Analysis of xx-top95-025-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 1.....7.9.4...72..8.........7..1..6.3.......5.6..4..2.........8..53...7.7.2....46 initial

Autosolve

position: 1.....7.9.4...72.18.7...6.427..1..633.......556..43.27........8..53...727.2....46 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # C2: 9 => SOL
* DIS # C6: 8 => CTR => C6: 1,9
* PRF # B7: 1,9 => SOL
* DIS # C4: 9 => CTR => C4: 4,8
* DIS # C6: 8,9 => CTR => C6: 1
* PRF # C6: 1 => SOL
* PRF # G6: 8,9 => SOL
* DIS # G6: 1 => CTR => G6: 8,9
* PRF # G4: 9 => SOL
* PRF # G6: 8 => SOL
* PRF # B7: 1,9 => SOL
* DIS # D7: 1,9 => CTR => D7: 2,4,5,6,7
* DIS # F7: 1,9 => CTR => F7: 2,4,5,6
* PRF # G6: 8 => SOL
* CNT  14 HDP CHAINS /  53 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # C2: 9 => SOL
* STA C2: 9
* CNT   1 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

1.....7.9.4...72..8.........7..1..6.3.......5.6..4..2.........8..53...7.7.2....46 initial
1.....7.9.4...72.18.7...6.427..1..633.......556..43.27........8..53...727.2....46 autosolve
123456789649837251857291634274518963398672415561943827416725398985364172732189546 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
B1: 2,5
C1: 3,6
A2: 6,9
B3: 2,5
H3: 3,5
B5: 1,9
C5: 4,8
F5: 2,6
D6: 8,9
G5: 4,8
H5: 1,9
G7: 3,5
H7: 1,9
G8: 1,9
G9: 3,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D3,F3: 1.. / D3 = 1  => 18 pairs (_) / F3 = 1  => 15 pairs (_)
B5,C6: 1.. / B5 = 1  =>  0 pairs (X) / C6 = 1  =>  0 pairs (_)
H5,G6: 1.. / H5 = 1  =>  0 pairs (*) / G6 = 1  =>  0 pairs (X)
H7,G8: 1.. / H7 = 1  =>  0 pairs (X) / G8 = 1  =>  0 pairs (_)
B5,H5: 1.. / B5 = 1  =>  0 pairs (X) / H5 = 1  =>  0 pairs (_)
C6,G6: 1.. / C6 = 1  =>  0 pairs (*) / G6 = 1  =>  0 pairs (X)
C6,C7: 1.. / C6 = 1  =>  0 pairs (*) / C7 = 1  =>  0 pairs (X)
G6,G8: 1.. / G6 = 1  =>  0 pairs (X) / G8 = 1  =>  0 pairs (_)
H5,H7: 1.. / H5 = 1  =>  0 pairs (*) / H7 = 1  =>  0 pairs (X)
B1,B3: 2.. / B1 = 2  => 15 pairs (_) / B3 = 2  => 17 pairs (_)
C1,C2: 3.. / C1 = 3  => 22 pairs (_) / C2 = 3  => 15 pairs (_)
B7,B9: 3.. / B7 = 3  => 13 pairs (_) / B9 = 3  =>  0 pairs (*)
G7,G9: 3.. / G7 = 3  =>  0 pairs (*) / G9 = 3  =>  0 pairs (X)
E3,H3: 3.. / E3 = 3  => 17 pairs (_) / H3 = 3  => 16 pairs (_)
B7,G7: 3.. / B7 = 3  => 13 pairs (_) / G7 = 3  =>  0 pairs (*)
B9,G9: 3.. / B9 = 3  =>  0 pairs (*) / G9 = 3  =>  0 pairs (X)
D1,F1: 4.. / D1 = 4  => 15 pairs (_) / F1 = 4  => 13 pairs (_)
C4,C5: 4.. / C4 = 4  => 15 pairs (_) / C5 = 4  => 15 pairs (_)
G4,G5: 4.. / G4 = 4  => 15 pairs (_) / G5 = 4  => 15 pairs (_)
A7,A8: 4.. / A7 = 4  => 16 pairs (_) / A8 = 4  => 16 pairs (_)
C4,G4: 4.. / C4 = 4  => 15 pairs (_) / G4 = 4  => 15 pairs (_)
C5,G5: 4.. / C5 = 4  => 15 pairs (_) / G5 = 4  => 15 pairs (_)
A8,F8: 4.. / A8 = 4  => 16 pairs (_) / F8 = 4  => 16 pairs (_)
D1,D7: 4.. / D1 = 4  => 15 pairs (_) / D7 = 4  => 13 pairs (_)
B1,B3: 5.. / B1 = 5  => 17 pairs (_) / B3 = 5  => 15 pairs (_)
D4,F4: 5.. / D4 = 5  => 17 pairs (_) / F4 = 5  => 18 pairs (_)
G7,G9: 5.. / G7 = 5  => 13 pairs (_) / G9 = 5  =>  0 pairs (*)
D5,E5: 7.. / D5 = 7  => 16 pairs (_) / E5 = 7  => 16 pairs (_)
D7,E7: 7.. / D7 = 7  => 16 pairs (_) / E7 = 7  => 16 pairs (_)
D5,D7: 7.. / D5 = 7  => 16 pairs (_) / D7 = 7  => 16 pairs (_)
E5,E7: 7.. / E5 = 7  => 16 pairs (_) / E7 = 7  => 16 pairs (_)
H1,H2: 8.. / H1 = 8  => 16 pairs (_) / H2 = 8  => 17 pairs (_)
B8,B9: 8.. / B8 = 8  => 16 pairs (_) / B9 = 8  => 17 pairs (_)
C5,G5: 8.. / C5 = 8  => 15 pairs (_) / G5 = 8  => 15 pairs (_)
A2,C2: 9.. / A2 = 9  => 16 pairs (_) / C2 = 9  =>  0 pairs (*)
H7,G8: 9.. / H7 = 9  =>  0 pairs (*) / G8 = 9  =>  0 pairs (X)
B5,H5: 9.. / B5 = 9  =>  0 pairs (*) / H5 = 9  =>  0 pairs (X)
H5,H7: 9.. / H5 = 9  =>  0 pairs (X) / H7 = 9  =>  0 pairs (_)
* DURATION: 0:01:04.666226  START: 23:21:16.390848  END: 23:22:21.057074 2017-05-03
* CP COUNT: (38)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B1,B3,B5,C1,C5,D6,F5,G5,G7,G8,G9,H3,H5,H7)
* 1.....7.9.4...72.18.7...6.427..1..633.......556..43.27........8..53...727.2....46
* PAIR B1: 2,5 ROW 1
D1: 2,5,4,6,8                            # reduction candidate for 2,5
D1: 2,5                                  # 17 pairs
E1: 2,5,3,6,8                            # reduction candidate for 2,5
E1: 2,5                                  # 17 pairs
F1: 2,5,4,6,8                            # reduction candidate for 2,5
F1: 2,5                                  # 17 pairs
* PAIR C1: 3,6 BLK 1
C2: 3,6,9                                # reduction candidate for 3,6
C2: 9 => SOLVED
* 123456789649837251857291634274518963398672415561943827416725398985364172732189546
C2: 3,6                                  # 16 pairs
* PAIR C1: 3,6 ROW 1
E1: 3,6,2,5,8                            # reduction candidate for 3,6
E1: 3,6                                  # 17 pairs
E1: 2,5,8                                # 15 pairs
* PAIR A2: 6,9 BLK 1
C2: 6,9,3                                # reduction candidate for 6,9
C2: 6,9                                  # 22 pairs
C2: 3                                    # 15 pairs
* PAIR A2: 6,9 COL A
A7: 6,9,4                                # reduction candidate for 6,9
A7: 6,9                                  # 16 pairs
A8: 6,9,4                                # reduction candidate for 6,9
A8: 6,9                                  # 16 pairs
* PAIR B3: 2,5 ROW 3
D3: 2,5,1,9                              # reduction candidate for 2,5
D3: 2,5                                  # 19 pairs
E3: 2,5,3,9                              # reduction candidate for 2,5
E3: 2,5                                  # 21 pairs
F3: 2,5,1,9                              # reduction candidate for 2,5
F3: 2,5                                  # 20 pairs
* PAIR H3: 3,5 BLK 3
H1: 3,5,8                                # reduction candidate for 3,5
H1: 3,5                                  # 17 pairs
H2: 3,5,8                                # reduction candidate for 3,5
H2: 3,5                                  # 16 pairs
* PAIR H3: 3,5 ROW 3
E3: 3,5,2,9                              # reduction candidate for 3,5
E3: 3,5                                  # 21 pairs
E3: 2,9                                  # 17 pairs
* PAIR B5: 1,9 BLK 4
C6: 1,9,8                                # reduction candidate for 1,9
C6: 8 => CTR
* 1.....7.9.4...72.18.7...6.427..1..6331.....95568943127..1.....8..53...727.2....46
C6: 1,9                                  # 17 pairs
* PAIR B5: 1,9 COL B
B7: 1,9,3                                # reduction candidate for 1,9
B7: 1,9 => SOLVED
* 123456789649837251857291634274518963398672415561943827416725398985364172732189546
B7: 3                                    # 13 pairs
B8: 1,9,8                                # reduction candidate for 1,9
B8: 1,9                                  # 17 pairs
B9: 1,9,3,8                              # reduction candidate for 1,9
B9: 1,9                                  # 15 pairs
* PAIR C5: 4,8 BLK 4
C4: 4,8,9                                # reduction candidate for 4,8
C4: 9 => CTR
* 1.....7.9.4...72.18.7...6.4279.1.463314...895568943127..1.....8..53...727.2....46
C4: 4,8                                  # 17 pairs
* PAIR F5: 2,6 BLK 5
D5: 2,6,7                                # reduction candidate for 2,6
D5: 2,6                                  # 16 pairs
E5: 2,6,7                                # reduction candidate for 2,6
E5: 2,6                                  # 16 pairs
* PAIR F5: 2,6 COL F
F1: 2,6,4,5,8                            # reduction candidate for 2,6
F1: 2,6                                  # 20 pairs
F7: 2,6,1,4,5,9                          # reduction candidate for 2,6
F7: 2,6                                  # 16 pairs
* PAIR D6: 8,9 BLK 5
D4: 8,9,5                                # reduction candidate for 8,9
D4: 8,9                                  # 18 pairs
F4: 8,9,5                                # reduction candidate for 8,9
F4: 8,9                                  # 17 pairs
* PAIR D6: 8,9 ROW 6
C6: 8,9,1                                # reduction candidate for 8,9
C6: 8,9 => CTR
* 1.....7.9.4...72.18.7...6.427..1..6331.....9556..43127..1.....8..53...727.2....46
C6: 1 => SOLVED
* 123456789649837251857291634274518963398672415561943827416725398985364172732189546
G6: 8,9,1                                # reduction candidate for 8,9
G6: 8,9 => SOLVED
* 123456789649837251857291634274518963398672415561943827416725398985364172732189546
G6: 1 => CTR
* 1.....7.9.4...72.18.7...6.427..1..633.......556..43127..1....98..53...727.2....46
* PAIR D6: 8,9 COL D
D9: 8,9,1,5                              # reduction candidate for 8,9
D9: 8,9                                  # 20 pairs
D9: 1,5                                  # 16 pairs
* PAIR G5: 4,8 BLK 6
G4: 4,8,9                                # reduction candidate for 4,8
G4: 9 => SOLVED
* 123456789649837251857291634274518963398672415561943827416725398985364172732189546
G4: 4,8                                  # 17 pairs
* PAIR H5: 1,9 BLK 6
G6: 1,9,8                                # reduction candidate for 1,9
G6: 8 => SOLVED
* 123456789649837251857291634274518963398672415561943827416725398985364172732189546
G6: 1,9                                  # 17 pairs
* PAIR H7: 1,9 ROW 7
B7: 1,9,3                                # reduction candidate for 1,9
B7: 1,9 => SOLVED
* 123456789649837251857291634274518963398672415561943827416725398985364172732189546
B7: 3                                    # 13 pairs
C7: 1,9,6                                # reduction candidate for 1,9
C7: 1,9                                  # 16 pairs
D7: 1,9,2,4,5,6,7                        # reduction candidate for 1,9
D7: 1,9 => CTR
* 1..4..7.9.4.6.72.18.72.16.427..1..633..726..556..43.27436.725.89.53.4.727.2...346
D7: 2,4,5,6,7                            # 15 pairs
F7: 1,9,2,4,5,6                          # reduction candidate for 1,9
F7: 1,9 => CTR
* 1.34.67.9649..72.18.71..6.427..1..6339.672.15561.43.27436...5.8985364172712...346
F7: 2,4,5,6                              # 15 pairs
* PAIR G8: 1,9 ROW 8
B8: 1,9,8                                # reduction candidate for 1,9
B8: 1,9                                  # 17 pairs
F8: 1,9,4,6,8                            # reduction candidate for 1,9
F8: 1,9                                  # 19 pairs
* PAIR G8: 1,9 COL G
G6: 1,9,8                                # reduction candidate for 1,9
G6: 8 => SOLVED
* 123456789649837251857291634274518963398672415561943827416725398985364172732189546
G6: 1,9                                  # 17 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top95-025-base-pr-000.dot
* REASONING
* PRF # C2: 9 => SOL
* DIS # C6: 8 => CTR => C6: 1,9
* PRF # B7: 1,9 => SOL
* DIS # C4: 9 => CTR => C4: 4,8
* DIS # C6: 8,9 => CTR => C6: 1
* PRF # C6: 1 => SOL
* PRF # G6: 8,9 => SOL
* DIS # G6: 1 => CTR => G6: 8,9
* PRF # G4: 9 => SOL
* PRF # G6: 8 => SOL
* PRF # B7: 1,9 => SOL
* DIS # D7: 1,9 => CTR => D7: 2,4,5,6,7
* DIS # F7: 1,9 => CTR => F7: 2,4,5,6
* PRF # G6: 8 => SOL
* CNT  14 HDP CHAINS /  53 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B1,B3,B5,C1,C5,D6,F5,G5,G7,G8,G9,H3,H5,H7)
* 1.....7.9.4...72.18.7...6.427..1..633.......556..43.27........8..53...727.2....46
* PAIR B1: 2,5 ROW 1
D1: 2,5,4,6,8                            # reduction candidate for 2,5
D1: 2,5                                  # 17 pairs
E1: 2,5,3,6,8                            # reduction candidate for 2,5
E1: 2,5                                  # 17 pairs
F1: 2,5,4,6,8                            # reduction candidate for 2,5
F1: 2,5                                  # 17 pairs
* PAIR C1: 3,6 BLK 1
C2: 3,6,9                                # reduction candidate for 3,6
C2: 9 => SOLVED
* 123456789649837251857291634274518963398672415561943827416725398985364172732189546
* DURATION: 0:00:06.181960  START: 23:23:12.450814  END: 23:23:18.632774 2017-05-03
* SOLUTION FOUND
* SAVE PR GRAPH xx-top95-025-base-pr-001.dot
* REASONING
* PRF # C2: 9 => SOL
* STA C2: 9
* CNT   1 HDP CHAINS /   5 HYP OPENED

Header Info

Top 95 Sudokus 025
[sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt

Solution

position: 123456789649837251857291634274518963398672415561943827416725398985364172732189546 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 # D1: 2,5 => UNS
* INC # E1: 2,5 => UNS
* INC # F1: 2,5 => UNS
* INC # C2: 3,6 => UNS
* PRF # C2: 9 => SOL
* INC # E1: 3,6 => UNS
* INC # E1: 2,5,8 => UNS
* INC # C2: 6,9 => UNS
* INC # C2: 3 => UNS
* INC # A7: 6,9 => UNS
* INC # A8: 6,9 => UNS
* INC # D3: 2,5 => UNS
* INC # E3: 2,5 => UNS
* INC # F3: 2,5 => UNS
* INC # H1: 3,5 => UNS
* INC # H2: 3,5 => UNS
* INC # E3: 3,5 => UNS
* INC # E3: 2,9 => UNS
* INC # C6: 1,9 => UNS
* DIS # C6: 8 => CTR => C6: 1,9
* PRF # B7: 1,9 => SOL
* INC # B7: 3 => UNS
* INC # B8: 1,9 => UNS
* INC # B9: 1,9 => UNS
* INC # C4: 4,8 => UNS
* DIS # C4: 9 => CTR => C4: 4,8
* INC # D5: 2,6 => UNS
* INC # E5: 2,6 => UNS
* INC # F1: 2,6 => UNS
* INC # F7: 2,6 => UNS
* INC # D4: 8,9 => UNS
* INC # F4: 8,9 => UNS
* DIS # C6: 8,9 => CTR => C6: 1
* PRF # C6: 1 => SOL
* PRF # G6: 8,9 => SOL
* DIS # G6: 1 => CTR => G6: 8,9
* INC # D9: 8,9 => UNS
* INC # D9: 1,5 => UNS
* INC # G4: 4,8 => UNS
* PRF # G4: 9 => SOL
* INC # G6: 1,9 => UNS
* PRF # G6: 8 => SOL
* PRF # B7: 1,9 => SOL
* INC # B7: 3 => UNS
* INC # C7: 1,9 => UNS
* DIS # D7: 1,9 => CTR => D7: 2,4,5,6,7
* INC # D7: 2,4,5,6,7 => UNS
* DIS # F7: 1,9 => CTR => F7: 2,4,5,6
* INC # F7: 2,4,5,6 => UNS
* INC # B8: 1,9 => UNS
* INC # F8: 1,9 => UNS
* INC # G6: 1,9 => UNS
* PRF # G6: 8 => SOL
* CNT  53 HDP CHAINS /  53 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D1: 2,5 => UNS
* INC # E1: 2,5 => UNS
* INC # F1: 2,5 => UNS
* INC # C2: 3,6 => UNS
* PRF # C2: 9 => SOL
* STA C2: 9
* CNT   5 HDP CHAINS /   5 HYP OPENED