 = 3 => 0 pairs (X) A4,G4: 3.. / A4 = 3 => 0 pairs (X) / G4 = 3 => 0 pairs (_) B6,G6: 3.. / B6 = 3 => 0 pairs (*) / G6 = 3 => 0 pairs (X) A2,A4: 3.. / A2 = 3 => 0 pairs (*) / A4 = 3 => 0 pairs (X) B2,B6: 3.. / B2 = 3 => 0 pairs (X) / B6 = 3 => 0 pairs (_) B2,C2: 9.. / B2 = 9 => 0 pairs (*) / C2 = 9 => 0 pairs (X) E1,D3: 9.. / E1 = 9 => 0 pairs (X) / D3 = 9 => 0 pairs (_) H1,I3: 9.. / H1 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) C5,B6: 9.. / C5 = 9 => 0 pairs (*) / B6 = 9 => 0 pairs (X) E4,F6: 9.. / E4 = 9 => 0 pairs (*) / F6 = 9 => 0 pairs (X) D9,F9: 9.. / D9 = 9 => 0 pairs (X) / F9 = 9 => 0 pairs (_) G8,I8: 9.. / G8 = 9 => 0 pairs (X) / I8 = 9 => 0 pairs (_) E1,H1: 9.. / E1 = 9 => 0 pairs (X) / H1 = 9 => 0 pairs (_) D3,I3: 9.. / D3 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) E4,G4: 9.. / E4 = 9 => 0 pairs (*) / G4 = 9 => 0 pairs (X) C5,H5: 9.. / C5 = 9 => 0 pairs (*) / H5 = 9 => 0 pairs (X) B2,B6: 9.. / B2 = 9 => 0 pairs (*) / B6 = 9 => 0 pairs (X) C2,C5: 9.. / C2 = 9 => 0 pairs (X) / C5 = 9 => 0 pairs (_) D3,D9: 9.. / D3 = 9 => 0 pairs (*) / D9 = 9 => 0 pairs (X) E1,E4: 9.. / E1 = 9 => 0 pairs (X) / E4 = 9 => 0 pairs (_) F6,F9: 9.. / F6 = 9 => 0 pairs (X) / F9 = 9 => 0 pairs (_) H1,H5: 9.. / H1 = 9 => 0 pairs (*) / H5 = 9 => 0 pairs (X) I3,I8: 9.. / I3 = 9 => 0 pairs (X) / I8 = 9 => 0 pairs (_) * DURATION: 0:01:09.557664 START: 14:46:57.287353 END: 14:48:06.845017 2017-05-04 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B2,B6,C2,C5,D3,D9,E1,E4,F6,F9,G8,H1,H5,I3,I8) * 8614.37.5...857461754.6183..876.5.1441.7385.65.614..78925314687173586.4.648.7.153 * PAIR A4: 2,3 ROW 4 G4: 2,3,9 # reduction candidate for 2,3 G4: 2,3 => SOLVED * 861423795392857461754961832287695314419738526536142978925314687173586249648279153 G4: 9 => CTR * 8614.37.5...857461754.6183.38762591441.7385.65.614..78925314687173586.4.648.7.153 * PAIR B6: 3,9 ROW 6 G6: 3,9,2 # reduction candidate for 3,9 G6: 3,9 => SOLVED * 861423795392857461754961832287695314419738526536142978925314687173586249648279153 G6: 2 => CTR * 8614.37.5...857461754.6183..876.531441.7385965.614..78925314687173586.4.648.7.153 * PAIR E4: 2,9 ROW 4 G4: 2,9,3 # reduction candidate for 2,9 G4: 2,9 => CTR * 8614.37.5...857461754.6183.3876.5.14412738596596142378925314687173586942648279153 G4: 3 => SOLVED * 861423795392857461754961832287695314419738526536142978925314687173586249648279153 * PAIR F6: 2,9 ROW 6 G6: 2,9,3 # reduction candidate for 2,9 G6: 2,9 => SOLVED * 861423795392857461754961832287695314419738526536142978925314687173586249648279153 G6: 3 => CTR * 861423795.39857461754961832387695.1441.7385.65.6142378925314687173586.4.648279153 * PAIR H5: 2,9 BLK 6 G4: 2,9,3 # reduction candidate for 2,9 G4: 2,9 => CTR * 8614.37.5...857461754.6183.3876.5.14412738596596142378925314687173586942648279153 G4: 3 => SOLVED * 861423795392857461754961832287695314419738526536142978925314687173586249648279153 G6: 2,9,3 # reduction candidate for 2,9 G6: 2,9 => SOLVED * 861423795392857461754961832287695314419738526536142978925314687173586249648279153 G6: 3 => CTR * 861423795.39857461754961832387695.1441.7385.65.6142378925314687173586.4.648279153 * PAIR G8: 2,9 COL G G4: 2,9,3 # reduction candidate for 2,9 G4: 2,9 => CTR * 8614.37.5...857461754.6183.3876.5.14412738596596142378925314687173586942648279153 G4: 3 => SOLVED * 861423795392857461754961832287695314419738526536142978925314687173586249648279153 G6: 2,9,3 # reduction candidate for 2,9 G6: 2,9 => SOLVED * 861423795392857461754961832287695314419738526536142978925314687173586249648279153 G6: 3 => CTR * 861423795.39857461754961832387695.1441.7385.65.6142378925314687173586.4.648279153 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-352-base-pr-000.dot * REASONING * PRF # G4: 2,3 => SOL * DIS # G4: 9 => CTR => G4: 2,3 * PRF # G6: 3,9 => SOL * DIS # G6: 2 => CTR => G6: 3,9 * DIS # G4: 2,9 => CTR => G4: 3 * PRF # G4: 3 => SOL * PRF # G6: 2,9 => SOL * DIS # G6: 3 => CTR => G6: 2,9 * DIS # G4: 2,9 => CTR => G4: 3 * PRF # G4: 3 => SOL * PRF # G6: 2,9 => SOL * DIS # G6: 3 => CTR => G6: 2,9 * DIS # G4: 2,9 => CTR => G4: 3 * PRF # G4: 3 => SOL * PRF # G6: 2,9 => SOL * DIS # G6: 3 => CTR => G6: 2,9 * CNT 16 HDP CHAINS / 16 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B2,B6,C2,C5,D3,D9,E1,E4,F6,F9,G8,H1,H5,I3,I8) * 8614.37.5...857461754.6183..876.5.1441.7385.65.614..78925314687173586.4.648.7.153 * PAIR A4: 2,3 ROW 4 G4: 2,3,9 # reduction candidate for 2,3 G4: 2,3 => SOLVED * 861423795392857461754961832287695314419738526536142978925314687173586249648279153 * DURATION: 0:00:02.244995 START: 14:48:25.799952 END: 14:48:28.044947 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-352-base-pr-001.dot * REASONING * PRF # G4: 2,3 => SOL * STA G4: 2,3 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 352 solution: 861423795392857461754961832287695314419738526536142978925314687173586249648279153 info: 4883 FNWX S8.f 47411 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 861423795392857461754961832287695314419738526536142978925314687173586249648279153 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 # G4: 2,3 => SOL * DIS # G4: 9 => CTR => G4: 2,3 * PRF # G6: 3,9 => SOL * DIS # G6: 2 => CTR => G6: 3,9 * DIS # G4: 2,9 => CTR => G4: 3 * PRF # G4: 3 => SOL * PRF # G6: 2,9 => SOL * DIS # G6: 3 => CTR => G6: 2,9 * DIS # G4: 2,9 => CTR => G4: 3 * PRF # G4: 3 => SOL * PRF # G6: 2,9 => SOL * DIS # G6: 3 => CTR => G6: 2,9 * DIS # G4: 2,9 => CTR => G4: 3 * PRF # G4: 3 => SOL * PRF # G6: 2,9 => SOL * DIS # G6: 3 => CTR => G6: 2,9 * CNT 16 HDP CHAINS / 16 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # G4: 2,3 => SOL * STA G4: 2,3 * CNT 1 HDP CHAINS / 1 HYP OPENED