Analysis of xx-top500-255-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .4.1.....5......2.....4.......5..1.48.7............6.......7.83..2.6.....1....... initial

Autosolve

position: .4.15....531.7842..7..4..159235861748674.1.5.15472.6.8496217583.82.65.41.158.4... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # G3: 3 => CTR => G3: 8,9
* PRF # D3: 6,9 => SOL
* DIS # D3: 3 => CTR => D3: 6,9
* PRF # H1: 6,9 => SOL
* DIS # H1: 3 => CTR => H1: 6,9
* DIS # I1: 6,9 => CTR => I1: 7
* DIS # I9: 6,9 => CTR => I9: 2,7
* PRF # G5: 2 => SOL
* PRF # F3: 3,9 => SOL
* PRF # G5: 2,9 => SOL
* DIS # G5: 3 => CTR => G5: 2,9
* PRF # I9: 2,9 => SOL
* PRF # G5: 2 => SOL
* DIS # H1: 6 => CTR => H1: 3,9
* PRF # D3: 6 => SOL
* PRF # G9: 7,9 => SOL
* DIS # G1: 7,9 => CTR => G1: 3,8
* DIS # I9: 6,9 => CTR => I9: 2,7
* PRF # H1: 6,9 => SOL
* DIS # H1: 3 => CTR => H1: 6,9
* CNT  20 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 # G3: 3 => CTR => G3: 8,9
* PRF G3: 8,9 # H1: 6,9 => SOL
* STA G3: 8,9 + H1: 6,9
* CNT   2 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

.4.1.....5......2.....4.......5..1.48.7............6.......7.83..2.6.....1....... initial
.4.15....531.7842..7..4..159235861748674.1.5.15472.6.8496217583.82.65.41.158.4... autosolve
648152397531978426279643815923586174867431259154729638496217583782365941315894762 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
A1: 2,6
C1: 8,9
A3: 2,6
C3: 8,9
D2: 6,9
I2: 6,9
E5: 3,9
F6: 3,9
I5: 2,9
H6: 3,9
A8: 3,7
A9: 3,7
D8: 3,9
E9: 3,9
G8: 7,9
H9: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,A3: 2.. / A1 = 2  => 18 pairs (_) / A3 = 2  =>  0 pairs (*)
F1,F3: 2.. / F1 = 2  =>  0 pairs (*) / F3 = 2  =>  0 pairs (X)
G5,I5: 2.. / G5 = 2  =>  0 pairs (*) / I5 = 2  =>  0 pairs (X)
G9,I9: 2.. / G9 = 2  => 16 pairs (_) / I9 = 2  =>  0 pairs (*)
A1,F1: 2.. / A1 = 2  => 18 pairs (_) / F1 = 2  =>  0 pairs (*)
A3,F3: 2.. / A3 = 2  =>  0 pairs (*) / F3 = 2  =>  0 pairs (X)
G5,G9: 2.. / G5 = 2  =>  0 pairs (*) / G9 = 2  =>  0 pairs (X)
I5,I9: 2.. / I5 = 2  => 16 pairs (_) / I9 = 2  =>  0 pairs (*)
E5,F6: 3.. / E5 = 3  =>  0 pairs (*) / F6 = 3  =>  0 pairs (X)
G5,H6: 3.. / G5 = 3  =>  0 pairs (X) / H6 = 3  =>  0 pairs (_)
A8,A9: 3.. / A8 = 3  =>  0 pairs (X) / A9 = 3  =>  0 pairs (_)
D8,E9: 3.. / D8 = 3  =>  0 pairs (*) / E9 = 3  =>  0 pairs (X)
E5,G5: 3.. / E5 = 3  =>  0 pairs (*) / G5 = 3  =>  0 pairs (X)
F6,H6: 3.. / F6 = 3  =>  0 pairs (X) / H6 = 3  =>  0 pairs (_)
A8,D8: 3.. / A8 = 3  =>  0 pairs (X) / D8 = 3  =>  0 pairs (_)
A9,E9: 3.. / A9 = 3  =>  0 pairs (*) / E9 = 3  =>  0 pairs (X)
D3,D8: 3.. / D3 = 3  =>  0 pairs (X) / D8 = 3  =>  0 pairs (_)
E5,E9: 3.. / E5 = 3  =>  0 pairs (*) / E9 = 3  =>  0 pairs (X)
H1,H6: 3.. / H1 = 3  =>  0 pairs (X) / H6 = 3  =>  0 pairs (_)
A1,A3: 6.. / A1 = 6  =>  0 pairs (*) / A3 = 6  =>  0 pairs (X)
D2,D3: 6.. / D2 = 6  => 18 pairs (_) / D3 = 6  =>  0 pairs (*)
H9,I9: 6.. / H9 = 6  => 16 pairs (_) / I9 = 6  =>  0 pairs (X)
D2,I2: 6.. / D2 = 6  => 18 pairs (_) / I2 = 6  =>  0 pairs (*)
A3,D3: 6.. / A3 = 6  => 18 pairs (_) / D3 = 6  =>  0 pairs (*)
H1,H9: 6.. / H1 = 6  =>  0 pairs (X) / H9 = 6  => 16 pairs (_)
G1,I1: 7.. / G1 = 7  =>  0 pairs (X) / I1 = 7  => 16 pairs (_)
A8,A9: 7.. / A8 = 7  =>  0 pairs (*) / A9 = 7  =>  0 pairs (X)
A8,G8: 7.. / A8 = 7  =>  0 pairs (*) / G8 = 7  =>  0 pairs (X)
I1,I9: 7.. / I1 = 7  => 16 pairs (_) / I9 = 7  =>  0 pairs (X)
C1,C3: 8.. / C1 = 8  => 17 pairs (_) / C3 = 8  => 17 pairs (_)
G1,G3: 8.. / G1 = 8  => 17 pairs (_) / G3 = 8  => 17 pairs (_)
C1,G1: 8.. / C1 = 8  => 17 pairs (_) / G1 = 8  => 17 pairs (_)
C3,G3: 8.. / C3 = 8  => 17 pairs (_) / G3 = 8  => 17 pairs (_)
C1,C3: 9.. / C1 = 9  => 17 pairs (_) / C3 = 9  => 17 pairs (_)
E5,F6: 9.. / E5 = 9  =>  0 pairs (X) / F6 = 9  =>  0 pairs (_)
D8,E9: 9.. / D8 = 9  =>  0 pairs (X) / E9 = 9  =>  0 pairs (_)
D2,I2: 9.. / D2 = 9  =>  0 pairs (*) / I2 = 9  =>  0 pairs (X)
F6,H6: 9.. / F6 = 9  =>  0 pairs (*) / H6 = 9  =>  0 pairs (X)
D8,G8: 9.. / D8 = 9  =>  0 pairs (X) / G8 = 9  =>  0 pairs (_)
E5,E9: 9.. / E5 = 9  =>  0 pairs (X) / E9 = 9  =>  0 pairs (_)
* DURATION: 0:01:18.249977  START: 11:29:47.271120  END: 11:31:05.521097 2017-05-04
* CP COUNT: (40)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A8,A9,C1,C3,D2,D8,E5,E9,F6,G8,H6,H9,I2,I5)
* .4.15....531.7842..7..4..159235861748674.1.5.15472.6.8496217583.82.65.41.158.4...
* PAIR C1: 8,9 ROW 1
G1: 8,9,3,7                              # reduction candidate for 8,9
G1: 8,9                                  # 19 pairs
G1: 3,7                                  # 18 pairs
* PAIR C3: 8,9 ROW 3
G3: 8,9,3                                # reduction candidate for 8,9
G3: 3 => CTR
* .4.15.8.7531.7842..78.4.315923586174867431.5.154729638496217583.82365941315894762
G3: 8,9                                  # 20 pairs
* PAIR D2: 6,9 BLK 2
D3: 6,9,3                                # reduction candidate for 6,9
D3: 6,9 => SOLVED
* 648152397531978426279643815923586174867431259154729638496217583782365941315894762
D3: 3 => CTR
* .4.15....53167842967.3428159235861748674.1.52154723698496217583382965741.158.4...
* PAIR I2: 6,9 BLK 3
H1: 6,9,3                                # reduction candidate for 6,9
H1: 6,9 => SOLVED
* 648152397531978426279643815923586174867431259154729638496217583782365941315894762
H1: 3 => CTR
* .4.15..3753197842..7..4..159235861748674.1352154723698496217583.82.65.41.15834269
I1: 6,9,7                                # reduction candidate for 6,9
I1: 6,9 => CTR
* .4.15.7..531.7842..7..4.8159235861748674.1352154723698496217583782365941315894...
I1: 7                                    # 16 pairs
* PAIR I2: 6,9 COL I
I9: 6,9,2,7                              # reduction candidate for 6,9
I9: 6,9 => CTR
* .4.15...7531.7842..7.34..15923586174867491352154723698496217583382965741715834269
I9: 2,7                                  # 19 pairs
* PAIR E5: 3,9 ROW 5
G5: 3,9,2                                # reduction candidate for 3,9
G5: 2 => SOLVED
* 648152397531978426279643815923586174867431259154729638496217583782365941315894762
G5: 3,9                                  # 16 pairs
* PAIR F6: 3,9 COL F
F1: 3,9,2                                # reduction candidate for 3,9
F1: 3,9                                  # 18 pairs
F3: 3,9,2                                # reduction candidate for 3,9
F3: 3,9 => SOLVED
* 648152397531978426279643815923586174867431259154729638496217583782365941315894762
F3: 2                                    # 18 pairs
* PAIR I5: 2,9 BLK 6
G5: 2,9,3                                # reduction candidate for 2,9
G5: 2,9 => SOLVED
* 648152397531978426279643815923586174867431259154729638496217583782365941315894762
G5: 3 => CTR
* .4.15..3753197842..7..4..159235861748674.1352154723698496217583.82.65.41.15834269
* PAIR I5: 2,9 COL I
I9: 2,9,6,7                              # reduction candidate for 2,9
I9: 2,9 => SOLVED
* 648152397531978426279643815923586174867431259154729638496217583782365941315894762
I9: 6,7                                  # 19 pairs
* PAIR H6: 3,9 BLK 6
G5: 3,9,2                                # reduction candidate for 3,9
G5: 2 => SOLVED
* 648152397531978426279643815923586174867431259154729638496217583782365941315894762
G5: 3,9                                  # 16 pairs
* PAIR H6: 3,9 COL H
H1: 3,9,6                                # reduction candidate for 3,9
H1: 6 => CTR
* .4.15..6.53167842967..42.159235861748674.1.5215472.638496217583.82.65.41.158.4296
H1: 3,9                                  # 16 pairs
* PAIR D8: 3,9 COL D
D3: 3,9,6                                # reduction candidate for 3,9
D3: 6 => SOLVED
* 648152397531978426279643815923586174867431259154729638496217583782365941315894762
D3: 3,9                                  # 18 pairs
* PAIR G8: 7,9 BLK 9
G9: 7,9,2                                # reduction candidate for 7,9
G9: 7,9 => SOLVED
* 648152397531978426279643815923586174867431259154729638496217583782365941315894762
G9: 2                                    # 16 pairs
I9: 7,9,2,6                              # reduction candidate for 7,9
I9: 7,9                                  # 17 pairs
* PAIR G8: 7,9 COL G
G1: 7,9,3,8                              # reduction candidate for 7,9
G1: 7,9 => CTR
* .481597..531.7842..79.4.8159235861748674.1352154723698496217583.82.65.41.15834269
G1: 3,8                                  # 17 pairs
* PAIR H9: 6,9 BLK 9
I9: 6,9,2,7                              # reduction candidate for 6,9
I9: 6,9 => CTR
* .4.15...7531.7842..7.34..15923586174867491352154723698496217583382965741715834269
I9: 2,7                                  # 19 pairs
* PAIR H9: 6,9 COL H
H1: 6,9,3                                # reduction candidate for 6,9
H1: 6,9 => SOLVED
* 648152397531978426279643815923586174867431259154729638496217583782365941315894762
H1: 3 => CTR
* .4.15..3753197842..7..4..159235861748674.1352154723698496217583.82.65.41.15834269
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-255-base-pr-000.dot
* REASONING
* DIS # G3: 3 => CTR => G3: 8,9
* PRF # D3: 6,9 => SOL
* DIS # D3: 3 => CTR => D3: 6,9
* PRF # H1: 6,9 => SOL
* DIS # H1: 3 => CTR => H1: 6,9
* DIS # I1: 6,9 => CTR => I1: 7
* DIS # I9: 6,9 => CTR => I9: 2,7
* PRF # G5: 2 => SOL
* PRF # F3: 3,9 => SOL
* PRF # G5: 2,9 => SOL
* DIS # G5: 3 => CTR => G5: 2,9
* PRF # I9: 2,9 => SOL
* PRF # G5: 2 => SOL
* DIS # H1: 6 => CTR => H1: 3,9
* PRF # D3: 6 => SOL
* PRF # G9: 7,9 => SOL
* DIS # G1: 7,9 => CTR => G1: 3,8
* DIS # I9: 6,9 => CTR => I9: 2,7
* PRF # H1: 6,9 => SOL
* DIS # H1: 3 => CTR => H1: 6,9
* CNT  20 HDP CHAINS /  36 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A8,A9,C1,C3,D2,D8,E5,E9,F6,G8,H6,H9,I2,I5)
* .4.15....531.7842..7..4..159235861748674.1.5.15472.6.8496217583.82.65.41.158.4...
* PAIR C1: 8,9 ROW 1
G1: 8,9,3,7                              # reduction candidate for 8,9
G1: 8,9                                  # 19 pairs
G1: 3,7                                  # 18 pairs
* PAIR C3: 8,9 ROW 3
G3: 8,9,3                                # reduction candidate for 8,9
G3: 3 => CTR
* .4.15.8.7531.7842..78.4.315923586174867431.5.154729638496217583.82365941315894762
* PAIR RESTART
* PAIR I2: 6,9 BLK 3
H1: 6,9,3                                # reduction candidate for 6,9
H1: 6,9 => SOLVED
* 648152397531978426279643815923586174867431259154729638496217583782365941315894762
* DURATION: 0:00:06.725410  START: 11:31:48.916471  END: 11:31:55.641881 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-255-base-pr-001.dot
* REASONING
* DIS # G3: 3 => CTR => G3: 8,9
* PRF G3: 8,9 # H1: 6,9 => SOL
* STA G3: 8,9 + H1: 6,9
* CNT   2 HDP CHAINS /   5 HYP OPENED

Header Info

Top 500 Minimum 17 255

solution: 648152397531978426279643815923586174867431259154729638496217583782365941315894762
info: 2077     FNBWXY   S8.f     46430

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

Solution

position: 648152397531978426279643815923586174867431259154729638496217583782365941315894762 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:

* INC # G1: 8,9 => UNS
* INC # G1: 3,7 => UNS
* INC # G3: 8,9 => UNS
* DIS # G3: 3 => CTR => G3: 8,9
* PRF # D3: 6,9 => SOL
* DIS # D3: 3 => CTR => D3: 6,9
* PRF # H1: 6,9 => SOL
* DIS # H1: 3 => CTR => H1: 6,9
* DIS # I1: 6,9 => CTR => I1: 7
* INC # I1: 7 => UNS
* DIS # I9: 6,9 => CTR => I9: 2,7
* INC # I9: 2,7 => UNS
* INC # G5: 3,9 => UNS
* PRF # G5: 2 => SOL
* INC # F1: 3,9 => UNS
* PRF # F3: 3,9 => SOL
* INC # F3: 2 => UNS
* PRF # G5: 2,9 => SOL
* DIS # G5: 3 => CTR => G5: 2,9
* PRF # I9: 2,9 => SOL
* INC # I9: 6,7 => UNS
* INC # G5: 3,9 => UNS
* PRF # G5: 2 => SOL
* INC # H1: 3,9 => UNS
* DIS # H1: 6 => CTR => H1: 3,9
* INC # D3: 3,9 => UNS
* PRF # D3: 6 => SOL
* PRF # G9: 7,9 => SOL
* INC # G9: 2 => UNS
* INC # I9: 7,9 => UNS
* DIS # G1: 7,9 => CTR => G1: 3,8
* INC # G1: 3,8 => UNS
* DIS # I9: 6,9 => CTR => I9: 2,7
* INC # I9: 2,7 => UNS
* PRF # H1: 6,9 => SOL
* DIS # H1: 3 => CTR => H1: 6,9
* CNT  36 HDP CHAINS /  36 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G1: 8,9 => UNS
* INC # G1: 3,7 => UNS
* INC # G3: 8,9 => UNS
* DIS # G3: 3 => CTR => G3: 8,9
* PRF G3: 8,9 # H1: 6,9 => SOL
* STA G3: 8,9 + H1: 6,9
* CNT   5 HDP CHAINS /   5 HYP OPENED