Analysis of xx-top500-352-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

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
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

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

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
Solution

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