Analysis of xx-top500-179-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .7...3....4..8..........6..6..5..1......7..4...1......5..6.1..........73...2..... initial

Autosolve

position: 276413...345986712.1.7..6346345.81.7.5.17.3467.1364...5.76314..16.84..734.32.7.61 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C5: 8,9 => CTR => C5: 2
* PRF # C5: 2 => SOL
* PRF # G6: 8,9 => SOL
* DIS # G6: 2 => CTR => G6: 8,9
* DIS # G9: 8,9 => CTR => G9: 5
* PRF # G9: 5 => SOL
* DIS # C5: 8,9 => CTR => C5: 2
* PRF # C5: 2 => SOL
* DIS # C5: 8 => CTR => C5: 2,9
* PRF # H6: 2,9 => SOL
* DIS # B7: 8 => CTR => B7: 2,9
* DIS # C5: 8 => CTR => C5: 2,9
* PRF # H6: 2,9 => SOL
* PRF # H7: 8 => SOL
* DIS # B7: 8 => CTR => B7: 2,9
* PRF # G8: 2,9 => SOL
* DIS # G8: 5 => CTR => G8: 2,9
* DIS # C5: 8 => CTR => C5: 2,9
* DIS # B7: 8,9 => CTR => B7: 2
* PRF # B7: 2 => SOL
* DIS # G9: 8,9 => CTR => G9: 5
* PRF # G9: 5 => SOL
* DIS # G8: 5,9 => CTR => G8: 2
* PRF # G8: 2 => SOL
* DIS # G9: 8 => CTR => G9: 5,9
* PRF # H7: 8,9 => SOL
* DIS # H7: 2 => CTR => H7: 8,9
* DIS # G9: 8,9 => CTR => G9: 5
* PRF # G9: 5 => SOL
* DIS # B7: 8,9 => CTR => B7: 2
* PRF # B7: 2 => SOL
* CNT  31 HDP CHAINS /  46 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 # C5: 8,9 => CTR => C5: 2
* PRF C5: 2 => SOL
* STA C5: 2
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

.7...3....4..8..........6..6..5..1......7..4...1......5..6.1..........73...2..... initial
276413...345986712.1.7..6346345.81.7.5.17.3467.1364...5.76314..16.84..734.32.7.61 autosolve
276413958345986712918752634634528197852179346791364825527631489169845273483297561 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
A3: 8,9
C3: 8,9
E3: 2,5
F3: 2,5
G1: 8,9
A5: 8,9
B6: 2,9
E4: 2,9
F5: 2,9
H4: 2,9
C8: 2,9
B9: 8,9
F8: 5,9
E9: 5,9
I7: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E3,F3: 2.. / E3 = 2  =>  0 pairs (X) / F3 = 2  =>  0 pairs (_)
C5,B6: 2.. / C5 = 2  =>  0 pairs (*) / B6 = 2  =>  0 pairs (X)
E4,F5: 2.. / E4 = 2  =>  0 pairs (*) / F5 = 2  =>  0 pairs (X)
B7,C8: 2.. / B7 = 2  =>  0 pairs (*) / C8 = 2  =>  0 pairs (X)
H7,G8: 2.. / H7 = 2  =>  0 pairs (X) / G8 = 2  =>  0 pairs (_)
E4,H4: 2.. / E4 = 2  =>  0 pairs (*) / H4 = 2  =>  0 pairs (X)
C5,F5: 2.. / C5 = 2  =>  0 pairs (*) / F5 = 2  =>  0 pairs (X)
B7,H7: 2.. / B7 = 2  =>  0 pairs (*) / H7 = 2  =>  0 pairs (X)
C8,G8: 2.. / C8 = 2  =>  0 pairs (X) / G8 = 2  =>  0 pairs (_)
B6,B7: 2.. / B6 = 2  =>  0 pairs (X) / B7 = 2  =>  0 pairs (_)
C5,C8: 2.. / C5 = 2  =>  0 pairs (*) / C8 = 2  =>  0 pairs (X)
E3,E4: 2.. / E3 = 2  =>  0 pairs (X) / E4 = 2  =>  0 pairs (_)
F3,F5: 2.. / F3 = 2  =>  0 pairs (*) / F5 = 2  =>  0 pairs (X)
G6,G8: 2.. / G6 = 2  =>  0 pairs (X) / G8 = 2  =>  0 pairs (_)
E3,F3: 5.. / E3 = 5  =>  0 pairs (*) / F3 = 5  =>  0 pairs (X)
H1,I1: 5.. / H1 = 5  => 16 pairs (_) / I1 = 5  => 17 pairs (_)
H6,I6: 5.. / H6 = 5  => 17 pairs (_) / I6 = 5  => 16 pairs (_)
F8,E9: 5.. / F8 = 5  =>  0 pairs (*) / E9 = 5  =>  0 pairs (X)
G8,G9: 5.. / G8 = 5  =>  0 pairs (X) / G9 = 5  =>  0 pairs (_)
F8,G8: 5.. / F8 = 5  =>  0 pairs (*) / G8 = 5  =>  0 pairs (X)
E9,G9: 5.. / E9 = 5  =>  0 pairs (X) / G9 = 5  =>  0 pairs (_)
E3,E9: 5.. / E3 = 5  =>  0 pairs (*) / E9 = 5  =>  0 pairs (X)
F3,F8: 5.. / F3 = 5  =>  0 pairs (X) / F8 = 5  =>  0 pairs (_)
H1,H6: 5.. / H1 = 5  => 16 pairs (_) / H6 = 5  => 17 pairs (_)
I1,I6: 5.. / I1 = 5  => 17 pairs (_) / I6 = 5  => 16 pairs (_)
A3,C3: 8.. / A3 = 8  =>  0 pairs (X) / C3 = 8  => 13 pairs (_)
A5,C5: 8.. / A5 = 8  => 13 pairs (_) / C5 = 8  =>  0 pairs (X)
B7,B9: 8.. / B7 = 8  =>  0 pairs (X) / B9 = 8  => 16 pairs (_)
B9,G9: 8.. / B9 = 8  => 16 pairs (_) / G9 = 8  =>  0 pairs (X)
A3,A5: 8.. / A3 = 8  =>  0 pairs (X) / A5 = 8  => 13 pairs (_)
C3,C5: 8.. / C3 = 8  => 13 pairs (_) / C5 = 8  =>  0 pairs (X)
A3,C3: 9.. / A3 = 9  => 13 pairs (_) / C3 = 9  =>  0 pairs (X)
E4,F5: 9.. / E4 = 9  =>  0 pairs (X) / F5 = 9  =>  0 pairs (_)
F8,E9: 9.. / F8 = 9  =>  0 pairs (X) / E9 = 9  =>  0 pairs (_)
E4,H4: 9.. / E4 = 9  =>  0 pairs (X) / H4 = 9  =>  0 pairs (_)
A3,A5: 9.. / A3 = 9  => 13 pairs (_) / A5 = 9  =>  0 pairs (X)
E4,E9: 9.. / E4 = 9  =>  0 pairs (X) / E9 = 9  =>  0 pairs (_)
F5,F8: 9.. / F5 = 9  =>  0 pairs (*) / F8 = 9  =>  0 pairs (X)
* DURATION: 0:01:12.543254  START: 08:48:41.082655  END: 08:49:53.625909 2017-05-04
* CP COUNT: (38)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,B6,B9,C3,C8,E3,E4,E9,F3,F5,F8,G1,H4,I7)
* 276413...345986712.1.7..6346345.81.7.5.17.3467.1364...5.76314..16.84..734.32.7.61
* PAIR C3: 8,9 COL C
C5: 8,9,2                                # reduction candidate for 8,9
C5: 8,9 => CTR
* 276413...345986712.1.7..6346345.81.7.5.172346721364...5.763142.1628495734.3257.61
C5: 2 => SOLVED
* 276413958345986712918752634634528197852179346791364825527631489169845273483297561
* PAIR G1: 8,9 BLK 3
H1: 8,9,5                                # reduction candidate for 8,9
H1: 8,9                                  # 17 pairs
I1: 8,9,5                                # reduction candidate for 8,9
I1: 8,9                                  # 16 pairs
* PAIR G1: 8,9 COL G
G6: 8,9,2                                # reduction candidate for 8,9
G6: 8,9 => SOLVED
* 276413958345986712918752634634528197852179346791364825527631489169845273483297561
G6: 2 => CTR
* 276413...345986712.1.7..6346345.81.7.5.17.3467.13642..5276314..169845.734.32.7.61
G9: 8,9,5                                # reduction candidate for 8,9
G9: 8,9 => CTR
* 276413...345986712.1.725634634598127.5.172346721364...5.76314..1628495734.3257.61
G9: 5 => SOLVED
* 276413958345986712918752634634528197852179346791364825527631489169845273483297561
* PAIR A5: 8,9 BLK 4
C5: 8,9,2                                # reduction candidate for 8,9
C5: 8,9 => CTR
* 276413...345986712.1.7..6346345.81.7.5.172346721364...5.763142.1628495734.3257.61
C5: 2 => SOLVED
* 276413958345986712918752634634528197852179346791364825527631489169845273483297561
* PAIR B6: 2,9 BLK 4
C5: 2,9,8                                # reduction candidate for 2,9
C5: 8 => CTR
* 276413...345986712.1.7..6346345.81.7.58172346721364...5.763142.1628495734.3257.61
C5: 2,9                                  # 13 pairs
* PAIR B6: 2,9 ROW 6
G6: 2,9,8                                # reduction candidate for 2,9
G6: 2,9                                  # 18 pairs
H6: 2,9,5,8                              # reduction candidate for 2,9
H6: 2,9 => SOLVED
* 276413958345986712918752634634528197852179346791364825527631489169845273483297561
H6: 5,8                                  # 16 pairs
* PAIR B6: 2,9 COL B
B7: 2,9,8                                # reduction candidate for 2,9
B7: 8 => CTR
* 276413...345986712.1.7..6346345.81.7.5.17.346721364...587631429162849573493257.61
B7: 2,9                                  # 16 pairs
* PAIR F5: 2,9 ROW 5
C5: 2,9,8                                # reduction candidate for 2,9
C5: 8 => CTR
* 276413...345986712.1.7..6346345.81.7.58172346721364...5.763142.1628495734.3257.61
C5: 2,9                                  # 13 pairs
* PAIR H4: 2,9 BLK 6
G6: 2,9,8                                # reduction candidate for 2,9
G6: 2,9                                  # 18 pairs
H6: 2,9,5,8                              # reduction candidate for 2,9
H6: 2,9 => SOLVED
* 276413958345986712918752634634528197852179346791364825527631489169845273483297561
H6: 5,8                                  # 16 pairs
* PAIR H4: 2,9 COL H
H7: 2,9,8                                # reduction candidate for 2,9
H7: 8 => SOLVED
* 276413958345986712918752634634528197852179346791364825527631489169845273483297561
H7: 2,9                                  # 18 pairs
* PAIR C8: 2,9 BLK 7
B7: 2,9,8                                # reduction candidate for 2,9
B7: 8 => CTR
* 276413...345986712.1.7..6346345.81.7.5.17.346721364...587631429162849573493257.61
B7: 2,9                                  # 16 pairs
* PAIR C8: 2,9 ROW 8
G8: 2,9,5                                # reduction candidate for 2,9
G8: 2,9 => SOLVED
* 276413958345986712918752634634528197852179346791364825527631489169845273483297561
G8: 5 => CTR
* 276413...345986712.1.7..6346345.81.7.5.17.3467.13642..5276314..169845.734.32.7.61
* PAIR C8: 2,9 COL C
C5: 2,9,8                                # reduction candidate for 2,9
C5: 8 => CTR
* 276413...345986712.1.7..6346345.81.7.58172346721364...5.763142.1628495734.3257.61
C5: 2,9                                  # 13 pairs
* PAIR B9: 8,9 BLK 7
B7: 8,9,2                                # reduction candidate for 8,9
B7: 8,9 => CTR
* 276413...345986712.1.7..6346345.81.7.5.17.346721364...5.763142.16284..734.32.7.61
B7: 2 => SOLVED
* 276413958345986712918752634634528197852179346791364825527631489169845273483297561
* PAIR B9: 8,9 ROW 9
G9: 8,9,5                                # reduction candidate for 8,9
G9: 8,9 => CTR
* 276413...345986712.1.725634634598127.5.172346721364...5.76314..1628495734.3257.61
G9: 5 => SOLVED
* 276413958345986712918752634634528197852179346791364825527631489169845273483297561
* PAIR F8: 5,9 ROW 8
G8: 5,9,2                                # reduction candidate for 5,9
G8: 5,9 => CTR
* 276413...345986712.1.7..6346345.81.7.5.17.3467.13642..5276314..169845.734.32.7.61
G8: 2 => SOLVED
* 276413958345986712918752634634528197852179346791364825527631489169845273483297561
* PAIR E9: 5,9 ROW 9
G9: 5,9,8                                # reduction candidate for 5,9
G9: 8 => CTR
* 2764139..345986712.1.725634634598127.5.17.3467.1364...5.76314..16.84.5734.3257861
G9: 5,9                                  # 16 pairs
* PAIR I7: 8,9 BLK 9
H7: 8,9,2                                # reduction candidate for 8,9
H7: 8,9 => SOLVED
* 276413958345986712918752634634528197852179346791364825527631489169845273483297561
H7: 2 => CTR
* 276413...345986712.1.7..634634528197.5.1793467.1364...5.763142.16284..734.32.7.61
G9: 8,9,5                                # reduction candidate for 8,9
G9: 8,9 => CTR
* 276413...345986712.1.725634634598127.5.172346721364...5.76314..1628495734.3257.61
G9: 5 => SOLVED
* 276413958345986712918752634634528197852179346791364825527631489169845273483297561
* PAIR I7: 8,9 ROW 7
B7: 8,9,2                                # reduction candidate for 8,9
B7: 8,9 => CTR
* 276413...345986712.1.7..6346345.81.7.5.17.346721364...5.763142.16284..734.32.7.61
B7: 2 => SOLVED
* 276413958345986712918752634634528197852179346791364825527631489169845273483297561
* PAIR I7: 8,9 COL I
I1: 8,9,5                                # reduction candidate for 8,9
I1: 8,9                                  # 16 pairs
I6: 8,9,5                                # reduction candidate for 8,9
I6: 8,9                                  # 17 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-179-base-pr-000.dot
* REASONING
* DIS # C5: 8,9 => CTR => C5: 2
* PRF # C5: 2 => SOL
* PRF # G6: 8,9 => SOL
* DIS # G6: 2 => CTR => G6: 8,9
* DIS # G9: 8,9 => CTR => G9: 5
* PRF # G9: 5 => SOL
* DIS # C5: 8,9 => CTR => C5: 2
* PRF # C5: 2 => SOL
* DIS # C5: 8 => CTR => C5: 2,9
* PRF # H6: 2,9 => SOL
* DIS # B7: 8 => CTR => B7: 2,9
* DIS # C5: 8 => CTR => C5: 2,9
* PRF # H6: 2,9 => SOL
* PRF # H7: 8 => SOL
* DIS # B7: 8 => CTR => B7: 2,9
* PRF # G8: 2,9 => SOL
* DIS # G8: 5 => CTR => G8: 2,9
* DIS # C5: 8 => CTR => C5: 2,9
* DIS # B7: 8,9 => CTR => B7: 2
* PRF # B7: 2 => SOL
* DIS # G9: 8,9 => CTR => G9: 5
* PRF # G9: 5 => SOL
* DIS # G8: 5,9 => CTR => G8: 2
* PRF # G8: 2 => SOL
* DIS # G9: 8 => CTR => G9: 5,9
* PRF # H7: 8,9 => SOL
* DIS # H7: 2 => CTR => H7: 8,9
* DIS # G9: 8,9 => CTR => G9: 5
* PRF # G9: 5 => SOL
* DIS # B7: 8,9 => CTR => B7: 2
* PRF # B7: 2 => SOL
* CNT  31 HDP CHAINS /  46 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,B6,B9,C3,C8,E3,E4,E9,F3,F5,F8,G1,H4,I7)
* 276413...345986712.1.7..6346345.81.7.5.17.3467.1364...5.76314..16.84..734.32.7.61
* PAIR C3: 8,9 COL C
C5: 8,9,2                                # reduction candidate for 8,9
C5: 8,9 => CTR
* 276413...345986712.1.7..6346345.81.7.5.172346721364...5.763142.1628495734.3257.61
C5: 2 => SOLVED
* 276413958345986712918752634634528197852179346791364825527631489169845273483297561
* DURATION: 0:00:03.173007  START: 08:50:47.807667  END: 08:50:50.980674 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-179-base-pr-001.dot
* REASONING
* DIS # C5: 8,9 => CTR => C5: 2
* PRF C5: 2 => SOL
* STA C5: 2
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 179

solution: 276413958345986712918752634634528197852179346791364825527631489169845273483297561
info: 1828     FNBWX    S8.f     22333

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

Solution

position: 276413958345986712918752634634528197852179346791364825527631489169845273483297561 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 # C5: 8,9 => CTR => C5: 2
* PRF # C5: 2 => SOL
* INC # H1: 8,9 => UNS
* INC # I1: 8,9 => UNS
* PRF # G6: 8,9 => SOL
* DIS # G6: 2 => CTR => G6: 8,9
* DIS # G9: 8,9 => CTR => G9: 5
* PRF # G9: 5 => SOL
* DIS # C5: 8,9 => CTR => C5: 2
* PRF # C5: 2 => SOL
* INC # C5: 2,9 => UNS
* DIS # C5: 8 => CTR => C5: 2,9
* INC # G6: 2,9 => UNS
* PRF # H6: 2,9 => SOL
* INC # H6: 5,8 => UNS
* INC # B7: 2,9 => UNS
* DIS # B7: 8 => CTR => B7: 2,9
* INC # C5: 2,9 => UNS
* DIS # C5: 8 => CTR => C5: 2,9
* INC # G6: 2,9 => UNS
* PRF # H6: 2,9 => SOL
* INC # H6: 5,8 => UNS
* INC # H7: 2,9 => UNS
* PRF # H7: 8 => SOL
* INC # B7: 2,9 => UNS
* DIS # B7: 8 => CTR => B7: 2,9
* PRF # G8: 2,9 => SOL
* DIS # G8: 5 => CTR => G8: 2,9
* INC # C5: 2,9 => UNS
* DIS # C5: 8 => CTR => C5: 2,9
* DIS # B7: 8,9 => CTR => B7: 2
* PRF # B7: 2 => SOL
* DIS # G9: 8,9 => CTR => G9: 5
* PRF # G9: 5 => SOL
* DIS # G8: 5,9 => CTR => G8: 2
* PRF # G8: 2 => SOL
* INC # G9: 5,9 => UNS
* DIS # G9: 8 => CTR => G9: 5,9
* PRF # H7: 8,9 => SOL
* DIS # H7: 2 => CTR => H7: 8,9
* DIS # G9: 8,9 => CTR => G9: 5
* PRF # G9: 5 => SOL
* DIS # B7: 8,9 => CTR => B7: 2
* PRF # B7: 2 => SOL
* INC # I1: 8,9 => UNS
* INC # I6: 8,9 => UNS
* CNT  46 HDP CHAINS /  46 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # C5: 8,9 => CTR => C5: 2
* PRF C5: 2 => SOL
* STA C5: 2
* CNT   2 HDP CHAINS /   1 HYP OPENED