Analysis of xx-top500-174-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .1.6........43.....5.......2.....57.4..3.........8.1..3......4.....5.7.......2... initial

Autosolve

position: .1467523.7.2438.51.532194.7281964573475321....3.58712432719684514.8537.25.874231. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # I5: 8,9 => SOL
* DIS # I5: 6 => CTR => I5: 8,9
* PRF # H5: 6,8 => SOL
* DIS # H5: 9 => CTR => H5: 6,8
* DIS # H5: 6,9 => CTR => H5: 8
* PRF # H5: 8 => SOL
* PRF # I5: 6,9 => SOL
* DIS # I5: 8 => CTR => I5: 6,9
* DIS # H5: 6,9 => CTR => H5: 8
* PRF # H5: 8 => SOL
* PRF # I5: 6,9 => SOL
* DIS # I5: 8 => CTR => I5: 6,9
* CNT  12 HDP CHAINS /  12 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 # I5: 8,9 => SOL
* STA I5: 8,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

.1.6........43.....5.......2.....57.4..3.........8.1..3......4.....5.7.......2... initial
.1467523.7.2438.51.532194.7281964573475321....3.58712432719684514.8537.25.874231. autosolve
914675238762438951853219467281964573475321689639587124327196845146853792598742316 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
A1: 8,9
B2: 6,9
A3: 6,8
I1: 8,9
G2: 6,9
H3: 6,8
A6: 6,9
C6: 6,9
G5: 6,9
C8: 6,9
B9: 6,9
H8: 6,9
I9: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B2,A3: 6.. / B2 = 6  =>  0 pairs (*) / A3 = 6  =>  0 pairs (X)
G2,H3: 6.. / G2 = 6  =>  0 pairs (X) / H3 = 6  =>  0 pairs (_)
A6,C6: 6.. / A6 = 6  =>  0 pairs (*) / C6 = 6  =>  0 pairs (X)
C8,B9: 6.. / C8 = 6  =>  0 pairs (*) / B9 = 6  =>  0 pairs (X)
H8,I9: 6.. / H8 = 6  =>  0 pairs (X) / I9 = 6  =>  0 pairs (_)
B2,G2: 6.. / B2 = 6  =>  0 pairs (*) / G2 = 6  =>  0 pairs (X)
A3,H3: 6.. / A3 = 6  =>  0 pairs (X) / H3 = 6  =>  0 pairs (_)
C8,H8: 6.. / C8 = 6  =>  0 pairs (*) / H8 = 6  =>  0 pairs (X)
B9,I9: 6.. / B9 = 6  =>  0 pairs (X) / I9 = 6  =>  0 pairs (_)
A3,A6: 6.. / A3 = 6  =>  0 pairs (X) / A6 = 6  =>  0 pairs (_)
B2,B9: 6.. / B2 = 6  =>  0 pairs (*) / B9 = 6  =>  0 pairs (X)
C6,C8: 6.. / C6 = 6  =>  0 pairs (X) / C8 = 6  =>  0 pairs (_)
G2,G5: 6.. / G2 = 6  =>  0 pairs (X) / G5 = 6  =>  0 pairs (_)
I5,I9: 6.. / I5 = 6  =>  0 pairs (X) / I9 = 6  =>  0 pairs (_)
A1,A3: 8.. / A1 = 8  =>  0 pairs (X) / A3 = 8  =>  0 pairs (_)
I1,H3: 8.. / I1 = 8  =>  0 pairs (*) / H3 = 8  =>  0 pairs (X)
H5,I5: 8.. / H5 = 8  =>  0 pairs (*) / I5 = 8  =>  0 pairs (X)
A1,I1: 8.. / A1 = 8  =>  0 pairs (X) / I1 = 8  =>  0 pairs (_)
A3,H3: 8.. / A3 = 8  =>  0 pairs (*) / H3 = 8  =>  0 pairs (X)
H3,H5: 8.. / H3 = 8  =>  0 pairs (X) / H5 = 8  =>  0 pairs (_)
I1,I5: 8.. / I1 = 8  =>  0 pairs (*) / I5 = 8  =>  0 pairs (X)
A1,B2: 9.. / A1 = 9  =>  0 pairs (*) / B2 = 9  =>  0 pairs (X)
I1,G2: 9.. / I1 = 9  =>  0 pairs (X) / G2 = 9  =>  0 pairs (_)
A6,C6: 9.. / A6 = 9  =>  0 pairs (X) / C6 = 9  =>  0 pairs (_)
C8,B9: 9.. / C8 = 9  =>  0 pairs (X) / B9 = 9  =>  0 pairs (_)
H8,I9: 9.. / H8 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
A1,I1: 9.. / A1 = 9  =>  0 pairs (*) / I1 = 9  =>  0 pairs (X)
B2,G2: 9.. / B2 = 9  =>  0 pairs (X) / G2 = 9  =>  0 pairs (_)
C8,H8: 9.. / C8 = 9  =>  0 pairs (X) / H8 = 9  =>  0 pairs (_)
B9,I9: 9.. / B9 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
A1,A6: 9.. / A1 = 9  =>  0 pairs (*) / A6 = 9  =>  0 pairs (X)
B2,B9: 9.. / B2 = 9  =>  0 pairs (X) / B9 = 9  =>  0 pairs (_)
C6,C8: 9.. / C6 = 9  =>  0 pairs (*) / C8 = 9  =>  0 pairs (X)
G2,G5: 9.. / G2 = 9  =>  0 pairs (*) / G5 = 9  =>  0 pairs (X)
H5,H8: 9.. / H5 = 9  =>  0 pairs (X) / H8 = 9  =>  0 pairs (_)
* DURATION: 0:01:11.091269  START: 08:39:37.992923  END: 08:40:49.084192 2017-05-04
* CP COUNT: (35)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A6,B2,B9,C6,C8,G2,G5,H3,H8,I1,I9)
* .1467523.7.2438.51.532194.7281964573475321....3.58712432719684514.8537.25.874231.
* PAIR I1: 8,9 COL I
I5: 8,9,6                                # reduction candidate for 8,9
I5: 8,9 => SOLVED
* 914675238762438951853219467281964573475321689639587124327196845146853792598742316
I5: 6 => CTR
* .146752387.2438951853219467281964573475321....3.58712432719684514.8537.25.874231.
* PAIR H3: 6,8 COL H
H5: 6,8,9                                # reduction candidate for 6,8
H5: 6,8 => SOLVED
* 914675238762438951853219467281964573475321689639587124327196845146853792598742316
H5: 9 => CTR
* .1467523.7.2438.51.53219487281964573475321.98.3.5871243271968451498537625.874231.
* PAIR G5: 6,9 BLK 6
H5: 6,9,8                                # reduction candidate for 6,9
H5: 6,9 => CTR
* 8146752397.2438.51.53219487281964573475321..8.3.58712432719684514.8537.25.8742316
H5: 8 => SOLVED
* 914675238762438951853219467281964573475321689639587124327196845146853792598742316
I5: 6,9,8                                # reduction candidate for 6,9
I5: 6,9 => SOLVED
* 914675238762438951853219467281964573475321689639587124327196845146853792598742316
I5: 8 => CTR
* 8146752397.2438.51.532194.7281964573475321..8.3.58712432719684514.8537.25.8742316
* PAIR H8: 6,9 COL H
H5: 6,9,8                                # reduction candidate for 6,9
H5: 6,9 => CTR
* 8146752397.2438.51.53219487281964573475321..8.3.58712432719684514.8537.25.8742316
H5: 8 => SOLVED
* 914675238762438951853219467281964573475321689639587124327196845146853792598742316
* PAIR I9: 6,9 COL I
I5: 6,9,8                                # reduction candidate for 6,9
I5: 6,9 => SOLVED
* 914675238762438951853219467281964573475321689639587124327196845146853792598742316
I5: 8 => CTR
* 8146752397.2438.51.532194.7281964573475321..8.3.58712432719684514.8537.25.8742316
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-174-base-pr-000.dot
* REASONING
* PRF # I5: 8,9 => SOL
* DIS # I5: 6 => CTR => I5: 8,9
* PRF # H5: 6,8 => SOL
* DIS # H5: 9 => CTR => H5: 6,8
* DIS # H5: 6,9 => CTR => H5: 8
* PRF # H5: 8 => SOL
* PRF # I5: 6,9 => SOL
* DIS # I5: 8 => CTR => I5: 6,9
* DIS # H5: 6,9 => CTR => H5: 8
* PRF # H5: 8 => SOL
* PRF # I5: 6,9 => SOL
* DIS # I5: 8 => CTR => I5: 6,9
* CNT  12 HDP CHAINS /  12 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A6,B2,B9,C6,C8,G2,G5,H3,H8,I1,I9)
* .1467523.7.2438.51.532194.7281964573475321....3.58712432719684514.8537.25.874231.
* PAIR I1: 8,9 COL I
I5: 8,9,6                                # reduction candidate for 8,9
I5: 8,9 => SOLVED
* 914675238762438951853219467281964573475321689639587124327196845146853792598742316
* DURATION: 0:00:02.114851  START: 08:41:06.629953  END: 08:41:08.744804 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-174-base-pr-001.dot
* REASONING
* PRF # I5: 8,9 => SOL
* STA I5: 8,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 174

solution: 914675238762438951853219467281964573475321689639587124327196845146853792598742316
info: 1827     FNTWX    S8.f     15651

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

Solution

position: 914675238762438951853219467281964573475321689639587124327196845146853792598742316 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 # I5: 8,9 => SOL
* DIS # I5: 6 => CTR => I5: 8,9
* PRF # H5: 6,8 => SOL
* DIS # H5: 9 => CTR => H5: 6,8
* DIS # H5: 6,9 => CTR => H5: 8
* PRF # H5: 8 => SOL
* PRF # I5: 6,9 => SOL
* DIS # I5: 8 => CTR => I5: 6,9
* DIS # H5: 6,9 => CTR => H5: 8
* PRF # H5: 8 => SOL
* PRF # I5: 6,9 => SOL
* DIS # I5: 8 => CTR => I5: 6,9
* CNT  12 HDP CHAINS /  12 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # I5: 8,9 => SOL
* STA I5: 8,9
* CNT   1 HDP CHAINS /   1 HYP OPENED