Analysis of xx-top95-019-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .237....68...6.59.9.....7......4.97.3.7.96..2.........5..47.........2....8....... initial

Autosolve

position: .23759..687.26.59.9.....72.....4.97.3.7.96..2....27...5..47.........2....8...5... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C6: 1,4 => CTR => C6: 5,8,9
* PRF # B4: 1 => SOL
* DIS # B6: 1,4 => CTR => B6: 5,9
* DIS # C6: 1,4 => CTR => C6: 5,8,9
* PRF # I6: 5,8 => SOL
* DIS # B8: 6,9 => CTR => B8: 1,3,4
* CNT   6 HDP CHAINS /  42 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 # C6: 1,4 => CTR => C6: 5,8,9
* PRF C6: 5,8,9 # B4: 1 => SOL
* STA C6: 5,8,9 + B4: 1
* CNT   2 HDP CHAINS /  13 HYP OPENED

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

Details

Positions

.237....68...6.59.9.....7......4.97.3.7.96..2.........5..47.........2....8....... initial
.23759..687.26.59.9.....72.....4.97.3.7.96..2....27...5..47.........2....8...5... autosolve
123759486874261593965384721216543978357896142498127365532478619641932857789615234 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (12)
A1: 1,4
C2: 1,4
B3: 5,6
C3: 5,6
A4: 2,6
A6: 1,4
G6: 3,6
H6: 3,6
A8: 6,7
D8: 6,9
D9: 6,9
E9: 1,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,C2: 1.. / A1 = 1  =>  0 pairs (*) / C2 = 1  =>  0 pairs (X)
A1,A6: 1.. / A1 = 1  =>  0 pairs (*) / A6 = 1  =>  0 pairs (X)
A4,C4: 2.. / A4 = 2  => 14 pairs (_) / C4 = 2  => 11 pairs (_)
G7,G9: 2.. / G7 = 2  => 12 pairs (_) / G9 = 2  => 14 pairs (_)
C7,G7: 2.. / C7 = 2  => 14 pairs (_) / G7 = 2  => 12 pairs (_)
A4,A9: 2.. / A4 = 2  => 14 pairs (_) / A9 = 2  => 11 pairs (_)
I2,I3: 3.. / I2 = 3  => 14 pairs (_) / I3 = 3  => 17 pairs (_)
D4,F4: 3.. / D4 = 3  => 14 pairs (_) / F4 = 3  => 16 pairs (_)
G6,H6: 3.. / G6 = 3  => 10 pairs (_) / H6 = 3  => 10 pairs (_)
B7,B8: 3.. / B7 = 3  => 14 pairs (_) / B8 = 3  =>  0 pairs (X)
F2,I2: 3.. / F2 = 3  => 17 pairs (_) / I2 = 3  => 14 pairs (_)
D3,D4: 3.. / D3 = 3  => 16 pairs (_) / D4 = 3  => 14 pairs (_)
A1,C2: 4.. / A1 = 4  =>  0 pairs (X) / C2 = 4  =>  0 pairs (_)
F2,F3: 4.. / F2 = 4  =>  0 pairs (X) / F3 = 4  => 14 pairs (_)
F3,I3: 4.. / F3 = 4  => 14 pairs (_) / I3 = 4  =>  0 pairs (X)
A1,A6: 4.. / A1 = 4  =>  0 pairs (X) / A6 = 4  =>  0 pairs (_)
B3,C3: 5.. / B3 = 5  => 14 pairs (_) / C3 = 5  => 14 pairs (_)
H8,I8: 5.. / H8 = 5  => 12 pairs (_) / I8 = 5  => 21 pairs (_)
H5,H8: 5.. / H5 = 5  => 21 pairs (_) / H8 = 5  => 12 pairs (_)
B3,C3: 6.. / B3 = 6  => 14 pairs (_) / C3 = 6  => 14 pairs (_)
G6,H6: 6.. / G6 = 6  => 10 pairs (_) / H6 = 6  => 10 pairs (_)
D8,D9: 6.. / D8 = 6  => 10 pairs (_) / D9 = 6  => 11 pairs (_)
A8,A9: 7.. / A8 = 7  => 12 pairs (_) / A9 = 7  => 13 pairs (_)
I8,I9: 7.. / I8 = 7  => 13 pairs (_) / I9 = 7  => 12 pairs (_)
A8,I8: 7.. / A8 = 7  => 12 pairs (_) / I8 = 7  => 13 pairs (_)
A9,I9: 7.. / A9 = 7  => 13 pairs (_) / I9 = 7  => 12 pairs (_)
G1,H1: 8.. / G1 = 8  => 14 pairs (_) / H1 = 8  => 13 pairs (_)
C4,C6: 8.. / C4 = 8  => 16 pairs (_) / C6 = 8  => 13 pairs (_)
F7,E8: 8.. / F7 = 8  => 16 pairs (_) / E8 = 8  => 14 pairs (_)
E3,E8: 8.. / E3 = 8  => 16 pairs (_) / E8 = 8  => 14 pairs (_)
B6,C6: 9.. / B6 = 9  => 12 pairs (_) / C6 = 9  =>  0 pairs (X)
D8,D9: 9.. / D8 = 9  => 11 pairs (_) / D9 = 9  => 10 pairs (_)
* DURATION: 0:00:57.405478  START: 23:15:05.077818  END: 23:16:02.483296 2017-05-03
* CP COUNT: (32)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,A6,A8,B3,C2,C3,D8,D9,E9,G6,H6)
* .23759..687.26.59.9.....72.....4.97.3.7.96..2....27...5..47.........2....8...5...
* PAIR A1: 1,4 ROW 1
G1: 1,4,8                                # reduction candidate for 1,4
G1: 1,4                                  # 13 pairs
H1: 1,4,8                                # reduction candidate for 1,4
H1: 1,4                                  # 14 pairs
* PAIR C2: 1,4 ROW 2
F2: 1,4,3                                # reduction candidate for 1,4
F2: 1,4                                  # 14 pairs
I2: 1,4,3                                # reduction candidate for 1,4
I2: 1,4                                  # 17 pairs
* PAIR C2: 1,4 COL C
C6: 1,4,5,8,9                            # reduction candidate for 1,4
C6: 1,4 => CTR
* .23759..687.26.59.9.5...72.268.4.97.3.7.96..2.9..27...5..47.........2....8...5...
C6: 5,8,9                                # 12 pairs
C8: 1,4,6,9                              # reduction candidate for 1,4
C8: 1,4                                  # 15 pairs
C9: 1,4,2,6,9                            # reduction candidate for 1,4
C9: 1,4                                  # 14 pairs
* PAIR B3: 5,6 COL B
B4: 5,6,1                                # reduction candidate for 5,6
B4: 1 => SOLVED
* 123759486874261593965384721216543978357896142498127365532478619641932857789615234
B4: 5,6                                  # 16 pairs
* PAIR C3: 5,6 COL C
C4: 5,6,1,2,8                            # reduction candidate for 5,6
C4: 5,6                                  # 15 pairs
C4: 1,2,8                                # 12 pairs
* PAIR A4: 2,6 BLK 4
C4: 2,6,1,5,8                            # reduction candidate for 2,6
C4: 2,6                                  # 14 pairs
C4: 1,5,8                                # 14 pairs
* PAIR A4: 2,6 COL A
A9: 2,6,7                                # reduction candidate for 2,6
A9: 7                                    # 13 pairs
A9: 2,6                                  # 12 pairs
* PAIR A6: 1,4 BLK 4
B5: 1,4,5                                # reduction candidate for 1,4
B5: 1,4                                  # 16 pairs
B6: 1,4,5,9                              # reduction candidate for 1,4
B6: 1,4 => CTR
* .23759..687.26.59.9.5...72.268.4.97.3.7.96..2..9.27...5..47.........2....8...5...
B6: 5,9                                  # 13 pairs
C6: 1,4,5,8,9                            # reduction candidate for 1,4
C6: 1,4 => CTR
* .23759..687.26.59.9.5...72.268.4.97.3.7.96..2.9..27...5..47.........2....8...5...
C6: 5,8,9                                # 12 pairs
* PAIR A6: 1,4 ROW 6
I6: 1,4,5,8                              # reduction candidate for 1,4
I6: 5,8 => SOLVED
* 123759486874261593965384721216543978357896142498127365532478619641932857789615234
I6: 1,4                                  # 18 pairs
* PAIR G6: 3,6 COL G
G7: 3,6,1,2,8                            # reduction candidate for 3,6
G7: 3,6                                  # 15 pairs
G8: 3,6,1,4,8                            # reduction candidate for 3,6
G8: 3,6                                  # 13 pairs
G9: 3,6,1,2,4                            # reduction candidate for 3,6
G9: 3,6                                  # 13 pairs
* PAIR H6: 3,6 COL H
H7: 3,6,1,8                              # reduction candidate for 3,6
H7: 3,6                                  # 14 pairs
H8: 3,6,1,4,5,8                          # reduction candidate for 3,6
H8: 3,6                                  # 26 pairs
H9: 3,6,1,4                              # reduction candidate for 3,6
H9: 3,6                                  # 14 pairs
* PAIR A8: 6,7 BLK 7
A9: 6,7,2                                # reduction candidate for 6,7
A9: 6,7                                  # 14 pairs
A9: 2                                    # 11 pairs
* PAIR D8: 6,9 ROW 8
B8: 6,9,1,3,4                            # reduction candidate for 6,9
B8: 6,9 => CTR
* .23759..687.26.59.9.....72.....4.97.3.7.96..2....27...53.47.........2....8...5...
B8: 1,3,4                                # 12 pairs
C8: 6,9,1,4                              # reduction candidate for 6,9
C8: 6,9                                  # 13 pairs
* PAIR D9: 6,9 ROW 9
C9: 6,9,1,2,4                            # reduction candidate for 6,9
C9: 6,9                                  # 14 pairs
C9: 1,2,4                                # 12 pairs
* PAIR E9: 1,3 BLK 8
F7: 1,3,8                                # reduction candidate for 1,3
F7: 1,3                                  # 14 pairs
E8: 1,3,8                                # reduction candidate for 1,3
E8: 1,3                                  # 16 pairs
* PAIR E9: 1,3 ROW 9
G9: 1,3,2,4,6                            # reduction candidate for 1,3
G9: 1,3                                  # 14 pairs
H9: 1,3,4,6                              # reduction candidate for 1,3
H9: 1,3                                  # 13 pairs
* PAIR E9: 1,3 COL E
E3: 1,3,8                                # reduction candidate for 1,3
E3: 8                                    # 16 pairs
E3: 1,3                                  # 14 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top95-019-base-pr-000.dot
* REASONING
* DIS # C6: 1,4 => CTR => C6: 5,8,9
* PRF # B4: 1 => SOL
* DIS # B6: 1,4 => CTR => B6: 5,9
* DIS # C6: 1,4 => CTR => C6: 5,8,9
* PRF # I6: 5,8 => SOL
* DIS # B8: 6,9 => CTR => B8: 1,3,4
* CNT   6 HDP CHAINS /  42 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,A6,A8,B3,C2,C3,D8,D9,E9,G6,H6)
* .23759..687.26.59.9.....72.....4.97.3.7.96..2....27...5..47.........2....8...5...
* PAIR A1: 1,4 ROW 1
G1: 1,4,8                                # reduction candidate for 1,4
G1: 1,4                                  # 13 pairs
H1: 1,4,8                                # reduction candidate for 1,4
H1: 1,4                                  # 14 pairs
* PAIR C2: 1,4 ROW 2
F2: 1,4,3                                # reduction candidate for 1,4
F2: 1,4                                  # 14 pairs
I2: 1,4,3                                # reduction candidate for 1,4
I2: 1,4                                  # 17 pairs
* PAIR C2: 1,4 COL C
C6: 1,4,5,8,9                            # reduction candidate for 1,4
C6: 1,4 => CTR
* .23759..687.26.59.9.5...72.268.4.97.3.7.96..2.9..27...5..47.........2....8...5...
C8: 1,4,6,9                              # reduction candidate for 1,4
C8: 1,4                                  # 15 pairs
C9: 1,4,2,6,9                            # reduction candidate for 1,4
C9: 1,4                                  # 14 pairs
* PAIR RESTART
* PAIR C2: 1,4 ROW 2
F2: 1,4,3                                # reduction candidate for 1,4
F2: 1,4                                  # 14 pairs
I2: 1,4,3                                # reduction candidate for 1,4
I2: 1,4                                  # 17 pairs
* PAIR C2: 1,4 COL C
C8: 1,4,6,9                              # reduction candidate for 1,4
C8: 1,4                                  # 15 pairs
C9: 1,4,2,6,9                            # reduction candidate for 1,4
C9: 1,4                                  # 14 pairs
* PAIR B3: 5,6 COL B
B4: 5,6,1                                # reduction candidate for 5,6
B4: 1 => SOLVED
* 123759486874261593965384721216543978357896142498127365532478619641932857789615234
* DURATION: 0:00:13.607631  START: 23:16:42.678408  END: 23:16:56.286039 2017-05-03
* SOLUTION FOUND
* SAVE PR GRAPH xx-top95-019-base-pr-001.dot
* REASONING
* DIS # C6: 1,4 => CTR => C6: 5,8,9
* PRF C6: 5,8,9 # B4: 1 => SOL
* STA C6: 5,8,9 + B4: 1
* CNT   2 HDP CHAINS /  13 HYP OPENED

Header Info

Top 95 Sudokus 019
[sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt

Solution

position: 123759486874261593965384721216543978357896142498127365532478619641932857789615234 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: 1,4 => UNS
* INC # H1: 1,4 => UNS
* INC # F2: 1,4 => UNS
* INC # I2: 1,4 => UNS
* DIS # C6: 1,4 => CTR => C6: 5,8,9
* INC # C6: 5,8,9 => UNS
* INC # C8: 1,4 => UNS
* INC # C9: 1,4 => UNS
* INC # B4: 5,6 => UNS
* PRF # B4: 1 => SOL
* INC # C4: 5,6 => UNS
* INC # C4: 1,2,8 => UNS
* INC # C4: 2,6 => UNS
* INC # C4: 1,5,8 => UNS
* INC # A9: 2,6 => UNS
* INC # A9: 7 => UNS
* INC # B5: 1,4 => UNS
* DIS # B6: 1,4 => CTR => B6: 5,9
* INC # B6: 5,9 => UNS
* DIS # C6: 1,4 => CTR => C6: 5,8,9
* INC # C6: 5,8,9 => UNS
* INC # I6: 1,4 => UNS
* PRF # I6: 5,8 => SOL
* INC # G7: 3,6 => UNS
* INC # G8: 3,6 => UNS
* INC # G9: 3,6 => UNS
* INC # H7: 3,6 => UNS
* INC # H8: 3,6 => UNS
* INC # H9: 3,6 => UNS
* INC # A9: 6,7 => UNS
* INC # A9: 2 => UNS
* DIS # B8: 6,9 => CTR => B8: 1,3,4
* INC # B8: 1,3,4 => UNS
* INC # C8: 6,9 => UNS
* INC # C9: 6,9 => UNS
* INC # C9: 1,2,4 => UNS
* INC # F7: 1,3 => UNS
* INC # E8: 1,3 => UNS
* INC # G9: 1,3 => UNS
* INC # H9: 1,3 => UNS
* INC # E3: 1,3 => UNS
* INC # E3: 8 => UNS
* CNT  42 HDP CHAINS /  42 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G1: 1,4 => UNS
* INC # H1: 1,4 => UNS
* INC # F2: 1,4 => UNS
* INC # I2: 1,4 => UNS
* DIS # C6: 1,4 => CTR => C6: 5,8,9
* INC C6: 5,8,9 # C8: 1,4 => UNS
* INC C6: 5,8,9 # C9: 1,4 => UNS
* INC C6: 5,8,9 # F2: 1,4 => UNS
* INC C6: 5,8,9 # I2: 1,4 => UNS
* INC C6: 5,8,9 # C8: 1,4 => UNS
* INC C6: 5,8,9 # C9: 1,4 => UNS
* INC C6: 5,8,9 # B4: 5,6 => UNS
* PRF C6: 5,8,9 # B4: 1 => SOL
* STA C6: 5,8,9 + B4: 1
* CNT  13 HDP CHAINS /  13 HYP OPENED