Analysis of xx-top500-005-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ....6...8.4.3......1....5.....1.5.4.6.....2..7....3...2...7...........1.......6.. initial

Autosolve

position: ...5641.854.31.9...1....5.4...1.57466.1.4.2.37.46.38.12639714854...5631.1.543.6.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B1: 3,9 => CTR => B1: 2,7
* DIS # A4: 3,9 => CTR => A4: 8
* DIS # A4: 9 => CTR => A4: 3,8
* DIS # F3: 2,7 => CTR => F3: 8,9
* DIS # H1: 2,7 => CTR => H1: 3
* DIS # H2: 2,7 => CTR => H2: 6
* DIS # C2: 2,7 => CTR => C2: 6,8
* PRF # I9: 2,7 => SOL
* DIS # F5: 9 => CTR => F5: 7,8
* PRF # D3: 7,8 => SOL
* DIS # D3: 2 => CTR => D3: 7,8
* DIS # E4: 8 => CTR => E4: 2,9
* DIS # B5: 8 => CTR => B5: 5,9
* PRF # D3: 7 => SOL
* DIS # F3: 2,8 => CTR => F3: 7,9
* PRF # I9: 2,7 => SOL
* DIS # H1: 2,7 => CTR => H1: 3
* DIS # H2: 2,7 => CTR => H2: 6
* CNT  18 HDP CHAINS /  46 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 # B1: 3,9 => CTR => B1: 2,7
* DIS B1: 2,7 # F3: 2,7 => CTR => F3: 8,9
* PRF B1: 2,7 + F3: 8,9 # I9: 2,7 => SOL
* STA B1: 2,7 + F3: 8,9 + I9: 2,7
* CNT   3 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

....6...8.4.3......1....5.....1.5.4.6.....2..7....3...2...7...........1.......6.. initial
...5641.854.31.9...1....5.4...1.57466.1.4.2.37.46.38.12639714854...5631.1.543.6.. autosolve
972564138548312967316789524839125746651847293724693851263971485487256319195438672 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
A1: 3,9
A3: 3,8
E3: 8,9
I2: 2,7
D5: 7,8
E6: 2,9
H5: 5,9
H6: 5,9
D8: 2,8
F9: 2,8
H9: 2,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E4,E6: 2.. / E4 = 2  => 12 pairs (_) / E6 = 2  => 15 pairs (_)
D8,F9: 2.. / D8 = 2  =>  0 pairs (*) / F9 = 2  =>  0 pairs (X)
B6,E6: 2.. / B6 = 2  => 12 pairs (_) / E6 = 2  => 15 pairs (_)
D8,I8: 2.. / D8 = 2  =>  0 pairs (*) / I8 = 2  =>  0 pairs (X)
D3,D8: 2.. / D3 = 2  =>  0 pairs (X) / D8 = 2  =>  0 pairs (_)
H1,H3: 3.. / H1 = 3  => 18 pairs (_) / H3 = 3  =>  0 pairs (X)
A4,B4: 3.. / A4 = 3  =>  0 pairs (X) / B4 = 3  => 12 pairs (_)
A3,H3: 3.. / A3 = 3  => 18 pairs (_) / H3 = 3  =>  0 pairs (X)
B1,B4: 3.. / B1 = 3  =>  0 pairs (X) / B4 = 3  => 12 pairs (_)
B5,B6: 5.. / B5 = 5  => 16 pairs (_) / B6 = 5  => 13 pairs (_)
H5,H6: 5.. / H5 = 5  => 13 pairs (_) / H6 = 5  => 16 pairs (_)
B5,H5: 5.. / B5 = 5  => 16 pairs (_) / H5 = 5  => 13 pairs (_)
B6,H6: 5.. / B6 = 5  => 13 pairs (_) / H6 = 5  => 16 pairs (_)
C2,C3: 6.. / C2 = 6  =>  0 pairs (X) / C3 = 6  => 11 pairs (_)
H2,H3: 6.. / H2 = 6  => 11 pairs (_) / H3 = 6  =>  0 pairs (X)
C2,H2: 6.. / C2 = 6  =>  0 pairs (X) / H2 = 6  => 11 pairs (_)
C3,H3: 6.. / C3 = 6  => 11 pairs (_) / H3 = 6  =>  0 pairs (X)
D5,F5: 7.. / D5 = 7  => 12 pairs (_) / F5 = 7  =>  0 pairs (*)
D3,D5: 7.. / D3 = 7  =>  0 pairs (*) / D5 = 7  =>  0 pairs (X)
D8,F9: 8.. / D8 = 8  =>  0 pairs (X) / F9 = 8  =>  0 pairs (_)
C2,F2: 8.. / C2 = 8  => 18 pairs (_) / F2 = 8  =>  0 pairs (X)
B9,F9: 8.. / B9 = 8  =>  0 pairs (X) / F9 = 8  =>  0 pairs (_)
A3,A4: 8.. / A3 = 8  =>  0 pairs (X) / A4 = 8  => 18 pairs (_)
E3,E4: 8.. / E3 = 8  => 18 pairs (_) / E4 = 8  =>  0 pairs (X)
E3,F3: 9.. / E3 = 9  =>  0 pairs (X) / F3 = 9  => 18 pairs (_)
H5,H6: 9.. / H5 = 9  => 16 pairs (_) / H6 = 9  => 13 pairs (_)
I8,I9: 9.. / I8 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
B9,I9: 9.. / B9 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
A1,A4: 9.. / A1 = 9  => 12 pairs (_) / A4 = 9  =>  0 pairs (X)
F3,F5: 9.. / F3 = 9  => 18 pairs (_) / F5 = 9  =>  0 pairs (X)
* DURATION: 0:00:49.263561  START: 02:44:55.070597  END: 02:45:44.334158 2017-05-04
* CP COUNT: (30)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,D5,D8,E3,E6,F9,H5,H6,H9,I2)
* ...5641.854.31.9...1....5.4...1.57466.1.4.2.37.46.38.12639714854...5631.1.543.6..
* PAIR A1: 3,9 BLK 1
B1: 3,9,2,7                              # reduction candidate for 3,9
B1: 3,9 => CTR
* ...5641.854.31896.816.9.534...1857466817492537546238912639714854.825631.1.543.6..
B1: 2,7                                  # 13 pairs
* PAIR A1: 3,9 COL A
A4: 3,9,8                                # reduction candidate for 3,9
A4: 3,9 => CTR
* ...5641.854.31.9..81..9.534...1857466817492537546238912639714854.825631.1.543.6..
A4: 8                                    # 18 pairs
* PAIR A3: 3,8 COL A
A4: 3,8,9                                # reduction candidate for 3,8
A4: 9 => CTR
* ...5641.854.31.9..81..9.53493.1857466817492537546238912639714854.825631.1.543.6..
A4: 3,8                                  # 12 pairs
* PAIR E3: 8,9 BLK 2
F3: 8,9,2,7                              # reduction candidate for 8,9
F3: 2,7 => CTR
* ...5641.854.31.9...1..9.5.4...1857466817492537546238912639714854.825631.1.54386..
F3: 8,9                                  # 18 pairs
* PAIR E3: 8,9 COL E
E4: 8,9,2                                # reduction candidate for 8,9
E4: 8,9                                  # 15 pairs
E4: 2                                    # 12 pairs
* PAIR I2: 2,7 BLK 3
H1: 2,7,3                                # reduction candidate for 2,7
H1: 2,7 => CTR
* ...5641.854.31.96.816.9.534...1857466817492537546238912639714854.825631.1.543.6..
H1: 3                                    # 18 pairs
H2: 2,7,6                                # reduction candidate for 2,7
H2: 2,7 => CTR
* ...5641.85463189...1..9.564...1857466817492537546238912639714854.825631.1.543.6..
H2: 6                                    # 11 pairs
H3: 2,7,3,6                              # reduction candidate for 2,7
H3: 2,7                                  # 18 pairs
* PAIR I2: 2,7 ROW 2
C2: 2,7,6,8                              # reduction candidate for 2,7
C2: 2,7 => CTR
* ...5641.854.31896..16.9.5.4...1857466817492537546238912639714854.825631.1.543.6..
C2: 6,8                                  # 12 pairs
F2: 2,7,8                                # reduction candidate for 2,7
F2: 2,7                                  # 18 pairs
* PAIR I2: 2,7 COL I
I8: 2,7,9                                # reduction candidate for 2,7
I8: 2,7                                  # 13 pairs
I9: 2,7,9                                # reduction candidate for 2,7
I9: 2,7 => SOLVED
* 972564138548312967316789524839125746651847293724693851263971485487256319195438672
I9: 9                                    # 13 pairs
* PAIR D5: 7,8 BLK 5
F5: 7,8,9                                # reduction candidate for 7,8
F5: 9 => CTR
* ...5641.854.31.9...1..9.5.4...1857466817492537546238912639714854.825631.1.54386..
F5: 7,8                                  # 18 pairs
* PAIR D5: 7,8 COL D
D3: 7,8,2                                # reduction candidate for 7,8
D3: 7,8 => SOLVED
* 972564138548312967316789524839125746651847293724693851263971485487256319195438672
D3: 2 => CTR
* ...5641.854.31.9.7.1.2.75.4...1.57466.174.2.37.46.38.12639714854..856312185432679
* PAIR E6: 2,9 BLK 5
E4: 2,9,8                                # reduction candidate for 2,9
E4: 8 => CTR
* ...5641.854.31.9...1....5.4...1857466817492537546238912639714854.825631.1.54386..
E4: 2,9                                  # 18 pairs
* PAIR E6: 2,9 ROW 6
B6: 2,9,5                                # reduction candidate for 2,9
B6: 2,9                                  # 16 pairs
B6: 5                                    # 13 pairs
* PAIR H5: 5,9 ROW 5
B5: 5,9,8                                # reduction candidate for 5,9
B5: 8 => CTR
* ...5641.854.31.9...1....5.4...1.57466817492537546238912639714854.825631.1.54386..
B5: 5,9                                  # 18 pairs
* PAIR H6: 5,9 ROW 6
B6: 5,9,2                                # reduction candidate for 5,9
B6: 5,9                                  # 15 pairs
B6: 2                                    # 12 pairs
* PAIR D8: 2,8 COL D
D3: 2,8,7                                # reduction candidate for 2,8
D3: 7 => SOLVED
* 972564138548312967316789524839125746651847293724693851263971485487256319195438672
D3: 2,8                                  # 12 pairs
* PAIR F9: 2,8 COL F
F2: 2,8,7                                # reduction candidate for 2,8
F2: 2,8                                  # 14 pairs
F3: 2,8,7,9                              # reduction candidate for 2,8
F3: 2,8 => CTR
* ...5641.854.31.9...1..9.5.4...1857466817492537546238912639714854.825631.1.54386..
F3: 7,9                                  # 12 pairs
* PAIR H9: 2,7 BLK 9
I8: 2,7,9                                # reduction candidate for 2,7
I8: 2,7                                  # 13 pairs
I9: 2,7,9                                # reduction candidate for 2,7
I9: 2,7 => SOLVED
* 972564138548312967316789524839125746651847293724693851263971485487256319195438672
I9: 9                                    # 13 pairs
* PAIR H9: 2,7 COL H
H1: 2,7,3                                # reduction candidate for 2,7
H1: 2,7 => CTR
* ...5641.854.31.96.816.9.534...1857466817492537546238912639714854.825631.1.543.6..
H1: 3                                    # 18 pairs
H2: 2,7,6                                # reduction candidate for 2,7
H2: 2,7 => CTR
* ...5641.85463189...1..9.564...1857466817492537546238912639714854.825631.1.543.6..
H2: 6                                    # 11 pairs
H3: 2,7,3,6                              # reduction candidate for 2,7
H3: 2,7                                  # 18 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-005-base-pr-000.dot
* REASONING
* DIS # B1: 3,9 => CTR => B1: 2,7
* DIS # A4: 3,9 => CTR => A4: 8
* DIS # A4: 9 => CTR => A4: 3,8
* DIS # F3: 2,7 => CTR => F3: 8,9
* DIS # H1: 2,7 => CTR => H1: 3
* DIS # H2: 2,7 => CTR => H2: 6
* DIS # C2: 2,7 => CTR => C2: 6,8
* PRF # I9: 2,7 => SOL
* DIS # F5: 9 => CTR => F5: 7,8
* PRF # D3: 7,8 => SOL
* DIS # D3: 2 => CTR => D3: 7,8
* DIS # E4: 8 => CTR => E4: 2,9
* DIS # B5: 8 => CTR => B5: 5,9
* PRF # D3: 7 => SOL
* DIS # F3: 2,8 => CTR => F3: 7,9
* PRF # I9: 2,7 => SOL
* DIS # H1: 2,7 => CTR => H1: 3
* DIS # H2: 2,7 => CTR => H2: 6
* CNT  18 HDP CHAINS /  46 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,D5,D8,E3,E6,F9,H5,H6,H9,I2)
* ...5641.854.31.9...1....5.4...1.57466.1.4.2.37.46.38.12639714854...5631.1.543.6..
* PAIR A1: 3,9 BLK 1
B1: 3,9,2,7                              # reduction candidate for 3,9
B1: 3,9 => CTR
* ...5641.854.31896.816.9.534...1857466817492537546238912639714854.825631.1.543.6..
* PAIR E3: 8,9 BLK 2
F3: 8,9,2,7                              # reduction candidate for 8,9
F3: 2,7 => CTR
* ...5641.854.31.9...1..9.5.4.3.1857466817492537546238912639714854.825631.1.54386..
* PAIR I2: 2,7 COL I
I8: 2,7,9                                # reduction candidate for 2,7
I8: 2,7                                  # 20 pairs
I9: 2,7,9                                # reduction candidate for 2,7
I9: 2,7 => SOLVED
* 972564138548312967316789524839125746651847293724693851263971485487256319195438672
* DURATION: 0:00:07.249894  START: 02:46:26.452251  END: 02:46:33.702145 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-005-base-pr-001.dot
* REASONING
* DIS # B1: 3,9 => CTR => B1: 2,7
* DIS B1: 2,7 # F3: 2,7 => CTR => F3: 8,9
* PRF B1: 2,7 + F3: 8,9 # I9: 2,7 => SOL
* STA B1: 2,7 + F3: 8,9 + I9: 2,7
* CNT   3 HDP CHAINS /   5 HYP OPENED

Header Info

Top 500 Minimum 17 005

solution: 972564138548312967316789524839125746651847293724693851263971485487256319195438672
info: 1305     FNBWX    S8.f     43167

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

Solution

position: 972564138548312967316789524839125746651847293724693851263971485487256319195438672 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 # B1: 3,9 => CTR => B1: 2,7
* INC # B1: 2,7 => UNS
* DIS # A4: 3,9 => CTR => A4: 8
* INC # A4: 8 => UNS
* INC # A4: 3,8 => UNS
* DIS # A4: 9 => CTR => A4: 3,8
* INC # F3: 8,9 => UNS
* DIS # F3: 2,7 => CTR => F3: 8,9
* INC # E4: 8,9 => UNS
* INC # E4: 2 => UNS
* DIS # H1: 2,7 => CTR => H1: 3
* INC # H1: 3 => UNS
* DIS # H2: 2,7 => CTR => H2: 6
* INC # H2: 6 => UNS
* INC # H3: 2,7 => UNS
* DIS # C2: 2,7 => CTR => C2: 6,8
* INC # C2: 6,8 => UNS
* INC # F2: 2,7 => UNS
* INC # I8: 2,7 => UNS
* PRF # I9: 2,7 => SOL
* INC # I9: 9 => UNS
* INC # F5: 7,8 => UNS
* DIS # F5: 9 => CTR => F5: 7,8
* PRF # D3: 7,8 => SOL
* DIS # D3: 2 => CTR => D3: 7,8
* INC # E4: 2,9 => UNS
* DIS # E4: 8 => CTR => E4: 2,9
* INC # B6: 2,9 => UNS
* INC # B6: 5 => UNS
* INC # B5: 5,9 => UNS
* DIS # B5: 8 => CTR => B5: 5,9
* INC # B6: 5,9 => UNS
* INC # B6: 2 => UNS
* INC # D3: 2,8 => UNS
* PRF # D3: 7 => SOL
* INC # F2: 2,8 => UNS
* DIS # F3: 2,8 => CTR => F3: 7,9
* INC # F3: 7,9 => UNS
* INC # I8: 2,7 => UNS
* PRF # I9: 2,7 => SOL
* INC # I9: 9 => UNS
* DIS # H1: 2,7 => CTR => H1: 3
* INC # H1: 3 => UNS
* DIS # H2: 2,7 => CTR => H2: 6
* INC # H2: 6 => UNS
* INC # H3: 2,7 => UNS
* CNT  46 HDP CHAINS /  46 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B1: 3,9 => CTR => B1: 2,7
* INC B1: 2,7 # F3: 8,9 => UNS
* DIS B1: 2,7 # F3: 2,7 => CTR => F3: 8,9
* INC B1: 2,7 + F3: 8,9 # I8: 2,7 => UNS
* PRF B1: 2,7 + F3: 8,9 # I9: 2,7 => SOL
* STA B1: 2,7 + F3: 8,9 + I9: 2,7
* CNT   5 HDP CHAINS /   5 HYP OPENED