Analysis of xx-top500-148-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .5.....1....2..4...........43....2.....5.1.6.....7....2.....3......3..5...7.....8 initial

Autosolve

position: .524.381717.25843.843.1752.431...2757285419635..3721842.57.4391..4.3.7523.7.25648 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # E4: 6,9 => SOL
* DIS # E4: 8 => CTR => E4: 6,9
* DIS # D4: 6,9 => CTR => D4: 8
* PRF # D4: 8 => SOL
* DIS # D4: 6,9 => CTR => D4: 8
* PRF # D4: 8 => SOL
* PRF # E4: 6,9 => SOL
* DIS # E4: 8 => CTR => E4: 6,9
* PRF # E4: 6,8 => SOL
* DIS # E4: 9 => CTR => E4: 6,8
* CNT  10 HDP CHAINS /  10 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 # E4: 6,9 => SOL
* STA E4: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

.5.....1....2..4...........43....2.....5.1.6.....7....2.....3......3..5...7.....8 initial
.524.381717.25843.843.1752.431...2757285419635..3721842.57.4391..4.3.7523.7.25648 autosolve
652493817179258436843617529431869275728541963596372184265784391984136752317925648 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (17)
A1: 6,9
C2: 6,9
E1: 6,9
D3: 6,9
I2: 6,9
I3: 6,9
B6: 6,9
C6: 6,9
F4: 6,9
B7: 6,8
A8: 6,9
B8: 1,8
B9: 1,9
E7: 6,8
D8: 1,8
F8: 6,9
D9: 1,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B8,B9: 1.. / B8 = 1  =>  0 pairs (X) / B9 = 1  =>  0 pairs (_)
D8,D9: 1.. / D8 = 1  =>  0 pairs (*) / D9 = 1  =>  0 pairs (X)
B8,D8: 1.. / B8 = 1  =>  0 pairs (X) / D8 = 1  =>  0 pairs (_)
B9,D9: 1.. / B9 = 1  =>  0 pairs (*) / D9 = 1  =>  0 pairs (X)
A1,C2: 6.. / A1 = 6  =>  0 pairs (*) / C2 = 6  =>  0 pairs (X)
E1,D3: 6.. / E1 = 6  =>  0 pairs (X) / D3 = 6  =>  0 pairs (_)
I2,I3: 6.. / I2 = 6  =>  0 pairs (*) / I3 = 6  =>  0 pairs (X)
B6,C6: 6.. / B6 = 6  =>  0 pairs (X) / C6 = 6  =>  0 pairs (_)
B7,A8: 6.. / B7 = 6  =>  0 pairs (*) / A8 = 6  =>  0 pairs (X)
E7,F8: 6.. / E7 = 6  =>  0 pairs (X) / F8 = 6  =>  0 pairs (_)
A1,E1: 6.. / A1 = 6  =>  0 pairs (*) / E1 = 6  =>  0 pairs (X)
C2,I2: 6.. / C2 = 6  =>  0 pairs (X) / I2 = 6  =>  0 pairs (_)
D3,I3: 6.. / D3 = 6  =>  0 pairs (*) / I3 = 6  =>  0 pairs (X)
B7,E7: 6.. / B7 = 6  =>  0 pairs (*) / E7 = 6  =>  0 pairs (X)
A8,F8: 6.. / A8 = 6  =>  0 pairs (X) / F8 = 6  =>  0 pairs (_)
A1,A8: 6.. / A1 = 6  =>  0 pairs (*) / A8 = 6  =>  0 pairs (X)
B6,B7: 6.. / B6 = 6  =>  0 pairs (X) / B7 = 6  =>  0 pairs (_)
C2,C6: 6.. / C2 = 6  =>  0 pairs (X) / C6 = 6  =>  0 pairs (_)
D3,D4: 6.. / D3 = 6  =>  0 pairs (*) / D4 = 6  =>  0 pairs (X)
F4,F8: 6.. / F4 = 6  =>  0 pairs (X) / F8 = 6  =>  0 pairs (_)
D4,E4: 8.. / D4 = 8  =>  0 pairs (*) / E4 = 8  =>  0 pairs (X)
B7,B8: 8.. / B7 = 8  =>  0 pairs (X) / B8 = 8  =>  0 pairs (_)
E7,D8: 8.. / E7 = 8  =>  0 pairs (*) / D8 = 8  =>  0 pairs (X)
B7,E7: 8.. / B7 = 8  =>  0 pairs (X) / E7 = 8  =>  0 pairs (_)
B8,D8: 8.. / B8 = 8  =>  0 pairs (*) / D8 = 8  =>  0 pairs (X)
D4,D8: 8.. / D4 = 8  =>  0 pairs (*) / D8 = 8  =>  0 pairs (X)
E4,E7: 8.. / E4 = 8  =>  0 pairs (X) / E7 = 8  =>  0 pairs (_)
A1,C2: 9.. / A1 = 9  =>  0 pairs (X) / C2 = 9  =>  0 pairs (_)
E1,D3: 9.. / E1 = 9  =>  0 pairs (*) / D3 = 9  =>  0 pairs (X)
I2,I3: 9.. / I2 = 9  =>  0 pairs (X) / I3 = 9  =>  0 pairs (_)
B6,C6: 9.. / B6 = 9  =>  0 pairs (*) / C6 = 9  =>  0 pairs (X)
A8,B9: 9.. / A8 = 9  =>  0 pairs (*) / B9 = 9  =>  0 pairs (X)
F8,D9: 9.. / F8 = 9  =>  0 pairs (X) / D9 = 9  =>  0 pairs (_)
A1,E1: 9.. / A1 = 9  =>  0 pairs (X) / E1 = 9  =>  0 pairs (_)
C2,I2: 9.. / C2 = 9  =>  0 pairs (*) / I2 = 9  =>  0 pairs (X)
D3,I3: 9.. / D3 = 9  =>  0 pairs (X) / I3 = 9  =>  0 pairs (_)
A8,F8: 9.. / A8 = 9  =>  0 pairs (*) / F8 = 9  =>  0 pairs (X)
B9,D9: 9.. / B9 = 9  =>  0 pairs (X) / D9 = 9  =>  0 pairs (_)
A1,A8: 9.. / A1 = 9  =>  0 pairs (X) / A8 = 9  =>  0 pairs (_)
B6,B9: 9.. / B6 = 9  =>  0 pairs (*) / B9 = 9  =>  0 pairs (X)
C2,C6: 9.. / C2 = 9  =>  0 pairs (*) / C6 = 9  =>  0 pairs (X)
E1,E4: 9.. / E1 = 9  =>  0 pairs (*) / E4 = 9  =>  0 pairs (X)
F4,F8: 9.. / F4 = 9  =>  0 pairs (*) / F8 = 9  =>  0 pairs (X)
* DURATION: 0:01:11.816571  START: 07:48:29.878405  END: 07:49:41.694976 2017-05-04
* CP COUNT: (43)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A8,B6,B7,B8,B9,C2,C6,D3,D8,D9,E1,E7,F4,F8,I2,I3)
* .524.381717.25843.843.1752.431...2757285419635..3721842.57.4391..4.3.7523.7.25648
* PAIR E1: 6,9 COL E
E4: 6,9,8                                # reduction candidate for 6,9
E4: 6,9 => SOLVED
* 652493817179258436843617529431869275728541963596372184265784391984136752317925648
E4: 8 => CTR
* .52493817179258436843617529431.862757285419635963721842.57.4391..4.3.7523.7.25648
* PAIR D3: 6,9 COL D
D4: 6,9,8                                # reduction candidate for 6,9
D4: 6,9 => CTR
* .524.381717.25843.843.1752.431.8.2757285419635..372184285764391614839752397125648
D4: 8 => SOLVED
* 652493817179258436843617529431869275728541963596372184265784391984136752317925648
* PAIR F4: 6,9 BLK 5
D4: 6,9,8                                # reduction candidate for 6,9
D4: 6,9 => CTR
* .524.381717.25843.843.1752.431.8.2757285419635..372184285764391614839752397125648
D4: 8 => SOLVED
* 652493817179258436843617529431869275728541963596372184265784391984136752317925648
E4: 6,9,8                                # reduction candidate for 6,9
E4: 6,9 => SOLVED
* 652493817179258436843617529431869275728541963596372184265784391984136752317925648
E4: 8 => CTR
* .52493817179258436843617529431.862757285419635963721842.57.4391..4.3.7523.7.25648
* PAIR E7: 6,8 COL E
E4: 6,8,9                                # reduction candidate for 6,8
E4: 6,8 => SOLVED
* 652493817179258436843617529431869275728541963596372184265784391984136752317925648
E4: 9 => CTR
* .524.381717.25843.843.1752.4318962757285419635..3721842.57.4391..4.3.7523.7.25648
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-148-base-pr-000.dot
* REASONING
* PRF # E4: 6,9 => SOL
* DIS # E4: 8 => CTR => E4: 6,9
* DIS # D4: 6,9 => CTR => D4: 8
* PRF # D4: 8 => SOL
* DIS # D4: 6,9 => CTR => D4: 8
* PRF # D4: 8 => SOL
* PRF # E4: 6,9 => SOL
* DIS # E4: 8 => CTR => E4: 6,9
* PRF # E4: 6,8 => SOL
* DIS # E4: 9 => CTR => E4: 6,8
* CNT  10 HDP CHAINS /  10 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A8,B6,B7,B8,B9,C2,C6,D3,D8,D9,E1,E7,F4,F8,I2,I3)
* .524.381717.25843.843.1752.431...2757285419635..3721842.57.4391..4.3.7523.7.25648
* PAIR E1: 6,9 COL E
E4: 6,9,8                                # reduction candidate for 6,9
E4: 6,9 => SOLVED
* 652493817179258436843617529431869275728541963596372184265784391984136752317925648
* DURATION: 0:00:01.912057  START: 07:49:54.827011  END: 07:49:56.739068 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-148-base-pr-001.dot
* REASONING
* PRF # E4: 6,9 => SOL
* STA E4: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 148

solution: 652493817179258436843617529431869275728541963596372184265784391984136752317925648
info: 1815     FNTWX    S8.f     47281

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

Solution

position: 652493817179258436843617529431869275728541963596372184265784391984136752317925648 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 # E4: 6,9 => SOL
* DIS # E4: 8 => CTR => E4: 6,9
* DIS # D4: 6,9 => CTR => D4: 8
* PRF # D4: 8 => SOL
* DIS # D4: 6,9 => CTR => D4: 8
* PRF # D4: 8 => SOL
* PRF # E4: 6,9 => SOL
* DIS # E4: 8 => CTR => E4: 6,9
* PRF # E4: 6,8 => SOL
* DIS # E4: 9 => CTR => E4: 6,8
* CNT  10 HDP CHAINS /  10 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # E4: 6,9 => SOL
* STA E4: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED