Analysis of xx-top95-059-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .47.2....8....1....3....9.2.....5...6..81..5.....4.....7....3.4...9...1.4..27.8.. initial

Autosolve

position: .47.2....8....1....3....9.2.....5...6..81..5.....4.....7.1..3.4...9.4.1.4..27.8.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A6: 1,5 => CTR => A6: 2,3,7,9
* DIS # F3: 6,8 => CTR => F3: 7
* DIS # H3: 6,8 => CTR => H3: 4,7
* DIS # C5: 2,9 => CTR => C5: 3,4
* DIS # F5: 3,7 => CTR => F5: 2,9
* DIS # F3: 6,8 => CTR => F3: 7
* DIS # I9: 6,9 => CTR => I9: 5
* CNT   7 HDP CHAINS /  47 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 # A6: 1,5 => CTR => A6: 2,3,7,9
* DIS A6: 2,3,7,9 # F3: 6,8 => CTR => F3: 7
* DIS A6: 2,3,7,9 + F3: 7 # H3: 6,8 => CTR => H3: 4
* DIS A6: 2,3,7,9 + F3: 7 + H3: 4 # B4: 2,9 => CTR => B4: 1,8
* DIS A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 # C5: 2,9 => CTR => C5: 3,4
* DIS A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 # B6: 2,9 => CTR => B6: 1,5,8
* DIS A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 # F5: 3 => CTR => F5: 2,9
* PRF A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 + F5: 2,9 # B2: 5,6 => SOL
* STA A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 + F5: 2,9 + B2: 5,6
* CNT   8 HDP CHAINS /  25 HYP OPENED

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

Details

Positions

.47.2....8....1....3....9.2.....5...6..81..5.....4.....7....3.4...9...1.4..27.8.. initial
.47.2....8....1....3....9.2.....5...6..81..5.....4.....7.1..3.4...9.4.1.4..27.8.. autosolve
947326581852491673136587942284735169693812457715649238579168324328954716461273895 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
A1: 5,9
A3: 1,5
E3: 6,8
B5: 2,9
F7: 6,8
F9: 3,6
H9: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A3,C3: 1.. / A3 = 1  =>  7 pairs (_) / C3 = 1  =>  0 pairs (X)
G1,I1: 1.. / G1 = 1  =>  7 pairs (_) / I1 = 1  =>  8 pairs (_)
B9,C9: 1.. / B9 = 1  =>  7 pairs (_) / C9 = 1  =>  8 pairs (_)
B2,C2: 2.. / B2 = 2  =>  8 pairs (_) / C2 = 2  =>  7 pairs (_)
F5,F6: 2.. / F5 = 2  =>  9 pairs (_) / F6 = 2  =>  7 pairs (_)
H7,G8: 2.. / H7 = 2  =>  9 pairs (_) / G8 = 2  => 13 pairs (_)
E8,F9: 3.. / E8 = 3  => 15 pairs (_) / F9 = 3  =>  8 pairs (_)
C9,F9: 3.. / C9 = 3  => 15 pairs (_) / F9 = 3  =>  8 pairs (_)
D2,D3: 4.. / D2 = 4  =>  7 pairs (_) / D3 = 4  =>  0 pairs (X)
C4,C5: 4.. / C4 = 4  =>  7 pairs (_) / C5 = 4  =>  8 pairs (_)
D3,H3: 4.. / D3 = 4  =>  0 pairs (X) / H3 = 4  =>  7 pairs (_)
C5,G5: 4.. / C5 = 4  =>  8 pairs (_) / G5 = 4  =>  7 pairs (_)
E7,E8: 5.. / E7 = 5  =>  8 pairs (_) / E8 = 5  => 12 pairs (_)
A4,A6: 7.. / A4 = 7  =>  8 pairs (_) / A6 = 7  =>  8 pairs (_)
G8,I8: 7.. / G8 = 7  => 11 pairs (_) / I8 = 7  =>  8 pairs (_)
F1,E2: 9.. / F1 = 9  => 14 pairs (_) / E2 = 9  => 13 pairs (_)
A1,F1: 9.. / A1 = 9  => 13 pairs (_) / F1 = 9  => 14 pairs (_)
E2,E4: 9.. / E2 = 9  => 13 pairs (_) / E4 = 9  => 14 pairs (_)
* DURATION: 0:00:19.162709  START: 00:07:16.105536  END: 00:07:35.268245 2017-05-04
* CP COUNT: (18)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B5,E3,F7,F9,H9)
* .47.2....8....1....3....9.2.....5...6..81..5.....4.....7.1..3.4...9.4.1.4..27.8..
* PAIR A1: 5,9 BLK 1
B2: 5,9,2,6                              # reduction candidate for 5,9
B2: 5,9                                  #  9 pairs
C2: 5,9,2,6                              # reduction candidate for 5,9
C2: 5,9                                  # 10 pairs
* PAIR A1: 5,9 COL A
A6: 5,9,1,2,3,7                          # reduction candidate for 5,9
A6: 5,9                                  # 15 pairs
A7: 5,9,2                                # reduction candidate for 5,9
A7: 5,9                                  #  9 pairs
* PAIR A3: 1,5 BLK 1
C3: 1,5,6                                # reduction candidate for 1,5
C3: 1,5                                  # 19 pairs
C3: 6                                    #  7 pairs
* PAIR A3: 1,5 COL A
A6: 1,5,2,3,7,9                          # reduction candidate for 1,5
A6: 1,5 => CTR
* 947.2..3.8..391476.364879.27..635...6.481.753..374....27.1..3.43..9.42174..2738.5
A6: 2,3,7,9                              #  7 pairs
* PAIR E3: 6,8 BLK 2
F1: 6,8,3,9                              # reduction candidate for 6,8
F1: 6,8                                  # 16 pairs
F3: 6,8,7                                # reduction candidate for 6,8
F3: 6,8 => CTR
* .47.2....8....1....3....9.2.....5...6..81..5.....4.....7.1..3.4...9.4.1.4..27.8..
F3: 7                                    #  7 pairs
* PAIR E3: 6,8 ROW 3
H3: 6,8,4,7                              # reduction candidate for 6,8
H3: 6,8 => CTR
* 94752..3.8..391475.3.4.79.2....35.4.6.481.753....4.....7.15.324...9.45174..2738..
H3: 4,7                                  #  8 pairs
* PAIR E3: 6,8 COL E
E7: 6,8,5                                # reduction candidate for 6,8
E7: 6,8                                  # 12 pairs
E8: 6,8,3,5                              # reduction candidate for 6,8
E8: 6,8                                  # 10 pairs
* PAIR B5: 2,9 BLK 4
A4: 2,9,1,3,7                            # reduction candidate for 2,9
A4: 2,9                                  # 12 pairs
B4: 2,9,1,8                              # reduction candidate for 2,9
B4: 2,9                                  # 15 pairs
C4: 2,9,1,3,4,8                          # reduction candidate for 2,9
C4: 2,9                                  # 10 pairs
C5: 2,9,3,4                              # reduction candidate for 2,9
C5: 2,9 => CTR
* 547.29...8....1...136587942..4.952..6..813457....42...97.1.83242..93471.4.32768..
C5: 3,4                                  #  8 pairs
A6: 2,9,1,3,5,7                          # reduction candidate for 2,9
A6: 2,9                                  # 13 pairs
B6: 2,9,1,5,8                            # reduction candidate for 2,9
B6: 2,9                                  # 17 pairs
C6: 2,9,1,3,5,8                          # reduction candidate for 2,9
C6: 2,9                                  # 11 pairs
* PAIR B5: 2,9 ROW 5
F5: 2,9,3,7                              # reduction candidate for 2,9
F5: 3,7 => CTR
* 547.29...8..4615..136587942....95...6..813.5.....42....7.15836426.934.1.4.3276895
F5: 2,9                                  # 11 pairs
* PAIR B5: 2,9 COL B
B2: 2,9,5,6                              # reduction candidate for 2,9
B2: 5,6                                  # 14 pairs
B2: 2,9                                  #  9 pairs
* PAIR F7: 6,8 BLK 8
E7: 6,8,5                                # reduction candidate for 6,8
E7: 6,8                                  # 12 pairs
E8: 6,8,3,5                              # reduction candidate for 6,8
E8: 6,8                                  # 10 pairs
* PAIR F7: 6,8 ROW 7
C7: 6,8,2,5,9                            # reduction candidate for 6,8
C7: 6,8                                  # 10 pairs
C7: 2,5,9                                #  7 pairs
* PAIR F7: 6,8 COL F
F1: 6,8,3,9                              # reduction candidate for 6,8
F1: 6,8                                  # 16 pairs
F3: 6,8,7                                # reduction candidate for 6,8
F3: 6,8 => CTR
* .47.2....8....1....3....9.2.....5...6..81..5.....4.....7.1..3.4...9.4.1.4..27.8..
F3: 7                                    #  7 pairs
* PAIR F9: 3,6 BLK 8
E8: 3,6,5,8                              # reduction candidate for 3,6
E8: 5,8                                  # 10 pairs
E8: 3,6                                  #  8 pairs
* PAIR F9: 3,6 ROW 9
C9: 3,6,1,5,9                            # reduction candidate for 3,6
C9: 3,6                                  #  9 pairs
C9: 1,5,9                                #  8 pairs
* PAIR F9: 3,6 COL F
F1: 3,6,8,9                              # reduction candidate for 3,6
F1: 3,6                                  # 14 pairs
F6: 3,6,2,7,9                            # reduction candidate for 3,6
F6: 3,6                                  # 15 pairs
* PAIR H9: 6,9 BLK 9
H7: 6,9,2                                # reduction candidate for 6,9
H7: 6,9                                  # 13 pairs
I9: 6,9,5                                # reduction candidate for 6,9
I9: 6,9 => CTR
* 547.29...8....1...1365879.2.....5...6..81..5.....4....97.15.324...9.4.1.4..2738..
I9: 5                                    #  8 pairs
* PAIR H9: 6,9 ROW 9
B9: 6,9,1,5                              # reduction candidate for 6,9
B9: 6,9                                  # 10 pairs
C9: 6,9,1,3,5                            # reduction candidate for 6,9
C9: 6,9                                  # 10 pairs
* PAIR H9: 6,9 COL H
H4: 6,9,2,3,4,7,8                        # reduction candidate for 6,9
H4: 6,9                                  # 11 pairs
H6: 6,9,2,3,7,8                          # reduction candidate for 6,9
H6: 6,9                                  # 11 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top95-059-base-pr-000.dot
* REASONING
* DIS # A6: 1,5 => CTR => A6: 2,3,7,9
* DIS # F3: 6,8 => CTR => F3: 7
* DIS # H3: 6,8 => CTR => H3: 4,7
* DIS # C5: 2,9 => CTR => C5: 3,4
* DIS # F5: 3,7 => CTR => F5: 2,9
* DIS # F3: 6,8 => CTR => F3: 7
* DIS # I9: 6,9 => CTR => I9: 5
* CNT   7 HDP CHAINS /  47 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B5,E3,F7,F9,H9)
* .47.2....8....1....3....9.2.....5...6..81..5.....4.....7.1..3.4...9.4.1.4..27.8..
* PAIR A1: 5,9 BLK 1
B2: 5,9,2,6                              # reduction candidate for 5,9
B2: 5,9                                  #  9 pairs
C2: 5,9,2,6                              # reduction candidate for 5,9
C2: 5,9                                  # 10 pairs
* PAIR A1: 5,9 COL A
A6: 5,9,1,2,3,7                          # reduction candidate for 5,9
A6: 5,9                                  # 15 pairs
A7: 5,9,2                                # reduction candidate for 5,9
A7: 5,9                                  #  9 pairs
* PAIR A3: 1,5 BLK 1
C3: 1,5,6                                # reduction candidate for 1,5
C3: 1,5                                  # 19 pairs
C3: 6                                    #  7 pairs
* PAIR A3: 1,5 COL A
A6: 1,5,2,3,7,9                          # reduction candidate for 1,5
A6: 1,5 => CTR
* 947.2..3.8..391476.364879.27..635...6.481.753..374....27.1..3.43..9.42174..2738.5
* PAIR RESTART
* PAIR A3: 1,5 BLK 1
C3: 1,5,6                                # reduction candidate for 1,5
C3: 1,5                                  # 19 pairs
C3: 6                                    #  7 pairs
* PAIR E3: 6,8 BLK 2
F1: 6,8,3,9                              # reduction candidate for 6,8
F1: 6,8                                  # 16 pairs
F3: 6,8,7                                # reduction candidate for 6,8
F3: 6,8 => CTR
* .47.2....8....1....3....9.2.....5...6..81..5.....4.....7.1..3.4...9.4.1.4..27.8..
* RESTART
* PAIR E3: 6,8 BLK 2
F1: 6,8,3,9                              # reduction candidate for 6,8
F1: 6,8                                  # 16 pairs
F1: 3,9                                  #  8 pairs
* PAIR E3: 6,8 ROW 3
H3: 6,8,4                                # reduction candidate for 6,8
H3: 6,8 => CTR
* 94752..3.8..391475.3.4.79.2....35.4.6.481.753....4.....7.15.324...9.45174..2738..
* PAIR RESTART
* PAIR B5: 2,9 BLK 4
A4: 2,9,1,3,7                            # reduction candidate for 2,9
A4: 2,9                                  # 19 pairs
B4: 2,9,1,8                              # reduction candidate for 2,9
B4: 2,9 => CTR
* 947.2....8.2491.73.3..87942.....5...6.381.4577...4.....7.1.83.43..9.4.1.4..27.8..
C4: 2,9,1,3,4,8                          # reduction candidate for 2,9
C4: 2,9                                  # 12 pairs
C5: 2,9,3,4                              # reduction candidate for 2,9
C5: 2,9 => CTR
* .47329...8..461573.36587942..4.952..6..813457..1.426.99751.8324...93471.4.3276895
A6: 2,9,3,7                              # reduction candidate for 2,9
A6: 2,9                                  # 22 pairs
B6: 2,9,1,5,8                            # reduction candidate for 2,9
B6: 2,9 => CTR
* 947.2....8.2491.73.3..87942..4..52..6.381.4577.5.4....5791683242..9.471.4..27.8..
C6: 2,9,1,3,5,8                          # reduction candidate for 2,9
C6: 2,9                                  # 20 pairs
* PAIR B5: 2,9 ROW 5
F5: 2,9,3                                # reduction candidate for 2,9
F5: 3 => CTR
* .47329...8..461573.36587942....95...6.4813.5.....42....7.158364.68934217413276895
* PAIR B5: 2,9 COL B
B2: 2,9,5,6                              # reduction candidate for 2,9
B2: 5,6 => SOLVED
* 947326581852491673136587942284735169693812457715649238579168324328954716461273895
* DURATION: 0:00:22.585343  START: 00:08:04.215848  END: 00:08:26.801191 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top95-059-base-pr-001.dot
* REASONING
* DIS # A6: 1,5 => CTR => A6: 2,3,7,9
* DIS A6: 2,3,7,9 # F3: 6,8 => CTR => F3: 7
* DIS A6: 2,3,7,9 + F3: 7 # H3: 6,8 => CTR => H3: 4
* DIS A6: 2,3,7,9 + F3: 7 + H3: 4 # B4: 2,9 => CTR => B4: 1,8
* DIS A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 # C5: 2,9 => CTR => C5: 3,4
* DIS A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 # B6: 2,9 => CTR => B6: 1,5,8
* DIS A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 # F5: 3 => CTR => F5: 2,9
* PRF A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 + F5: 2,9 # B2: 5,6 => SOL
* STA A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 + F5: 2,9 + B2: 5,6
* CNT   8 HDP CHAINS /  25 HYP OPENED

Header Info

Top 95 Sudokus 059
[sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt

Solution

position: 947326581852491673136587942284735169693812457715649238579168324328954716461273895 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 # B2: 5,9 => UNS
* INC # C2: 5,9 => UNS
* INC # A6: 5,9 => UNS
* INC # A7: 5,9 => UNS
* INC # C3: 1,5 => UNS
* INC # C3: 6 => UNS
* DIS # A6: 1,5 => CTR => A6: 2,3,7,9
* INC # A6: 2,3,7,9 => UNS
* INC # F1: 6,8 => UNS
* DIS # F3: 6,8 => CTR => F3: 7
* INC # F3: 7 => UNS
* DIS # H3: 6,8 => CTR => H3: 4,7
* INC # H3: 4,7 => UNS
* INC # E7: 6,8 => UNS
* INC # E8: 6,8 => UNS
* INC # A4: 2,9 => UNS
* INC # B4: 2,9 => UNS
* INC # C4: 2,9 => UNS
* DIS # C5: 2,9 => CTR => C5: 3,4
* INC # C5: 3,4 => UNS
* INC # A6: 2,9 => UNS
* INC # B6: 2,9 => UNS
* INC # C6: 2,9 => UNS
* INC # F5: 2,9 => UNS
* DIS # F5: 3,7 => CTR => F5: 2,9
* INC # B2: 2,9 => UNS
* INC # B2: 5,6 => UNS
* INC # E7: 6,8 => UNS
* INC # E8: 6,8 => UNS
* INC # C7: 6,8 => UNS
* INC # C7: 2,5,9 => UNS
* INC # F1: 6,8 => UNS
* DIS # F3: 6,8 => CTR => F3: 7
* INC # F3: 7 => UNS
* INC # E8: 3,6 => UNS
* INC # E8: 5,8 => UNS
* INC # C9: 3,6 => UNS
* INC # C9: 1,5,9 => UNS
* INC # F1: 3,6 => UNS
* INC # F6: 3,6 => UNS
* INC # H7: 6,9 => UNS
* DIS # I9: 6,9 => CTR => I9: 5
* INC # I9: 5 => UNS
* INC # B9: 6,9 => UNS
* INC # C9: 6,9 => UNS
* INC # H4: 6,9 => UNS
* INC # H6: 6,9 => UNS
* CNT  47 HDP CHAINS /  47 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 5,9 => UNS
* INC # C2: 5,9 => UNS
* INC # A6: 5,9 => UNS
* INC # A7: 5,9 => UNS
* INC # C3: 1,5 => UNS
* INC # C3: 6 => UNS
* DIS # A6: 1,5 => CTR => A6: 2,3,7,9
* INC A6: 2,3,7,9 # C3: 1,5 => UNS
* INC A6: 2,3,7,9 # C3: 6 => UNS
* INC A6: 2,3,7,9 # F1: 6,8 => UNS
* DIS A6: 2,3,7,9 # F3: 6,8 => CTR => F3: 7
* INC A6: 2,3,7,9 + F3: 7 # F1: 6,8 => UNS
* INC A6: 2,3,7,9 + F3: 7 # F1: 3,9 => UNS
* DIS A6: 2,3,7,9 + F3: 7 # H3: 6,8 => CTR => H3: 4
* INC A6: 2,3,7,9 + F3: 7 + H3: 4 # A4: 2,9 => UNS
* DIS A6: 2,3,7,9 + F3: 7 + H3: 4 # B4: 2,9 => CTR => B4: 1,8
* INC A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 # C4: 2,9 => UNS
* DIS A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 # C5: 2,9 => CTR => C5: 3,4
* INC A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 # A6: 2,9 => UNS
* DIS A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 # B6: 2,9 => CTR => B6: 1,5,8
* INC A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 # C6: 2,9 => UNS
* INC A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 # F5: 2,9 => UNS
* DIS A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 # F5: 3 => CTR => F5: 2,9
* INC A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 + F5: 2,9 # B2: 2,9 => UNS
* PRF A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 + F5: 2,9 # B2: 5,6 => SOL
* STA A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 + F5: 2,9 + B2: 5,6
* CNT  25 HDP CHAINS /  25 HYP OPENED