Analysis of xx-top500-436-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ......8.1...7........6........5...6..9.....5..2..3....4...8.1..6.....3..5.7...... initial

Autosolve

position: 763.5.8.1.5.7..6...4.6..5.73745.1.681968...53825.3671.43..8517668.1..3.551736..8. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E2: 2,9 => CTR => E2: 1,4
* DIS # H2: 2,9 => CTR => H2: 3,4
* DIS # E2: 2,9 => CTR => E2: 1,4
* DIS # E8: 2,9 => CTR => E8: 4,7
* PRF # D1: 2 => SOL
* PRF # I9: 4,9 => SOL
* DIS # E8: 2,9 => CTR => E8: 4,7
* DIS # F8: 2,9 => CTR => F8: 4,7
* DIS # E8: 2,9 => CTR => E8: 4,7
* DIS # F8: 2,9 => CTR => F8: 4,7
* DIS # D1: 4 => CTR => D1: 2,9
* PRF # I9: 4,9 => SOL
* PRF # F9: 2 => SOL
* CNT  13 HDP CHAINS /  36 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 # E2: 2,9 => CTR => E2: 1,4
* DIS E2: 1,4 # H2: 2,9 => CTR => H2: 3,4
* PRF E2: 1,4 + H2: 3,4 # H3: 2,9 => SOL
* STA E2: 1,4 + H2: 3,4 + H3: 2,9
* CNT   3 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

......8.1...7........6........5...6..9.....5..2..3....4...8.1..6.....3..5.7...... initial
763.5.8.1.5.7..6...4.6..5.73745.1.681968...53825.3671.43..8517668.1..3.551736..8. autosolve
763259841951748632248613597374591268196827453825436719432985176689174325517362984 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
A2: 2,9
C2: 1,8
A3: 2,9
C3: 1,8
F2: 3,8
F3: 3,8
E4: 2,9
D6: 4,9
G4: 2,9
G5: 2,4
I6: 4,9
C7: 2,9
C8: 2,9
D7: 2,9
G9: 4,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C2,C3: 1.. / C2 = 1  => 12 pairs (_) / C3 = 1  => 15 pairs (_)
E2,E3: 1.. / E2 = 1  => 15 pairs (_) / E3 = 1  => 12 pairs (_)
C2,E2: 1.. / C2 = 1  => 12 pairs (_) / E2 = 1  => 15 pairs (_)
C3,E3: 1.. / C3 = 1  => 15 pairs (_) / E3 = 1  => 12 pairs (_)
A2,A3: 2.. / A2 = 2  => 18 pairs (_) / A3 = 2  => 18 pairs (_)
G4,G5: 2.. / G4 = 2  => 20 pairs (_) / G5 = 2  =>  0 pairs (X)
C7,C8: 2.. / C7 = 2  =>  0 pairs (*) / C8 = 2  =>  0 pairs (X)
H8,I9: 2.. / H8 = 2  =>  0 pairs (*) / I9 = 2  =>  0 pairs (X)
E4,G4: 2.. / E4 = 2  =>  0 pairs (X) / G4 = 2  => 20 pairs (_)
C7,D7: 2.. / C7 = 2  =>  0 pairs (*) / D7 = 2  =>  0 pairs (X)
F9,I9: 2.. / F9 = 2  =>  0 pairs (*) / I9 = 2  =>  0 pairs (X)
D1,D7: 2.. / D1 = 2  =>  0 pairs (*) / D7 = 2  =>  0 pairs (X)
I2,I9: 2.. / I2 = 2  =>  0 pairs (*) / I9 = 2  =>  0 pairs (X)
F2,F3: 3.. / F2 = 3  => 15 pairs (_) / F3 = 3  => 12 pairs (_)
H2,H3: 3.. / H2 = 3  => 12 pairs (_) / H3 = 3  => 15 pairs (_)
F2,H2: 3.. / F2 = 3  => 15 pairs (_) / H2 = 3  => 12 pairs (_)
F3,H3: 3.. / F3 = 3  => 12 pairs (_) / H3 = 3  => 15 pairs (_)
G5,I6: 4.. / G5 = 4  => 20 pairs (_) / I6 = 4  =>  0 pairs (X)
D6,I6: 4.. / D6 = 4  => 20 pairs (_) / I6 = 4  =>  0 pairs (X)
D1,D6: 4.. / D1 = 4  =>  0 pairs (X) / D6 = 4  => 20 pairs (_)
G5,G9: 4.. / G5 = 4  => 20 pairs (_) / G9 = 4  =>  0 pairs (X)
E5,F5: 7.. / E5 = 7  => 16 pairs (_) / F5 = 7  => 19 pairs (_)
E8,F8: 7.. / E8 = 7  => 19 pairs (_) / F8 = 7  => 16 pairs (_)
E5,E8: 7.. / E5 = 7  => 16 pairs (_) / E8 = 7  => 19 pairs (_)
F5,F8: 7.. / F5 = 7  => 19 pairs (_) / F8 = 7  => 16 pairs (_)
C2,C3: 8.. / C2 = 8  => 15 pairs (_) / C3 = 8  => 12 pairs (_)
F2,F3: 8.. / F2 = 8  => 12 pairs (_) / F3 = 8  => 15 pairs (_)
C2,F2: 8.. / C2 = 8  => 15 pairs (_) / F2 = 8  => 12 pairs (_)
C3,F3: 8.. / C3 = 8  => 12 pairs (_) / F3 = 8  => 15 pairs (_)
A2,A3: 9.. / A2 = 9  => 18 pairs (_) / A3 = 9  => 18 pairs (_)
E4,D6: 9.. / E4 = 9  => 20 pairs (_) / D6 = 9  =>  0 pairs (X)
G4,I6: 9.. / G4 = 9  =>  0 pairs (X) / I6 = 9  => 20 pairs (_)
C7,C8: 9.. / C7 = 9  => 16 pairs (_) / C8 = 9  =>  0 pairs (*)
E4,G4: 9.. / E4 = 9  => 20 pairs (_) / G4 = 9  =>  0 pairs (X)
D6,I6: 9.. / D6 = 9  =>  0 pairs (X) / I6 = 9  => 20 pairs (_)
C7,D7: 9.. / C7 = 9  => 16 pairs (_) / D7 = 9  =>  0 pairs (*)
G4,G9: 9.. / G4 = 9  =>  0 pairs (X) / G9 = 9  => 20 pairs (_)
* DURATION: 0:01:17.052500  START: 17:39:41.291119  END: 17:40:58.343619 2017-05-04
* CP COUNT: (37)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,C2,C3,C7,C8,D6,D7,E4,F2,F3,G4,G5,G9,I6)
* 763.5.8.1.5.7..6...4.6..5.73745.1.681968...53825.3671.43..8517668.1..3.551736..8.
* PAIR A2: 2,9 ROW 2
E2: 2,9,1,4                              # reduction candidate for 2,9
E2: 2,9 => CTR
* 763.5.8.1.517.8634.486135.73745.1.681968..45382543671943..8517668.1473.551736.982
E2: 1,4                                  # 16 pairs
H2: 2,9,3,4                              # reduction candidate for 2,9
H2: 2,9 => CTR
* 763.5.8.1.587136.4.416.85373745.1.681968..45382543671943..8517668.1473.551736.982
H2: 3,4                                  # 16 pairs
I2: 2,9,4                                # reduction candidate for 2,9
I2: 2,9                                  # 22 pairs
* PAIR A3: 2,9 ROW 3
E3: 2,9,1                                # reduction candidate for 2,9
E3: 2,9                                  # 15 pairs
H3: 2,9,3                                # reduction candidate for 2,9
H3: 2,9                                  # 12 pairs
* PAIR E4: 2,9 COL E
E2: 2,9,1,4                              # reduction candidate for 2,9
E2: 2,9 => CTR
* 763.5.8.1.517.8634.486135.73745.1.681968..45382543671943..8517668.1473.551736.982
E2: 1,4                                  # 16 pairs
E3: 2,9,1                                # reduction candidate for 2,9
E3: 2,9                                  # 15 pairs
E8: 2,9,4,7                              # reduction candidate for 2,9
E8: 2,9 => CTR
* 763459821.5.7..6.4.4.6..5.73745.1.6819687..53825.3671.43..8517668.1.7345517364982
E8: 4,7                                  # 16 pairs
* PAIR D6: 4,9 COL D
D1: 4,9,2                                # reduction candidate for 4,9
D1: 2 => SOLVED
* 763259841951748632248613597374591268196827453825436719432985176689174325517362984
D1: 4,9                                  # 16 pairs
* PAIR G5: 2,4 ROW 5
E5: 2,4,7                                # reduction candidate for 2,4
E5: 2,4                                  # 19 pairs
F5: 2,4,7                                # reduction candidate for 2,4
F5: 2,4                                  # 16 pairs
* PAIR I6: 4,9 COL I
I2: 4,9,2                                # reduction candidate for 4,9
I2: 4,9                                  # 18 pairs
I9: 4,9,2                                # reduction candidate for 4,9
I9: 4,9 => SOLVED
* 763259841951748632248613597374591268196827453825436719432985176689174325517362984
I9: 2                                    # 18 pairs
* PAIR C8: 2,9 ROW 8
E8: 2,9,4,7                              # reduction candidate for 2,9
E8: 2,9 => CTR
* 763459821.5.7..6.4.4.6..5.73745.1.6819687..53825.3671.43..8517668.1.7345517364982
E8: 4,7                                  # 16 pairs
F8: 2,9,4,7                              # reduction candidate for 2,9
F8: 2,9 => CTR
* 76345.8.1.5.7..6.4.4.6..5.73745.1.681968.7.53825.3671.43..8517668.17.345517364982
F8: 4,7                                  # 16 pairs
H8: 2,9,4                                # reduction candidate for 2,9
H8: 2,9                                  # 22 pairs
* PAIR D7: 2,9 BLK 8
E8: 2,9,4,7                              # reduction candidate for 2,9
E8: 2,9 => CTR
* 763459821.5.7..6.4.4.6..5.73745.1.6819687..53825.3671.43..8517668.1.7345517364982
E8: 4,7                                  # 16 pairs
F8: 2,9,4,7                              # reduction candidate for 2,9
F8: 2,9 => CTR
* 76345.8.1.5.7..6.4.4.6..5.73745.1.681968.7.53825.3671.43..8517668.17.345517364982
F8: 4,7                                  # 16 pairs
F9: 2,9,4                                # reduction candidate for 2,9
F9: 2,9                                  # 22 pairs
* PAIR D7: 2,9 COL D
D1: 2,9,4                                # reduction candidate for 2,9
D1: 4 => CTR
* 76345.8.1.5.7..64994.6..5373745219681968..25382593671443928517668219.3.551736.482
D1: 2,9                                  # 20 pairs
* PAIR G9: 4,9 BLK 9
H8: 4,9,2                                # reduction candidate for 4,9
H8: 4,9                                  # 18 pairs
I9: 4,9,2                                # reduction candidate for 4,9
I9: 4,9 => SOLVED
* 763259841951748632248613597374591268196827453825436719432985176689174325517362984
I9: 2                                    # 18 pairs
* PAIR G9: 4,9 ROW 9
F9: 4,9,2                                # reduction candidate for 4,9
F9: 2 => SOLVED
* 763259841951748632248613597374591268196827453825436719432985176689174325517362984
F9: 4,9                                  # 18 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-436-base-pr-000.dot
* REASONING
* DIS # E2: 2,9 => CTR => E2: 1,4
* DIS # H2: 2,9 => CTR => H2: 3,4
* DIS # E2: 2,9 => CTR => E2: 1,4
* DIS # E8: 2,9 => CTR => E8: 4,7
* PRF # D1: 2 => SOL
* PRF # I9: 4,9 => SOL
* DIS # E8: 2,9 => CTR => E8: 4,7
* DIS # F8: 2,9 => CTR => F8: 4,7
* DIS # E8: 2,9 => CTR => E8: 4,7
* DIS # F8: 2,9 => CTR => F8: 4,7
* DIS # D1: 4 => CTR => D1: 2,9
* PRF # I9: 4,9 => SOL
* PRF # F9: 2 => SOL
* CNT  13 HDP CHAINS /  36 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,C2,C3,C7,C8,D6,D7,E4,F2,F3,G4,G5,G9,I6)
* 763.5.8.1.5.7..6...4.6..5.73745.1.681968...53825.3671.43..8517668.1..3.551736..8.
* PAIR A2: 2,9 ROW 2
E2: 2,9,1,4                              # reduction candidate for 2,9
E2: 2,9 => CTR
* 763.5.8.1.517.8634.486135.73745.1.681968..45382543671943..8517668.1473.551736.982
H2: 2,9,3,4                              # reduction candidate for 2,9
H2: 2,9 => CTR
* 763.5.8.1.587136.4.416.85373745.1.681968..45382543671943..8517668.1473.551736.982
* RESTART
* PAIR RESTART
* PAIR A3: 2,9 ROW 3
E3: 2,9,1                                # reduction candidate for 2,9
E3: 2,9                                  # 19 pairs
H3: 2,9,3                                # reduction candidate for 2,9
H3: 2,9 => SOLVED
* 763259841951748632248613597374591268196827453825436719432985176689174325517362984
* DURATION: 0:00:06.745998  START: 17:41:40.195254  END: 17:41:46.941252 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-436-base-pr-001.dot
* REASONING
* DIS # E2: 2,9 => CTR => E2: 1,4
* DIS E2: 1,4 # H2: 2,9 => CTR => H2: 3,4
* PRF E2: 1,4 + H2: 3,4 # H3: 2,9 => SOL
* STA E2: 1,4 + H2: 3,4 + H3: 2,9
* CNT   3 HDP CHAINS /   4 HYP OPENED

Header Info

Top 500 Minimum 17 436

solution: 763259841951748632248613597374591268196827453825436719432985176689174325517362984
info: 95230    FNBTHWXK S8.f     1621

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

Solution

position: 763259841951748632248613597374591268196827453825436719432985176689174325517362984 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 # E2: 2,9 => CTR => E2: 1,4
* INC # E2: 1,4 => UNS
* DIS # H2: 2,9 => CTR => H2: 3,4
* INC # H2: 3,4 => UNS
* INC # I2: 2,9 => UNS
* INC # E3: 2,9 => UNS
* INC # H3: 2,9 => UNS
* DIS # E2: 2,9 => CTR => E2: 1,4
* INC # E2: 1,4 => UNS
* INC # E3: 2,9 => UNS
* DIS # E8: 2,9 => CTR => E8: 4,7
* INC # E8: 4,7 => UNS
* INC # D1: 4,9 => UNS
* PRF # D1: 2 => SOL
* INC # E5: 2,4 => UNS
* INC # F5: 2,4 => UNS
* INC # I2: 4,9 => UNS
* PRF # I9: 4,9 => SOL
* INC # I9: 2 => UNS
* DIS # E8: 2,9 => CTR => E8: 4,7
* INC # E8: 4,7 => UNS
* DIS # F8: 2,9 => CTR => F8: 4,7
* INC # F8: 4,7 => UNS
* INC # H8: 2,9 => UNS
* DIS # E8: 2,9 => CTR => E8: 4,7
* INC # E8: 4,7 => UNS
* DIS # F8: 2,9 => CTR => F8: 4,7
* INC # F8: 4,7 => UNS
* INC # F9: 2,9 => UNS
* INC # D1: 2,9 => UNS
* DIS # D1: 4 => CTR => D1: 2,9
* INC # H8: 4,9 => UNS
* PRF # I9: 4,9 => SOL
* INC # I9: 2 => UNS
* INC # F9: 4,9 => UNS
* PRF # F9: 2 => SOL
* CNT  36 HDP CHAINS /  36 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # E2: 2,9 => CTR => E2: 1,4
* DIS E2: 1,4 # H2: 2,9 => CTR => H2: 3,4
* INC E2: 1,4 + H2: 3,4 # E3: 2,9 => UNS
* PRF E2: 1,4 + H2: 3,4 # H3: 2,9 => SOL
* STA E2: 1,4 + H2: 3,4 + H3: 2,9
* CNT   4 HDP CHAINS /   4 HYP OPENED