Analysis of xx-top500-009-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .31.....5...8...2..........2.....1..7..4............83....319..64...........5.... initial

Autosolve

position: .31...8.55..893421...1.5.3.25.3..14.7.341.5..1.45...838..6319546459..31.319.54..8 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # E1: 2,7 => SOL
* DIS # F1: 2,7 => CTR => F1: 6
* PRF # I3: 6,7 => SOL
* PRF # E3: 4 => SOL
* DIS # G6: 6,7 => CTR => G6: 2
* PRF # G6: 2 => SOL
* PRF # G9: 6,7 => SOL
* DIS # G9: 2 => CTR => G9: 6,7
* DIS # B5: 9 => CTR => B5: 6,8
* DIS # F4: 6,8 => CTR => F4: 7,9
* DIS # B5: 6,9 => CTR => B5: 8
* DIS # I4: 6,9 => CTR => I4: 7
* PRF # I4: 7 => SOL
* PRF # I5: 6,9 => SOL
* DIS # I5: 2 => CTR => I5: 6,9
* DIS # B5: 6,9 => CTR => B5: 8
* DIS # F5: 6,9 => CTR => F5: 2,8
* PRF # H1: 6,9 => SOL
* DIS # H1: 7 => CTR => H1: 6,9
* DIS # G9: 2,7 => CTR => G9: 6
* PRF # G9: 6 => SOL
* DIS # G9: 2,7 => CTR => G9: 6
* PRF # G9: 6 => SOL
* PRF # G9: 6,7 => SOL
* DIS # G9: 2 => CTR => G9: 6,7
* PRF # H1: 9 => SOL
* CNT  26 HDP CHAINS /  44 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 # E1: 2,7 => SOL
* STA E1: 2,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

.31.....5...8...2..........2.....1..7..4............83....319..64...........5.... initial
.31...8.55..893421...1.5.3.25.3..14.7.341.5..1.45...838..6319546459..31.319.54..8 autosolve
431726895567893421928145736256389147783412569194567283872631954645978312319254678 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
A1: 4,9
B2: 6,7
C2: 6,7
A3: 4,9
B3: 2,8
C3: 2,8
D1: 2,7
G3: 6,7
C4: 6,8
B6: 6,9
H5: 6,9
B7: 2,7
C7: 2,7
D9: 2,7
I8: 2,7
H9: 6,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B3,C3: 2.. / B3 = 2  => 10 pairs (_) / C3 = 2  =>  0 pairs (X)
I5,G6: 2.. / I5 = 2  =>  0 pairs (X) / G6 = 2  =>  0 pairs (_)
B7,C7: 2.. / B7 = 2  =>  0 pairs (X) / C7 = 2  => 10 pairs (_)
I8,G9: 2.. / I8 = 2  =>  0 pairs (*) / G9 = 2  =>  0 pairs (X)
F5,I5: 2.. / F5 = 2  =>  0 pairs (*) / I5 = 2  =>  0 pairs (X)
D9,G9: 2.. / D9 = 2  =>  0 pairs (*) / G9 = 2  =>  0 pairs (X)
B3,B7: 2.. / B3 = 2  => 10 pairs (_) / B7 = 2  =>  0 pairs (X)
C3,C7: 2.. / C3 = 2  =>  0 pairs (X) / C7 = 2  => 10 pairs (_)
D1,D9: 2.. / D1 = 2  =>  0 pairs (X) / D9 = 2  =>  0 pairs (_)
G6,G9: 2.. / G6 = 2  =>  0 pairs (*) / G9 = 2  =>  0 pairs (X)
I5,I8: 2.. / I5 = 2  =>  0 pairs (X) / I8 = 2  =>  0 pairs (_)
A1,A3: 4.. / A1 = 4  =>  0 pairs (*) / A3 = 4  =>  0 pairs (X)
E1,E3: 4.. / E1 = 4  => 20 pairs (_) / E3 = 4  =>  0 pairs (*)
A1,E1: 4.. / A1 = 4  =>  0 pairs (*) / E1 = 4  =>  0 pairs (X)
A3,E3: 4.. / A3 = 4  => 20 pairs (_) / E3 = 4  =>  0 pairs (*)
B2,C2: 6.. / B2 = 6  => 10 pairs (_) / C2 = 6  =>  0 pairs (X)
G9,H9: 6.. / G9 = 6  =>  0 pairs (*) / H9 = 6  =>  0 pairs (X)
C2,C4: 6.. / C2 = 6  =>  0 pairs (X) / C4 = 6  => 10 pairs (_)
B2,C2: 7.. / B2 = 7  =>  0 pairs (X) / C2 = 7  => 10 pairs (_)
I4,G6: 7.. / I4 = 7  =>  0 pairs (*) / G6 = 7  =>  0 pairs (X)
B7,C7: 7.. / B7 = 7  => 10 pairs (_) / C7 = 7  =>  0 pairs (X)
B2,B7: 7.. / B2 = 7  =>  0 pairs (X) / B7 = 7  => 10 pairs (_)
C2,C7: 7.. / C2 = 7  => 10 pairs (_) / C7 = 7  =>  0 pairs (X)
D1,D9: 7.. / D1 = 7  =>  0 pairs (*) / D9 = 7  =>  0 pairs (X)
H1,H9: 7.. / H1 = 7  =>  0 pairs (X) / H9 = 7  =>  0 pairs (_)
B3,C3: 8.. / B3 = 8  =>  0 pairs (X) / C3 = 8  => 10 pairs (_)
C4,B5: 8.. / C4 = 8  =>  0 pairs (X) / B5 = 8  => 10 pairs (_)
E8,F8: 8.. / E8 = 8  => 18 pairs (_) / F8 = 8  => 11 pairs (_)
B5,F5: 8.. / B5 = 8  => 10 pairs (_) / F5 = 8  =>  0 pairs (X)
B3,B5: 8.. / B3 = 8  =>  0 pairs (X) / B5 = 8  => 10 pairs (_)
C3,C4: 8.. / C3 = 8  => 10 pairs (_) / C4 = 8  =>  0 pairs (X)
E4,E8: 8.. / E4 = 8  => 11 pairs (_) / E8 = 8  => 18 pairs (_)
A1,A3: 9.. / A1 = 9  => 20 pairs (_) / A3 = 9  =>  0 pairs (*)
H1,I3: 9.. / H1 = 9  =>  0 pairs (*) / I3 = 9  =>  0 pairs (X)
B5,B6: 9.. / B5 = 9  =>  0 pairs (X) / B6 = 9  => 16 pairs (_)
A1,H1: 9.. / A1 = 9  => 20 pairs (_) / H1 = 9  =>  0 pairs (*)
A3,I3: 9.. / A3 = 9  =>  0 pairs (*) / I3 = 9  =>  0 pairs (X)
F4,I4: 9.. / F4 = 9  => 17 pairs (_) / I4 = 9  =>  0 pairs (X)
B6,F6: 9.. / B6 = 9  => 16 pairs (_) / F6 = 9  =>  0 pairs (X)
H1,H5: 9.. / H1 = 9  =>  0 pairs (*) / H5 = 9  =>  0 pairs (X)
* DURATION: 0:01:10.979536  START: 02:54:06.809298  END: 02:55:17.788834 2017-05-04
* CP COUNT: (40)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B2,B3,B6,B7,C2,C3,C4,C7,D1,D9,G3,H5,H9,I8)
* .31...8.55..893421...1.5.3.25.3..14.7.341.5..1.45...838..6319546459..31.319.54..8
* PAIR D1: 2,7 BLK 2
E1: 2,7,4,6                              # reduction candidate for 2,7
E1: 2,7 => SOLVED
* 431726895567893421928145736256389147783412569194567283872631954645978312319254678
E1: 4,6                                  # 17 pairs
F1: 2,7,6                                # reduction candidate for 2,7
F1: 2,7 => CTR
* .317.28.55..893421...1.573.25.3..1477.341.5.21.45...838..6319546459..31.319.54678
F1: 6                                    # 18 pairs
* PAIR G3: 6,7 BLK 3
H1: 6,7,9                                # reduction candidate for 6,7
H1: 6,7                                  # 20 pairs
I3: 6,7,9                                # reduction candidate for 6,7
I3: 6,7 => SOLVED
* 431726895567893421928145736256389147783412569194567283872631954645978312319254678
I3: 9                                    # 20 pairs
* PAIR G3: 6,7 ROW 3
E3: 6,7,4                                # reduction candidate for 6,7
E3: 4 => SOLVED
* 431726895567893421928145736256389147783412569194567283872631954645978312319254678
E3: 6,7                                  # 20 pairs
* PAIR G3: 6,7 COL G
G6: 6,7,2                                # reduction candidate for 6,7
G6: 6,7 => CTR
* .312..8755..893421...17563925.3..14.7.341.5.21.45...838..6319546459..317319754268
G6: 2 => SOLVED
* 431726895567893421928145736256389147783412569194567283872631954645978312319254678
G9: 6,7,2                                # reduction candidate for 6,7
G9: 6,7 => SOLVED
* 431726895567893421928145736256389147783412569194567283872631954645978312319254678
G9: 2 => CTR
* .312..8755..893421...17563925.3.91477.341.5..1.45...838..6319546459..31.319.54268
* PAIR C4: 6,8 BLK 4
B5: 6,8,9                                # reduction candidate for 6,8
B5: 9 => CTR
* .31...8.55..893421.821.5.3.2583..14.7934185621645.97838..6319546459..31.319.54..8
B5: 6,8                                  # 16 pairs
* PAIR C4: 6,8 ROW 4
E4: 6,8,7                                # reduction candidate for 6,8
E4: 6,8                                  # 19 pairs
F4: 6,8,7,9                              # reduction candidate for 6,8
F4: 6,8 => CTR
* .31...8.55..893421...1.5.3.25.3..1497.341.5621.45..7838..6319546459..31.319.54..8
F4: 7,9                                  # 17 pairs
* PAIR B6: 6,9 BLK 4
B5: 6,9,8                                # reduction candidate for 6,9
B5: 6,9 => CTR
* .312..875576893421.8217563925836.14.7.34185.21.45...83827631954645982317319754268
B5: 8                                    # 10 pairs
* PAIR B6: 6,9 ROW 6
F6: 6,9,2,7                              # reduction candidate for 6,9
F6: 6,9                                  # 19 pairs
F6: 2,7                                  # 17 pairs
* PAIR H5: 6,9 BLK 6
I4: 6,9,7                                # reduction candidate for 6,9
I4: 6,9 => CTR
* .312..8755..893421...17563925.3..14.7.341.5..1.45..7838..6319546459..31.319.54268
I4: 7 => SOLVED
* 431726895567893421928145736256389147783412569194567283872631954645978312319254678
I5: 6,9,2                                # reduction candidate for 6,9
I5: 6,9 => SOLVED
* 431726895567893421928145736256389147783412569194567283872631954645978312319254678
I5: 2 => CTR
* .312..8755..893421...17563925.3..14.7.341.5.21.45...838..6319546459..317319754268
* PAIR H5: 6,9 ROW 5
B5: 6,9,8                                # reduction candidate for 6,9
B5: 6,9 => CTR
* .312..875576893421.8217563925836.14.7.34185.21.45...83827631954645982317319754268
B5: 8                                    # 10 pairs
F5: 6,9,2,8                              # reduction candidate for 6,9
F5: 6,9 => CTR
* .312..875567893421.281756392563..14.78341.5.21945...838..6319546459..317319754268
F5: 2,8                                  # 17 pairs
* PAIR H5: 6,9 COL H
H1: 6,9,7                                # reduction candidate for 6,9
H1: 6,9 => SOLVED
* 431726895567893421928145736256389147783412569194567283872631954645978312319254678
H1: 7 => CTR
* 931.468755..8934214..17563925.3.91477.341.5961945672838..63195464592.31.319.54..8
* PAIR D9: 2,7 BLK 8
E8: 2,7,8                                # reduction candidate for 2,7
E8: 2,7                                  # 11 pairs
F8: 2,7,8                                # reduction candidate for 2,7
F8: 2,7                                  # 18 pairs
* PAIR D9: 2,7 ROW 9
G9: 2,7,6                                # reduction candidate for 2,7
G9: 2,7 => CTR
* .31...8755..893421...17563925.3.91477.341.5961945.72838..6319546459..312319.54.68
G9: 6 => SOLVED
* 431726895567893421928145736256389147783412569194567283872631954645978312319254678
* PAIR I8: 2,7 BLK 9
G9: 2,7,6                                # reduction candidate for 2,7
G9: 2,7 => CTR
* .31...8755..893421...17563925.3.91477.341.5961945.72838..6319546459..312319.54.68
G9: 6 => SOLVED
* 431726895567893421928145736256389147783412569194567283872631954645978312319254678
* PAIR I8: 2,7 ROW 8
E8: 2,7,8                                # reduction candidate for 2,7
E8: 2,7                                  # 11 pairs
F8: 2,7,8                                # reduction candidate for 2,7
F8: 2,7                                  # 18 pairs
* PAIR H9: 6,7 BLK 9
G9: 6,7,2                                # reduction candidate for 6,7
G9: 6,7 => SOLVED
* 431726895567893421928145736256389147783412569194567283872631954645978312319254678
G9: 2 => CTR
* .312..8755..893421...17563925.3.91477.341.5..1.45...838..6319546459..31.319.54268
* PAIR H9: 6,7 COL H
H1: 6,7,9                                # reduction candidate for 6,7
H1: 9 => SOLVED
* 431726895567893421928145736256389147783412569194567283872631954645978312319254678
H1: 6,7                                  # 20 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-009-base-pr-000.dot
* REASONING
* PRF # E1: 2,7 => SOL
* DIS # F1: 2,7 => CTR => F1: 6
* PRF # I3: 6,7 => SOL
* PRF # E3: 4 => SOL
* DIS # G6: 6,7 => CTR => G6: 2
* PRF # G6: 2 => SOL
* PRF # G9: 6,7 => SOL
* DIS # G9: 2 => CTR => G9: 6,7
* DIS # B5: 9 => CTR => B5: 6,8
* DIS # F4: 6,8 => CTR => F4: 7,9
* DIS # B5: 6,9 => CTR => B5: 8
* DIS # I4: 6,9 => CTR => I4: 7
* PRF # I4: 7 => SOL
* PRF # I5: 6,9 => SOL
* DIS # I5: 2 => CTR => I5: 6,9
* DIS # B5: 6,9 => CTR => B5: 8
* DIS # F5: 6,9 => CTR => F5: 2,8
* PRF # H1: 6,9 => SOL
* DIS # H1: 7 => CTR => H1: 6,9
* DIS # G9: 2,7 => CTR => G9: 6
* PRF # G9: 6 => SOL
* DIS # G9: 2,7 => CTR => G9: 6
* PRF # G9: 6 => SOL
* PRF # G9: 6,7 => SOL
* DIS # G9: 2 => CTR => G9: 6,7
* PRF # H1: 9 => SOL
* CNT  26 HDP CHAINS /  44 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B2,B3,B6,B7,C2,C3,C4,C7,D1,D9,G3,H5,H9,I8)
* .31...8.55..893421...1.5.3.25.3..14.7.341.5..1.45...838..6319546459..31.319.54..8
* PAIR D1: 2,7 BLK 2
E1: 2,7,4,6                              # reduction candidate for 2,7
E1: 2,7 => SOLVED
* 431726895567893421928145736256389147783412569194567283872631954645978312319254678
* DURATION: 0:00:02.521341  START: 02:56:04.417491  END: 02:56:06.938832 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-009-base-pr-001.dot
* REASONING
* PRF # E1: 2,7 => SOL
* STA E1: 2,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 009

solution: 431726895567893421928145736256389147783412569194567283872631954645978312319254678
info: 1307     FNBWXY   S8.f     18192

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

Solution

position: 431726895567893421928145736256389147783412569194567283872631954645978312319254678 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 # E1: 2,7 => SOL
* INC # E1: 4,6 => UNS
* DIS # F1: 2,7 => CTR => F1: 6
* INC # F1: 6 => UNS
* INC # H1: 6,7 => UNS
* PRF # I3: 6,7 => SOL
* INC # I3: 9 => UNS
* INC # E3: 6,7 => UNS
* PRF # E3: 4 => SOL
* DIS # G6: 6,7 => CTR => G6: 2
* PRF # G6: 2 => SOL
* PRF # G9: 6,7 => SOL
* DIS # G9: 2 => CTR => G9: 6,7
* INC # B5: 6,8 => UNS
* DIS # B5: 9 => CTR => B5: 6,8
* INC # E4: 6,8 => UNS
* DIS # F4: 6,8 => CTR => F4: 7,9
* INC # F4: 7,9 => UNS
* DIS # B5: 6,9 => CTR => B5: 8
* INC # B5: 8 => UNS
* INC # F6: 6,9 => UNS
* INC # F6: 2,7 => UNS
* DIS # I4: 6,9 => CTR => I4: 7
* PRF # I4: 7 => SOL
* PRF # I5: 6,9 => SOL
* DIS # I5: 2 => CTR => I5: 6,9
* DIS # B5: 6,9 => CTR => B5: 8
* INC # B5: 8 => UNS
* DIS # F5: 6,9 => CTR => F5: 2,8
* INC # F5: 2,8 => UNS
* PRF # H1: 6,9 => SOL
* DIS # H1: 7 => CTR => H1: 6,9
* INC # E8: 2,7 => UNS
* INC # F8: 2,7 => UNS
* DIS # G9: 2,7 => CTR => G9: 6
* PRF # G9: 6 => SOL
* DIS # G9: 2,7 => CTR => G9: 6
* PRF # G9: 6 => SOL
* INC # E8: 2,7 => UNS
* INC # F8: 2,7 => UNS
* PRF # G9: 6,7 => SOL
* DIS # G9: 2 => CTR => G9: 6,7
* INC # H1: 6,7 => UNS
* PRF # H1: 9 => SOL
* CNT  44 HDP CHAINS /  44 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # E1: 2,7 => SOL
* STA E1: 2,7
* CNT   1 HDP CHAINS /   1 HYP OPENED