Analysis of xx-top500-141-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .....48.....5.1...2............3.2...1....4...5.6.....3.1.4.......7...5.........6 initial

Autosolve

position: 1.526483..3.5.16242463.85.16..43.215.1385246.45261.3.8361945782..47.61535..1.3946 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A2: 7,9 => CTR => A2: 8
* PRF # A2: 8 => SOL
* PRF # C2: 7,9 => SOL
* DIS # C2: 8 => CTR => C2: 7,9
* DIS # B4: 7,9 => CTR => B4: 8
* DIS # A2: 7,9 => CTR => A2: 8
* PRF # A2: 8 => SOL
* PRF # C2: 7,9 => SOL
* DIS # C2: 8 => CTR => C2: 7,9
* DIS # B4: 7,9 => CTR => B4: 8
* DIS # A2: 7,9 => CTR => A2: 8
* PRF # A2: 8 => SOL
* DIS # B4: 7,9 => CTR => B4: 8
* PRF # B8: 2 => SOL
* PRF # A2: 8,9 => SOL
* DIS # A2: 7 => CTR => A2: 8,9
* PRF # B9: 7,8 => SOL
* PRF # C2: 7,8 => SOL
* DIS # C2: 9 => CTR => C2: 7,8
* DIS # C4: 7,8 => CTR => C4: 9
* PRF # C4: 9 => SOL
* PRF # B8: 2,8 => SOL
* DIS # B8: 9 => CTR => B8: 2,8
* PRF # B9: 7 => 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 # A2: 7,9 => CTR => A2: 8
* PRF A2: 8 => SOL
* STA A2: 8
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

.....48.....5.1...2............3.2...1....4...5.6.....3.1.4.......7...5.........6 initial
1.526483..3.5.16242463.85.16..43.215.1385246.45261.3.8361945782..47.61535..1.3946 autosolve
195264837837591624246378591689437215713852469452619378361945782924786153578123946 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
B1: 7,9
E2: 7,9
E3: 7,9
I1: 7,9
H3: 7,9
A5: 7,9
F4: 7,9
F6: 7,9
I5: 7,9
H6: 7,9
A8: 8,9
C9: 7,8
E8: 2,8
E9: 2,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B8,B9: 2.. / B8 = 2  =>  0 pairs (*) / B9 = 2  =>  0 pairs (X)
E8,E9: 2.. / E8 = 2  => 14 pairs (_) / E9 = 2  =>  0 pairs (*)
B8,E8: 2.. / B8 = 2  =>  0 pairs (*) / E8 = 2  =>  0 pairs (X)
B9,E9: 2.. / B9 = 2  => 14 pairs (_) / E9 = 2  =>  0 pairs (*)
E2,E3: 7.. / E2 = 7  =>  0 pairs (X) / E3 = 7  =>  0 pairs (_)
I1,H3: 7.. / I1 = 7  =>  0 pairs (*) / H3 = 7  =>  0 pairs (X)
F4,F6: 7.. / F4 = 7  =>  0 pairs (*) / F6 = 7  =>  0 pairs (X)
I5,H6: 7.. / I5 = 7  =>  0 pairs (X) / H6 = 7  =>  0 pairs (_)
B9,C9: 7.. / B9 = 7  =>  0 pairs (*) / C9 = 7  =>  0 pairs (X)
B1,I1: 7.. / B1 = 7  =>  0 pairs (X) / I1 = 7  =>  0 pairs (_)
E3,H3: 7.. / E3 = 7  =>  0 pairs (*) / H3 = 7  =>  0 pairs (X)
A5,I5: 7.. / A5 = 7  =>  0 pairs (*) / I5 = 7  =>  0 pairs (X)
F6,H6: 7.. / F6 = 7  =>  0 pairs (X) / H6 = 7  =>  0 pairs (_)
A2,A5: 7.. / A2 = 7  =>  0 pairs (X) / A5 = 7  =>  0 pairs (_)
H3,H6: 7.. / H3 = 7  =>  0 pairs (X) / H6 = 7  =>  0 pairs (_)
I1,I5: 7.. / I1 = 7  =>  0 pairs (*) / I5 = 7  =>  0 pairs (X)
A2,C2: 8.. / A2 = 8  =>  0 pairs (*) / C2 = 8  =>  0 pairs (X)
B4,C4: 8.. / B4 = 8  => 17 pairs (_) / C4 = 8  =>  0 pairs (X)
E8,E9: 8.. / E8 = 8  =>  0 pairs (*) / E9 = 8  =>  0 pairs (X)
A2,A8: 8.. / A2 = 8  =>  0 pairs (*) / A8 = 8  =>  0 pairs (X)
E2,E3: 9.. / E2 = 9  =>  0 pairs (*) / E3 = 9  =>  0 pairs (X)
I1,H3: 9.. / I1 = 9  =>  0 pairs (X) / H3 = 9  =>  0 pairs (_)
F4,F6: 9.. / F4 = 9  =>  0 pairs (X) / F6 = 9  =>  0 pairs (_)
I5,H6: 9.. / I5 = 9  =>  0 pairs (*) / H6 = 9  =>  0 pairs (X)
A8,B8: 9.. / A8 = 9  =>  0 pairs (*) / B8 = 9  =>  0 pairs (X)
B1,I1: 9.. / B1 = 9  =>  0 pairs (*) / I1 = 9  =>  0 pairs (X)
E3,H3: 9.. / E3 = 9  =>  0 pairs (X) / H3 = 9  =>  0 pairs (_)
A5,I5: 9.. / A5 = 9  =>  0 pairs (X) / I5 = 9  =>  0 pairs (_)
F6,H6: 9.. / F6 = 9  =>  0 pairs (*) / H6 = 9  =>  0 pairs (X)
C2,C4: 9.. / C2 = 9  =>  0 pairs (X) / C4 = 9  =>  0 pairs (_)
H3,H6: 9.. / H3 = 9  =>  0 pairs (*) / H6 = 9  =>  0 pairs (X)
I1,I5: 9.. / I1 = 9  =>  0 pairs (X) / I5 = 9  =>  0 pairs (_)
* DURATION: 0:00:56.259761  START: 07:33:49.147680  END: 07:34:45.407441 2017-05-04
* CP COUNT: (32)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B1,C9,E2,E3,E8,E9,F4,F6,H3,H6,I1,I5)
* 1.526483..3.5.16242463.85.16..43.215.1385246.45261.3.8361945782..47.61535..1.3946
* PAIR B1: 7,9 BLK 1
A2: 7,9,8                                # reduction candidate for 7,9
A2: 7,9 => CTR
* 1.526483..385.16242463.85.16894372157138524694526193783619457828947.61535..1.3946
A2: 8 => SOLVED
* 195264837837591624246378591689437215713852469452619378361945782924786153578123946
C2: 7,9,8                                # reduction candidate for 7,9
C2: 7,9 => SOLVED
* 195264837837591624246378591689437215713852469452619378361945782924786153578123946
C2: 8 => CTR
* 1.526483..385.16242463.85.16894372157138524694526193783619457828947.61535..1.3946
* PAIR B1: 7,9 COL B
B4: 7,9,8                                # reduction candidate for 7,9
B4: 7,9 => CTR
* 1.526483.8395716242463985716.843.21571385246945261.3.8361945782..47.61535.71.3946
B4: 8                                    # 17 pairs
* PAIR E2: 7,9 ROW 2
A2: 7,9,8                                # reduction candidate for 7,9
A2: 7,9 => CTR
* 1.526483..385.16242463.85.16894372157138524694526193783619457828947.61535..1.3946
A2: 8 => SOLVED
* 195264837837591624246378591689437215713852469452619378361945782924786153578123946
C2: 7,9,8                                # reduction candidate for 7,9
C2: 7,9 => SOLVED
* 195264837837591624246378591689437215713852469452619378361945782924786153578123946
C2: 8 => CTR
* 1.526483..385.16242463.85.16894372157138524694526193783619457828947.61535..1.3946
* PAIR A5: 7,9 BLK 4
B4: 7,9,8                                # reduction candidate for 7,9
B4: 7,9 => CTR
* 1.526483.8395716242463985716.843.21571385246945261.3.8361945782..47.61535.71.3946
B4: 8                                    # 17 pairs
C4: 7,9,8                                # reduction candidate for 7,9
C4: 7,9                                  # 17 pairs
* PAIR A5: 7,9 COL A
A2: 7,9,8                                # reduction candidate for 7,9
A2: 7,9 => CTR
* 1.526483..385.16242463.85.16894372157138524694526193783619457828947.61535..1.3946
A2: 8 => SOLVED
* 195264837837591624246378591689437215713852469452619378361945782924786153578123946
* PAIR F4: 7,9 ROW 4
B4: 7,9,8                                # reduction candidate for 7,9
B4: 7,9 => CTR
* 1.526483.8395716242463985716.843.21571385246945261.3.8361945782..47.61535.71.3946
B4: 8                                    # 17 pairs
C4: 7,9,8                                # reduction candidate for 7,9
C4: 7,9                                  # 17 pairs
* PAIR A8: 8,9 BLK 7
B8: 8,9,2                                # reduction candidate for 8,9
B8: 2 => SOLVED
* 195264837837591624246378591689437215713852469452619378361945782924786153578123946
B8: 8,9                                  # 14 pairs
* PAIR A8: 8,9 COL A
A2: 8,9,7                                # reduction candidate for 8,9
A2: 8,9 => SOLVED
* 195264837837591624246378591689437215713852469452619378361945782924786153578123946
A2: 7 => CTR
* 1.526483.73859162424637859168.43.215.1385246.45261.3.8361945782..47.61535..1.3946
* PAIR C9: 7,8 BLK 7
B9: 7,8,2                                # reduction candidate for 7,8
B9: 7,8 => SOLVED
* 195264837837591624246378591689437215713852469452619378361945782924786153578123946
B9: 2                                    # 14 pairs
* PAIR C9: 7,8 COL C
C2: 7,8,9                                # reduction candidate for 7,8
C2: 7,8 => SOLVED
* 195264837837591624246378591689437215713852469452619378361945782924786153578123946
C2: 9 => CTR
* 1.526483.8395716242463985716..43.21571385246945261.3.8361945782..47.61535..1.3946
C4: 7,8,9                                # reduction candidate for 7,8
C4: 7,8 => CTR
* 1.526483..395716242463985716..43.21571385246945261.3.8361945782..47.61535..1.3946
C4: 9 => SOLVED
* 195264837837591624246378591689437215713852469452619378361945782924786153578123946
* PAIR E8: 2,8 ROW 8
B8: 2,8,9                                # reduction candidate for 2,8
B8: 2,8 => SOLVED
* 195264837837591624246378591689437215713852469452619378361945782924786153578123946
B8: 9 => CTR
* 175264839.3.57162424639857168.43.215.1385246.45261.3.8361945782.94726153527183946
* PAIR E9: 2,8 ROW 9
B9: 2,8,7                                # reduction candidate for 2,8
B9: 7 => SOLVED
* 195264837837591624246378591689437215713852469452619378361945782924786153578123946
B9: 2,8                                  # 16 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-141-base-pr-000.dot
* REASONING
* DIS # A2: 7,9 => CTR => A2: 8
* PRF # A2: 8 => SOL
* PRF # C2: 7,9 => SOL
* DIS # C2: 8 => CTR => C2: 7,9
* DIS # B4: 7,9 => CTR => B4: 8
* DIS # A2: 7,9 => CTR => A2: 8
* PRF # A2: 8 => SOL
* PRF # C2: 7,9 => SOL
* DIS # C2: 8 => CTR => C2: 7,9
* DIS # B4: 7,9 => CTR => B4: 8
* DIS # A2: 7,9 => CTR => A2: 8
* PRF # A2: 8 => SOL
* DIS # B4: 7,9 => CTR => B4: 8
* PRF # B8: 2 => SOL
* PRF # A2: 8,9 => SOL
* DIS # A2: 7 => CTR => A2: 8,9
* PRF # B9: 7,8 => SOL
* PRF # C2: 7,8 => SOL
* DIS # C2: 9 => CTR => C2: 7,8
* DIS # C4: 7,8 => CTR => C4: 9
* PRF # C4: 9 => SOL
* PRF # B8: 2,8 => SOL
* DIS # B8: 9 => CTR => B8: 2,8
* PRF # B9: 7 => SOL
* CNT  24 HDP CHAINS /  32 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B1,C9,E2,E3,E8,E9,F4,F6,H3,H6,I1,I5)
* 1.526483..3.5.16242463.85.16..43.215.1385246.45261.3.8361945782..47.61535..1.3946
* PAIR B1: 7,9 BLK 1
A2: 7,9,8                                # reduction candidate for 7,9
A2: 7,9 => CTR
* 1.526483..385.16242463.85.16894372157138524694526193783619457828947.61535..1.3946
A2: 8 => SOLVED
* 195264837837591624246378591689437215713852469452619378361945782924786153578123946
* DURATION: 0:00:01.678434  START: 07:35:24.446127  END: 07:35:26.124561 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-141-base-pr-001.dot
* REASONING
* DIS # A2: 7,9 => CTR => A2: 8
* PRF A2: 8 => SOL
* STA A2: 8
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 141

solution: 195264837837591624246378591689437215713852469452619378361945782924786153578123946
info: 1813     FNBWX    S8.f     49017

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

Solution

position: 195264837837591624246378591689437215713852469452619378361945782924786153578123946 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 # A2: 7,9 => CTR => A2: 8
* PRF # A2: 8 => SOL
* PRF # C2: 7,9 => SOL
* DIS # C2: 8 => CTR => C2: 7,9
* DIS # B4: 7,9 => CTR => B4: 8
* INC # B4: 8 => UNS
* DIS # A2: 7,9 => CTR => A2: 8
* PRF # A2: 8 => SOL
* PRF # C2: 7,9 => SOL
* DIS # C2: 8 => CTR => C2: 7,9
* DIS # B4: 7,9 => CTR => B4: 8
* INC # B4: 8 => UNS
* INC # C4: 7,9 => UNS
* DIS # A2: 7,9 => CTR => A2: 8
* PRF # A2: 8 => SOL
* DIS # B4: 7,9 => CTR => B4: 8
* INC # B4: 8 => UNS
* INC # C4: 7,9 => UNS
* INC # B8: 8,9 => UNS
* PRF # B8: 2 => SOL
* PRF # A2: 8,9 => SOL
* DIS # A2: 7 => CTR => A2: 8,9
* PRF # B9: 7,8 => SOL
* INC # B9: 2 => UNS
* PRF # C2: 7,8 => SOL
* DIS # C2: 9 => CTR => C2: 7,8
* DIS # C4: 7,8 => CTR => C4: 9
* PRF # C4: 9 => SOL
* PRF # B8: 2,8 => SOL
* DIS # B8: 9 => CTR => B8: 2,8
* INC # B9: 2,8 => UNS
* PRF # B9: 7 => SOL
* CNT  32 HDP CHAINS /  32 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A2: 7,9 => CTR => A2: 8
* PRF A2: 8 => SOL
* STA A2: 8
* CNT   2 HDP CHAINS /   1 HYP OPENED