Analysis of zz-www.sudokuwiki.org-0074-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=74

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=74

position: .7.3.....4...8.5...8...9..6.....6.9...3.4.1...2.7.....8..9...4...5.1...3.....5.2. initial

Autosolve

position: .7.3.....4...8.5...8...9..6.....6.9...3.4.1...2.79..5.8..9...45..5.1...3.....5.21 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C6: 1,6 => CTR => C6: 4,8
* DIS # G6: 4,8 => CTR => G6: 3,6
* DIS # C6: 1,6 => CTR => C6: 4,8
* CNT   3 HDP CHAINS /  33 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: 1,6 => CTR => C6: 4,8
* PRF C6: 4,8 # G9: 6,7 => SOL
* STA C6: 4,8 + G9: 6,7
* CNT   2 HDP CHAINS /  26 HYP OPENED

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

Details

Positions

.7.3.....4...8.5...8...9..6.....6.9...3.4.1...2.7.....8..9...4...5.1...3.....5.2. initial
.7.3.....4...8.5...8...9..6.....6.9...3.4.1...2.79..5.8..9...45..5.1...3.....5.21 autosolve
976354218431682579582179436154236897793548162628791354817923645265417983349865721 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
C3: 1,2
H1: 1,8
A4: 1,7
A6: 1,6
F5: 2,8
I6: 4,8
G7: 6,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D4,F6: 1.. / D4 = 1  => 11 pairs (_) / F6 = 1  => 14 pairs (_)
B7,C7: 1.. / B7 = 1  =>  9 pairs (_) / C7 = 1  => 18 pairs (_)
C7,A8: 2.. / C7 = 2  =>  0 pairs (X) / A8 = 2  =>  7 pairs (_)
B2,A3: 3.. / B2 = 3  => 10 pairs (_) / A3 = 3  => 10 pairs (_)
H2,H3: 3.. / H2 = 3  => 10 pairs (_) / H3 = 3  => 10 pairs (_)
E4,F6: 3.. / E4 = 3  => 13 pairs (_) / F6 = 3  => 15 pairs (_)
G4,G6: 3.. / G4 = 3  => 15 pairs (_) / G6 = 3  => 13 pairs (_)
B2,H2: 3.. / B2 = 3  => 10 pairs (_) / H2 = 3  => 10 pairs (_)
A3,H3: 3.. / A3 = 3  => 10 pairs (_) / H3 = 3  => 10 pairs (_)
E4,G4: 3.. / E4 = 3  => 13 pairs (_) / G4 = 3  => 15 pairs (_)
F6,G6: 3.. / F6 = 3  => 15 pairs (_) / G6 = 3  => 13 pairs (_)
A3,A9: 3.. / A3 = 3  => 10 pairs (_) / A9 = 3  => 10 pairs (_)
F6,F7: 3.. / F6 = 3  => 15 pairs (_) / F7 = 3  => 13 pairs (_)
F1,D3: 4.. / F1 = 4  =>  8 pairs (_) / D3 = 4  => 13 pairs (_)
D3,G3: 4.. / D3 = 4  => 13 pairs (_) / G3 = 4  =>  8 pairs (_)
F1,F8: 4.. / F1 = 4  =>  8 pairs (_) / F8 = 4  => 13 pairs (_)
A1,A3: 5.. / A1 = 5  =>  8 pairs (_) / A3 = 5  => 13 pairs (_)
B4,B5: 5.. / B4 = 5  => 13 pairs (_) / B5 = 5  => 14 pairs (_)
A1,E1: 5.. / A1 = 5  =>  8 pairs (_) / E1 = 5  => 13 pairs (_)
B5,D5: 5.. / B5 = 5  => 14 pairs (_) / D5 = 5  => 13 pairs (_)
E1,D2: 6.. / E1 = 6  => 16 pairs (_) / D2 = 6  =>  9 pairs (_)
H5,G6: 6.. / H5 = 6  => 10 pairs (_) / G6 = 6  =>  0 pairs (X)
H5,H8: 6.. / H5 = 6  => 10 pairs (_) / H8 = 6  =>  0 pairs (X)
F2,E3: 7.. / F2 = 7  => 12 pairs (_) / E3 = 7  => 11 pairs (_)
C4,C6: 8.. / C4 = 8  =>  7 pairs (_) / C6 = 8  =>  8 pairs (_)
D9,G9: 8.. / D9 = 8  =>  9 pairs (_) / G9 = 8  => 11 pairs (_)
I1,I2: 9.. / I1 = 9  => 10 pairs (_) / I2 = 9  => 10 pairs (_)
A5,B5: 9.. / A5 = 9  =>  8 pairs (_) / B5 = 9  => 16 pairs (_)
G8,G9: 9.. / G8 = 9  =>  8 pairs (_) / G9 = 9  =>  9 pairs (_)
* DURATION: 0:00:31.573687  START: 04:44:43.939515  END: 04:45:15.513202 2017-05-01
* CP COUNT: (29)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,C3,F5,G7,H1,I6)
* .7.3.....4...8.5...8...9..6.....6.9...3.4.1...2.79..5.8..9...45..5.1...3.....5.21
* PAIR C3: 1,2 BLK 1
A1: 1,2,5,6,9                            # reduction candidate for 1,2
A1: 1,2                                  # 18 pairs
C1: 1,2,6,9                              # reduction candidate for 1,2
C1: 1,2                                  # 20 pairs
C2: 1,2,6,9                              # reduction candidate for 1,2
C2: 1,2                                  # 15 pairs
A3: 1,2,3,5                              # reduction candidate for 1,2
A3: 1,2                                  # 18 pairs
* PAIR C3: 1,2 ROW 3
D3: 1,2,4,5                              # reduction candidate for 1,2
D3: 1,2                                  # 13 pairs
D3: 4,5                                  #  8 pairs
* PAIR C3: 1,2 COL C
C7: 1,2,6,7                              # reduction candidate for 1,2
C7: 1,2                                  # 15 pairs
C7: 6,7                                  # 12 pairs
* PAIR A4: 1,7 BLK 4
C4: 1,7,4,8                              # reduction candidate for 1,7
C4: 1,7                                  # 19 pairs
C4: 4,8                                  #  8 pairs
* PAIR A6: 1,6 BLK 4
C6: 1,6,4,8                              # reduction candidate for 1,6
C6: 1,6 => CTR
* 57.3.....4...8.5.9.8.5.94.6748156392953248167.2.7938548179326452.5417983.94865721
C6: 4,8                                  # 10 pairs
* PAIR A6: 1,6 COL A
A1: 1,6,2,5,9                            # reduction candidate for 1,6
A1: 1,6                                  # 22 pairs
A1: 2,5,9                                #  7 pairs
* PAIR F5: 2,8 BLK 5
D4: 2,8,1,5                              # reduction candidate for 2,8
D4: 2,8                                  # 17 pairs
D5: 2,8,5                                # reduction candidate for 2,8
D5: 2,8                                  # 14 pairs
* PAIR F5: 2,8 ROW 5
I5: 2,8,7                                # reduction candidate for 2,8
I5: 2,8                                  # 15 pairs
I5: 7                                    # 11 pairs
* PAIR F5: 2,8 COL F
F8: 2,8,4,7                              # reduction candidate for 2,8
F8: 2,8                                  # 12 pairs
F8: 4,7                                  #  9 pairs
* PAIR I6: 4,8 BLK 6
G4: 4,8,2,3,7                            # reduction candidate for 4,8
G4: 4,8                                  # 30 pairs
I4: 4,8,2,7                              # reduction candidate for 4,8
I4: 4,8                                  # 14 pairs
G6: 4,8,3,6                              # reduction candidate for 4,8
G6: 4,8 => CTR
* 57.3.42184...81579.8.579436748156392953248167.2.7938548179...45..5.1..83..48.5.21
G6: 3,6                                  #  8 pairs
* PAIR I6: 4,8 ROW 6
C6: 4,8,1,6                              # reduction candidate for 4,8
C6: 1,6 => CTR
* 57.3.....4...8.5.9.8.5.94.6748156392953248167.2.7938548179326452.5417983.94865721
C6: 4,8                                  # 10 pairs
* PAIR I6: 4,8 COL I
I1: 4,8,2,9                              # reduction candidate for 4,8
I1: 4,8                                  # 13 pairs
I1: 2,9                                  # 10 pairs
* PAIR G7: 6,7 BLK 9
G8: 6,7,8,9                              # reduction candidate for 6,7
G8: 6,7                                  # 16 pairs
H8: 6,7,8                                # reduction candidate for 6,7
H8: 6,7                                  # 11 pairs
G9: 6,7,8,9                              # reduction candidate for 6,7
G9: 6,7                                  # 19 pairs
* PAIR G7: 6,7 ROW 7
C7: 6,7,1,2                              # reduction candidate for 6,7
C7: 6,7                                  # 12 pairs
E7: 6,7,2,3                              # reduction candidate for 6,7
E7: 6,7                                  # 20 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0074-base-pr-000.dot
* REASONING
* DIS # C6: 1,6 => CTR => C6: 4,8
* DIS # G6: 4,8 => CTR => G6: 3,6
* DIS # C6: 1,6 => CTR => C6: 4,8
* CNT   3 HDP CHAINS /  33 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,C3,F5,G7,H1,I6)
* .7.3.....4...8.5...8...9..6.....6.9...3.4.1...2.79..5.8..9...45..5.1...3.....5.21
* PAIR C3: 1,2 BLK 1
A1: 1,2,5,6,9                            # reduction candidate for 1,2
A1: 1,2                                  # 18 pairs
C1: 1,2,6,9                              # reduction candidate for 1,2
C1: 1,2                                  # 20 pairs
C2: 1,2,6,9                              # reduction candidate for 1,2
C2: 1,2                                  # 15 pairs
A3: 1,2,3,5                              # reduction candidate for 1,2
A3: 1,2                                  # 18 pairs
* PAIR C3: 1,2 ROW 3
D3: 1,2,4,5                              # reduction candidate for 1,2
D3: 1,2                                  # 13 pairs
D3: 4,5                                  #  8 pairs
* PAIR C3: 1,2 COL C
C7: 1,2,6,7                              # reduction candidate for 1,2
C7: 1,2                                  # 15 pairs
C7: 6,7                                  # 12 pairs
* PAIR A4: 1,7 BLK 4
C4: 1,7,4,8                              # reduction candidate for 1,7
C4: 1,7                                  # 19 pairs
C4: 4,8                                  #  8 pairs
* PAIR A6: 1,6 BLK 4
C6: 1,6,4,8                              # reduction candidate for 1,6
C6: 1,6 => CTR
* 57.3.....4...8.5.9.8.5.94.6748156392953248167.2.7938548179326452.5417983.94865721
* PAIR A6: 1,6 COL A
A1: 1,6,2,5,9                            # reduction candidate for 1,6
A1: 1,6                                  # 26 pairs
A1: 2,5,9                                # 10 pairs
* PAIR F5: 2,8 BLK 5
D4: 2,8,1,5                              # reduction candidate for 2,8
D4: 2,8                                  # 17 pairs
D5: 2,8,5                                # reduction candidate for 2,8
D5: 2,8                                  # 17 pairs
* PAIR F5: 2,8 ROW 5
I5: 2,8,7                                # reduction candidate for 2,8
I5: 2,8                                  # 15 pairs
I5: 7                                    # 14 pairs
* PAIR F5: 2,8 COL F
F8: 2,8,4,7                              # reduction candidate for 2,8
F8: 2,8                                  # 14 pairs
F8: 4,7                                  # 13 pairs
* PAIR I6: 4,8 BLK 6
G4: 4,8,2,3,7                            # reduction candidate for 4,8
G4: 4,8                                  # 30 pairs
I4: 4,8,2,7                              # reduction candidate for 4,8
I4: 4,8                                  # 14 pairs
* PAIR I6: 4,8 COL I
I1: 4,8,2,9                              # reduction candidate for 4,8
I1: 4,8                                  # 16 pairs
I1: 2,9                                  # 12 pairs
* PAIR G7: 6,7 BLK 9
G8: 6,7,8,9                              # reduction candidate for 6,7
G8: 6,7                                  # 27 pairs
H8: 6,7,8                                # reduction candidate for 6,7
H8: 6,7                                  # 14 pairs
G9: 6,7,8,9                              # reduction candidate for 6,7
G9: 6,7 => SOLVED
* 976354218431682579582179436154236897793548162628791354817923645265417983349865721
* DURATION: 0:00:20.121010  START: 04:45:37.640233  END: 04:45:57.761243 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0074-base-pr-001.dot
* REASONING
* DIS # C6: 1,6 => CTR => C6: 4,8
* PRF C6: 4,8 # G9: 6,7 => SOL
* STA C6: 4,8 + G9: 6,7
* CNT   2 HDP CHAINS /  26 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=74

Solution

position: 976354218431682579582179436154236897793548162628791354817923645265417983349865721 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: 1,2 => UNS
* INC # C1: 1,2 => UNS
* INC # C2: 1,2 => UNS
* INC # A3: 1,2 => UNS
* INC # D3: 1,2 => UNS
* INC # D3: 4,5 => UNS
* INC # C7: 1,2 => UNS
* INC # C7: 6,7 => UNS
* INC # C4: 1,7 => UNS
* INC # C4: 4,8 => UNS
* DIS # C6: 1,6 => CTR => C6: 4,8
* INC # C6: 4,8 => UNS
* INC # A1: 1,6 => UNS
* INC # A1: 2,5,9 => UNS
* INC # D4: 2,8 => UNS
* INC # D5: 2,8 => UNS
* INC # I5: 2,8 => UNS
* INC # I5: 7 => UNS
* INC # F8: 2,8 => UNS
* INC # F8: 4,7 => UNS
* INC # G4: 4,8 => UNS
* INC # I4: 4,8 => UNS
* DIS # G6: 4,8 => CTR => G6: 3,6
* INC # G6: 3,6 => UNS
* INC # C6: 4,8 => UNS
* DIS # C6: 1,6 => CTR => C6: 4,8
* INC # I1: 4,8 => UNS
* INC # I1: 2,9 => UNS
* INC # G8: 6,7 => UNS
* INC # H8: 6,7 => UNS
* INC # G9: 6,7 => UNS
* INC # C7: 6,7 => UNS
* INC # E7: 6,7 => UNS
* CNT  33 HDP CHAINS /  33 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 1,2 => UNS
* INC # C1: 1,2 => UNS
* INC # C2: 1,2 => UNS
* INC # A3: 1,2 => UNS
* INC # D3: 1,2 => UNS
* INC # D3: 4,5 => UNS
* INC # C7: 1,2 => UNS
* INC # C7: 6,7 => UNS
* INC # C4: 1,7 => UNS
* INC # C4: 4,8 => UNS
* DIS # C6: 1,6 => CTR => C6: 4,8
* INC C6: 4,8 # A1: 1,6 => UNS
* INC C6: 4,8 # A1: 2,5,9 => UNS
* INC C6: 4,8 # D4: 2,8 => UNS
* INC C6: 4,8 # D5: 2,8 => UNS
* INC C6: 4,8 # I5: 2,8 => UNS
* INC C6: 4,8 # I5: 7 => UNS
* INC C6: 4,8 # F8: 2,8 => UNS
* INC C6: 4,8 # F8: 4,7 => UNS
* INC C6: 4,8 # G4: 4,8 => UNS
* INC C6: 4,8 # I4: 4,8 => UNS
* INC C6: 4,8 # I1: 4,8 => UNS
* INC C6: 4,8 # I1: 2,9 => UNS
* INC C6: 4,8 # G8: 6,7 => UNS
* INC C6: 4,8 # H8: 6,7 => UNS
* PRF C6: 4,8 # G9: 6,7 => SOL
* STA C6: 4,8 + G9: 6,7
* CNT  26 HDP CHAINS /  26 HYP OPENED