Analysis of zz-www.sudokuwiki.org-0097-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=97

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=97

position: .....46....35.....1......89..8..9.2..3..2..9..9.3..4..28......6.....85....47..... initial

Autosolve

position: .2...465..635.....145....89..8..9.2..3..2..9..923..46.28......6.....85....47..... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A1: 8 => SOL
* DIS # E1: 8,9 => CTR => E1: 1,3
* DIS # E1: 8,9 => CTR => E1: 1,3
* DIS # A5: 5,7 => CTR => A5: 4,6
* DIS # I6: 5,7 => CTR => I6: 1,8
* DIS # C8: 1,7 => CTR => C8: 6,9
* DIS # I8: 1,7 => CTR => I8: 2,4
* DIS # F9: 1,3 => CTR => F9: 2,6
* CNT   8 HDP CHAINS /  40 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 # A1: 8 => SOL
* STA A1: 8
* CNT   1 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

.....46....35.....1......89..8..9.2..3..2..9..9.3..4..28......6.....85....47..... initial
.2...465..635.....145....89..8..9.2..3..2..9..923..46.28......6.....85....47..... autosolve
827914653963587214145236789718649325436825197592371468281453976379168542654792831 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
C1: 7,9
A2: 8,9
E2: 8,9
D3: 2,6
I1: 1,3
A6: 5,7
B8: 1,7
B9: 1,5
H9: 1,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B4,C5: 1.. / B4 = 1  => 11 pairs (_) / C5 = 1  => 14 pairs (_)
D8,F9: 2.. / D8 = 2  =>  0 pairs (X) / F9 = 2  => 14 pairs (_)
D8,I8: 2.. / D8 = 2  =>  0 pairs (X) / I8 = 2  => 14 pairs (_)
D3,D8: 2.. / D3 = 2  => 14 pairs (_) / D8 = 2  =>  0 pairs (X)
I1,G3: 3.. / I1 = 3  => 10 pairs (_) / G3 = 3  =>  0 pairs (X)
G4,I4: 3.. / G4 = 3  => 10 pairs (_) / I4 = 3  =>  0 pairs (X)
A8,A9: 3.. / A8 = 3  =>  9 pairs (_) / A9 = 3  => 13 pairs (_)
E1,I1: 3.. / E1 = 3  =>  0 pairs (X) / I1 = 3  => 10 pairs (_)
G3,G4: 3.. / G3 = 3  =>  0 pairs (X) / G4 = 3  => 10 pairs (_)
I1,I4: 3.. / I1 = 3  => 10 pairs (_) / I4 = 3  =>  0 pairs (X)
H2,I2: 4.. / H2 = 4  =>  0 pairs (X) / I2 = 4  => 10 pairs (_)
A4,A5: 4.. / A4 = 4  => 13 pairs (_) / A5 = 4  =>  9 pairs (_)
A5,D5: 4.. / A5 = 4  =>  9 pairs (_) / D5 = 4  => 13 pairs (_)
I2,I8: 4.. / I2 = 4  => 10 pairs (_) / I8 = 4  =>  0 pairs (X)
A9,B9: 5.. / A9 = 5  => 18 pairs (_) / B9 = 5  =>  9 pairs (_)
E7,F7: 5.. / E7 = 5  => 10 pairs (_) / F7 = 5  => 10 pairs (_)
B4,B9: 5.. / B4 = 5  => 18 pairs (_) / B9 = 5  =>  9 pairs (_)
C5,C8: 6.. / C5 = 6  => 13 pairs (_) / C8 = 6  => 12 pairs (_)
A1,C1: 7.. / A1 = 7  => 13 pairs (_) / C1 = 7  => 11 pairs (_)
B4,B8: 7.. / B4 = 7  => 13 pairs (_) / B8 = 7  => 10 pairs (_)
A1,A2: 8.. / A1 = 8  =>  0 pairs (*) / A2 = 8  =>  0 pairs (X)
D5,E6: 8.. / D5 = 8  => 16 pairs (_) / E6 = 8  =>  9 pairs (_)
G9,I9: 8.. / G9 = 8  => 14 pairs (_) / I9 = 8  => 12 pairs (_)
A2,E2: 8.. / A2 = 8  =>  9 pairs (_) / E2 = 8  =>  0 pairs (*)
E6,I6: 8.. / E6 = 8  =>  9 pairs (_) / I6 = 8  => 16 pairs (_)
D1,D5: 8.. / D1 = 8  =>  9 pairs (_) / D5 = 8  => 16 pairs (_)
G5,G9: 8.. / G5 = 8  => 12 pairs (_) / G9 = 8  => 14 pairs (_)
G7,G9: 9.. / G7 = 9  => 12 pairs (_) / G9 = 9  => 13 pairs (_)
A2,E2: 9.. / A2 = 9  =>  0 pairs (*) / E2 = 9  =>  0 pairs (X)
* DURATION: 0:00:44.302516  START: 05:14:07.990255  END: 05:14:52.292771 2017-05-01
* CP COUNT: (29)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,B8,B9,C1,D3,E2,H9,I1)
* .2...465..635.....145....89..8..9.2..3..2..9..923..46.28......6.....85....47.....
* PAIR C1: 7,9 BLK 1
A1: 7,9,8                                # reduction candidate for 7,9
A1: 8 => SOLVED
* 827914653963587214145236789718649325436825197592371468281453976379168542654792831
A1: 7,9                                  #  9 pairs
* PAIR C1: 7,9 COL C
C7: 7,9,1                                # reduction candidate for 7,9
C7: 7,9                                  # 12 pairs
C8: 7,9,1,6                              # reduction candidate for 7,9
C8: 7,9                                  # 14 pairs
* PAIR A2: 8,9 BLK 1
A1: 8,9,7                                # reduction candidate for 8,9
A1: 7                                    # 13 pairs
A1: 8,9                                  # 11 pairs
* PAIR E2: 8,9 BLK 2
D1: 8,9,1                                # reduction candidate for 8,9
D1: 8,9                                  # 11 pairs
E1: 8,9,1,3                              # reduction candidate for 8,9
E1: 8,9 => CTR
* .291846538635972141452..789..864932.43682.197.9237146828.453976...9.85.29547.28.1
E1: 1,3                                  # 11 pairs
* PAIR D3: 2,6 BLK 2
F3: 2,6,3,7                              # reduction candidate for 2,6
F3: 2,6                                  # 13 pairs
F3: 3,7                                  # 10 pairs
* PAIR D3: 2,6 COL D
D8: 2,6,1,4,9                            # reduction candidate for 2,6
D8: 1,4,9                                # 15 pairs
D8: 2,6                                  # 11 pairs
* PAIR I1: 1,3 ROW 1
E1: 1,3,8,9                              # reduction candidate for 1,3
E1: 8,9 => CTR
* .291846538635972141452..789..864932.43682.197.9237146828.453976...9.85.29547.28.1
E1: 1,3                                  # 11 pairs
* PAIR I1: 1,3 COL I
I4: 1,3,5,7                              # reduction candidate for 1,3
I4: 1,3                                  # 12 pairs
I4: 5,7                                  # 11 pairs
* PAIR A6: 5,7 BLK 4
A4: 5,7,4,6                              # reduction candidate for 5,7
A4: 5,7                                  # 16 pairs
B4: 5,7,1                                # reduction candidate for 5,7
B4: 5,7                                  # 14 pairs
A5: 5,7,4,6                              # reduction candidate for 5,7
A5: 5,7 => CTR
* 9278.465.86359.2.41452.6.894186.9.2..3642.89..9238.46.28..531.6.7...85.2.547.29.8
A5: 4,6                                  # 10 pairs
* PAIR A6: 5,7 ROW 6
E6: 5,7,1,8                              # reduction candidate for 5,7
E6: 5,7                                  # 19 pairs
F6: 5,7,1                                # reduction candidate for 5,7
F6: 5,7                                  # 12 pairs
I6: 5,7,1,8                              # reduction candidate for 5,7
I6: 5,7 => CTR
* .2.81465386359....1452.6789..8.7932..3..25.9..9238146.287.53.46.1.9485729547.....
I6: 1,8                                  # 10 pairs
* PAIR B8: 1,7 BLK 7
C7: 1,7,9                                # reduction candidate for 1,7
C7: 1,7                                  # 11 pairs
C8: 1,7,6,9                              # reduction candidate for 1,7
C8: 1,7 => CTR
* .278.465.86359.2.41452.6.89.18..9.2..36.2.89..9238.46.289..3176.719.8542.54712938
C8: 6,9                                  # 10 pairs
* PAIR B8: 1,7 ROW 8
H8: 1,7,3,4                              # reduction candidate for 1,7
H8: 1,7                                  # 12 pairs
I8: 1,7,2,4                              # reduction candidate for 1,7
I8: 1,7 => CTR
* 8279.465.96358...41456...89..8..9.2.43682..9..923..4682814..976.792.8541.5479.8.2
I8: 2,4                                  # 10 pairs
* PAIR B8: 1,7 COL B
B4: 1,7,5                                # reduction candidate for 1,7
B4: 5                                    # 18 pairs
B4: 1,7                                  #  9 pairs
* PAIR B9: 1,5 COL B
B4: 1,5,7                                # reduction candidate for 1,5
B4: 7                                    # 13 pairs
B4: 1,5                                  # 10 pairs
* PAIR H9: 1,3 BLK 9
H7: 1,3,4,7                              # reduction candidate for 1,3
H7: 1,3                                  # 14 pairs
H8: 1,3,4,7                              # reduction candidate for 1,3
H8: 1,3                                  # 16 pairs
* PAIR H9: 1,3 ROW 9
E9: 1,3,6,9                              # reduction candidate for 1,3
E9: 1,3                                  # 13 pairs
F9: 1,3,2,6                              # reduction candidate for 1,3
F9: 1,3 => CTR
* .2...465..635.....1456...896.8..9.2.43..26.95.923..46.28....9.63.62985..95476....
F9: 2,6                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0097-base-pr-000.dot
* REASONING
* PRF # A1: 8 => SOL
* DIS # E1: 8,9 => CTR => E1: 1,3
* DIS # E1: 8,9 => CTR => E1: 1,3
* DIS # A5: 5,7 => CTR => A5: 4,6
* DIS # I6: 5,7 => CTR => I6: 1,8
* DIS # C8: 1,7 => CTR => C8: 6,9
* DIS # I8: 1,7 => CTR => I8: 2,4
* DIS # F9: 1,3 => CTR => F9: 2,6
* CNT   8 HDP CHAINS /  40 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,B8,B9,C1,D3,E2,H9,I1)
* .2...465..635.....145....89..8..9.2..3..2..9..923..46.28......6.....85....47.....
* PAIR C1: 7,9 BLK 1
A1: 7,9,8                                # reduction candidate for 7,9
A1: 8 => SOLVED
* 827914653963587214145236789718649325436825197592371468281453976379168542654792831
* DURATION: 0:00:03.091412  START: 05:15:24.116285  END: 05:15:27.207697 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0097-base-pr-001.dot
* REASONING
* PRF # A1: 8 => SOL
* STA A1: 8
* CNT   1 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=97

Solution

position: 827914653963587214145236789718649325436825197592371468281453976379168542654792831 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 # A1: 7,9 => UNS
* PRF # A1: 8 => SOL
* INC # C7: 7,9 => UNS
* INC # C8: 7,9 => UNS
* INC # A1: 8,9 => UNS
* INC # A1: 7 => UNS
* INC # D1: 8,9 => UNS
* DIS # E1: 8,9 => CTR => E1: 1,3
* INC # E1: 1,3 => UNS
* INC # F3: 2,6 => UNS
* INC # F3: 3,7 => UNS
* INC # D8: 2,6 => UNS
* INC # D8: 1,4,9 => UNS
* INC # E1: 1,3 => UNS
* DIS # E1: 8,9 => CTR => E1: 1,3
* INC # I4: 1,3 => UNS
* INC # I4: 5,7 => UNS
* INC # A4: 5,7 => UNS
* INC # B4: 5,7 => UNS
* DIS # A5: 5,7 => CTR => A5: 4,6
* INC # A5: 4,6 => UNS
* INC # E6: 5,7 => UNS
* INC # F6: 5,7 => UNS
* DIS # I6: 5,7 => CTR => I6: 1,8
* INC # I6: 1,8 => UNS
* INC # C7: 1,7 => UNS
* DIS # C8: 1,7 => CTR => C8: 6,9
* INC # C8: 6,9 => UNS
* INC # H8: 1,7 => UNS
* DIS # I8: 1,7 => CTR => I8: 2,4
* INC # I8: 2,4 => UNS
* INC # B4: 1,7 => UNS
* INC # B4: 5 => UNS
* INC # B4: 1,5 => UNS
* INC # B4: 7 => UNS
* INC # H7: 1,3 => UNS
* INC # H8: 1,3 => UNS
* INC # E9: 1,3 => UNS
* DIS # F9: 1,3 => CTR => F9: 2,6
* INC # F9: 2,6 => UNS
* CNT  40 HDP CHAINS /  40 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 7,9 => UNS
* PRF # A1: 8 => SOL
* STA A1: 8
* CNT   2 HDP CHAINS /   2 HYP OPENED