Analysis of xx-top500-487-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ....7.81..42...............8......6....4.2......5....1...36.4...25......1........ initial

Autosolve

position: 5..674812.42158......923...85.7.926.3..4.2...2..5.6..19..3614254258971361..245... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # G2: 6,7 => SOL
* DIS # G2: 3,9 => CTR => G2: 6,7
* DIS # G3: 6,7 => CTR => G3: 5
* PRF # G3: 5 => SOL
* DIS # G2: 7,9 => CTR => G2: 3,6
* DIS # I2: 7,9 => CTR => I2: 3
* PRF # I2: 3 => SOL
* DIS # H5: 7,9 => CTR => H5: 5,8
* PRF # H6: 7,9 => SOL
* PRF # H3: 4,7 => SOL
* DIS # H3: 5 => CTR => H3: 4,7
* PRF # B5: 7,9 => SOL
* DIS # C5: 7,9 => CTR => C5: 1,6
* DIS # C6: 7,9 => CTR => C6: 4
* PRF # C6: 4 => SOL
* DIS # G6: 7,9 => CTR => G6: 3
* PRF # G6: 3 => SOL
* PRF # H6: 7,9 => SOL
* PRF # I9: 7,9 => SOL
* DIS # G2: 7,9 => CTR => G2: 3,6
* PRF # G5: 7,9 => SOL
* DIS # G5: 5 => CTR => G5: 7,9
* DIS # G6: 7,9 => CTR => G6: 3
* PRF # G6: 3 => SOL
* CNT  24 HDP CHAINS /  34 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 # G2: 6,7 => SOL
* STA G2: 6,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

....7.81..42...............8......6....4.2......5....1...36.4...25......1........ initial
5..674812.42158......923...85.7.926.3..4.2...2..5.6..19..3614254258971361..245... autosolve
539674812742158693618923547851739264376412958294586371987361425425897136163245789 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (19)
B1: 3,9
C1: 3,9
A2: 6,7
A3: 6,7
B3: 1,8
C3: 1,8
H2: 7,9
I3: 4,7
C4: 1,4
B6: 7,9
E4: 1,3
E5: 1,8
E6: 3,8
I4: 3,4
B7: 7,8
C7: 7,8
B9: 3,6
C9: 3,6
G9: 7,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B3,C3: 1.. / B3 = 1  => 16 pairs (_) / C3 = 1  =>  0 pairs (X)
E4,E5: 1.. / E4 = 1  =>  0 pairs (X) / E5 = 1  =>  0 pairs (_)
C4,E4: 1.. / C4 = 1  =>  0 pairs (*) / E4 = 1  =>  0 pairs (X)
B3,B5: 1.. / B3 = 1  => 16 pairs (_) / B5 = 1  =>  0 pairs (X)
B1,C1: 3.. / B1 = 3  => 16 pairs (_) / C1 = 3  => 13 pairs (_)
G2,I2: 3.. / G2 = 3  =>  0 pairs (X) / I2 = 3  =>  0 pairs (_)
E4,E6: 3.. / E4 = 3  =>  0 pairs (*) / E6 = 3  =>  0 pairs (X)
I4,G6: 3.. / I4 = 3  =>  0 pairs (X) / G6 = 3  =>  0 pairs (_)
B9,C9: 3.. / B9 = 3  => 13 pairs (_) / C9 = 3  => 16 pairs (_)
E4,I4: 3.. / E4 = 3  =>  0 pairs (*) / I4 = 3  =>  0 pairs (X)
E6,G6: 3.. / E6 = 3  =>  0 pairs (X) / G6 = 3  =>  0 pairs (_)
B1,B9: 3.. / B1 = 3  => 16 pairs (_) / B9 = 3  => 13 pairs (_)
C1,C9: 3.. / C1 = 3  => 13 pairs (_) / C9 = 3  => 16 pairs (_)
G2,G6: 3.. / G2 = 3  =>  0 pairs (X) / G6 = 3  =>  0 pairs (_)
I2,I4: 3.. / I2 = 3  =>  0 pairs (*) / I4 = 3  =>  0 pairs (X)
H3,I3: 4.. / H3 = 4  =>  0 pairs (*) / I3 = 4  =>  0 pairs (X)
C4,C6: 4.. / C4 = 4  =>  0 pairs (X) / C6 = 4  =>  0 pairs (_)
I4,H6: 4.. / I4 = 4  =>  0 pairs (*) / H6 = 4  =>  0 pairs (X)
C4,I4: 4.. / C4 = 4  =>  0 pairs (X) / I4 = 4  =>  0 pairs (_)
C6,H6: 4.. / C6 = 4  =>  0 pairs (*) / H6 = 4  =>  0 pairs (X)
H3,H6: 4.. / H3 = 4  =>  0 pairs (*) / H6 = 4  =>  0 pairs (X)
I3,I4: 4.. / I3 = 4  =>  0 pairs (X) / I4 = 4  =>  0 pairs (_)
G3,H3: 5.. / G3 = 5  =>  0 pairs (*) / H3 = 5  =>  0 pairs (X)
G5,H5: 5.. / G5 = 5  =>  0 pairs (X) / H5 = 5  =>  0 pairs (_)
G3,G5: 5.. / G3 = 5  =>  0 pairs (*) / G5 = 5  =>  0 pairs (X)
H3,H5: 5.. / H3 = 5  =>  0 pairs (X) / H5 = 5  =>  0 pairs (_)
A2,A3: 6.. / A2 = 6  =>  0 pairs (X) / A3 = 6  =>  0 pairs (_)
G2,G3: 6.. / G2 = 6  =>  0 pairs (*) / G3 = 6  =>  0 pairs (X)
B5,C5: 6.. / B5 = 6  => 13 pairs (_) / C5 = 6  => 16 pairs (_)
B9,C9: 6.. / B9 = 6  => 16 pairs (_) / C9 = 6  => 13 pairs (_)
A2,G2: 6.. / A2 = 6  =>  0 pairs (X) / G2 = 6  =>  0 pairs (_)
A3,G3: 6.. / A3 = 6  =>  0 pairs (*) / G3 = 6  =>  0 pairs (X)
B5,B9: 6.. / B5 = 6  => 13 pairs (_) / B9 = 6  => 16 pairs (_)
C5,C9: 6.. / C5 = 6  => 16 pairs (_) / C9 = 6  => 13 pairs (_)
A2,A3: 7.. / A2 = 7  =>  0 pairs (*) / A3 = 7  =>  0 pairs (X)
B7,C7: 7.. / B7 = 7  =>  0 pairs (X) / C7 = 7  => 16 pairs (_)
B3,C3: 8.. / B3 = 8  =>  0 pairs (X) / C3 = 8  => 16 pairs (_)
E5,E6: 8.. / E5 = 8  =>  0 pairs (X) / E6 = 8  =>  0 pairs (_)
B7,C7: 8.. / B7 = 8  => 16 pairs (_) / C7 = 8  =>  0 pairs (X)
H9,I9: 8.. / H9 = 8  =>  0 pairs (*) / I9 = 8  =>  0 pairs (X)
E6,H6: 8.. / E6 = 8  =>  0 pairs (*) / H6 = 8  =>  0 pairs (X)
B3,B7: 8.. / B3 = 8  =>  0 pairs (X) / B7 = 8  => 16 pairs (_)
C3,C7: 8.. / C3 = 8  => 16 pairs (_) / C7 = 8  =>  0 pairs (X)
I5,I9: 8.. / I5 = 8  =>  0 pairs (*) / I9 = 8  =>  0 pairs (X)
B1,C1: 9.. / B1 = 9  => 13 pairs (_) / C1 = 9  => 16 pairs (_)
* DURATION: 0:01:50.637565  START: 19:16:41.555573  END: 19:18:32.193138 2017-05-04
* CP COUNT: (45)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B1,B3,B6,B7,B9,C1,C3,C4,C7,C9,E4,E5,E6,G9,H2,I3,I4)
* 5..674812.42158......923...85.7.926.3..4.2...2..5.6..19..3614254258971361..245...
* PAIR A2: 6,7 ROW 2
G2: 6,7,3,9                              # reduction candidate for 6,7
G2: 6,7 => SOLVED
* 539674812742158693618923547851739264376412958294586371987361425425897136163245789
G2: 3,9 => CTR
* 5..674812642158...7..9236548547192633..4825..2..5.6..19..3614254258971361..245...
* PAIR A3: 6,7 ROW 3
G3: 6,7,5                                # reduction candidate for 6,7
G3: 6,7 => CTR
* 5..674812.42158......923.548547192633..4825..2..5.6..19..3614254258971361..245...
G3: 5 => SOLVED
* 539674812742158693618923547851739264376412958294586371987361425425897136163245789
* PAIR H2: 7,9 BLK 3
G2: 7,9,3,6                              # reduction candidate for 7,9
G2: 7,9 => CTR
* 5..674812642158..37..92365485.7.926.3..4.2...2..5.6..19..3614254258971361..245...
G2: 3,6                                  # 20 pairs
I2: 7,9,3                                # reduction candidate for 7,9
I2: 7,9 => CTR
* 5..674812.421583.....9236548547192633..4825..2..5.6..19..3614254258971361..245...
I2: 3 => SOLVED
* 539674812742158693618923547851739264376412958294586371987361425425897136163245789
* PAIR H2: 7,9 COL H
H5: 7,9,5,8                              # reduction candidate for 7,9
H5: 7,9 => CTR
* 5..674812.42158......923.548547192633..4825..2..5.6..19..3614254258971361..245...
H5: 5,8                                  # 20 pairs
H6: 7,9,4,8                              # reduction candidate for 7,9
H6: 7,9 => SOLVED
* 539674812742158693618923547851739264376412958294586371987361425425897136163245789
H6: 4,8                                  # 20 pairs
H9: 7,9,8                                # reduction candidate for 7,9
H9: 7,9                                  # 24 pairs
* PAIR I3: 4,7 BLK 3
H3: 4,7,5                                # reduction candidate for 4,7
H3: 4,7 => SOLVED
* 539674812742158693618923547851739264376412958294586371987361425425897136163245789
H3: 5 => CTR
* 5..674812.42158......923.548547192633..4825..2..5.6..19..3614254258971361..245...
* PAIR B6: 7,9 BLK 4
B5: 7,9,1,6                              # reduction candidate for 7,9
B5: 7,9 => SOLVED
* 539674812742158693618923547851739264376412958294586371987361425425897136163245789
B5: 1,6                                  # 20 pairs
C5: 7,9,1,6                              # reduction candidate for 7,9
C5: 7,9 => CTR
* 593674812.42158..3.18923...85173926436.412...274586391987361425425897136136245..9
C5: 1,6                                  # 20 pairs
C6: 7,9,4                                # reduction candidate for 7,9
C6: 7,9 => CTR
* 5..674812.42158......923...8547192633..482...2..536..19..3614254258971361..245...
C6: 4 => SOLVED
* 539674812742158693618923547851739264376412958294586371987361425425897136163245789
* PAIR B6: 7,9 ROW 6
G6: 7,9,3                                # reduction candidate for 7,9
G6: 7,9 => CTR
* 5..674812.421583.....9236548547192633..4825..2..5.6..19..3614254258971361..245...
G6: 3 => SOLVED
* 539674812742158693618923547851739264376412958294586371987361425425897136163245789
H6: 7,9,4,8                              # reduction candidate for 7,9
H6: 7,9 => SOLVED
* 539674812742158693618923547851739264376412958294586371987361425425897136163245789
H6: 4,8                                  # 20 pairs
* PAIR G9: 7,9 BLK 9
H9: 7,9,8                                # reduction candidate for 7,9
H9: 7,9                                  # 24 pairs
I9: 7,9,8                                # reduction candidate for 7,9
I9: 7,9 => SOLVED
* 539674812742158693618923547851739264376412958294586371987361425425897136163245789
I9: 8                                    # 24 pairs
* PAIR G9: 7,9 COL G
G2: 7,9,3,6                              # reduction candidate for 7,9
G2: 7,9 => CTR
* 5..674812642158..37..92365485.7.926.3..4.2...2..5.6..19..3614254258971361..245...
G2: 3,6                                  # 20 pairs
G5: 7,9,5                                # reduction candidate for 7,9
G5: 7,9 => SOLVED
* 539674812742158693618923547851739264376412958294586371987361425425897136163245789
G5: 5 => CTR
* 5..674812.42158......923.548547192633..4825..2..536..19..3614254258971361..245...
G6: 7,9,3                                # reduction candidate for 7,9
G6: 7,9 => CTR
* 5..674812.421583.....9236548547192633..4825..2..5.6..19..3614254258971361..245...
G6: 3 => SOLVED
* 539674812742158693618923547851739264376412958294586371987361425425897136163245789
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-487-base-pr-000.dot
* REASONING
* PRF # G2: 6,7 => SOL
* DIS # G2: 3,9 => CTR => G2: 6,7
* DIS # G3: 6,7 => CTR => G3: 5
* PRF # G3: 5 => SOL
* DIS # G2: 7,9 => CTR => G2: 3,6
* DIS # I2: 7,9 => CTR => I2: 3
* PRF # I2: 3 => SOL
* DIS # H5: 7,9 => CTR => H5: 5,8
* PRF # H6: 7,9 => SOL
* PRF # H3: 4,7 => SOL
* DIS # H3: 5 => CTR => H3: 4,7
* PRF # B5: 7,9 => SOL
* DIS # C5: 7,9 => CTR => C5: 1,6
* DIS # C6: 7,9 => CTR => C6: 4
* PRF # C6: 4 => SOL
* DIS # G6: 7,9 => CTR => G6: 3
* PRF # G6: 3 => SOL
* PRF # H6: 7,9 => SOL
* PRF # I9: 7,9 => SOL
* DIS # G2: 7,9 => CTR => G2: 3,6
* PRF # G5: 7,9 => SOL
* DIS # G5: 5 => CTR => G5: 7,9
* DIS # G6: 7,9 => CTR => G6: 3
* PRF # G6: 3 => SOL
* CNT  24 HDP CHAINS /  34 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B1,B3,B6,B7,B9,C1,C3,C4,C7,C9,E4,E5,E6,G9,H2,I3,I4)
* 5..674812.42158......923...85.7.926.3..4.2...2..5.6..19..3614254258971361..245...
* PAIR A2: 6,7 ROW 2
G2: 6,7,3,9                              # reduction candidate for 6,7
G2: 6,7 => SOLVED
* 539674812742158693618923547851739264376412958294586371987361425425897136163245789
* DURATION: 0:00:02.734341  START: 19:19:24.639073  END: 19:19:27.373414 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-487-base-pr-001.dot
* REASONING
* PRF # G2: 6,7 => SOL
* STA G2: 6,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 487

solution: 539674812742158693618923547851739264376412958294586371987361425425897136163245789
info: 96136    FNBYK    S8.f     42986

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

Solution

position: 539674812742158693618923547851739264376412958294586371987361425425897136163245789 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 # G2: 6,7 => SOL
* DIS # G2: 3,9 => CTR => G2: 6,7
* DIS # G3: 6,7 => CTR => G3: 5
* PRF # G3: 5 => SOL
* DIS # G2: 7,9 => CTR => G2: 3,6
* INC # G2: 3,6 => UNS
* DIS # I2: 7,9 => CTR => I2: 3
* PRF # I2: 3 => SOL
* DIS # H5: 7,9 => CTR => H5: 5,8
* INC # H5: 5,8 => UNS
* PRF # H6: 7,9 => SOL
* INC # H6: 4,8 => UNS
* INC # H9: 7,9 => UNS
* PRF # H3: 4,7 => SOL
* DIS # H3: 5 => CTR => H3: 4,7
* PRF # B5: 7,9 => SOL
* INC # B5: 1,6 => UNS
* DIS # C5: 7,9 => CTR => C5: 1,6
* INC # C5: 1,6 => UNS
* DIS # C6: 7,9 => CTR => C6: 4
* PRF # C6: 4 => SOL
* DIS # G6: 7,9 => CTR => G6: 3
* PRF # G6: 3 => SOL
* PRF # H6: 7,9 => SOL
* INC # H6: 4,8 => UNS
* INC # H9: 7,9 => UNS
* PRF # I9: 7,9 => SOL
* INC # I9: 8 => UNS
* DIS # G2: 7,9 => CTR => G2: 3,6
* INC # G2: 3,6 => UNS
* PRF # G5: 7,9 => SOL
* DIS # G5: 5 => CTR => G5: 7,9
* DIS # G6: 7,9 => CTR => G6: 3
* PRF # G6: 3 => SOL
* CNT  34 HDP CHAINS /  34 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # G2: 6,7 => SOL
* STA G2: 6,7
* CNT   1 HDP CHAINS /   1 HYP OPENED