Analysis of xx-top95-005-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ....14....3....2...7..........9...3.6.1.............8.2.....1.4....5.6.....7.8... initial

Autosolve

position: .623148.7.3....2...7.2..4.3...9...3.6.1....42.......8.2..6..1.4....5.6.8.167.83.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A2: 5,9 => CTR => A2: 1,4,8
* PRF # A3: 5,9 => SOL
* DIS # A6: 5,9 => CTR => A6: 3,4,7
* DIS # A2: 5,8 => CTR => A2: 1,4,9
* DIS # C2: 5,8 => CTR => C2: 4,9
* PRF # H9: 5,9 => SOL
* DIS # A2: 5,9 => CTR => A2: 1,4,8
* DIS # C7: 7 => CTR => C7: 5,8
* DIS # A8: 4,9 => CTR => A8: 3,7
* DIS # C8: 4,9 => CTR => C8: 3,7
* DIS # C7: 8 => CTR => C7: 5,7
* PRF # H9: 5,9 => SOL
* PRF # A9: 4 => SOL
* CNT  13 HDP CHAINS /  51 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: 5,9 => CTR => A2: 1,4,8
* PRF A2: 1,4,8 # A3: 5,9 => SOL
* STA A2: 1,4,8 + A3: 5,9
* CNT   2 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

....14....3....2...7..........9...3.6.1.............8.2.....1.4....5.6.....7.8... initial
.623148.7.3....2...7.2..4.3...9...3.6.1....42.......8.2..6..1.4....5.6.8.167.83.. autosolve
962314857134587269578296413847962531651873942329145786285639174793451628416728395 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (20)
A1: 5,9
D2: 5,8
H1: 5,9
H2: 1,6
I2: 5,9
H3: 1,6
D5: 5,8
D6: 1,4
G4: 5,7
I4: 1,6
I6: 1,6
B7: 5,8
B8: 4,9
E7: 3,9
F7: 3,9
D8: 1,4
F8: 1,2
E9: 2,4
H7: 5,7
I9: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A2,A3: 1.. / A2 = 1  => 19 pairs (_) / A3 = 1  => 23 pairs (_)
H2,H3: 1.. / H2 = 1  => 23 pairs (_) / H3 = 1  => 19 pairs (_)
I4,I6: 1.. / I4 = 1  => 18 pairs (_) / I6 = 1  => 18 pairs (_)
D8,F8: 1.. / D8 = 1  => 20 pairs (_) / F8 = 1  =>  0 pairs (*)
A2,H2: 1.. / A2 = 1  => 19 pairs (_) / H2 = 1  => 23 pairs (_)
A3,H3: 1.. / A3 = 1  => 23 pairs (_) / H3 = 1  => 19 pairs (_)
F4,I4: 1.. / F4 = 1  => 18 pairs (_) / I4 = 1  => 18 pairs (_)
D6,D8: 1.. / D6 = 1  =>  0 pairs (*) / D8 = 1  =>  0 pairs (X)
B4,B6: 2.. / B4 = 2  => 20 pairs (_) / B6 = 2  => 22 pairs (_)
F8,E9: 2.. / F8 = 2  => 20 pairs (_) / E9 = 2  =>  0 pairs (*)
H8,H9: 2.. / H8 = 2  =>  0 pairs (*) / H9 = 2  =>  0 pairs (X)
F8,H8: 2.. / F8 = 2  => 20 pairs (_) / H8 = 2  =>  0 pairs (*)
E9,H9: 2.. / E9 = 2  =>  0 pairs (*) / H9 = 2  =>  0 pairs (X)
A6,C6: 3.. / A6 = 3  => 20 pairs (_) / C6 = 3  => 20 pairs (_)
E5,F5: 3.. / E5 = 3  => 20 pairs (_) / F5 = 3  => 20 pairs (_)
A8,C8: 3.. / A8 = 3  => 20 pairs (_) / C8 = 3  => 20 pairs (_)
E7,F7: 3.. / E7 = 3  => 20 pairs (_) / F7 = 3  => 20 pairs (_)
A6,A8: 3.. / A6 = 3  => 20 pairs (_) / A8 = 3  => 20 pairs (_)
C6,C8: 3.. / C6 = 3  => 20 pairs (_) / C8 = 3  => 20 pairs (_)
E5,E7: 3.. / E5 = 3  => 20 pairs (_) / E7 = 3  => 20 pairs (_)
F5,F7: 3.. / F5 = 3  => 20 pairs (_) / F7 = 3  => 20 pairs (_)
A2,C2: 4.. / A2 = 4  => 26 pairs (_) / C2 = 4  => 20 pairs (_)
D8,E9: 4.. / D8 = 4  =>  0 pairs (*) / E9 = 4  =>  0 pairs (X)
A9,E9: 4.. / A9 = 4  =>  0 pairs (*) / E9 = 4  =>  0 pairs (X)
D6,D8: 4.. / D6 = 4  => 20 pairs (_) / D8 = 4  =>  0 pairs (*)
H1,I2: 5.. / H1 = 5  =>  0 pairs (*) / I2 = 5  =>  0 pairs (X)
A1,H1: 5.. / A1 = 5  =>  0 pairs (X) / H1 = 5  =>  0 pairs (_)
D2,D5: 5.. / D2 = 5  =>  0 pairs (*) / D5 = 5  =>  0 pairs (X)
I2,I9: 5.. / I2 = 5  =>  0 pairs (X) / I9 = 5  =>  0 pairs (_)
H2,H3: 6.. / H2 = 6  => 19 pairs (_) / H3 = 6  => 23 pairs (_)
I4,I6: 6.. / I4 = 6  => 18 pairs (_) / I6 = 6  => 18 pairs (_)
E2,F2: 7.. / E2 = 7  => 21 pairs (_) / F2 = 7  => 21 pairs (_)
H7,H8: 7.. / H7 = 7  => 24 pairs (_) / H8 = 7  =>  0 pairs (X)
C7,H7: 7.. / C7 = 7  =>  0 pairs (X) / H7 = 7  => 24 pairs (_)
B7,C7: 8.. / B7 = 8  => 21 pairs (_) / C7 = 8  =>  0 pairs (X)
D2,D5: 8.. / D2 = 8  => 22 pairs (_) / D5 = 8  =>  0 pairs (*)
H1,I2: 9.. / H1 = 9  =>  0 pairs (X) / I2 = 9  =>  0 pairs (_)
G5,G6: 9.. / G5 = 9  => 25 pairs (_) / G6 = 9  => 23 pairs (_)
E7,F7: 9.. / E7 = 9  => 20 pairs (_) / F7 = 9  => 20 pairs (_)
A1,H1: 9.. / A1 = 9  =>  0 pairs (*) / H1 = 9  =>  0 pairs (X)
B5,G5: 9.. / B5 = 9  => 23 pairs (_) / G5 = 9  => 25 pairs (_)
I2,I9: 9.. / I2 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
* DURATION: 0:01:42.163175  START: 22:53:13.397832  END: 22:54:55.561007 2017-05-03
* CP COUNT: (42)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B7,B8,D2,D5,D6,D8,E7,E9,F7,F8,G4,H1,H2,H3,H7,I2,I4,I6,I9)
* .623148.7.3....2...7.2..4.3...9...3.6.1....42.......8.2..6..1.4....5.6.8.167.83..
* PAIR A1: 5,9 BLK 1
A2: 5,9,1,4,8                            # reduction candidate for 5,9
A2: 5,9 => CTR
* .623148.7.348..21.1782954638..9..53.691583742.53...98.285639174..9.5.6.8.167.83..
A2: 1,4,8                                # 20 pairs
C2: 5,9,4,8                              # reduction candidate for 5,9
C2: 5,9                                  # 18 pairs
A3: 5,9,1,8                              # reduction candidate for 5,9
A3: 5,9 => SOLVED
* 962314857134587269578296413847962531651873942329145786285639174793451628416728395
A3: 1,8                                  # 21 pairs
C3: 5,9,8                                # reduction candidate for 5,9
C3: 5,9                                  # 23 pairs
* PAIR A1: 5,9 COL A
A6: 5,9,3,4,7                            # reduction candidate for 5,9
A6: 5,9 => CTR
* 562314897.34...2.5.792.54.37.89..53.6.15837429.3....8.2856..1743.7.5.6.84167283..
A6: 3,4,7                                # 20 pairs
A9: 5,9,4                                # reduction candidate for 5,9
A9: 5,9                                  # 20 pairs
* PAIR D2: 5,8 ROW 2
A2: 5,8,1,4,9                            # reduction candidate for 5,8
A2: 5,8 => CTR
* 9623148575348..2191782954638.79..531651...9423.91..7862..6..174793451628416728395
A2: 1,4,9                                # 20 pairs
C2: 5,8,4,9                              # reduction candidate for 5,8
C2: 5,8 => CTR
* .6231485743....21917.2..4638..9...3.6.1....42...4...8.2856..1.4...1526.8.1674832.
C2: 4,9                                  # 21 pairs
* PAIR H1: 5,9 COL H
H9: 5,9,2                                # reduction candidate for 5,9
H9: 5,9 => SOLVED
* 962314857134587269578296413847962531651873942329145786285639174793451628416728395
H9: 2                                    # 20 pairs
* PAIR I2: 5,9 ROW 2
A2: 5,9,1,4,8                            # reduction candidate for 5,9
A2: 5,9 => CTR
* .623148.7.348..21.1782954638..9..53.691583742.53...98.285639174..9.5.6.8.167.83..
A2: 1,4,8                                # 20 pairs
C2: 5,9,4,8                              # reduction candidate for 5,9
C2: 5,9                                  # 18 pairs
F2: 5,9,6,7                              # reduction candidate for 5,9
F2: 5,9                                  # 22 pairs
* PAIR D5: 5,8 ROW 5
B5: 5,8,9                                # reduction candidate for 5,8
B5: 5,8                                  # 25 pairs
B5: 9                                    # 23 pairs
* PAIR G4: 5,7 BLK 6
G5: 5,7,9                                # reduction candidate for 5,7
G5: 5,7                                  # 23 pairs
G6: 5,7,9                                # reduction candidate for 5,7
G6: 5,7                                  # 25 pairs
* PAIR G4: 5,7 ROW 4
A4: 5,7,4,8                              # reduction candidate for 5,7
A4: 5,7                                  # 27 pairs
C4: 5,7,4,8                              # reduction candidate for 5,7
C4: 5,7                                  # 24 pairs
F4: 5,7,1,2,6                            # reduction candidate for 5,7
F4: 5,7                                  # 26 pairs
* PAIR I4: 1,6 ROW 4
F4: 1,6,2,5,7                            # reduction candidate for 1,6
F4: 2,5,7                                # 21 pairs
F4: 1,6                                  # 21 pairs
* PAIR I6: 1,6 ROW 6
F6: 1,6,2,5,7                            # reduction candidate for 1,6
F6: 1,6                                  # 22 pairs
F6: 2,5,7                                # 20 pairs
* PAIR B7: 5,8 BLK 7
C7: 5,8,7                                # reduction candidate for 5,8
C7: 7 => CTR
* .623148.7.3....2...7.2..4.3...9...3.6.1....42.......8.2876..154....5.678516748329
C7: 5,8                                  # 24 pairs
* PAIR B7: 5,8 COL B
B4: 5,8,2,4                              # reduction candidate for 5,8
B4: 5,8                                  # 25 pairs
B5: 5,8,9                                # reduction candidate for 5,8
B5: 5,8                                  # 25 pairs
* PAIR B8: 4,9 BLK 7
A8: 4,9,3,7                              # reduction candidate for 4,9
A8: 4,9 => CTR
* .62314897.3....2.5.7.2.54.37..9..53.6.15...423......8.2.76..154..3.526785167.8329
A8: 3,7                                  # 21 pairs
C8: 4,9,3,7                              # reduction candidate for 4,9
C8: 4,9 => CTR
* .62314897.3....2.5.7.2.54.3...9...3.6.15...42..3....8.2.76..1543...526785167.8329
C8: 3,7                                  # 21 pairs
A9: 4,9,5                                # reduction candidate for 4,9
A9: 4,9                                  # 24 pairs
* PAIR B8: 4,9 COL B
B6: 4,9,2,5                              # reduction candidate for 4,9
B6: 4,9                                  # 25 pairs
B6: 2,5                                  # 21 pairs
* PAIR F8: 1,2 COL F
F4: 1,2,5,6,7                            # reduction candidate for 1,2
F4: 1,2                                  # 21 pairs
F6: 1,2,5,6,7                            # reduction candidate for 1,2
F6: 1,2                                  # 19 pairs
* PAIR E9: 2,4 COL E
E4: 2,4,6,7,8                            # reduction candidate for 2,4
E4: 2,4                                  # 24 pairs
E6: 2,4,6,7                              # reduction candidate for 2,4
E6: 2,4                                  # 21 pairs
* PAIR H7: 5,7 ROW 7
C7: 5,7,8                                # reduction candidate for 5,7
C7: 8 => CTR
* .623148.7.34...2...7.2..4.34..9...3.6.1....42.......8.2586..174.4.152698916748325
C7: 5,7                                  # 21 pairs
* PAIR I9: 5,9 BLK 9
H9: 5,9,2                                # reduction candidate for 5,9
H9: 5,9 => SOLVED
* 962314857134587269578296413847962531651873942329145786285639174793451628416728395
H9: 2                                    # 20 pairs
* PAIR I9: 5,9 ROW 9
A9: 5,9,4                                # reduction candidate for 5,9
A9: 4 => SOLVED
* 962314857134587269578296413847962531651873942329145786285639174793451628416728395
A9: 5,9                                  # 20 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top95-005-base-pr-000.dot
* REASONING
* DIS # A2: 5,9 => CTR => A2: 1,4,8
* PRF # A3: 5,9 => SOL
* DIS # A6: 5,9 => CTR => A6: 3,4,7
* DIS # A2: 5,8 => CTR => A2: 1,4,9
* DIS # C2: 5,8 => CTR => C2: 4,9
* PRF # H9: 5,9 => SOL
* DIS # A2: 5,9 => CTR => A2: 1,4,8
* DIS # C7: 7 => CTR => C7: 5,8
* DIS # A8: 4,9 => CTR => A8: 3,7
* DIS # C8: 4,9 => CTR => C8: 3,7
* DIS # C7: 8 => CTR => C7: 5,7
* PRF # H9: 5,9 => SOL
* PRF # A9: 4 => SOL
* CNT  13 HDP CHAINS /  51 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B7,B8,D2,D5,D6,D8,E7,E9,F7,F8,G4,H1,H2,H3,H7,I2,I4,I6,I9)
* .623148.7.3....2...7.2..4.3...9...3.6.1....42.......8.2..6..1.4....5.6.8.167.83..
* PAIR A1: 5,9 BLK 1
A2: 5,9,1,4,8                            # reduction candidate for 5,9
A2: 5,9 => CTR
* .623148.7.348..21.1782954638..9..53.691583742.53...98.285639174..9.5.6.8.167.83..
C2: 5,9,4,8                              # reduction candidate for 5,9
C2: 5,9                                  # 18 pairs
A3: 5,9,1,8                              # reduction candidate for 5,9
A3: 5,9 => SOLVED
* 962314857134587269578296413847962531651873942329145786285639174793451628416728395
* DURATION: 0:00:06.221203  START: 22:56:04.435517  END: 22:56:10.656720 2017-05-03
* SOLUTION FOUND
* SAVE PR GRAPH xx-top95-005-base-pr-001.dot
* REASONING
* DIS # A2: 5,9 => CTR => A2: 1,4,8
* PRF A2: 1,4,8 # A3: 5,9 => SOL
* STA A2: 1,4,8 + A3: 5,9
* CNT   2 HDP CHAINS /   3 HYP OPENED

Header Info

Top 95 Sudokus 005
[sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt

Solution

position: 962314857134587269578296413847962531651873942329145786285639174793451628416728395 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: 5,9 => CTR => A2: 1,4,8
* INC # A2: 1,4,8 => UNS
* INC # C2: 5,9 => UNS
* PRF # A3: 5,9 => SOL
* INC # A3: 1,8 => UNS
* INC # C3: 5,9 => UNS
* DIS # A6: 5,9 => CTR => A6: 3,4,7
* INC # A6: 3,4,7 => UNS
* INC # A9: 5,9 => UNS
* DIS # A2: 5,8 => CTR => A2: 1,4,9
* INC # A2: 1,4,9 => UNS
* DIS # C2: 5,8 => CTR => C2: 4,9
* INC # C2: 4,9 => UNS
* PRF # H9: 5,9 => SOL
* INC # H9: 2 => UNS
* DIS # A2: 5,9 => CTR => A2: 1,4,8
* INC # A2: 1,4,8 => UNS
* INC # C2: 5,9 => UNS
* INC # F2: 5,9 => UNS
* INC # B5: 5,8 => UNS
* INC # B5: 9 => UNS
* INC # G5: 5,7 => UNS
* INC # G6: 5,7 => UNS
* INC # A4: 5,7 => UNS
* INC # C4: 5,7 => UNS
* INC # F4: 5,7 => UNS
* INC # F4: 1,6 => UNS
* INC # F4: 2,5,7 => UNS
* INC # F6: 1,6 => UNS
* INC # F6: 2,5,7 => UNS
* INC # C7: 5,8 => UNS
* DIS # C7: 7 => CTR => C7: 5,8
* INC # B4: 5,8 => UNS
* INC # B5: 5,8 => UNS
* DIS # A8: 4,9 => CTR => A8: 3,7
* INC # A8: 3,7 => UNS
* DIS # C8: 4,9 => CTR => C8: 3,7
* INC # C8: 3,7 => UNS
* INC # A9: 4,9 => UNS
* INC # B6: 4,9 => UNS
* INC # B6: 2,5 => UNS
* INC # F4: 1,2 => UNS
* INC # F6: 1,2 => UNS
* INC # E4: 2,4 => UNS
* INC # E6: 2,4 => UNS
* INC # C7: 5,7 => UNS
* DIS # C7: 8 => CTR => C7: 5,7
* PRF # H9: 5,9 => SOL
* INC # H9: 2 => UNS
* INC # A9: 5,9 => UNS
* PRF # A9: 4 => SOL
* CNT  51 HDP CHAINS /  51 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A2: 5,9 => CTR => A2: 1,4,8
* INC A2: 1,4,8 # C2: 5,9 => UNS
* PRF A2: 1,4,8 # A3: 5,9 => SOL
* STA A2: 1,4,8 + A3: 5,9
* CNT   3 HDP CHAINS /   3 HYP OPENED