Analysis of xx-top500-142-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 26..8.....5......7.......1.4.1...2.....75....7.........38...........48.....1..... initial

Autosolve

position: 267.814..15.24..8784...7.124918..275386752194725419368.38.25741.12.748...741.8.2. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D3: 3,9 => CTR => D3: 5,6
* PRF # D3: 5,6 => SOL
* PRF # E3: 3,9 => SOL
* DIS # E3: 6 => CTR => E3: 3,9
* DIS # D3: 5,9 => CTR => D3: 3,6
* PRF # D3: 3,6 => SOL
* PRF # D3: 3,6 => SOL
* DIS # D3: 5,9 => CTR => D3: 3,6
* DIS # E3: 3,6 => CTR => E3: 9
* PRF # E3: 9 => SOL
* DIS # I8: 3,9 => CTR => I8: 6
* PRF # I8: 6 => SOL
* PRF # I9: 3,9 => SOL
* DIS # I9: 6 => CTR => I9: 3,9
* DIS # G3: 6,9 => CTR => G3: 5
* PRF # G3: 5 => SOL
* DIS # E3: 3,6 => CTR => E3: 9
* PRF # E3: 9 => SOL
* PRF # E9: 3,6 => SOL
* DIS # E9: 9 => CTR => E9: 3,6
* PRF # A8: 6,9 => SOL
* DIS # A8: 5 => CTR => A8: 6,9
* DIS # A9: 6,9 => CTR => A9: 5
* PRF # A9: 5 => SOL
* DIS # D8: 6,9 => CTR => D8: 3
* PRF # D8: 3 => SOL
* PRF # E9: 6,9 => SOL
* DIS # E9: 3 => CTR => E9: 6,9
* PRF # D3: 6,9 => SOL
* PRF # A9: 5,9 => SOL
* DIS # A9: 6 => CTR => A9: 5,9
* PRF # G3: 5,9 => SOL
* DIS # G3: 6 => CTR => G3: 5,9
* CNT  33 HDP CHAINS /  34 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # D3: 3,9 => CTR => D3: 5,6
* PRF D3: 5,6 => SOL
* STA D3: 5,6
* CNT   2 HDP CHAINS /   1 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

26..8.....5......7.......1.4.1...2.....75....7.........38...........48.....1..... initial
267.814..15.24..8784...7.124918..275386752194725419368.38.25741.12.748...741.8.2. autosolve
267581439159243687843697512491836275386752194725419368638925741912374856574168923 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
C2: 3,9
C3: 3,9
D1: 5,9
F2: 3,6
H1: 3,5
I1: 3,9
G2: 6,9
E4: 3,6
F4: 3,6
A7: 6,9
D7: 6,9
H8: 3,5
G9: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C2,C3: 3.. / C2 = 3  =>  0 pairs (X) / C3 = 3  =>  0 pairs (_)
H1,I1: 3.. / H1 = 3  =>  0 pairs (*) / I1 = 3  =>  0 pairs (X)
E4,F4: 3.. / E4 = 3  =>  0 pairs (*) / F4 = 3  =>  0 pairs (X)
D8,E9: 3.. / D8 = 3  =>  0 pairs (*) / E9 = 3  =>  0 pairs (X)
C2,F2: 3.. / C2 = 3  =>  0 pairs (X) / F2 = 3  =>  0 pairs (_)
E9,I9: 3.. / E9 = 3  =>  0 pairs (X) / I9 = 3  =>  0 pairs (_)
D3,D8: 3.. / D3 = 3  =>  0 pairs (X) / D8 = 3  =>  0 pairs (_)
F2,F4: 3.. / F2 = 3  =>  0 pairs (*) / F4 = 3  =>  0 pairs (X)
H1,H8: 3.. / H1 = 3  =>  0 pairs (*) / H8 = 3  =>  0 pairs (X)
D1,D3: 5.. / D1 = 5  =>  0 pairs (*) / D3 = 5  =>  0 pairs (X)
H1,G3: 5.. / H1 = 5  =>  0 pairs (X) / G3 = 5  =>  0 pairs (_)
A8,A9: 5.. / A8 = 5  =>  0 pairs (X) / A9 = 5  =>  0 pairs (_)
H8,G9: 5.. / H8 = 5  =>  0 pairs (*) / G9 = 5  =>  0 pairs (X)
D1,H1: 5.. / D1 = 5  =>  0 pairs (*) / H1 = 5  =>  0 pairs (X)
D3,G3: 5.. / D3 = 5  =>  0 pairs (X) / G3 = 5  =>  0 pairs (_)
A8,H8: 5.. / A8 = 5  =>  0 pairs (X) / H8 = 5  =>  0 pairs (_)
A9,G9: 5.. / A9 = 5  =>  0 pairs (*) / G9 = 5  =>  0 pairs (X)
G3,G9: 5.. / G3 = 5  =>  0 pairs (*) / G9 = 5  =>  0 pairs (X)
H1,H8: 5.. / H1 = 5  =>  0 pairs (X) / H8 = 5  =>  0 pairs (_)
G2,G3: 6.. / G2 = 6  =>  0 pairs (*) / G3 = 6  =>  0 pairs (X)
E4,F4: 6.. / E4 = 6  =>  0 pairs (X) / F4 = 6  =>  0 pairs (_)
I8,I9: 6.. / I8 = 6  =>  0 pairs (*) / I9 = 6  =>  0 pairs (X)
F2,G2: 6.. / F2 = 6  =>  0 pairs (X) / G2 = 6  =>  0 pairs (_)
A7,D7: 6.. / A7 = 6  =>  0 pairs (*) / D7 = 6  =>  0 pairs (X)
F2,F4: 6.. / F2 = 6  =>  0 pairs (X) / F4 = 6  =>  0 pairs (_)
C2,C3: 9.. / C2 = 9  =>  0 pairs (*) / C3 = 9  =>  0 pairs (X)
D1,I1: 9.. / D1 = 9  =>  0 pairs (X) / I1 = 9  =>  0 pairs (_)
C2,G2: 9.. / C2 = 9  =>  0 pairs (*) / G2 = 9  =>  0 pairs (X)
A7,D7: 9.. / A7 = 9  => 15 pairs (_) / D7 = 9  =>  0 pairs (*)
E3,E9: 9.. / E3 = 9  =>  0 pairs (*) / E9 = 9  =>  0 pairs (X)
* DURATION: 0:00:49.815979  START: 07:35:40.944932  END: 07:36:30.760911 2017-05-04
* CP COUNT: (30)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,C2,C3,D1,D7,E4,F2,F4,G2,G9,H1,H8,I1)
* 267.814..15.24..8784...7.124918..275386752194725419368.38.25741.12.748...741.8.2.
* PAIR C3: 3,9 ROW 3
D3: 3,9,5,6                              # reduction candidate for 3,9
D3: 3,9 => CTR
* 267581439159243687843967512491836275386752194725419368938625741.12374856.741.8.2.
D3: 5,6 => SOLVED
* 267581439159243687843697512491836275386752194725419368638925741912374856574168923
E3: 3,9,6                                # reduction candidate for 3,9
E3: 3,9 => SOLVED
* 267581439159243687843697512491836275386752194725419368638925741912374856574168923
E3: 6 => CTR
* 267.814..15.24..8784..67.12491836275386752194725419368.38.25741.1237485.574198.2.
* PAIR D1: 5,9 BLK 2
D3: 5,9,3,6                              # reduction candidate for 5,9
D3: 5,9 => CTR
* 267.814..15.24..8784...7.124918..275386752194725419368.38.25741.1237485.5741.8923
D3: 3,6 => SOLVED
* 267581439159243687843697512491836275386752194725419368638925741912374856574168923
* PAIR F2: 3,6 BLK 2
D3: 3,6,5,9                              # reduction candidate for 3,6
D3: 3,6 => SOLVED
* 267581439159243687843697512491836275386752194725419368638925741912374856574168923
D3: 5,9 => CTR
* 267.814..15.24..8784...7.124918..275386752194725419368.38.25741.1237485.5741.8923
E3: 3,6,9                                # reduction candidate for 3,6
E3: 3,6 => CTR
* 267.814..15.24..8784...7.124918..275386752194725419368.38.25741.12.748...74198523
E3: 9 => SOLVED
* 267581439159243687843697512491836275386752194725419368638925741912374856574168923
* PAIR I1: 3,9 COL I
I8: 3,9,6                                # reduction candidate for 3,9
I8: 3,9 => CTR
* 267.814..15.24..8784.397.124918..275386752194725419368.38.25741.12.748...74138.26
I8: 6 => SOLVED
* 267581439159243687843697512491836275386752194725419368638925741912374856574168923
I9: 3,9,6                                # reduction candidate for 3,9
I9: 3,9 => SOLVED
* 267581439159243687843697512491836275386752194725419368638925741912374856574168923
I9: 6 => CTR
* 267.814..15.24..8784.397.124918..275386752194725419368.38.25741.12.748...74138.26
* PAIR G2: 6,9 BLK 3
G3: 6,9,5                                # reduction candidate for 6,9
G3: 6,9 => CTR
* 267.8145315.24..8784.5.7.124918..275386752194725419368.38.257415123748...741.8.2.
G3: 5 => SOLVED
* 267581439159243687843697512491836275386752194725419368638925741912374856574168923
* PAIR E4: 3,6 COL E
E3: 3,6,9                                # reduction candidate for 3,6
E3: 3,6 => CTR
* 267.814..15.24..8784...7.124918..275386752194725419368.38.25741.12.748...74198523
E3: 9 => SOLVED
* 267581439159243687843697512491836275386752194725419368638925741912374856574168923
E9: 3,6,9                                # reduction candidate for 3,6
E9: 3,6 => SOLVED
* 267581439159243687843697512491836275386752194725419368638925741912374856574168923
E9: 9 => CTR
* 267.814..15.24..8784...7.124918..275386752194725419368.38.25741.1237485.574198.2.
* PAIR A7: 6,9 BLK 7
A8: 6,9,5                                # reduction candidate for 6,9
A8: 6,9 => SOLVED
* 267581439159243687843697512491836275386752194725419368638925741912374856574168923
A8: 5 => CTR
* 267.814..15.24..8784...7.124918..275386752194725419368.38.25741512.7483..7413852.
A9: 6,9,5                                # reduction candidate for 6,9
A9: 6,9 => CTR
* 267.814..15.24..8784...7.124918..275386752194725419368.38.25741512.7483..7413852.
A9: 5 => SOLVED
* 267581439159243687843697512491836275386752194725419368638925741912374856574168923
* PAIR D7: 6,9 BLK 8
D8: 6,9,3                                # reduction candidate for 6,9
D8: 6,9 => CTR
* 267.814..15.24..8784.3.75124918.3275386752194725419368.38.25741.12.74853574138926
D8: 3 => SOLVED
* 267581439159243687843697512491836275386752194725419368638925741912374856574168923
E9: 6,9,3                                # reduction candidate for 6,9
E9: 6,9 => SOLVED
* 267581439159243687843697512491836275386752194725419368638925741912374856574168923
E9: 3 => CTR
* 267.814..15.24..8784..97.12491863275386752194725419368.38.25741.12.748...74138.2.
* PAIR D7: 6,9 COL D
D3: 6,9,3,5                              # reduction candidate for 6,9
D3: 6,9 => SOLVED
* 267581439159243687843697512491836275386752194725419368638925741912374856574168923
D3: 3,5                                  # 15 pairs
* PAIR G9: 5,9 ROW 9
A9: 5,9,6                                # reduction candidate for 5,9
A9: 5,9 => SOLVED
* 267581439159243687843697512491836275386752194725419368638925741912374856574168923
A9: 6 => CTR
* 267.814..15.24..8784...7.124918..275386752194725419368.38.25741512.7483.674138529
* PAIR G9: 5,9 COL G
G3: 5,9,6                                # reduction candidate for 5,9
G3: 5,9 => SOLVED
* 267581439159243687843697512491836275386752194725419368638925741912374856574168923
G3: 6 => CTR
* 267.8145315.24.987849537.124918..275386752194725419368.38.25741.12.748...741.8.2.
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-142-base-pr-000.dot
* REASONING
* DIS # D3: 3,9 => CTR => D3: 5,6
* PRF # D3: 5,6 => SOL
* PRF # E3: 3,9 => SOL
* DIS # E3: 6 => CTR => E3: 3,9
* DIS # D3: 5,9 => CTR => D3: 3,6
* PRF # D3: 3,6 => SOL
* PRF # D3: 3,6 => SOL
* DIS # D3: 5,9 => CTR => D3: 3,6
* DIS # E3: 3,6 => CTR => E3: 9
* PRF # E3: 9 => SOL
* DIS # I8: 3,9 => CTR => I8: 6
* PRF # I8: 6 => SOL
* PRF # I9: 3,9 => SOL
* DIS # I9: 6 => CTR => I9: 3,9
* DIS # G3: 6,9 => CTR => G3: 5
* PRF # G3: 5 => SOL
* DIS # E3: 3,6 => CTR => E3: 9
* PRF # E3: 9 => SOL
* PRF # E9: 3,6 => SOL
* DIS # E9: 9 => CTR => E9: 3,6
* PRF # A8: 6,9 => SOL
* DIS # A8: 5 => CTR => A8: 6,9
* DIS # A9: 6,9 => CTR => A9: 5
* PRF # A9: 5 => SOL
* DIS # D8: 6,9 => CTR => D8: 3
* PRF # D8: 3 => SOL
* PRF # E9: 6,9 => SOL
* DIS # E9: 3 => CTR => E9: 6,9
* PRF # D3: 6,9 => SOL
* PRF # A9: 5,9 => SOL
* DIS # A9: 6 => CTR => A9: 5,9
* PRF # G3: 5,9 => SOL
* DIS # G3: 6 => CTR => G3: 5,9
* CNT  33 HDP CHAINS /  34 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,C2,C3,D1,D7,E4,F2,F4,G2,G9,H1,H8,I1)
* 267.814..15.24..8784...7.124918..275386752194725419368.38.25741.12.748...741.8.2.
* PAIR C3: 3,9 ROW 3
D3: 3,9,5,6                              # reduction candidate for 3,9
D3: 3,9 => CTR
* 267581439159243687843967512491836275386752194725419368938625741.12374856.741.8.2.
D3: 5,6 => SOLVED
* 267581439159243687843697512491836275386752194725419368638925741912374856574168923
* DURATION: 0:00:02.357328  START: 07:37:11.630017  END: 07:37:13.987345 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-142-base-pr-001.dot
* REASONING
* DIS # D3: 3,9 => CTR => D3: 5,6
* PRF D3: 5,6 => SOL
* STA D3: 5,6
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 142

solution: 267581439159243687843697512491836275386752194725419368638925741912374856574168923
info: 1814     FNBWY    S8.f     28499

http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/

Solution

position: 267581439159243687843697512491836275386752194725419368638925741912374856574168923 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:

* DIS # D3: 3,9 => CTR => D3: 5,6
* PRF # D3: 5,6 => SOL
* PRF # E3: 3,9 => SOL
* DIS # E3: 6 => CTR => E3: 3,9
* DIS # D3: 5,9 => CTR => D3: 3,6
* PRF # D3: 3,6 => SOL
* PRF # D3: 3,6 => SOL
* DIS # D3: 5,9 => CTR => D3: 3,6
* DIS # E3: 3,6 => CTR => E3: 9
* PRF # E3: 9 => SOL
* DIS # I8: 3,9 => CTR => I8: 6
* PRF # I8: 6 => SOL
* PRF # I9: 3,9 => SOL
* DIS # I9: 6 => CTR => I9: 3,9
* DIS # G3: 6,9 => CTR => G3: 5
* PRF # G3: 5 => SOL
* DIS # E3: 3,6 => CTR => E3: 9
* PRF # E3: 9 => SOL
* PRF # E9: 3,6 => SOL
* DIS # E9: 9 => CTR => E9: 3,6
* PRF # A8: 6,9 => SOL
* DIS # A8: 5 => CTR => A8: 6,9
* DIS # A9: 6,9 => CTR => A9: 5
* PRF # A9: 5 => SOL
* DIS # D8: 6,9 => CTR => D8: 3
* PRF # D8: 3 => SOL
* PRF # E9: 6,9 => SOL
* DIS # E9: 3 => CTR => E9: 6,9
* PRF # D3: 6,9 => SOL
* INC # D3: 3,5 => UNS
* PRF # A9: 5,9 => SOL
* DIS # A9: 6 => CTR => A9: 5,9
* PRF # G3: 5,9 => SOL
* DIS # G3: 6 => CTR => G3: 5,9
* CNT  34 HDP CHAINS /  34 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # D3: 3,9 => CTR => D3: 5,6
* PRF D3: 5,6 => SOL
* STA D3: 5,6
* CNT   2 HDP CHAINS /   1 HYP OPENED