Analysis of xx-top500-461-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...6...1..72.......8..4....5..3.9.......7.8..6........3..9....5.4....7........... initial

Autosolve

position: .536...17.72.......8674....51.3.9...2.4.7.8..6........3.19.7..584.2..7..7........ autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A2: 4,9 => CTR => A2: 1
* PRF # A2: 1 => SOL
* PRF # G1: 4,9 => SOL
* DIS # G1: 2 => CTR => G1: 4,9
* PRF # A2: 1,9 => SOL
* DIS # A2: 4 => CTR => A2: 1,9
* PRF # E1: 2,8 => SOL
* DIS # E1: 9 => CTR => E1: 2,8
* PRF # F6: 2,8 => SOL
* DIS # E2: 1,5 => CTR => E2: 3,9
* DIS # F2: 1,5 => CTR => F2: 3
* PRF # F3: 1,5 => SOL
* DIS # F3: 2,3 => CTR => F3: 1,5
* DIS # F5: 1,5 => CTR => F5: 6
* DIS # F6: 1,5 => CTR => F6: 2,4,8
* PRF # F6: 1,2,5 => SOL
* DIS # G7: 2,6 => CTR => G7: 4
* PRF # G7: 4 => SOL
* DIS # H7: 2,6 => CTR => H7: 4,8
* DIS # G9: 2,6 => CTR => G9: 1,3,9
* DIS # E9: 6,8 => CTR => E9: 1,3,5
* PRF # H7: 6,8 => SOL
* DIS # H7: 2,4 => CTR => H7: 6,8
* PRF # F9: 4,8 => SOL
* DIS # F9: 1,3,5,6 => CTR => F9: 4,8
* CNT  25 HDP CHAINS /  45 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 # A2: 4,9 => CTR => A2: 1
* PRF A2: 1 => SOL
* STA A2: 1
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

...6...1..72.......8..4....5..3.9.......7.8..6........3..9....5.4....7........... initial
.536...17.72.......8674....51.3.9...2.4.7.8..6........3.19.7..584.2..7..7........ autosolve
453628917172593648986741523517389264234176859698452371321967485849215736765834192 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
A1: 4,9
A3: 1,9
F1: 2,8
D2: 1,5
C4: 7,8
B5: 3,9
B6: 3,9
C6: 7,8
D5: 1,5
D6: 4,8
B7: 2,6
C8: 5,9
B9: 2,6
C9: 5,9
E7: 6,8
D9: 4,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A2,A3: 1.. / A2 = 1  =>  0 pairs (*) / A3 = 1  =>  0 pairs (X)
A3,F3: 1.. / A3 = 1  =>  0 pairs (X) / F3 = 1  =>  0 pairs (_)
D2,D5: 1.. / D2 = 1  =>  0 pairs (X) / D5 = 1  => 16 pairs (_)
G6,G9: 1.. / G6 = 1  => 16 pairs (_) / G9 = 1  => 16 pairs (_)
B7,B9: 2.. / B7 = 2  => 15 pairs (_) / B9 = 2  =>  0 pairs (X)
B5,B6: 3.. / B5 = 3  => 14 pairs (_) / B6 = 3  => 14 pairs (_)
A1,A2: 4.. / A1 = 4  =>  0 pairs (*) / A2 = 4  =>  0 pairs (X)
D6,F6: 4.. / D6 = 4  =>  0 pairs (*) / F6 = 4  =>  0 pairs (X)
D9,F9: 4.. / D9 = 4  => 14 pairs (_) / F9 = 4  =>  0 pairs (*)
G7,H7: 4.. / G7 = 4  =>  0 pairs (*) / H7 = 4  =>  0 pairs (X)
A1,G1: 4.. / A1 = 4  =>  0 pairs (*) / G1 = 4  =>  0 pairs (X)
D6,D9: 4.. / D6 = 4  =>  0 pairs (*) / D9 = 4  =>  0 pairs (X)
F6,F9: 4.. / F6 = 4  => 14 pairs (_) / F9 = 4  =>  0 pairs (*)
I2,I4: 4.. / I2 = 4  =>  0 pairs (X) / I4 = 4  => 17 pairs (_)
C8,C9: 5.. / C8 = 5  => 14 pairs (_) / C9 = 5  => 15 pairs (_)
D2,D5: 5.. / D2 = 5  => 16 pairs (_) / D5 = 5  =>  0 pairs (X)
E4,F5: 6.. / E4 = 6  =>  0 pairs (X) / F5 = 6  => 17 pairs (_)
B7,B9: 6.. / B7 = 6  =>  0 pairs (X) / B9 = 6  => 15 pairs (_)
C4,C6: 7.. / C4 = 7  =>  0 pairs (*) / C6 = 7  =>  0 pairs (X)
H4,H6: 7.. / H4 = 7  => 15 pairs (_) / H6 = 7  =>  0 pairs (*)
C4,H4: 7.. / C4 = 7  =>  0 pairs (*) / H4 = 7  =>  0 pairs (X)
C6,H6: 7.. / C6 = 7  => 15 pairs (_) / H6 = 7  =>  0 pairs (*)
E1,F1: 8.. / E1 = 8  =>  0 pairs (X) / F1 = 8  => 16 pairs (_)
H2,I2: 8.. / H2 = 8  =>  0 pairs (X) / I2 = 8  => 17 pairs (_)
C4,C6: 8.. / C4 = 8  => 15 pairs (_) / C6 = 8  =>  0 pairs (*)
C4,E4: 8.. / C4 = 8  => 15 pairs (_) / E4 = 8  =>  0 pairs (*)
E7,H7: 8.. / E7 = 8  =>  0 pairs (X) / H7 = 8  =>  0 pairs (_)
D6,D9: 8.. / D6 = 8  => 14 pairs (_) / D9 = 8  =>  0 pairs (*)
I2,I9: 8.. / I2 = 8  => 17 pairs (_) / I9 = 8  =>  0 pairs (X)
E1,E2: 9.. / E1 = 9  =>  0 pairs (X) / E2 = 9  =>  0 pairs (_)
B5,B6: 9.. / B5 = 9  => 14 pairs (_) / B6 = 9  => 14 pairs (_)
C8,C9: 9.. / C8 = 9  => 15 pairs (_) / C9 = 9  => 14 pairs (_)
* DURATION: 0:01:04.731472  START: 18:28:25.755076  END: 18:29:30.486548 2017-05-04
* CP COUNT: (32)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B5,B6,B7,B9,C4,C6,C8,C9,D2,D5,D6,D9,E7,F1)
* .536...17.72.......8674....51.3.9...2.4.7.8..6........3.19.7..584.2..7..7........
* PAIR A1: 4,9 BLK 1
A2: 4,9,1                                # reduction candidate for 4,9
A2: 4,9 => CTR
* 953628417472.9....18674....51.3.9..42.4.7.8..6........3.1987.4584.2..7..7..4.....
A2: 1 => SOLVED
* 453628917172593648986741523517389264234176859698452371321967485849215736765834192
* PAIR A1: 4,9 ROW 1
G1: 4,9,2                                # reduction candidate for 4,9
G1: 4,9 => SOLVED
* 453628917172593648986741523517389264234176859698452371321967485849215736765834192
G1: 2 => CTR
* 453698217972......186742...51.3.9...2.4.7.8..6........3.19.7..584.2..7..7........
* PAIR A3: 1,9 BLK 1
A2: 1,9,4                                # reduction candidate for 1,9
A2: 1,9 => SOLVED
* 453628917172593648986741523517389264234176859698452371321967485849215736765834192
A2: 4 => CTR
* 953628417472.9....18674....51.3.9..42.4.7.8..6........3.1987.4584.2..7..7..4.....
* PAIR F1: 2,8 BLK 2
E1: 2,8,9                                # reduction candidate for 2,8
E1: 2,8 => SOLVED
* 453628917172593648986741523517389264234176859698452371321967485849215736765834192
E1: 9 => CTR
* 453698217972......186742...51.3.9...2.4.7.8..6........3.19.7..584.2..7..7........
* PAIR F1: 2,8 COL F
F6: 2,8,1,4,5                            # reduction candidate for 2,8
F6: 2,8 => SOLVED
* 453628917172593648986741523517389264234176859698452371321967485849215736765834192
F6: 1,4,5                                # 17 pairs
* PAIR D2: 1,5 BLK 2
E2: 1,5,3,9                              # reduction candidate for 1,5
E2: 1,5 => CTR
* 453698217972..3...186742...51.3.9...2.4.7.8..6........3.19.7..584.2..7..7........
E2: 3,9                                  # 17 pairs
F2: 1,5,3                                # reduction candidate for 1,5
F2: 1,5 => CTR
* 953628417472.9.3..186743...51.3.9..42.4.7.8..6........3.1987.4584.2..7..7..4.....
F2: 3                                    # 16 pairs
F3: 1,5,2,3                              # reduction candidate for 1,5
F3: 1,5 => SOLVED
* 453628917172593648986741523517389264234176859698452371321967485849215736765834192
F3: 2,3 => CTR
* 953628417472.9.3..186743...51.3.9..42.4.7.8..6........3.1987.4584.2..7..7..4.....
* PAIR B5: 3,9 ROW 5
H5: 3,9,5,6                              # reduction candidate for 3,9
H5: 3,9                                  # 18 pairs
I5: 3,9,1,6                              # reduction candidate for 3,9
I5: 3,9                                  # 18 pairs
* PAIR B6: 3,9 ROW 6
G6: 3,9,1,2,5                            # reduction candidate for 3,9
G6: 3,9                                  # 18 pairs
H6: 3,9,2,5,7                            # reduction candidate for 3,9
H6: 3,9                                  # 17 pairs
I6: 3,9,1,2                              # reduction candidate for 3,9
I6: 3,9                                  # 17 pairs
* PAIR D5: 1,5 BLK 5
F5: 1,5,6                                # reduction candidate for 1,5
F5: 1,5 => CTR
* 453698217972....8.186742...5183694722.4.7.8..6.7824...3.198764584.2.67..76.4...28
F5: 6                                    # 17 pairs
E6: 1,5,2,8                              # reduction candidate for 1,5
E6: 1,5                                  # 18 pairs
F6: 1,5,2,4,8                            # reduction candidate for 1,5
F6: 1,5 => CTR
* .53698217.72....48186742...51.3.96.42.4.768..6..4.....32196748584.2..76.76.8.4...
F6: 2,4,8                                # 16 pairs
* PAIR D6: 4,8 BLK 5
F6: 4,8,1,2,5                            # reduction candidate for 4,8
F6: 1,2,5 => SOLVED
* 453628917172593648986741523517389264234176859698452371321967485849215736765834192
F6: 4,8                                  # 17 pairs
* PAIR B7: 2,6 ROW 7
G7: 2,6,4                                # reduction candidate for 2,6
G7: 2,6 => CTR
* 453698217972.....4186742...5183.947.2.4.7.8..6.78.4...32198764584.2..7..76.4....8
G7: 4 => SOLVED
* 453628917172593648986741523517389264234176859698452371321967485849215736765834192
H7: 2,6,4,8                              # reduction candidate for 2,6
H7: 2,6 => CTR
* 453698217.72...648.86742...5183.9.742.4.7.8..6.78.4...3.19874.584.2..7..7..4...8.
H7: 4,8                                  # 17 pairs
* PAIR B9: 2,6 ROW 9
G9: 2,6,1,3,9                            # reduction candidate for 2,6
G9: 2,6 => CTR
* .536...17.72.......8674....51.3.9...2.4.7.8..6.....1..3.19.7..584.2..7..7........
G9: 1,3,9                                # 16 pairs
H9: 2,6,3,8,9                            # reduction candidate for 2,6
H9: 2,6                                  # 17 pairs
I9: 2,6,1,3,8,9                          # reduction candidate for 2,6
I9: 2,6                                  # 18 pairs
* PAIR E7: 6,8 BLK 8
E9: 6,8,1,3,5                            # reduction candidate for 6,8
E9: 6,8 => CTR
* 453698217972......186742...518329.7.2.4.768..6.78.4...3.19.74.584.2..7..7..4.....
E9: 1,3,5                                # 16 pairs
F9: 6,8,1,3,4,5                          # reduction candidate for 6,8
F9: 6,8                                  # 16 pairs
* PAIR E7: 6,8 ROW 7
H7: 6,8,2,4                              # reduction candidate for 6,8
H7: 6,8 => SOLVED
* 453628917172593648986741523517389264234176859698452371321967485849215736765834192
H7: 2,4 => CTR
* 453698217972......186742...5183.9.7.2.4.7.8..6.78.4...3.1987..584.2..7..7..4.....
* PAIR E7: 6,8 COL E
E4: 6,8,2                                # reduction candidate for 6,8
E4: 6,8                                  # 17 pairs
E4: 2                                    # 17 pairs
* PAIR D9: 4,8 BLK 8
F9: 4,8,1,3,5,6                          # reduction candidate for 4,8
F9: 4,8 => SOLVED
* 453628917172593648986741523517389264234176859698452371321967485849215736765834192
F9: 1,3,5,6 => CTR
* 453698217972......186742...5183.9.7.2.4.7.8..6.78.4...3.19.7..584.2..7..7..4.....
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-461-base-pr-000.dot
* REASONING
* DIS # A2: 4,9 => CTR => A2: 1
* PRF # A2: 1 => SOL
* PRF # G1: 4,9 => SOL
* DIS # G1: 2 => CTR => G1: 4,9
* PRF # A2: 1,9 => SOL
* DIS # A2: 4 => CTR => A2: 1,9
* PRF # E1: 2,8 => SOL
* DIS # E1: 9 => CTR => E1: 2,8
* PRF # F6: 2,8 => SOL
* DIS # E2: 1,5 => CTR => E2: 3,9
* DIS # F2: 1,5 => CTR => F2: 3
* PRF # F3: 1,5 => SOL
* DIS # F3: 2,3 => CTR => F3: 1,5
* DIS # F5: 1,5 => CTR => F5: 6
* DIS # F6: 1,5 => CTR => F6: 2,4,8
* PRF # F6: 1,2,5 => SOL
* DIS # G7: 2,6 => CTR => G7: 4
* PRF # G7: 4 => SOL
* DIS # H7: 2,6 => CTR => H7: 4,8
* DIS # G9: 2,6 => CTR => G9: 1,3,9
* DIS # E9: 6,8 => CTR => E9: 1,3,5
* PRF # H7: 6,8 => SOL
* DIS # H7: 2,4 => CTR => H7: 6,8
* PRF # F9: 4,8 => SOL
* DIS # F9: 1,3,5,6 => CTR => F9: 4,8
* CNT  25 HDP CHAINS /  45 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B5,B6,B7,B9,C4,C6,C8,C9,D2,D5,D6,D9,E7,F1)
* .536...17.72.......8674....51.3.9...2.4.7.8..6........3.19.7..584.2..7..7........
* PAIR A1: 4,9 BLK 1
A2: 4,9,1                                # reduction candidate for 4,9
A2: 4,9 => CTR
* 953628417472.9....18674....51.3.9..42.4.7.8..6........3.1987.4584.2..7..7..4.....
A2: 1 => SOLVED
* 453628917172593648986741523517389264234176859698452371321967485849215736765834192
* DURATION: 0:00:03.888392  START: 18:30:23.339287  END: 18:30:27.227679 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-461-base-pr-001.dot
* REASONING
* DIS # A2: 4,9 => CTR => A2: 1
* PRF A2: 1 => SOL
* STA A2: 1
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 461

solution: 453628917172593648986741523517389264234176859698452371321967485849215736765834192
info: 95544    FNBTYK   S8.f     10358

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

Solution

position: 453628917172593648986741523517389264234176859698452371321967485849215736765834192 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 # A2: 4,9 => CTR => A2: 1
* PRF # A2: 1 => SOL
* PRF # G1: 4,9 => SOL
* DIS # G1: 2 => CTR => G1: 4,9
* PRF # A2: 1,9 => SOL
* DIS # A2: 4 => CTR => A2: 1,9
* PRF # E1: 2,8 => SOL
* DIS # E1: 9 => CTR => E1: 2,8
* PRF # F6: 2,8 => SOL
* INC # F6: 1,4,5 => UNS
* DIS # E2: 1,5 => CTR => E2: 3,9
* INC # E2: 3,9 => UNS
* DIS # F2: 1,5 => CTR => F2: 3
* INC # F2: 3 => UNS
* PRF # F3: 1,5 => SOL
* DIS # F3: 2,3 => CTR => F3: 1,5
* INC # H5: 3,9 => UNS
* INC # I5: 3,9 => UNS
* INC # G6: 3,9 => UNS
* INC # H6: 3,9 => UNS
* INC # I6: 3,9 => UNS
* DIS # F5: 1,5 => CTR => F5: 6
* INC # F5: 6 => UNS
* INC # E6: 1,5 => UNS
* DIS # F6: 1,5 => CTR => F6: 2,4,8
* INC # F6: 2,4,8 => UNS
* INC # F6: 4,8 => UNS
* PRF # F6: 1,2,5 => SOL
* DIS # G7: 2,6 => CTR => G7: 4
* PRF # G7: 4 => SOL
* DIS # H7: 2,6 => CTR => H7: 4,8
* INC # H7: 4,8 => UNS
* DIS # G9: 2,6 => CTR => G9: 1,3,9
* INC # G9: 1,3,9 => UNS
* INC # H9: 2,6 => UNS
* INC # I9: 2,6 => UNS
* DIS # E9: 6,8 => CTR => E9: 1,3,5
* INC # E9: 1,3,5 => UNS
* INC # F9: 6,8 => UNS
* PRF # H7: 6,8 => SOL
* DIS # H7: 2,4 => CTR => H7: 6,8
* INC # E4: 6,8 => UNS
* INC # E4: 2 => UNS
* PRF # F9: 4,8 => SOL
* DIS # F9: 1,3,5,6 => CTR => F9: 4,8
* CNT  45 HDP CHAINS /  45 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A2: 4,9 => CTR => A2: 1
* PRF A2: 1 => SOL
* STA A2: 1
* CNT   2 HDP CHAINS /   1 HYP OPENED