Analysis of zz-www.sudokuwiki.org-0071-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=71

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=71

position: ....792...5.8....37......6.2....1.9...8...1...6.3....4.7......29....7.3...614.... initial

Autosolve

position: ....792...5.8....37......6.24...139...8...1...6.3....4.7......29....7.3...614.... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C6: 1,9 => CTR => C6: 5,7
* DIS # C6: 1,5 => CTR => C6: 7,9
* CNT   2 HDP CHAINS /  10 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: 1,9 => CTR => C6: 5,7
* DIS C6: 5,7 # A1: 8 => CTR => A1: 4,6
* PRF C6: 5,7 + A1: 4,6 # F2: 2 => SOL
* STA C6: 5,7 + A1: 4,6 + F2: 2
* CNT   3 HDP CHAINS /   8 HYP OPENED

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

Details

Positions

....792...5.8....37......6.2....1.9...8...1...6.3....4.7......29....7.3...614.... initial
....792...5.8....37......6.24...139...8...1...6.3....4.7......29....7.3...614.... autosolve
431679285659812743782534961245781396398426157167395824573968412914257638826143579 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (4)
C4: 5,7
A5: 3,5
B5: 3,9
A6: 1,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E2,E3: 1.. / E2 = 1  =>  6 pairs (_) / E3 = 1  =>  8 pairs (_)
A6,C6: 1.. / A6 = 1  =>  4 pairs (_) / C6 = 1  =>  0 pairs (X)
H7,I8: 1.. / H7 = 1  =>  9 pairs (_) / I8 = 1  =>  8 pairs (_)
H5,H6: 2.. / H5 = 2  =>  4 pairs (_) / H6 = 2  =>  6 pairs (_)
B9,F9: 2.. / B9 = 2  =>  5 pairs (_) / F9 = 2  =>  9 pairs (_)
E3,F3: 3.. / E3 = 3  =>  6 pairs (_) / F3 = 3  =>  5 pairs (_)
A5,B5: 3.. / A5 = 3  =>  5 pairs (_) / B5 = 3  =>  0 pairs (X)
C1,C7: 3.. / C1 = 3  =>  5 pairs (_) / C7 = 3  =>  9 pairs (_)
E3,E7: 3.. / E3 = 3  =>  6 pairs (_) / E7 = 3  =>  5 pairs (_)
D5,F5: 4.. / D5 = 4  =>  9 pairs (_) / F5 = 4  =>  5 pairs (_)
C8,G8: 4.. / C8 = 4  =>  9 pairs (_) / G8 = 4  =>  6 pairs (_)
A1,A2: 6.. / A1 = 6  =>  8 pairs (_) / A2 = 6  => 11 pairs (_)
I4,I5: 6.. / I4 = 6  =>  7 pairs (_) / I5 = 6  =>  4 pairs (_)
G7,G8: 6.. / G7 = 6  =>  5 pairs (_) / G8 = 6  => 10 pairs (_)
A1,D1: 6.. / A1 = 6  =>  8 pairs (_) / D1 = 6  => 11 pairs (_)
G2,H2: 7.. / G2 = 7  =>  8 pairs (_) / H2 = 7  => 11 pairs (_)
C4,C6: 7.. / C4 = 7  =>  0 pairs (X) / C6 = 7  =>  7 pairs (_)
D4,D5: 7.. / D4 = 7  =>  7 pairs (_) / D5 = 7  =>  8 pairs (_)
E4,I4: 8.. / E4 = 8  =>  5 pairs (_) / I4 = 8  => 14 pairs (_)
B5,C6: 9.. / B5 = 9  =>  5 pairs (_) / C6 = 9  =>  0 pairs (X)
D7,E7: 9.. / D7 = 9  =>  4 pairs (_) / E7 = 9  =>  0 pairs (X)
G9,I9: 9.. / G9 = 9  =>  7 pairs (_) / I9 = 9  => 11 pairs (_)
C2,G2: 9.. / C2 = 9  =>  7 pairs (_) / G2 = 9  => 14 pairs (_)
C6,E6: 9.. / C6 = 9  =>  0 pairs (X) / E6 = 9  =>  5 pairs (_)
B3,B5: 9.. / B3 = 9  =>  0 pairs (X) / B5 = 9  =>  5 pairs (_)
D5,D7: 9.. / D5 = 9  =>  0 pairs (X) / D7 = 9  =>  4 pairs (_)
I3,I9: 9.. / I3 = 9  =>  7 pairs (_) / I9 = 9  => 11 pairs (_)
* DURATION: 0:00:28.948304  START: 04:42:40.172458  END: 04:43:09.120762 2017-05-01
* CP COUNT: (27)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B5,C4)
* ....792...5.8....37......6.24...139...8...1...6.3....4.7......29....7.3...614....
* PAIR C4: 5,7 BLK 4
C6: 5,7,1,9                              # reduction candidate for 5,7
C6: 1,9 => CTR
* ....792...598....37.....569247..139.3987.412.561392..4.7.9....29....7.3.8.614.957
C6: 5,7                                  #  6 pairs
* PAIR C4: 5,7 ROW 4
D4: 5,7,6                                # reduction candidate for 5,7
D4: 5,7                                  #  7 pairs
I4: 5,7,6,8                              # reduction candidate for 5,7
I4: 5,7                                  # 18 pairs
* PAIR A5: 3,5 COL A
A7: 3,5,1,4,8                            # reduction candidate for 3,5
A7: 3,5                                  # 12 pairs
A9: 3,5,8                                # reduction candidate for 3,5
A9: 3,5                                  #  6 pairs
* PAIR A6: 1,5 BLK 4
C6: 1,5,7,9                              # reduction candidate for 1,5
C6: 1,5 => CTR
* .3.6792..659812..37124358692475.139.398724156.6.398724.739.6..298.257631526143987
C6: 7,9                                  #  5 pairs
* PAIR A6: 1,5 COL A
A7: 1,5,3,4,8                            # reduction candidate for 1,5
A7: 1,5                                  # 11 pairs
A7: 3,4,8                                #  4 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0071-base-pr-000.dot
* REASONING
* DIS # C6: 1,9 => CTR => C6: 5,7
* DIS # C6: 1,5 => CTR => C6: 7,9
* CNT   2 HDP CHAINS /  10 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B5,C4)
* ....792...5.8....37......6.24...139...8...1...6.3....4.7......29....7.3...614....
* PAIR C4: 5,7 BLK 4
C6: 5,7,1,9                              # reduction candidate for 5,7
C6: 1,9 => CTR
* ....792...598....37.....569247..139.3987.412.561392..4.7.9....29....7.3.8.614.957
* PAIR C4: 5,7 ROW 4
D4: 5,7,6                                # reduction candidate for 5,7
D4: 5,7                                  #  9 pairs
I4: 5,7,6,8                              # reduction candidate for 5,7
I4: 5,7                                  # 20 pairs

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,A9,B9,C4,C6,F9)
* ....792...5.8....37......6.24...139.398...1..16.39...4.7.9....29....7.3...614....
* PAIR A2: 4,6 BLK 1
A1: 4,6,8                                # reduction candidate for 4,6
A1: 8 => CTR
* 8..6792..65.8....37......6.24578139639845612716739258447.9386.298..6743.5.614....
* PAIR A2: 4,6 ROW 2
F2: 4,6,2                                # reduction candidate for 4,6
F2: 2 => SOLVED
* 431679285659812743782534961245781396398426157167395824573968412914257638826143579
* DURATION: 0:00:08.020300  START: 04:43:16.064494  END: 04:43:24.084794 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0071-base-pr-001.dot
* REASONING
* DIS # C6: 1,9 => CTR => C6: 5,7
* DIS C6: 5,7 # A1: 8 => CTR => A1: 4,6
* PRF C6: 5,7 + A1: 4,6 # F2: 2 => SOL
* STA C6: 5,7 + A1: 4,6 + F2: 2
* CNT   3 HDP CHAINS /   8 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=71

Solution

position: 431679285659812743782534961245781396398426157167395824573968412914257638826143579 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 # C6: 5,7 => UNS
* DIS # C6: 1,9 => CTR => C6: 5,7
* INC # D4: 5,7 => UNS
* INC # I4: 5,7 => UNS
* INC # A7: 3,5 => UNS
* INC # A9: 3,5 => UNS
* DIS # C6: 1,5 => CTR => C6: 7,9
* INC # C6: 7,9 => UNS
* INC # A7: 1,5 => UNS
* INC # A7: 3,4,8 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C6: 5,7 => UNS
* DIS # C6: 1,9 => CTR => C6: 5,7
* INC C6: 5,7 # D4: 5,7 => UNS
* INC C6: 5,7 # I4: 5,7 => UNS
* INC C6: 5,7 # A1: 4,6 => UNS
* DIS C6: 5,7 # A1: 8 => CTR => A1: 4,6
* INC C6: 5,7 + A1: 4,6 # F2: 4,6 => UNS
* PRF C6: 5,7 + A1: 4,6 # F2: 2 => SOL
* STA C6: 5,7 + A1: 4,6 + F2: 2
* CNT   8 HDP CHAINS /   8 HYP OPENED