Analysis of xx-top95-016-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 6..3.2....4.....1..........7.26............543.........8.15........4.2........7.. initial

Autosolve

position: 6..3.2....4.....12.2.4.....7526.4..........543.4....2728.15........4.2..4.....7.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # G1: 8,9 => CTR => G1: 4,5
* PRF # G2: 8,9 => SOL
* DIS # I3: 8,9 => CTR => I3: 3,6
* DIS # C1: 8,9 => CTR => C1: 1,5,7
* DIS # I4: 3 => CTR => I4: 8,9
* DIS # G4: 3,9 => CTR => G4: 1,8
* DIS # I4: 3,9 => CTR => I4: 8
* DIS # E4: 1,8 => CTR => E4: 3,9
* PRF # H3: 3,9 => SOL
* DIS # H7: 3,9 => CTR => H7: 4,6
* DIS # C8: 1,5 => CTR => C8: 6,7,9
* DIS # C9: 6,9 => CTR => C9: 1,5
* CNT  12 HDP CHAINS /  30 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 # G1: 8,9 => CTR => G1: 4,5
* PRF G1: 4,5 # G2: 8,9 => SOL
* STA G1: 4,5 + G2: 8,9
* CNT   2 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

6..3.2....4.....1..........7.26............543.........8.15........4.2........7.. initial
6..3.2....4.....12.2.4.....7526.4..........543.4....2728.15........4.2..4.....7.. autosolve
615382479943765812827491536752634198168279354394518627286157943579843261431926785 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (4)
I1: 8,9
H4: 3,9
I8: 1,5
I9: 1,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I8,I9: 1.. / I8 = 1  =>  3 pairs (_) / I9 = 1  =>  0 pairs (X)
E4,G4: 1.. / E4 = 1  =>  0 pairs (X) / G4 = 1  =>  4 pairs (_)
D5,E5: 2.. / D5 = 2  =>  5 pairs (_) / E5 = 2  =>  5 pairs (_)
D9,E9: 2.. / D9 = 2  =>  5 pairs (_) / E9 = 2  =>  5 pairs (_)
D5,D9: 2.. / D5 = 2  =>  5 pairs (_) / D9 = 2  =>  5 pairs (_)
E5,E9: 2.. / E5 = 2  =>  5 pairs (_) / E9 = 2  =>  5 pairs (_)
C2,C3: 3.. / C2 = 3  =>  0 pairs (*) / C3 = 3  =>  0 pairs (X)
B8,B9: 3.. / B8 = 3  =>  0 pairs (X) / B9 = 3  =>  5 pairs (_)
C2,G2: 3.. / C2 = 3  =>  0 pairs (*) / G2 = 3  =>  0 pairs (X)
G1,H1: 4.. / G1 = 4  =>  5 pairs (_) / H1 = 4  =>  0 pairs (X)
G7,H7: 4.. / G7 = 4  =>  0 pairs (X) / H7 = 4  =>  5 pairs (_)
G1,G7: 4.. / G1 = 4  =>  5 pairs (_) / G7 = 4  =>  0 pairs (X)
H1,H7: 4.. / H1 = 4  =>  0 pairs (X) / H7 = 4  =>  5 pairs (_)
D6,F6: 5.. / D6 = 5  =>  4 pairs (_) / F6 = 5  =>  6 pairs (_)
I8,I9: 5.. / I8 = 5  =>  0 pairs (X) / I9 = 5  =>  3 pairs (_)
C1,G1: 5.. / C1 = 5  =>  3 pairs (_) / G1 = 5  =>  0 pairs (X)
C9,I9: 5.. / C9 = 5  =>  0 pairs (X) / I9 = 5  =>  3 pairs (_)
D2,D6: 5.. / D2 = 5  =>  6 pairs (_) / D6 = 5  =>  4 pairs (_)
E2,F2: 6.. / E2 = 6  =>  4 pairs (_) / F2 = 6  =>  0 pairs (X)
H3,I3: 6.. / H3 = 6  =>  0 pairs (X) / I3 = 6  =>  5 pairs (_)
G5,G6: 6.. / G5 = 6  =>  0 pairs (X) / G6 = 6  =>  5 pairs (_)
B6,G6: 6.. / B6 = 6  =>  0 pairs (X) / G6 = 6  =>  5 pairs (_)
E2,E9: 6.. / E2 = 6  =>  4 pairs (_) / E9 = 6  =>  0 pairs (X)
I3,I7: 6.. / I3 = 6  =>  5 pairs (_) / I7 = 6  =>  0 pairs (X)
H1,H3: 7.. / H1 = 7  =>  0 pairs (*) / H3 = 7  =>  0 pairs (X)
C7,F7: 7.. / C7 = 7  =>  0 pairs (X) / F7 = 7  =>  8 pairs (_)
B1,B8: 7.. / B1 = 7  =>  0 pairs (X) / B8 = 7  =>  0 pairs (_)
A5,C5: 8.. / A5 = 8  =>  5 pairs (_) / C5 = 8  =>  5 pairs (_)
H8,H9: 8.. / H8 = 8  =>  5 pairs (_) / H9 = 8  =>  5 pairs (_)
* DURATION: 0:00:44.709608  START: 23:11:01.336946  END: 23:11:46.046554 2017-05-03
* CP COUNT: (29)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (H4,I1,I8,I9)
* 6..3.2....4.....12.2.4.....7526.4..........543.4....2728.15........4.2..4.....7..
* PAIR I1: 8,9 BLK 3
G1: 8,9,4,5                              # reduction candidate for 8,9
G1: 8,9 => CTR
* 615372.4..47.6.312.234..5767526.4...1.8....543.4....2728.1574..57..4.2.1431.2.7.5
G1: 4,5                                  #  5 pairs
G2: 8,9,3,5                              # reduction candidate for 8,9
G2: 8,9 => SOLVED
* 615382479943765812827491536752634198168279354394518627286157943579843261431926785
G2: 3,5                                  #  5 pairs
G3: 8,9,3,5                              # reduction candidate for 8,9
G3: 8,9                                  #  9 pairs
I3: 8,9,3,6                              # reduction candidate for 8,9
I3: 8,9 => CTR
* 6..3.247..4.....12.2.4...6.7526.4.93....3..543.4....27289157346.7..4328.43....7..
I3: 3,6                                  #  5 pairs
* PAIR I1: 8,9 ROW 1
C1: 8,9,1,5,7                            # reduction candidate for 8,9
C1: 8,9 => CTR
* 61.37254..47.6.312.234...767526.4..........543.4....2728.1574...7..4.2..43..2.7..
C1: 1,5,7                                #  4 pairs
E1: 8,9,1,7                              # reduction candidate for 8,9
E1: 8,9                                  #  8 pairs
* PAIR I1: 8,9 COL I
I4: 8,9,3                                # reduction candidate for 8,9
I4: 3 => CTR
* 6..3.2....47.6.312.234.....7526.4.93.......543.4....27286157.39.7..432..4.....7..
I4: 8,9                                  #  7 pairs
* PAIR H4: 3,9 BLK 6
G4: 3,9,1,8                              # reduction candidate for 3,9
G4: 3,9 => CTR
* 6..3.2..9.47.6.312.234.1..6752614938.......543.4....2728.1574.3.7..432..4.....7..
G4: 1,8                                  #  5 pairs
I4: 3,9,8                                # reduction candidate for 3,9
I4: 3,9 => CTR
* 6..3.2....47.6.312.234.....7526.4..........543.4....2728.157....7..4.2..43..2.7..
I4: 8                                    #  7 pairs
G5: 3,9,1,6                              # reduction candidate for 3,9
G5: 3,9                                  # 10 pairs
* PAIR H4: 3,9 ROW 4
E4: 3,9,1,8                              # reduction candidate for 3,9
E4: 1,8 => CTR
* 6..3.2....47.6.312.234.....7526.4..........543.4....2728.157....7..4.2..43..2.7..
E4: 3,9                                  #  9 pairs
* PAIR H4: 3,9 COL H
H3: 3,9,6,7                              # reduction candidate for 3,9
H3: 3,9 => SOLVED
* 615382479943765812827491536752634198168279354394518627286157943579843261431926785
H3: 6,7                                  #  5 pairs
H7: 3,9,4,6                              # reduction candidate for 3,9
H7: 3,9 => CTR
* 6..372.4..47.6.312.234...767526.4..........543.4....272861574...7..432..4.....7..
H7: 4,6                                  #  5 pairs
H8: 3,9,6,8                              # reduction candidate for 3,9
H8: 3,9                                  # 10 pairs
H9: 3,9,6,8                              # reduction candidate for 3,9
H9: 3,9                                  # 10 pairs
* PAIR I8: 1,5 ROW 8
A8: 1,5,9                                # reduction candidate for 1,5
A8: 1,5                                  #  5 pairs
C8: 1,5,6,7,9                            # reduction candidate for 1,5
C8: 1,5 => CTR
* 6..37254..47.6.312.234...767526.4..........543.4....272861574..97.84.2..43..2.78.
C8: 6,7,9                                #  4 pairs
* PAIR I9: 1,5 ROW 9
C9: 1,5,6,9                              # reduction candidate for 1,5
C9: 6,9 => CTR
* 67.3.2....4.....12.2.4...767526.4..........543.4....2728.15.....3..4.2.141....7.5
C9: 1,5                                  #  5 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top95-016-base-pr-000.dot
* REASONING
* DIS # G1: 8,9 => CTR => G1: 4,5
* PRF # G2: 8,9 => SOL
* DIS # I3: 8,9 => CTR => I3: 3,6
* DIS # C1: 8,9 => CTR => C1: 1,5,7
* DIS # I4: 3 => CTR => I4: 8,9
* DIS # G4: 3,9 => CTR => G4: 1,8
* DIS # I4: 3,9 => CTR => I4: 8
* DIS # E4: 1,8 => CTR => E4: 3,9
* PRF # H3: 3,9 => SOL
* DIS # H7: 3,9 => CTR => H7: 4,6
* DIS # C8: 1,5 => CTR => C8: 6,7,9
* DIS # C9: 6,9 => CTR => C9: 1,5
* CNT  12 HDP CHAINS /  30 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (H4,I1,I8,I9)
* 6..3.2....4.....12.2.4.....7526.4..........543.4....2728.15........4.2..4.....7..
* PAIR I1: 8,9 BLK 3
G1: 8,9,4,5                              # reduction candidate for 8,9
G1: 8,9 => CTR
* 615372.4..47.6.312.234..5767526.4...1.8....543.4....2728.1574..57..4.2.1431.2.7.5
G2: 8,9,3,5                              # reduction candidate for 8,9
G2: 8,9 => SOLVED
* 615382479943765812827491536752634198168279354394518627286157943579843261431926785
* DURATION: 0:00:03.866436  START: 23:12:11.866373  END: 23:12:15.732809 2017-05-03
* SOLUTION FOUND
* SAVE PR GRAPH xx-top95-016-base-pr-001.dot
* REASONING
* DIS # G1: 8,9 => CTR => G1: 4,5
* PRF G1: 4,5 # G2: 8,9 => SOL
* STA G1: 4,5 + G2: 8,9
* CNT   2 HDP CHAINS /   2 HYP OPENED

Header Info

Top 95 Sudokus 016
[sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt

Solution

position: 615382479943765812827491536752634198168279354394518627286157943579843261431926785 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 # G1: 8,9 => CTR => G1: 4,5
* INC # G1: 4,5 => UNS
* PRF # G2: 8,9 => SOL
* INC # G2: 3,5 => UNS
* INC # G3: 8,9 => UNS
* DIS # I3: 8,9 => CTR => I3: 3,6
* INC # I3: 3,6 => UNS
* DIS # C1: 8,9 => CTR => C1: 1,5,7
* INC # C1: 1,5,7 => UNS
* INC # E1: 8,9 => UNS
* INC # I4: 8,9 => UNS
* DIS # I4: 3 => CTR => I4: 8,9
* DIS # G4: 3,9 => CTR => G4: 1,8
* INC # G4: 1,8 => UNS
* DIS # I4: 3,9 => CTR => I4: 8
* INC # I4: 8 => UNS
* INC # G5: 3,9 => UNS
* INC # E4: 3,9 => UNS
* DIS # E4: 1,8 => CTR => E4: 3,9
* PRF # H3: 3,9 => SOL
* INC # H3: 6,7 => UNS
* DIS # H7: 3,9 => CTR => H7: 4,6
* INC # H7: 4,6 => UNS
* INC # H8: 3,9 => UNS
* INC # H9: 3,9 => UNS
* INC # A8: 1,5 => UNS
* DIS # C8: 1,5 => CTR => C8: 6,7,9
* INC # C8: 6,7,9 => UNS
* INC # C9: 1,5 => UNS
* DIS # C9: 6,9 => CTR => C9: 1,5
* CNT  30 HDP CHAINS /  30 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # G1: 8,9 => CTR => G1: 4,5
* PRF G1: 4,5 # G2: 8,9 => SOL
* STA G1: 4,5 + G2: 8,9
* CNT   2 HDP CHAINS /   2 HYP OPENED