Analysis of xx-top500-163-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 7..5....4...1..3......7....61.....7....3....8.....2.......1.25.4.3............... initial

Autosolve

position: 72.53.814..512.3.713..7.5.26128459735..3916283..762145...41325.4.325.781251.8743. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B2: 6,9 => CTR => B2: 4,8
* PRF # B2: 4,8 => SOL
* DIS # C7: 6,9 => CTR => C7: 7,8
* PRF # C7: 7,8 => SOL
* DIS # B2: 8,9 => CTR => B2: 4,6
* PRF # B2: 4,8 => SOL
* DIS # B2: 6,9 => CTR => B2: 4,8
* PRF # B2: 4,8 => SOL
* DIS # B2: 6,9 => CTR => B2: 4,8
* DIS # B2: 6,9 => CTR => B2: 4,8
* PRF # B2: 4,8 => SOL
* DIS # B2: 8,9 => CTR => B2: 4,6
* DIS # B7: 8,9 => CTR => B7: 6,7
* DIS # C7: 8,9 => CTR => C7: 6,7
* DIS # B7: 8,9 => CTR => B7: 6,7
* DIS # C7: 8,9 => CTR => C7: 6,7
* PRF # B7: 6,9 => SOL
* DIS # C7: 6,9 => CTR => C7: 7,8
* PRF # C7: 7,8 => SOL
* DIS # B2: 6,9 => CTR => B2: 4,8
* PRF # B2: 4,8 => SOL
* PRF # B7: 6,9 => SOL
* DIS # C7: 6,9 => CTR => C7: 7,8
* PRF # C7: 7,8 => SOL
* CNT  24 HDP CHAINS /  32 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 # B2: 6,9 => CTR => B2: 4,8
* PRF B2: 4,8 => SOL
* STA B2: 4,8
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

7..5....4...1..3......7....61.....7....3....8.....2.......1.25.4.3............... initial
72.53.814..512.3.713..7.5.26128459735..3916283..762145...41325.4.325.781251.8743. autosolve
726539814945128367138674592612845973574391628389762145867413259493256781251987436 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (19)
C1: 6,9
A2: 8,9
C3: 4,8
F1: 6,9
F2: 4,8
D3: 6,9
F3: 4,8
H2: 6,9
H3: 6,9
B5: 4,7
C5: 4,7
B6: 8,9
C6: 8,9
A7: 8,9
B8: 6,9
F8: 6,9
D9: 6,9
I7: 6,9
I9: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B2,C3: 4.. / B2 = 4  =>  0 pairs (*) / C3 = 4  =>  0 pairs (X)
F2,F3: 4.. / F2 = 4  => 14 pairs (_) / F3 = 4  =>  0 pairs (*)
B5,C5: 4.. / B5 = 4  => 14 pairs (_) / C5 = 4  =>  0 pairs (*)
B2,F2: 4.. / B2 = 4  =>  0 pairs (*) / F2 = 4  =>  0 pairs (X)
C3,F3: 4.. / C3 = 4  => 14 pairs (_) / F3 = 4  =>  0 pairs (*)
B2,B5: 4.. / B2 = 4  =>  0 pairs (*) / B5 = 4  =>  0 pairs (X)
C3,C5: 4.. / C3 = 4  => 14 pairs (_) / C5 = 4  =>  0 pairs (*)
C1,B2: 6.. / C1 = 6  =>  0 pairs (*) / B2 = 6  =>  0 pairs (X)
F1,D3: 6.. / F1 = 6  =>  0 pairs (X) / D3 = 6  =>  0 pairs (_)
H2,H3: 6.. / H2 = 6  =>  0 pairs (*) / H3 = 6  =>  0 pairs (X)
F8,D9: 6.. / F8 = 6  =>  0 pairs (*) / D9 = 6  =>  0 pairs (X)
I7,I9: 6.. / I7 = 6  =>  0 pairs (X) / I9 = 6  =>  0 pairs (_)
C1,F1: 6.. / C1 = 6  =>  0 pairs (*) / F1 = 6  =>  0 pairs (X)
B2,H2: 6.. / B2 = 6  =>  0 pairs (X) / H2 = 6  =>  0 pairs (_)
D3,H3: 6.. / D3 = 6  =>  0 pairs (*) / H3 = 6  =>  0 pairs (X)
B8,F8: 6.. / B8 = 6  =>  0 pairs (X) / F8 = 6  =>  0 pairs (_)
D9,I9: 6.. / D9 = 6  =>  0 pairs (X) / I9 = 6  =>  0 pairs (_)
C1,C7: 6.. / C1 = 6  =>  0 pairs (*) / C7 = 6  =>  0 pairs (X)
D3,D9: 6.. / D3 = 6  =>  0 pairs (*) / D9 = 6  =>  0 pairs (X)
F1,F8: 6.. / F1 = 6  =>  0 pairs (X) / F8 = 6  =>  0 pairs (_)
B5,C5: 7.. / B5 = 7  =>  0 pairs (*) / C5 = 7  =>  0 pairs (X)
B7,C7: 7.. / B7 = 7  => 14 pairs (_) / C7 = 7  =>  0 pairs (*)
B5,B7: 7.. / B5 = 7  =>  0 pairs (*) / B7 = 7  =>  0 pairs (X)
C5,C7: 7.. / C5 = 7  => 14 pairs (_) / C7 = 7  =>  0 pairs (*)
F2,F3: 8.. / F2 = 8  =>  0 pairs (*) / F3 = 8  =>  0 pairs (X)
B6,C6: 8.. / B6 = 8  =>  0 pairs (*) / C6 = 8  =>  0 pairs (X)
C3,F3: 8.. / C3 = 8  =>  0 pairs (*) / F3 = 8  =>  0 pairs (X)
A2,A7: 8.. / A2 = 8  =>  0 pairs (X) / A7 = 8  =>  0 pairs (_)
F1,D3: 9.. / F1 = 9  =>  0 pairs (*) / D3 = 9  =>  0 pairs (X)
H2,H3: 9.. / H2 = 9  =>  0 pairs (X) / H3 = 9  =>  0 pairs (_)
B6,C6: 9.. / B6 = 9  =>  0 pairs (X) / C6 = 9  =>  0 pairs (_)
F8,D9: 9.. / F8 = 9  =>  0 pairs (X) / D9 = 9  =>  0 pairs (_)
I7,I9: 9.. / I7 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
C1,F1: 9.. / C1 = 9  =>  0 pairs (X) / F1 = 9  =>  0 pairs (_)
D3,H3: 9.. / D3 = 9  =>  0 pairs (X) / H3 = 9  =>  0 pairs (_)
B8,F8: 9.. / B8 = 9  =>  0 pairs (*) / F8 = 9  =>  0 pairs (X)
D9,I9: 9.. / D9 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
A2,A7: 9.. / A2 = 9  =>  0 pairs (*) / A7 = 9  =>  0 pairs (X)
D3,D9: 9.. / D3 = 9  =>  0 pairs (X) / D9 = 9  =>  0 pairs (_)
F1,F8: 9.. / F1 = 9  =>  0 pairs (*) / F8 = 9  =>  0 pairs (X)
* DURATION: 0:01:08.763876  START: 08:19:06.068829  END: 08:20:14.832705 2017-05-04
* CP COUNT: (40)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B5,B6,B8,C1,C3,C5,C6,D3,D9,F1,F2,F3,F8,H2,H3,I7,I9)
* 72.53.814..512.3.713..7.5.26128459735..3916283..762145...41325.4.325.781251.8743.
* PAIR C1: 6,9 BLK 1
B2: 6,9,4,8                              # reduction candidate for 6,9
B2: 6,9 => CTR
* 72.53.8148.51243.7134.785.2612845973547391628389762145978413256463259781251.8743.
B2: 4,8 => SOLVED
* 726539814945128367138674592612845973574391628389762145867413259493256781251987436
* PAIR C1: 6,9 COL C
C7: 6,9,7,8                              # reduction candidate for 6,9
C7: 6,9 => CTR
* 72.53.8149851243671346785926128459735473916283987621458794132564.325.781251.8743.
C7: 7,8 => SOLVED
* 726539814945128367138674592612845973574391628389762145867413259493256781251987436
* PAIR A2: 8,9 BLK 1
B2: 8,9,4,6                              # reduction candidate for 8,9
B2: 8,9 => CTR
* 726539814..51243671346785926128459735473916283..762145.7.4132564.325.781251.8743.
B2: 4,6                                  # 20 pairs
* PAIR C3: 4,8 BLK 1
B2: 4,8,6,9                              # reduction candidate for 4,8
B2: 4,8 => SOLVED
* 726539814945128367138674592612845973574391628389762145867413259493256781251987436
B2: 6,9 => CTR
* 72.53.8148.51243.7134.785.2612845973547391628389762145978413256463259781251.8743.
* PAIR F2: 4,8 ROW 2
B2: 4,8,6,9                              # reduction candidate for 4,8
B2: 4,8 => SOLVED
* 726539814945128367138674592612845973574391628389762145867413259493256781251987436
B2: 6,9 => CTR
* 72.53.8148.51243.7134.785.2612845973547391628389762145978413256463259781251.8743.
* PAIR H2: 6,9 ROW 2
B2: 6,9,4,8                              # reduction candidate for 6,9
B2: 6,9 => CTR
* 72.53.8148.51243.7134.785.2612845973547391628389762145978413256463259781251.8743.
B2: 4,8 => SOLVED
* 726539814945128367138674592612845973574391628389762145867413259493256781251987436
* PAIR B6: 8,9 COL B
B2: 8,9,4,6                              # reduction candidate for 8,9
B2: 8,9 => CTR
* 726539814..51243671346785926128459735473916283..762145.7.4132564.325.781251.8743.
B2: 4,6                                  # 20 pairs
B7: 8,9,6,7                              # reduction candidate for 8,9
B7: 8,9 => CTR
* 72.53.814..512.3.713..7.5.26128459735743916283..762145..7413256463259781251687439
B7: 6,7                                  # 20 pairs
* PAIR C6: 8,9 COL C
C7: 8,9,6,7                              # reduction candidate for 8,9
C7: 8,9 => CTR
* 726539814..512.36713.67.5926128459735.73916283..762145.7.4132564.325.781251.8743.
C7: 6,7                                  # 20 pairs
* PAIR A7: 8,9 BLK 7
B7: 8,9,6,7                              # reduction candidate for 8,9
B7: 8,9 => CTR
* 72.53.814..512.3.713..7.5.26128459735743916283..762145..7413256463259781251687439
B7: 6,7                                  # 20 pairs
C7: 8,9,6,7                              # reduction candidate for 8,9
C7: 8,9 => CTR
* 726539814..512.36713.67.5926128459735.73916283..762145.7.4132564.325.781251.8743.
C7: 6,7                                  # 20 pairs
* PAIR B8: 6,9 BLK 7
B7: 6,9,7,8                              # reduction candidate for 6,9
B7: 6,9 => SOLVED
* 726539814945128367138674592612845973574391628389762145867413259493256781251987436
B7: 7,8                                  # 20 pairs
C7: 6,9,7,8                              # reduction candidate for 6,9
C7: 6,9 => CTR
* 72.53.8149851243671346785926128459735473916283987621458794132564.325.781251.8743.
C7: 7,8 => SOLVED
* 726539814945128367138674592612845973574391628389762145867413259493256781251987436
* PAIR B8: 6,9 COL B
B2: 6,9,4,8                              # reduction candidate for 6,9
B2: 6,9 => CTR
* 72.53.8148.51243.7134.785.2612845973547391628389762145978413256463259781251.8743.
B2: 4,8 => SOLVED
* 726539814945128367138674592612845973574391628389762145867413259493256781251987436
* PAIR I7: 6,9 ROW 7
B7: 6,9,7,8                              # reduction candidate for 6,9
B7: 6,9 => SOLVED
* 726539814945128367138674592612845973574391628389762145867413259493256781251987436
B7: 7,8                                  # 20 pairs
C7: 6,9,7,8                              # reduction candidate for 6,9
C7: 6,9 => CTR
* 72.53.8149851243671346785926128459735473916283987621458794132564.325.781251.8743.
C7: 7,8 => SOLVED
* 726539814945128367138674592612845973574391628389762145867413259493256781251987436
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-163-base-pr-000.dot
* REASONING
* DIS # B2: 6,9 => CTR => B2: 4,8
* PRF # B2: 4,8 => SOL
* DIS # C7: 6,9 => CTR => C7: 7,8
* PRF # C7: 7,8 => SOL
* DIS # B2: 8,9 => CTR => B2: 4,6
* PRF # B2: 4,8 => SOL
* DIS # B2: 6,9 => CTR => B2: 4,8
* PRF # B2: 4,8 => SOL
* DIS # B2: 6,9 => CTR => B2: 4,8
* DIS # B2: 6,9 => CTR => B2: 4,8
* PRF # B2: 4,8 => SOL
* DIS # B2: 8,9 => CTR => B2: 4,6
* DIS # B7: 8,9 => CTR => B7: 6,7
* DIS # C7: 8,9 => CTR => C7: 6,7
* DIS # B7: 8,9 => CTR => B7: 6,7
* DIS # C7: 8,9 => CTR => C7: 6,7
* PRF # B7: 6,9 => SOL
* DIS # C7: 6,9 => CTR => C7: 7,8
* PRF # C7: 7,8 => SOL
* DIS # B2: 6,9 => CTR => B2: 4,8
* PRF # B2: 4,8 => SOL
* PRF # B7: 6,9 => SOL
* DIS # C7: 6,9 => CTR => C7: 7,8
* PRF # C7: 7,8 => SOL
* CNT  24 HDP CHAINS /  32 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B5,B6,B8,C1,C3,C5,C6,D3,D9,F1,F2,F3,F8,H2,H3,I7,I9)
* 72.53.814..512.3.713..7.5.26128459735..3916283..762145...41325.4.325.781251.8743.
* PAIR C1: 6,9 BLK 1
B2: 6,9,4,8                              # reduction candidate for 6,9
B2: 6,9 => CTR
* 72.53.8148.51243.7134.785.2612845973547391628389762145978413256463259781251.8743.
B2: 4,8 => SOLVED
* 726539814945128367138674592612845973574391628389762145867413259493256781251987436
* DURATION: 0:00:03.080462  START: 08:20:51.361767  END: 08:20:54.442229 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-163-base-pr-001.dot
* REASONING
* DIS # B2: 6,9 => CTR => B2: 4,8
* PRF B2: 4,8 => SOL
* STA B2: 4,8
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 163

solution: 726539814945128367138674592612845973574391628389762145867413259493256781251987436
info: 1821     FNTWX    S8.f     37007

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

Solution

position: 726539814945128367138674592612845973574391628389762145867413259493256781251987436 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 # B2: 6,9 => CTR => B2: 4,8
* PRF # B2: 4,8 => SOL
* DIS # C7: 6,9 => CTR => C7: 7,8
* PRF # C7: 7,8 => SOL
* DIS # B2: 8,9 => CTR => B2: 4,6
* INC # B2: 4,6 => UNS
* PRF # B2: 4,8 => SOL
* DIS # B2: 6,9 => CTR => B2: 4,8
* PRF # B2: 4,8 => SOL
* DIS # B2: 6,9 => CTR => B2: 4,8
* DIS # B2: 6,9 => CTR => B2: 4,8
* PRF # B2: 4,8 => SOL
* DIS # B2: 8,9 => CTR => B2: 4,6
* INC # B2: 4,6 => UNS
* DIS # B7: 8,9 => CTR => B7: 6,7
* INC # B7: 6,7 => UNS
* DIS # C7: 8,9 => CTR => C7: 6,7
* INC # C7: 6,7 => UNS
* DIS # B7: 8,9 => CTR => B7: 6,7
* INC # B7: 6,7 => UNS
* DIS # C7: 8,9 => CTR => C7: 6,7
* INC # C7: 6,7 => UNS
* PRF # B7: 6,9 => SOL
* INC # B7: 7,8 => UNS
* DIS # C7: 6,9 => CTR => C7: 7,8
* PRF # C7: 7,8 => SOL
* DIS # B2: 6,9 => CTR => B2: 4,8
* PRF # B2: 4,8 => SOL
* PRF # B7: 6,9 => SOL
* INC # B7: 7,8 => UNS
* DIS # C7: 6,9 => CTR => C7: 7,8
* PRF # C7: 7,8 => SOL
* CNT  32 HDP CHAINS /  32 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B2: 6,9 => CTR => B2: 4,8
* PRF B2: 4,8 => SOL
* STA B2: 4,8
* CNT   2 HDP CHAINS /   1 HYP OPENED