Analysis of xx-top500-137-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...8..4...67...................17.6.....6.5..4.........9.....718..4.5......2..... initial

Autosolve

position: 1..8.64.7.6714..58.4875.1.6.8..17.647...645824.6...71.5946..2718..4756..673291845 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # F3: 2,3 => SOL
* PRF # B1: 2,3 => SOL
* DIS # B1: 5 => CTR => B1: 2,3
* DIS # H1: 2,3 => CTR => H1: 9
* PRF # H1: 9 => SOL
* DIS # H3: 3,9 => CTR => H3: 2
* PRF # F2: 3,9 => SOL
* DIS # D6: 3,5 => CTR => D6: 9
* PRF # D6: 9 => SOL
* PRF # B1: 3,5 => SOL
* DIS # B1: 2 => CTR => B1: 3,5
* DIS # D4: 3,9 => CTR => D4: 5
* PRF # D4: 5 => SOL
* PRF # D6: 3,9 => SOL
* DIS # D6: 5 => CTR => D6: 3,9
* PRF # A4: 3,9 => SOL
* DIS # A4: 2 => CTR => A4: 3,9
* DIS # D4: 3,9 => CTR => D4: 5
* PRF # D4: 5 => SOL
* PRF # D6: 3,9 => SOL
* DIS # D6: 5 => CTR => D6: 3,9
* DIS # H3: 3,9 => CTR => H3: 2
* CNT  22 HDP CHAINS /  30 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 # F3: 2,3 => SOL
* STA F3: 2,3
* CNT   1 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

...8..4...67...................17.6.....6.5..4.........9.....718..4.5......2..... initial
1..8.64.7.6714..58.4875.1.6.8..17.647...645824.6...71.5946..2718..4756..673291845 autosolve
135826497267149358948753126382517964719364582456982713594638271821475639673291845 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
E1: 2,3
G2: 3,9
B5: 1,3
C5: 1,9
B6: 3,5
D5: 3,9
E6: 2,8
F6: 2,8
G4: 3,9
I6: 3,9
B8: 1,2
C8: 1,2
E7: 3,8
F7: 3,8
H8: 3,9
I8: 3,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B5,C5: 1.. / B5 = 1  =>  0 pairs (*) / C5 = 1  =>  0 pairs (X)
B8,C8: 1.. / B8 = 1  =>  0 pairs (X) / C8 = 1  =>  0 pairs (_)
B5,B8: 1.. / B5 = 1  =>  0 pairs (*) / B8 = 1  =>  0 pairs (X)
C5,C8: 1.. / C5 = 1  =>  0 pairs (X) / C8 = 1  =>  0 pairs (_)
H1,H3: 2.. / H1 = 2  =>  0 pairs (X) / H3 = 2  => 19 pairs (_)
A4,C4: 2.. / A4 = 2  =>  0 pairs (X) / C4 = 2  =>  0 pairs (_)
E6,F6: 2.. / E6 = 2  => 16 pairs (_) / F6 = 2  =>  0 pairs (*)
B8,C8: 2.. / B8 = 2  =>  0 pairs (*) / C8 = 2  =>  0 pairs (X)
A2,F2: 2.. / A2 = 2  =>  0 pairs (*) / F2 = 2  =>  0 pairs (X)
B1,B8: 2.. / B1 = 2  =>  0 pairs (X) / B8 = 2  =>  0 pairs (_)
E1,E6: 2.. / E1 = 2  =>  0 pairs (*) / E6 = 2  =>  0 pairs (X)
G4,I6: 3.. / G4 = 3  =>  0 pairs (X) / I6 = 3  =>  0 pairs (_)
E7,F7: 3.. / E7 = 3  =>  0 pairs (*) / F7 = 3  =>  0 pairs (X)
H8,I8: 3.. / H8 = 3  =>  0 pairs (*) / I8 = 3  =>  0 pairs (X)
B5,D5: 3.. / B5 = 3  =>  0 pairs (X) / D5 = 3  =>  0 pairs (_)
E1,E7: 3.. / E1 = 3  => 16 pairs (_) / E7 = 3  =>  0 pairs (*)
G2,G4: 3.. / G2 = 3  =>  0 pairs (*) / G4 = 3  =>  0 pairs (X)
I6,I8: 3.. / I6 = 3  =>  0 pairs (*) / I8 = 3  =>  0 pairs (X)
B1,C1: 5.. / B1 = 5  =>  0 pairs (X) / C1 = 5  =>  0 pairs (_)
C4,B6: 5.. / C4 = 5  =>  0 pairs (X) / B6 = 5  =>  0 pairs (_)
D4,D6: 5.. / D4 = 5  =>  0 pairs (*) / D6 = 5  =>  0 pairs (X)
C4,D4: 5.. / C4 = 5  =>  0 pairs (X) / D4 = 5  =>  0 pairs (_)
B6,D6: 5.. / B6 = 5  =>  0 pairs (*) / D6 = 5  =>  0 pairs (X)
B1,B6: 5.. / B1 = 5  =>  0 pairs (X) / B6 = 5  =>  0 pairs (_)
C1,C4: 5.. / C1 = 5  =>  0 pairs (*) / C4 = 5  =>  0 pairs (X)
E6,F6: 8.. / E6 = 8  =>  0 pairs (*) / F6 = 8  =>  0 pairs (X)
E7,F7: 8.. / E7 = 8  => 16 pairs (_) / F7 = 8  =>  0 pairs (*)
E6,E7: 8.. / E6 = 8  =>  0 pairs (*) / E7 = 8  =>  0 pairs (X)
F6,F7: 8.. / F6 = 8  => 16 pairs (_) / F7 = 8  =>  0 pairs (*)
F2,F3: 9.. / F2 = 9  =>  0 pairs (*) / F3 = 9  =>  0 pairs (X)
G4,I6: 9.. / G4 = 9  =>  0 pairs (*) / I6 = 9  =>  0 pairs (X)
H8,I8: 9.. / H8 = 9  =>  0 pairs (X) / I8 = 9  =>  0 pairs (_)
C1,H1: 9.. / C1 = 9  =>  0 pairs (X) / H1 = 9  =>  0 pairs (_)
C5,D5: 9.. / C5 = 9  =>  0 pairs (*) / D5 = 9  =>  0 pairs (X)
D6,I6: 9.. / D6 = 9  =>  0 pairs (*) / I6 = 9  =>  0 pairs (X)
G2,G4: 9.. / G2 = 9  =>  0 pairs (X) / G4 = 9  =>  0 pairs (_)
I6,I8: 9.. / I6 = 9  =>  0 pairs (X) / I8 = 9  =>  0 pairs (_)
* DURATION: 0:01:01.380716  START: 07:25:19.188939  END: 07:26:20.569655 2017-05-04
* CP COUNT: (37)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,B6,B8,C5,C8,D5,E1,E6,E7,F6,F7,G2,G4,H8,I6,I8)
* 1..8.64.7.6714..58.4875.1.6.8..17.647...645824.6...71.5946..2718..4756..673291845
* PAIR E1: 2,3 BLK 2
F2: 2,3,9                                # reduction candidate for 2,3
F2: 2,3                                  # 19 pairs
F3: 2,3,9                                # reduction candidate for 2,3
F3: 2,3 => SOLVED
* 135826497267149358948753126382517964719364582456982713594638271821475639673291845
F3: 9                                    # 19 pairs
* PAIR E1: 2,3 ROW 1
B1: 2,3,5                                # reduction candidate for 2,3
B1: 2,3 => SOLVED
* 135826497267149358948753126382517964719364582456982713594638271821475639673291845
B1: 5 => CTR
* 15.8.64.7.6714..58.4875.1.6.85.17.647...645824365..7195946..271821475693673291845
H1: 2,3,9                                # reduction candidate for 2,3
H1: 2,3 => CTR
* 1.98.64.7.6714..58.4875.1.698..17.647...645824.6...71.5946..2718..4756..673291845
H1: 9 => SOLVED
* 135826497267149358948753126382517964719364582456982713594638271821475639673291845
* PAIR G2: 3,9 BLK 3
H1: 3,9,2                                # reduction candidate for 3,9
H1: 3,9                                  # 19 pairs
H3: 3,9,2                                # reduction candidate for 3,9
H3: 3,9 => CTR
* 1.98.6427.6714..58.4875.1.6.8..17.647...645824.6.2871.5946832718214756..673291845
H3: 2                                    # 19 pairs
* PAIR G2: 3,9 ROW 2
A2: 3,9,2                                # reduction candidate for 3,9
A2: 3,9                                  # 17 pairs
F2: 3,9,2                                # reduction candidate for 3,9
F2: 3,9 => SOLVED
* 135826497267149358948753126382517964719364582456982713594638271821475639673291845
F2: 2                                    # 17 pairs
* PAIR B6: 3,5 ROW 6
D6: 3,5,9                                # reduction candidate for 3,5
D6: 3,5 => CTR
* 1.98.64.7.6714.958.487591.698..17.647...645824.6...7195946..2718..475693673291845
D6: 9 => SOLVED
* 135826497267149358948753126382517964719364582456982713594638271821475639673291845
* PAIR B6: 3,5 COL B
B1: 3,5,2                                # reduction candidate for 3,5
B1: 3,5 => SOLVED
* 135826497267149358948753126382517964719364582456982713594638271821475639673291845
B1: 2 => CTR
* 125836497.6714235834875912628..17.647...645824.6...71.5946..2718..4756..673291845
* PAIR D5: 3,9 BLK 5
D4: 3,9,5                                # reduction candidate for 3,9
D4: 3,9 => CTR
* 1598.64.7.6714.958.487591.6.85.17.647...645824365..7195946..2718..475693673291845
D4: 5 => SOLVED
* 135826497267149358948753126382517964719364582456982713594638271821475639673291845
D6: 3,9,5                                # reduction candidate for 3,9
D6: 3,9 => SOLVED
* 135826497267149358948753126382517964719364582456982713594638271821475639673291845
D6: 5 => CTR
* 1598.64.7.6714.958.487591.698..17.647...645824.65..7195946..2718..475693673291845
* PAIR G4: 3,9 ROW 4
A4: 3,9,2                                # reduction candidate for 3,9
A4: 3,9 => SOLVED
* 135826497267149358948753126382517964719364582456982713594638271821475639673291845
A4: 2 => CTR
* 1..83649796714235834875912628.31796473..645824.6.2871.5946832718..4756..673291845
D4: 3,9,5                                # reduction candidate for 3,9
D4: 3,9 => CTR
* 1598.64.7.6714.958.487591.6.85.17.647...645824365..7195946..2718..475693673291845
D4: 5 => SOLVED
* 135826497267149358948753126382517964719364582456982713594638271821475639673291845
* PAIR I6: 3,9 ROW 6
D6: 3,9,5                                # reduction candidate for 3,9
D6: 3,9 => SOLVED
* 135826497267149358948753126382517964719364582456982713594638271821475639673291845
D6: 5 => CTR
* 1598.64.7.6714.958.487591.698..17.647...645824.65..7195946..2718..475693673291845
* PAIR H8: 3,9 COL H
H1: 3,9,2                                # reduction candidate for 3,9
H1: 3,9                                  # 19 pairs
H3: 3,9,2                                # reduction candidate for 3,9
H3: 3,9 => CTR
* 1.98.6427.6714..58.4875.1.6.8..17.647...645824.6.2871.5946832718214756..673291845
H3: 2                                    # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-137-base-pr-000.dot
* REASONING
* PRF # F3: 2,3 => SOL
* PRF # B1: 2,3 => SOL
* DIS # B1: 5 => CTR => B1: 2,3
* DIS # H1: 2,3 => CTR => H1: 9
* PRF # H1: 9 => SOL
* DIS # H3: 3,9 => CTR => H3: 2
* PRF # F2: 3,9 => SOL
* DIS # D6: 3,5 => CTR => D6: 9
* PRF # D6: 9 => SOL
* PRF # B1: 3,5 => SOL
* DIS # B1: 2 => CTR => B1: 3,5
* DIS # D4: 3,9 => CTR => D4: 5
* PRF # D4: 5 => SOL
* PRF # D6: 3,9 => SOL
* DIS # D6: 5 => CTR => D6: 3,9
* PRF # A4: 3,9 => SOL
* DIS # A4: 2 => CTR => A4: 3,9
* DIS # D4: 3,9 => CTR => D4: 5
* PRF # D4: 5 => SOL
* PRF # D6: 3,9 => SOL
* DIS # D6: 5 => CTR => D6: 3,9
* DIS # H3: 3,9 => CTR => H3: 2
* CNT  22 HDP CHAINS /  30 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,B6,B8,C5,C8,D5,E1,E6,E7,F6,F7,G2,G4,H8,I6,I8)
* 1..8.64.7.6714..58.4875.1.6.8..17.647...645824.6...71.5946..2718..4756..673291845
* PAIR E1: 2,3 BLK 2
F2: 2,3,9                                # reduction candidate for 2,3
F2: 2,3                                  # 19 pairs
F3: 2,3,9                                # reduction candidate for 2,3
F3: 2,3 => SOLVED
* 135826497267149358948753126382517964719364582456982713594638271821475639673291845
* DURATION: 0:00:02.823219  START: 07:26:52.450636  END: 07:26:55.273855 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-137-base-pr-001.dot
* REASONING
* PRF # F3: 2,3 => SOL
* STA F3: 2,3
* CNT   1 HDP CHAINS /   2 HYP OPENED

Header Info

Top 500 Minimum 17 137

solution: 135826497267149358948753126382517964719364582456982713594638271821475639673291845
info: 1813     FNBWY    S8.f     12183

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

Solution

position: 135826497267149358948753126382517964719364582456982713594638271821475639673291845 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:

* INC # F2: 2,3 => UNS
* PRF # F3: 2,3 => SOL
* INC # F3: 9 => UNS
* PRF # B1: 2,3 => SOL
* DIS # B1: 5 => CTR => B1: 2,3
* DIS # H1: 2,3 => CTR => H1: 9
* PRF # H1: 9 => SOL
* INC # H1: 3,9 => UNS
* DIS # H3: 3,9 => CTR => H3: 2
* INC # H3: 2 => UNS
* INC # A2: 3,9 => UNS
* PRF # F2: 3,9 => SOL
* INC # F2: 2 => UNS
* DIS # D6: 3,5 => CTR => D6: 9
* PRF # D6: 9 => SOL
* PRF # B1: 3,5 => SOL
* DIS # B1: 2 => CTR => B1: 3,5
* DIS # D4: 3,9 => CTR => D4: 5
* PRF # D4: 5 => SOL
* PRF # D6: 3,9 => SOL
* DIS # D6: 5 => CTR => D6: 3,9
* PRF # A4: 3,9 => SOL
* DIS # A4: 2 => CTR => A4: 3,9
* DIS # D4: 3,9 => CTR => D4: 5
* PRF # D4: 5 => SOL
* PRF # D6: 3,9 => SOL
* DIS # D6: 5 => CTR => D6: 3,9
* INC # H1: 3,9 => UNS
* DIS # H3: 3,9 => CTR => H3: 2
* INC # H3: 2 => UNS
* CNT  30 HDP CHAINS /  30 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F2: 2,3 => UNS
* PRF # F3: 2,3 => SOL
* STA F3: 2,3
* CNT   2 HDP CHAINS /   2 HYP OPENED