Analysis of zz-www.sudokuwiki.org-0075-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=75

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=75

position: ..61...7.4.......6....7.31...9..2....5..8..4....5..7...12.4....6.......4.3...59.. initial

Autosolve

position: 3.61..47.471.....6....7.31...9..2....5..8..4....5..7...12.4....6.......4.34..59.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C8: 5,8 => CTR => C8: 7
* DIS # F6: 1,3,9 => CTR => F6: 4,6
* DIS # F6: 1,3,9 => CTR => F6: 4,6
* DIS # C8: 5 => CTR => C8: 7,8
* CNT   4 HDP CHAINS /  30 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 # C8: 5,8 => CTR => C8: 7
* DIS C8: 7 # F6: 1,3,9 => CTR => F6: 4,6
* DIS C8: 7 + F6: 4,6 # D4: 4,6 => CTR => D4: 3,7
* DIS C8: 7 + F6: 4,6 + D4: 3,7 # I1: 2,8 => CTR => I1: 5,9
* PRF C8: 7 + F6: 4,6 + D4: 3,7 + I1: 5,9 # D2: 8,9 => SOL
* STA C8: 7 + F6: 4,6 + D4: 3,7 + I1: 5,9 + D2: 8,9
* CNT   5 HDP CHAINS /  14 HYP OPENED

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

Details

Positions

..61...7.4.......6....7.31...9..2....5..8..4....5..7...12.4....6.......4.3...59.. initial
3.61..47.471.....6....7.31...9..2....5..8..4....5..7...12.4....6.......4.34..59.. autosolve
386129475471853296925476318749362581253781649168594732512947863697238154834615927 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (12)
A3: 5,9
C3: 5,8
F1: 8,9
D3: 4,6
F3: 4,6
B4: 4,6
C5: 3,7
B6: 4,6
C6: 3,8
A7: 5,9
B8: 8,9
A9: 7,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G8,I9: 1.. / G8 = 1  => 19 pairs (_) / I9 = 1  => 13 pairs (_)
E9,I9: 1.. / E9 = 1  => 19 pairs (_) / I9 = 1  => 13 pairs (_)
B1,B3: 2.. / B1 = 2  => 15 pairs (_) / B3 = 2  => 16 pairs (_)
A5,A6: 2.. / A5 = 2  => 14 pairs (_) / A6 = 2  => 13 pairs (_)
B3,I3: 2.. / B3 = 2  => 16 pairs (_) / I3 = 2  => 15 pairs (_)
C5,C6: 3.. / C5 = 3  => 12 pairs (_) / C6 = 3  =>  0 pairs (X)
D3,F3: 4.. / D3 = 4  =>  8 pairs (_) / F3 = 4  => 11 pairs (_)
B4,B6: 4.. / B4 = 4  =>  8 pairs (_) / B6 = 4  => 11 pairs (_)
D4,F6: 4.. / D4 = 4  => 11 pairs (_) / F6 = 4  =>  8 pairs (_)
B4,D4: 4.. / B4 = 4  =>  8 pairs (_) / D4 = 4  => 11 pairs (_)
B6,F6: 4.. / B6 = 4  => 11 pairs (_) / F6 = 4  =>  8 pairs (_)
D3,D4: 4.. / D3 = 4  =>  8 pairs (_) / D4 = 4  => 11 pairs (_)
F3,F6: 4.. / F3 = 4  => 11 pairs (_) / F6 = 4  =>  8 pairs (_)
A3,C3: 5.. / A3 = 5  =>  0 pairs (X) / C3 = 5  => 13 pairs (_)
E1,E2: 5.. / E1 = 5  => 13 pairs (_) / E2 = 5  => 14 pairs (_)
A7,C8: 5.. / A7 = 5  => 13 pairs (_) / C8 = 5  =>  0 pairs (X)
E1,I1: 5.. / E1 = 5  => 13 pairs (_) / I1 = 5  => 14 pairs (_)
A3,A7: 5.. / A3 = 5  =>  0 pairs (X) / A7 = 5  => 13 pairs (_)
C3,C8: 5.. / C3 = 5  => 13 pairs (_) / C8 = 5  =>  0 pairs (X)
D3,F3: 6.. / D3 = 6  => 11 pairs (_) / F3 = 6  =>  8 pairs (_)
B4,B6: 6.. / B4 = 6  => 11 pairs (_) / B6 = 6  =>  8 pairs (_)
C8,A9: 7.. / C8 = 7  => 12 pairs (_) / A9 = 7  =>  0 pairs (X)
I7,I9: 7.. / I7 = 7  => 12 pairs (_) / I9 = 7  =>  0 pairs (*)
A4,D4: 7.. / A4 = 7  => 12 pairs (_) / D4 = 7  =>  9 pairs (_)
C5,C8: 7.. / C5 = 7  =>  0 pairs (X) / C8 = 7  => 12 pairs (_)
A7,B8: 9.. / A7 = 9  =>  0 pairs (X) / B8 = 9  => 13 pairs (_)
A3,A7: 9.. / A3 = 9  => 13 pairs (_) / A7 = 9  =>  0 pairs (X)
H2,H6: 9.. / H2 = 9  => 15 pairs (_) / H6 = 9  => 15 pairs (_)
* DURATION: 0:00:40.483701  START: 04:46:12.972391  END: 04:46:53.456092 2017-05-01
* CP COUNT: (28)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A7,A9,B4,B6,B8,C3,C5,C6,D3,F1,F3)
* 3.61..47.471.....6....7.31...9..2....5..8..4....5..7...12.4....6.......4.34..59..
* PAIR C3: 5,8 COL C
C8: 5,8,7                                # reduction candidate for 5,8
C8: 5,8 => CTR
* 3.61.9475471.53.96...47631..49762..3257381649.635947...12.485376.5.371.4734.15968
C8: 7                                    # 12 pairs
* PAIR F1: 8,9 BLK 2
D2: 8,9,2,3                              # reduction candidate for 8,9
D2: 8,9                                  # 16 pairs
F2: 8,9,3                                # reduction candidate for 8,9
F2: 8,9                                  # 15 pairs
* PAIR F1: 8,9 ROW 1
B1: 8,9,2                                # reduction candidate for 8,9
B1: 8,9                                  # 16 pairs
I1: 8,9,2,5                              # reduction candidate for 8,9
I1: 8,9                                  # 15 pairs
* PAIR F1: 8,9 COL F
F7: 8,9,3,6,7                            # reduction candidate for 8,9
F7: 8,9                                  # 14 pairs
F8: 8,9,1,3,7                            # reduction candidate for 8,9
F8: 8,9                                  # 16 pairs
* PAIR D3: 4,6 COL D
D4: 4,6,3,7                              # reduction candidate for 4,6
D4: 4,6                                  # 16 pairs
D4: 3,7                                  #  9 pairs
* PAIR F3: 4,6 COL F
F6: 4,6,1,3,9                            # reduction candidate for 4,6
F6: 1,3,9 => CTR
* 3.61..47.471.....69.567431.7694.2....53786.49.485..76.5129476..697.....48342.59..
F6: 4,6                                  # 13 pairs
* PAIR B4: 4,6 ROW 4
D4: 4,6,3,7                              # reduction candidate for 4,6
D4: 4,6                                  # 16 pairs
D4: 3,7                                  #  9 pairs
* PAIR C5: 3,7 ROW 5
D5: 3,7,6,9                              # reduction candidate for 3,7
D5: 3,7                                  # 14 pairs
F5: 3,7,1,6,9                            # reduction candidate for 3,7
F5: 3,7                                  # 15 pairs
* PAIR B6: 4,6 ROW 6
F6: 4,6,1,3,9                            # reduction candidate for 4,6
F6: 1,3,9 => CTR
* 3.61..47.471.....69.567431.7694.2....53786.49.485..76.5129476..697.....48342.59..
F6: 4,6                                  # 13 pairs
* PAIR C6: 3,8 ROW 6
H6: 3,8,2,6,9                            # reduction candidate for 3,8
H6: 3,8                                  # 17 pairs
I6: 3,8,1,2,9                            # reduction candidate for 3,8
I6: 3,8                                  # 14 pairs
* PAIR B8: 8,9 ROW 8
D8: 8,9,2,3,7                            # reduction candidate for 8,9
D8: 8,9                                  # 14 pairs
F8: 8,9,1,3,7                            # reduction candidate for 8,9
F8: 8,9                                  # 16 pairs
* PAIR B8: 8,9 COL B
B1: 8,9,2                                # reduction candidate for 8,9
B1: 8,9                                  # 16 pairs
B3: 8,9,2                                # reduction candidate for 8,9
B3: 8,9                                  # 15 pairs
* PAIR A9: 7,8 BLK 7
C8: 7,8,5                                # reduction candidate for 7,8
C8: 5 => CTR
* 326159478471....96598476312.497.2...257.81649.6359472.912.4...76859.7234734..59.1
C8: 7,8                                  # 13 pairs
* PAIR A9: 7,8 ROW 9
D9: 7,8,2,6                              # reduction candidate for 7,8
D9: 7,8                                  # 15 pairs
I9: 7,8,1,2                              # reduction candidate for 7,8
I9: 7,8                                  # 22 pairs
* PAIR A9: 7,8 COL A
A4: 7,8,1                                # reduction candidate for 7,8
A4: 7,8                                  # 15 pairs
A4: 1                                    # 11 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0075-base-pr-000.dot
* REASONING
* DIS # C8: 5,8 => CTR => C8: 7
* DIS # F6: 1,3,9 => CTR => F6: 4,6
* DIS # F6: 1,3,9 => CTR => F6: 4,6
* DIS # C8: 5 => CTR => C8: 7,8
* CNT   4 HDP CHAINS /  30 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A7,A9,B4,B6,B8,C3,C5,C6,D3,F1,F3)
* 3.61..47.471.....6....7.31...9..2....5..8..4....5..7...12.4....6.......4.34..59..
* PAIR C3: 5,8 COL C
C8: 5,8,7                                # reduction candidate for 5,8
C8: 5,8 => CTR
* 3.61.9475471.53.96...47631..49762..3257381649.635947...12.485376.5.371.4734.15968
* PAIR RESTART
* PAIR F1: 8,9 BLK 2
D2: 8,9,2,3                              # reduction candidate for 8,9
D2: 8,9                                  # 21 pairs
F2: 8,9,3                                # reduction candidate for 8,9
F2: 8,9                                  # 17 pairs
* PAIR F1: 8,9 ROW 1
I1: 8,9,2,5                              # reduction candidate for 8,9
I1: 2,5                                  # 14 pairs
I1: 8,9                                  # 13 pairs
* PAIR F1: 8,9 COL F
F7: 8,9,3,6,7                            # reduction candidate for 8,9
F7: 8,9                                  # 22 pairs
F7: 3,6,7                                # 13 pairs
* PAIR D3: 4,6 COL D
D4: 4,6,3,7                              # reduction candidate for 4,6
D4: 4,6                                  # 16 pairs
D4: 3,7                                  #  9 pairs
* PAIR F3: 4,6 COL F
F6: 4,6,1,3,9                            # reduction candidate for 4,6
F6: 1,3,9 => CTR
* 3.61..47.471.....69.567431.7694.2....53786.49.485..76.5129476..697.....48342.59..
* PAIR RESTART
* PAIR B4: 4,6 ROW 4
D4: 4,6,3,7                              # reduction candidate for 4,6
D4: 4,6 => CTR
* 3.61..47.471...2.6925.7.3187.9..2185.53.8.64...85..7..512.4.86769721...4834.65921
* PAIR RESTART

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A4,A6,B1,B3,D4,F1,G7,H9,I3)
* 3.61..47.471.....69.547631..49..2....53.8..4..685.47..512.4....697.....4834..59..
* PAIR B1: 2,8 ROW 1
I1: 2,8,5,9                              # reduction candidate for 2,8
I1: 2,8 => CTR
* 3.615947.471...5969.547631.1497.2..5.53.8.24926859473151294...3697...154834.15927
* PAIR RESTART
* PAIR F1: 8,9 BLK 2
D2: 8,9,2,3                              # reduction candidate for 8,9
D2: 8,9 => SOLVED
* 386129475471853296925476318749362581253781649168594732512947863697238154834615927
* DURATION: 0:00:17.943748  START: 04:47:16.479489  END: 04:47:34.423237 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0075-base-pr-001.dot
* REASONING
* DIS # C8: 5,8 => CTR => C8: 7
* DIS C8: 7 # F6: 1,3,9 => CTR => F6: 4,6
* DIS C8: 7 + F6: 4,6 # D4: 4,6 => CTR => D4: 3,7
* DIS C8: 7 + F6: 4,6 + D4: 3,7 # I1: 2,8 => CTR => I1: 5,9
* PRF C8: 7 + F6: 4,6 + D4: 3,7 + I1: 5,9 # D2: 8,9 => SOL
* STA C8: 7 + F6: 4,6 + D4: 3,7 + I1: 5,9 + D2: 8,9
* CNT   5 HDP CHAINS /  14 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=75

Solution

position: 386129475471853296925476318749362581253781649168594732512947863697238154834615927 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 # C8: 5,8 => CTR => C8: 7
* INC # C8: 7 => UNS
* INC # D2: 8,9 => UNS
* INC # F2: 8,9 => UNS
* INC # B1: 8,9 => UNS
* INC # I1: 8,9 => UNS
* INC # F7: 8,9 => UNS
* INC # F8: 8,9 => UNS
* INC # D4: 4,6 => UNS
* INC # D4: 3,7 => UNS
* INC # F6: 4,6 => UNS
* DIS # F6: 1,3,9 => CTR => F6: 4,6
* INC # D4: 4,6 => UNS
* INC # D4: 3,7 => UNS
* INC # D5: 3,7 => UNS
* INC # F5: 3,7 => UNS
* INC # F6: 4,6 => UNS
* DIS # F6: 1,3,9 => CTR => F6: 4,6
* INC # H6: 3,8 => UNS
* INC # I6: 3,8 => UNS
* INC # D8: 8,9 => UNS
* INC # F8: 8,9 => UNS
* INC # B1: 8,9 => UNS
* INC # B3: 8,9 => UNS
* INC # C8: 7,8 => UNS
* DIS # C8: 5 => CTR => C8: 7,8
* INC # D9: 7,8 => UNS
* INC # I9: 7,8 => UNS
* INC # A4: 7,8 => UNS
* INC # A4: 1 => UNS
* CNT  30 HDP CHAINS /  30 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # C8: 5,8 => CTR => C8: 7
* INC C8: 7 # D2: 8,9 => UNS
* INC C8: 7 # F2: 8,9 => UNS
* INC C8: 7 # I1: 8,9 => UNS
* INC C8: 7 # I1: 2,5 => UNS
* INC C8: 7 # F7: 8,9 => UNS
* INC C8: 7 # F7: 3,6,7 => UNS
* INC C8: 7 # D4: 4,6 => UNS
* INC C8: 7 # D4: 3,7 => UNS
* INC C8: 7 # F6: 4,6 => UNS
* DIS C8: 7 # F6: 1,3,9 => CTR => F6: 4,6
* DIS C8: 7 + F6: 4,6 # D4: 4,6 => CTR => D4: 3,7
* DIS C8: 7 + F6: 4,6 + D4: 3,7 # I1: 2,8 => CTR => I1: 5,9
* PRF C8: 7 + F6: 4,6 + D4: 3,7 + I1: 5,9 # D2: 8,9 => SOL
* STA C8: 7 + F6: 4,6 + D4: 3,7 + I1: 5,9 + D2: 8,9
* CNT  14 HDP CHAINS /  14 HYP OPENED