Analysis of xx-top95-090-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ..........72.6.1....51...82.8...13..4.........37.9..1.....238..5.4..9.........79. initial

Autosolve

position: 1.........72.6.1....51...82.8...13..451.......37.9..1.7...238..5.4..9....2..1.79. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A2: 9 => CTR => A2: 3,8
* DIS # E1: 3,8 => CTR => E1: 4,5
* DIS # E3: 4,7 => CTR => E3: 3
* DIS # G6: 2,6 => CTR => G6: 4,5
* DIS # A2: 9 => CTR => A2: 3,8
* DIS # D5: 7,8 => CTR => D5: 2,3,6
* DIS # E5: 3 => CTR => E5: 7,8
* DIS # G6: 2,6 => CTR => G6: 4,5
* CNT   8 HDP CHAINS /  32 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: 9 => CTR => A2: 3,8
* DIS A2: 3,8 # G6: 2,6 => CTR => G6: 4,5
* PRF A2: 3,8 + G6: 4,5 # B3: 6,9 => SOL
* STA A2: 3,8 + G6: 4,5 + B3: 6,9
* CNT   3 HDP CHAINS /  25 HYP OPENED

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

Details

Positions

..........72.6.1....51...82.8...13..4.........37.9..1.....238..5.4..9.........79. initial
1.........72.6.1....51...82.8...13..451.......37.9..1.7...238..5.4..9....2..1.79. autosolve
143258679872964153695137482986541327451372968237896514719623845564789231328415796 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
C1: 3,8
F3: 4,7
C4: 6,9
A6: 2,6
C7: 6,9
B8: 1,6
A9: 3,8
C9: 3,8
D8: 7,8
E8: 7,8
G8: 2,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B7,B8: 1.. / B7 = 1  => 14 pairs (_) / B8 = 1  => 15 pairs (_)
I7,I8: 1.. / I7 = 1  => 15 pairs (_) / I8 = 1  => 14 pairs (_)
B7,I7: 1.. / B7 = 1  => 14 pairs (_) / I7 = 1  => 15 pairs (_)
B8,I8: 1.. / B8 = 1  => 15 pairs (_) / I8 = 1  => 14 pairs (_)
D1,F1: 2.. / D1 = 2  => 16 pairs (_) / F1 = 2  => 11 pairs (_)
A4,A6: 2.. / A4 = 2  => 14 pairs (_) / A6 = 2  => 11 pairs (_)
G8,H8: 2.. / G8 = 2  => 12 pairs (_) / H8 = 2  => 21 pairs (_)
D5,E5: 3.. / D5 = 3  => 13 pairs (_) / E5 = 3  =>  0 pairs (X)
A9,C9: 3.. / A9 = 3  => 14 pairs (_) / C9 = 3  =>  9 pairs (_)
H8,I8: 3.. / H8 = 3  => 13 pairs (_) / I8 = 3  => 15 pairs (_)
A3,E3: 3.. / A3 = 3  =>  0 pairs (X) / E3 = 3  => 15 pairs (_)
C1,C9: 3.. / C1 = 3  => 14 pairs (_) / C9 = 3  =>  9 pairs (_)
B1,B3: 4.. / B1 = 4  => 13 pairs (_) / B3 = 4  => 20 pairs (_)
E1,E4: 5.. / E1 = 5  =>  0 pairs (*) / E4 = 5  =>  0 pairs (X)
G1,G6: 5.. / G1 = 5  =>  0 pairs (X) / G6 = 5  =>  0 pairs (_)
C4,C7: 6.. / C4 = 6  => 15 pairs (_) / C7 = 6  => 16 pairs (_)
E3,F3: 7.. / E3 = 7  =>  0 pairs (X) / F3 = 7  => 11 pairs (_)
H1,I1: 7.. / H1 = 7  => 12 pairs (_) / I1 = 7  => 11 pairs (_)
D8,E8: 7.. / D8 = 7  => 10 pairs (_) / E8 = 7  => 11 pairs (_)
F3,F5: 7.. / F3 = 7  => 11 pairs (_) / F5 = 7  =>  0 pairs (X)
C1,A2: 8.. / C1 = 8  =>  9 pairs (_) / A2 = 8  => 14 pairs (_)
I5,I6: 8.. / I5 = 8  => 16 pairs (_) / I6 = 8  => 11 pairs (_)
A9,C9: 8.. / A9 = 8  =>  9 pairs (_) / C9 = 8  => 14 pairs (_)
D8,E8: 8.. / D8 = 8  => 11 pairs (_) / E8 = 8  => 10 pairs (_)
A2,A9: 8.. / A2 = 8  => 14 pairs (_) / A9 = 8  =>  9 pairs (_)
C1,C9: 8.. / C1 = 8  =>  9 pairs (_) / C9 = 8  => 14 pairs (_)
D1,D2: 9.. / D1 = 9  => 12 pairs (_) / D2 = 9  => 15 pairs (_)
A4,C4: 9.. / A4 = 9  => 15 pairs (_) / C4 = 9  => 16 pairs (_)
G5,I5: 9.. / G5 = 9  => 17 pairs (_) / I5 = 9  => 18 pairs (_)
B7,C7: 9.. / B7 = 9  => 16 pairs (_) / C7 = 9  => 15 pairs (_)
C4,C7: 9.. / C4 = 9  => 16 pairs (_) / C7 = 9  => 15 pairs (_)
* DURATION: 0:00:45.727218  START: 01:03:30.128261  END: 01:04:15.855479 2017-05-04
* CP COUNT: (31)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,B8,C1,C4,C7,C9,D8,E8,F3,G8)
* 1.........72.6.1....51...82.8...13..451.......37.9..1.7...238..5.4..9....2..1.79.
* PAIR C1: 3,8 BLK 1
A2: 3,8,9                                # reduction candidate for 3,8
A2: 9 => CTR
* 1489.25..972.6.1..3651..982.89.513..451.....9.37.96418796.23851514..9...823615794
A2: 3,8                                  # 15 pairs
* PAIR C1: 3,8 ROW 1
D1: 3,8,2,4,5,9                          # reduction candidate for 3,8
D1: 3,8                                  # 11 pairs
E1: 3,8,4,5                              # reduction candidate for 3,8
E1: 3,8 => CTR
* 14........72.6.1..365147982.8..513..451.....9.37.9.41.7...238..5.4..9....2..1.79.
E1: 4,5                                  # 12 pairs
* PAIR F3: 4,7 BLK 2
E3: 4,7,3                                # reduction candidate for 4,7
E3: 4,7 => CTR
* 1489.25..972.6.1..3651..982.89.513..451.....9.37.96418796.23851514..9...823615794
E3: 3                                    # 15 pairs
* PAIR C4: 6,9 BLK 4
A4: 6,9,2                                # reduction candidate for 6,9
A4: 2                                    # 14 pairs
A4: 6,9                                  # 11 pairs
* PAIR A6: 2,6 BLK 4
A4: 2,6,9                                # reduction candidate for 2,6
A4: 2,6                                  # 16 pairs
A4: 9                                    # 15 pairs
* PAIR A6: 2,6 ROW 6
D6: 2,6,4,5,8                            # reduction candidate for 2,6
D6: 2,6                                  # 13 pairs
F6: 2,6,4,5,8                            # reduction candidate for 2,6
F6: 2,6                                  # 13 pairs
G6: 2,6,4,5                              # reduction candidate for 2,6
G6: 2,6 => CTR
* 14....5...72.6.139..51.7482.8..5134.451...9.8.37.9..157...2385.5.4..9..3.2..1.79.
G6: 4,5                                  # 12 pairs
* PAIR C7: 6,9 BLK 7
B7: 6,9,1                                # reduction candidate for 6,9
B7: 6,9                                  # 15 pairs
B7: 1                                    # 14 pairs
* PAIR B8: 1,6 BLK 7
B7: 1,6,9                                # reduction candidate for 1,6
B7: 9                                    # 16 pairs
B7: 1,6                                  # 15 pairs
* PAIR B8: 1,6 ROW 8
I8: 1,6,3                                # reduction candidate for 1,6
I8: 3                                    # 15 pairs
I8: 1,6                                  # 13 pairs
* PAIR A9: 3,8 COL A
A2: 3,8,9                                # reduction candidate for 3,8
A2: 9 => CTR
* 1489.25..972.6.1..3651..982.89.513..451.....9.37.96418796.23851514..9...823615794
A2: 3,8                                  # 15 pairs
* PAIR D8: 7,8 COL D
D5: 7,8,2,3,6                            # reduction candidate for 7,8
D5: 7,8 => CTR
* 1489526..9723681..3651..982.89..13..45183...9.37.9..18796.238.1514789...823.1.79.
D5: 2,3,6                                # 11 pairs
* PAIR E8: 7,8 COL E
E5: 7,8,3                                # reduction candidate for 7,8
E5: 3 => CTR
* 1489526..9723681..3651..982.89..13..45183...9.37.9..18796.238.1514789...823.1.79.
E5: 7,8                                  # 13 pairs
* PAIR G8: 2,6 BLK 9
H8: 2,6,3                                # reduction candidate for 2,6
H8: 2,6                                  # 15 pairs
H8: 3                                    # 13 pairs
* PAIR G8: 2,6 COL G
G5: 2,6,9                                # reduction candidate for 2,6
G5: 2,6                                  # 18 pairs
G6: 2,6,4,5                              # reduction candidate for 2,6
G6: 2,6 => CTR
* 14....5...72.6.139..51.7482.8..5134.451...9.8.37.9..157...2385.5.4..9..3.2..1.79.
G6: 4,5                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top95-090-base-pr-000.dot
* REASONING
* DIS # A2: 9 => CTR => A2: 3,8
* DIS # E1: 3,8 => CTR => E1: 4,5
* DIS # E3: 4,7 => CTR => E3: 3
* DIS # G6: 2,6 => CTR => G6: 4,5
* DIS # A2: 9 => CTR => A2: 3,8
* DIS # D5: 7,8 => CTR => D5: 2,3,6
* DIS # E5: 3 => CTR => E5: 7,8
* DIS # G6: 2,6 => CTR => G6: 4,5
* CNT   8 HDP CHAINS /  32 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,B8,C1,C4,C7,C9,D8,E8,F3,G8)
* 1.........72.6.1....51...82.8...13..451.......37.9..1.7...238..5.4..9....2..1.79.
* PAIR C1: 3,8 BLK 1
A2: 3,8,9                                # reduction candidate for 3,8
A2: 9 => CTR
* 1489.25..972.6.1..3651..982.89.513..451.....9.37.96418796.23851514..9...823615794
* PAIR C4: 6,9 BLK 4
A4: 6,9,2                                # reduction candidate for 6,9
A4: 2                                    # 17 pairs
A4: 6,9                                  # 15 pairs
* PAIR A6: 2,6 BLK 4
A4: 2,6,9                                # reduction candidate for 2,6
A4: 2,6                                  # 19 pairs
A4: 9                                    # 15 pairs
* PAIR A6: 2,6 ROW 6
D6: 2,6,4,5,8                            # reduction candidate for 2,6
D6: 2,6                                  # 17 pairs
F6: 2,6,4,5,8                            # reduction candidate for 2,6
F6: 2,6                                  # 17 pairs
G6: 2,6,4,5                              # reduction candidate for 2,6
G6: 2,6 => CTR
* 14....5...72.6.1....5137482.8..513..4513..9...37.9..157...2385.5.4..9....2..1.79.
* PAIR RESTART
* PAIR A6: 2,6 BLK 4
A4: 2,6,9                                # reduction candidate for 2,6
A4: 2,6                                  # 20 pairs
A4: 9                                    # 16 pairs
* PAIR A6: 2,6 ROW 6
D6: 2,6,4,5,8                            # reduction candidate for 2,6
D6: 2,6                                  # 17 pairs
F6: 2,6,4,5,8                            # reduction candidate for 2,6
F6: 2,6                                  # 17 pairs
* PAIR C7: 6,9 BLK 7
B7: 6,9,1                                # reduction candidate for 6,9
B7: 6,9                                  # 20 pairs
B7: 1                                    # 15 pairs
* PAIR B8: 1,6 BLK 7
B7: 1,6,9                                # reduction candidate for 1,6
B7: 9                                    # 20 pairs
B7: 1,6                                  # 16 pairs
* PAIR B8: 1,6 ROW 8
I8: 1,6,3                                # reduction candidate for 1,6
I8: 3                                    # 20 pairs
I8: 1,6                                  # 18 pairs
* PAIR G8: 2,6 BLK 9
H8: 2,6,3                                # reduction candidate for 2,6
H8: 2,6                                  # 20 pairs
H8: 3                                    # 18 pairs
* PAIR G8: 2,6 COL G
G5: 2,6,9                                # reduction candidate for 2,6
G5: 2,6                                  # 20 pairs
G5: 9                                    # 18 pairs

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,A3,A6,A9,B8,C1,C4,C7,C9,D8,E1,E4,E5,E8,G6,G8)
* 1.........72.6.1....5137.82.8...13..4513......37.9..1.7...238..5.4..9....2..1.79.
* PAIR A3: 6,9 BLK 1
B1: 6,9,4                                # reduction candidate for 6,9
B1: 6,9                                  # 20 pairs
B3: 6,9,4                                # reduction candidate for 6,9
B3: 6,9 => SOLVED
* 143258679872964153695137482986541327451372968237896514719623845564789231328415796
* DURATION: 0:00:24.460627  START: 01:04:41.716679  END: 01:05:06.177306 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top95-090-base-pr-001.dot
* REASONING
* DIS # A2: 9 => CTR => A2: 3,8
* DIS A2: 3,8 # G6: 2,6 => CTR => G6: 4,5
* PRF A2: 3,8 + G6: 4,5 # B3: 6,9 => SOL
* STA A2: 3,8 + G6: 4,5 + B3: 6,9
* CNT   3 HDP CHAINS /  25 HYP OPENED

Header Info

Top 95 Sudokus 090
[sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt

Solution

position: 143258679872964153695137482986541327451372968237896514719623845564789231328415796 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 # A2: 3,8 => UNS
* DIS # A2: 9 => CTR => A2: 3,8
* INC # D1: 3,8 => UNS
* DIS # E1: 3,8 => CTR => E1: 4,5
* INC # E1: 4,5 => UNS
* DIS # E3: 4,7 => CTR => E3: 3
* INC # E3: 3 => UNS
* INC # A4: 6,9 => UNS
* INC # A4: 2 => UNS
* INC # A4: 2,6 => UNS
* INC # A4: 9 => UNS
* INC # D6: 2,6 => UNS
* INC # F6: 2,6 => UNS
* DIS # G6: 2,6 => CTR => G6: 4,5
* INC # G6: 4,5 => UNS
* INC # B7: 6,9 => UNS
* INC # B7: 1 => UNS
* INC # B7: 1,6 => UNS
* INC # B7: 9 => UNS
* INC # I8: 1,6 => UNS
* INC # I8: 3 => UNS
* INC # A2: 3,8 => UNS
* DIS # A2: 9 => CTR => A2: 3,8
* DIS # D5: 7,8 => CTR => D5: 2,3,6
* INC # D5: 2,3,6 => UNS
* INC # E5: 7,8 => UNS
* DIS # E5: 3 => CTR => E5: 7,8
* INC # H8: 2,6 => UNS
* INC # H8: 3 => UNS
* INC # G5: 2,6 => UNS
* DIS # G6: 2,6 => CTR => G6: 4,5
* INC # G6: 4,5 => UNS
* CNT  32 HDP CHAINS /  32 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 3,8 => UNS
* DIS # A2: 9 => CTR => A2: 3,8
* INC A2: 3,8 # A4: 6,9 => UNS
* INC A2: 3,8 # A4: 2 => UNS
* INC A2: 3,8 # A4: 2,6 => UNS
* INC A2: 3,8 # A4: 9 => UNS
* INC A2: 3,8 # D6: 2,6 => UNS
* INC A2: 3,8 # F6: 2,6 => UNS
* DIS A2: 3,8 # G6: 2,6 => CTR => G6: 4,5
* INC A2: 3,8 + G6: 4,5 # A4: 2,6 => UNS
* INC A2: 3,8 + G6: 4,5 # A4: 9 => UNS
* INC A2: 3,8 + G6: 4,5 # D6: 2,6 => UNS
* INC A2: 3,8 + G6: 4,5 # F6: 2,6 => UNS
* INC A2: 3,8 + G6: 4,5 # B7: 6,9 => UNS
* INC A2: 3,8 + G6: 4,5 # B7: 1 => UNS
* INC A2: 3,8 + G6: 4,5 # B7: 1,6 => UNS
* INC A2: 3,8 + G6: 4,5 # B7: 9 => UNS
* INC A2: 3,8 + G6: 4,5 # I8: 1,6 => UNS
* INC A2: 3,8 + G6: 4,5 # I8: 3 => UNS
* INC A2: 3,8 + G6: 4,5 # H8: 2,6 => UNS
* INC A2: 3,8 + G6: 4,5 # H8: 3 => UNS
* INC A2: 3,8 + G6: 4,5 # G5: 2,6 => UNS
* INC A2: 3,8 + G6: 4,5 # G5: 9 => UNS
* INC A2: 3,8 + G6: 4,5 # B1: 6,9 => UNS
* PRF A2: 3,8 + G6: 4,5 # B3: 6,9 => SOL
* STA A2: 3,8 + G6: 4,5 + B3: 6,9
* CNT  25 HDP CHAINS /  25 HYP OPENED