Analysis of zz-www.sudokuwiki.org-0090-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=90

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=90

position: .....1.8.1...5...364.3.......8....4...28.39...7....6.......8.578...6...2.9.2..... initial

Autosolve

position: .....1.8.18..5...364.38...9..8....4..628.397..7....6.8..6..8.578...6..92.9.2..8.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E6: 1,4 => CTR => E6: 2,9
* CNT   1 HDP CHAINS /  31 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 # E6: 1,4 => CTR => E6: 2,9
* PRF E6: 2,9 # G3: 1,2 => SOL
* STA E6: 2,9 + G3: 1,2
* CNT   2 HDP CHAINS /  40 HYP OPENED

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

Details

Positions

.....1.8.1...5...364.3.......8....4...28.39...7....6.......8.578...6...2.9.2..... initial
.....1.8.18..5...364.38...9..8....4..628.397..7....6.8..6..8.578...6..92.9.2..8.. autosolve
723691584189452763645387129938716245562843971471529638216938457857164392394275816 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
C2: 7,9
C3: 5,7
F3: 2,7
I1: 4,6
H2: 2,6
H3: 1,2
A5: 4,5
E5: 1,4
G4: 2,3
I4: 1,5
I5: 1,5
H6: 2,3
I9: 4,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G3,H3: 1.. / G3 = 1  =>  0 pairs (*) / H3 = 1  =>  0 pairs (X)
B4,C6: 1.. / B4 = 1  => 14 pairs (_) / C6 = 1  => 15 pairs (_)
I4,I5: 1.. / I4 = 1  =>  0 pairs (X) / I5 = 1  => 13 pairs (_)
E5,I5: 1.. / E5 = 1  =>  0 pairs (X) / I5 = 1  => 13 pairs (_)
H3,H9: 1.. / H3 = 1  => 13 pairs (_) / H9 = 1  =>  0 pairs (*)
A1,B1: 2.. / A1 = 2  => 17 pairs (_) / B1 = 2  => 14 pairs (_)
F2,F3: 2.. / F2 = 2  => 16 pairs (_) / F3 = 2  => 13 pairs (_)
E4,E6: 2.. / E4 = 2  => 18 pairs (_) / E6 = 2  => 13 pairs (_)
G4,H6: 2.. / G4 = 2  => 13 pairs (_) / H6 = 2  => 18 pairs (_)
A7,B7: 2.. / A7 = 2  => 14 pairs (_) / B7 = 2  => 17 pairs (_)
E4,G4: 2.. / E4 = 2  => 18 pairs (_) / G4 = 2  => 13 pairs (_)
E6,H6: 2.. / E6 = 2  => 13 pairs (_) / H6 = 2  => 18 pairs (_)
A1,A7: 2.. / A1 = 2  => 17 pairs (_) / A7 = 2  => 14 pairs (_)
B1,B7: 2.. / B1 = 2  => 14 pairs (_) / B7 = 2  => 17 pairs (_)
G4,H6: 3.. / G4 = 3  => 18 pairs (_) / H6 = 3  => 13 pairs (_)
E7,E9: 3.. / E7 = 3  => 16 pairs (_) / E9 = 3  => 13 pairs (_)
H6,H9: 3.. / H6 = 3  => 13 pairs (_) / H9 = 3  => 18 pairs (_)
A5,E5: 4.. / A5 = 4  =>  0 pairs (X) / E5 = 4  => 13 pairs (_)
I1,I9: 4.. / I1 = 4  => 14 pairs (_) / I9 = 4  => 11 pairs (_)
G1,G3: 5.. / G1 = 5  => 13 pairs (_) / G3 = 5  => 13 pairs (_)
I4,I5: 5.. / I4 = 5  => 13 pairs (_) / I5 = 5  =>  0 pairs (X)
C3,G3: 5.. / C3 = 5  => 13 pairs (_) / G3 = 5  => 13 pairs (_)
A5,I5: 5.. / A5 = 5  => 13 pairs (_) / I5 = 5  =>  0 pairs (X)
I1,H2: 6.. / I1 = 6  => 11 pairs (_) / H2 = 6  => 14 pairs (_)
D4,F4: 6.. / D4 = 6  => 12 pairs (_) / F4 = 6  => 13 pairs (_)
H9,I9: 6.. / H9 = 6  => 11 pairs (_) / I9 = 6  => 14 pairs (_)
D1,I1: 6.. / D1 = 6  => 14 pairs (_) / I1 = 6  => 11 pairs (_)
F2,F4: 6.. / F2 = 6  => 12 pairs (_) / F4 = 6  => 13 pairs (_)
H2,H9: 6.. / H2 = 6  => 14 pairs (_) / H9 = 6  => 11 pairs (_)
I1,I9: 6.. / I1 = 6  => 11 pairs (_) / I9 = 6  => 14 pairs (_)
A1,A9: 7.. / A1 = 7  => 14 pairs (_) / A9 = 7  => 14 pairs (_)
D7,E7: 9.. / D7 = 9  => 13 pairs (_) / E7 = 9  =>  0 pairs (X)
* DURATION: 0:00:47.286777  START: 05:04:41.846329  END: 05:05:29.133106 2017-05-01
* CP COUNT: (32)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C2,C3,E5,F3,G4,H2,H3,H6,I1,I4,I5,I9)
* .....1.8.18..5...364.38...9..8....4..628.397..7....6.8..6..8.578...6..92.9.2..8..
* PAIR C2: 7,9 BLK 1
A1: 7,9,2,3,5                            # reduction candidate for 7,9
A1: 7,9                                  # 14 pairs
C1: 7,9,3,5                              # reduction candidate for 7,9
C1: 7,9                                  # 18 pairs
* PAIR C2: 7,9 ROW 2
D2: 7,9,4,6                              # reduction candidate for 7,9
D2: 7,9                                  # 17 pairs
F2: 7,9,2,4,6                            # reduction candidate for 7,9
F2: 7,9                                  # 17 pairs
* PAIR C3: 5,7 BLK 1
A1: 5,7,2,3,9                            # reduction candidate for 5,7
A1: 5,7                                  # 14 pairs
C1: 5,7,3,9                              # reduction candidate for 5,7
C1: 5,7                                  # 18 pairs
* PAIR C3: 5,7 ROW 3
G3: 5,7,1,2                              # reduction candidate for 5,7
G3: 1,2                                  # 16 pairs
G3: 5,7                                  # 13 pairs
* PAIR C3: 5,7 COL C
C8: 5,7,1,3,4                            # reduction candidate for 5,7
C8: 5,7                                  # 16 pairs
C9: 5,7,1,3,4                            # reduction candidate for 5,7
C9: 5,7                                  # 17 pairs
* PAIR F3: 2,7 BLK 2
F2: 2,7,4,6,9                            # reduction candidate for 2,7
F2: 2,7                                  # 19 pairs
F2: 4,6,9                                # 13 pairs
* PAIR F3: 2,7 ROW 3
G3: 2,7,1,5                              # reduction candidate for 2,7
G3: 2,7                                  # 14 pairs
G3: 1,5                                  # 14 pairs
* PAIR I1: 4,6 ROW 1
D1: 4,6,7,9                              # reduction candidate for 4,6
D1: 4,6                                  # 16 pairs
D1: 7,9                                  # 12 pairs
* PAIR H2: 2,6 ROW 2
F2: 2,6,4,7,9                            # reduction candidate for 2,6
F2: 2,6                                  # 15 pairs
F2: 4,7,9                                # 13 pairs
* PAIR H3: 1,2 BLK 3
G3: 1,2,5,7                              # reduction candidate for 1,2
G3: 1,2                                  # 16 pairs
G3: 5,7                                  # 13 pairs
* PAIR A5: 4,5 BLK 4
A6: 4,5,3,9                              # reduction candidate for 4,5
A6: 4,5                                  # 18 pairs
C6: 4,5,1,3,9                            # reduction candidate for 4,5
C6: 4,5                                  # 18 pairs
* PAIR A5: 4,5 COL A
A9: 4,5,3,7                              # reduction candidate for 4,5
A9: 4,5                                  # 20 pairs
A9: 3,7                                  # 14 pairs
* PAIR E5: 1,4 BLK 5
D6: 1,4,5,9                              # reduction candidate for 1,4
D6: 1,4                                  # 16 pairs
E6: 1,4,2,9                              # reduction candidate for 1,4
E6: 1,4 => CTR
* 72369158418945..6364538..199.872634..628.397.37.5.962821693845783716..92.9.27.836
E6: 2,9                                  # 14 pairs
* PAIR E5: 1,4 COL E
E7: 1,4,3,9                              # reduction candidate for 1,4
E7: 1,4                                  # 16 pairs
E9: 1,4,3,7                              # reduction candidate for 1,4
E9: 1,4                                  # 19 pairs
* PAIR I4: 1,5 ROW 4
B4: 1,5,3                                # reduction candidate for 1,5
B4: 1,5                                  # 15 pairs
D4: 1,5,6,7,9                            # reduction candidate for 1,5
D4: 1,5                                  # 21 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0090-base-pr-000.dot
* REASONING
* DIS # E6: 1,4 => CTR => E6: 2,9
* CNT   1 HDP CHAINS /  31 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C2,C3,E5,F3,G4,H2,H3,H6,I1,I4,I5,I9)
* .....1.8.18..5...364.38...9..8....4..628.397..7....6.8..6..8.578...6..92.9.2..8..
* PAIR C2: 7,9 BLK 1
A1: 7,9,2,3,5                            # reduction candidate for 7,9
A1: 7,9                                  # 14 pairs
C1: 7,9,3,5                              # reduction candidate for 7,9
C1: 7,9                                  # 18 pairs
* PAIR C2: 7,9 ROW 2
D2: 7,9,4,6                              # reduction candidate for 7,9
D2: 7,9                                  # 17 pairs
F2: 7,9,2,4,6                            # reduction candidate for 7,9
F2: 7,9                                  # 17 pairs
* PAIR C3: 5,7 BLK 1
A1: 5,7,2,3,9                            # reduction candidate for 5,7
A1: 5,7                                  # 14 pairs
C1: 5,7,3,9                              # reduction candidate for 5,7
C1: 5,7                                  # 18 pairs
* PAIR C3: 5,7 ROW 3
G3: 5,7,1,2                              # reduction candidate for 5,7
G3: 1,2                                  # 16 pairs
G3: 5,7                                  # 13 pairs
* PAIR C3: 5,7 COL C
C8: 5,7,1,3,4                            # reduction candidate for 5,7
C8: 5,7                                  # 16 pairs
C9: 5,7,1,3,4                            # reduction candidate for 5,7
C9: 5,7                                  # 17 pairs
* PAIR F3: 2,7 BLK 2
F2: 2,7,4,6,9                            # reduction candidate for 2,7
F2: 2,7                                  # 19 pairs
F2: 4,6,9                                # 13 pairs
* PAIR F3: 2,7 ROW 3
G3: 2,7,1,5                              # reduction candidate for 2,7
G3: 2,7                                  # 14 pairs
G3: 1,5                                  # 14 pairs
* PAIR I1: 4,6 ROW 1
D1: 4,6,7,9                              # reduction candidate for 4,6
D1: 4,6                                  # 16 pairs
D1: 7,9                                  # 12 pairs
* PAIR H2: 2,6 ROW 2
F2: 2,6,4,7,9                            # reduction candidate for 2,6
F2: 2,6                                  # 15 pairs
F2: 4,7,9                                # 13 pairs
* PAIR H3: 1,2 BLK 3
G3: 1,2,5,7                              # reduction candidate for 1,2
G3: 1,2                                  # 16 pairs
G3: 5,7                                  # 13 pairs
* PAIR A5: 4,5 BLK 4
A6: 4,5,3,9                              # reduction candidate for 4,5
A6: 4,5                                  # 18 pairs
C6: 4,5,1,3,9                            # reduction candidate for 4,5
C6: 4,5                                  # 18 pairs
* PAIR A5: 4,5 COL A
A9: 4,5,3,7                              # reduction candidate for 4,5
A9: 4,5                                  # 20 pairs
A9: 3,7                                  # 14 pairs
* PAIR E5: 1,4 BLK 5
D6: 1,4,5,9                              # reduction candidate for 1,4
D6: 1,4                                  # 16 pairs
E6: 1,4,2,9                              # reduction candidate for 1,4
E6: 1,4 => CTR
* 72369158418945..6364538..199.872634..628.397.37.5.962821693845783716..92.9.27.836
* RESTART
* PAIR E5: 1,4 BLK 5
D6: 1,4,5,9                              # reduction candidate for 1,4
D6: 5,9                                  # 17 pairs
D6: 1,4                                  # 16 pairs
* PAIR E5: 1,4 COL E
E7: 1,4,3,9                              # reduction candidate for 1,4
E7: 1,4                                  # 16 pairs
E9: 1,4,3,7                              # reduction candidate for 1,4
E9: 1,4                                  # 19 pairs
* PAIR I4: 1,5 ROW 4
B4: 1,5,3                                # reduction candidate for 1,5
B4: 1,5                                  # 19 pairs
D4: 1,5,6,7,9                            # reduction candidate for 1,5
D4: 1,5                                  # 21 pairs

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A5,C2,C3,E5,E6,F3,G4,H2,H3,H6,I1,I4,I5,I9)
* .....1.8.18..5...364.38...9..8....4..628.397..7....6.8..6..8.578...6..92.9.2..8..
* PAIR C2: 7,9 BLK 1
A1: 7,9,2,3,5                            # reduction candidate for 7,9
A1: 7,9                                  # 15 pairs
C1: 7,9,3,5                              # reduction candidate for 7,9
C1: 7,9                                  # 19 pairs
* PAIR C2: 7,9 ROW 2
D2: 7,9,4,6                              # reduction candidate for 7,9
D2: 7,9                                  # 13 pairs
F2: 7,9,2,4,6                            # reduction candidate for 7,9
F2: 7,9                                  # 18 pairs
* PAIR C3: 5,7 BLK 1
A1: 5,7,2,3,9                            # reduction candidate for 5,7
A1: 5,7                                  # 15 pairs
C1: 5,7,3,9                              # reduction candidate for 5,7
C1: 5,7                                  # 22 pairs
* PAIR C3: 5,7 ROW 3
G3: 5,7,1,2                              # reduction candidate for 5,7
G3: 1,2 => SOLVED
* 723691584189452763645387129938716245562843971471529638216938457857164392394275816
* DURATION: 0:00:33.127631  START: 05:05:54.021853  END: 05:06:27.149484 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0090-base-pr-001.dot
* REASONING
* DIS # E6: 1,4 => CTR => E6: 2,9
* PRF E6: 2,9 # G3: 1,2 => SOL
* STA E6: 2,9 + G3: 1,2
* CNT   2 HDP CHAINS /  40 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=90

Solution

position: 723691584189452763645387129938716245562843971471529638216938457857164392394275816 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
* INC # C1: 7,9 => UNS
* INC # D2: 7,9 => UNS
* INC # F2: 7,9 => UNS
* INC # A1: 5,7 => UNS
* INC # C1: 5,7 => UNS
* INC # G3: 5,7 => UNS
* INC # G3: 1,2 => UNS
* INC # C8: 5,7 => UNS
* INC # C9: 5,7 => UNS
* INC # F2: 2,7 => UNS
* INC # F2: 4,6,9 => UNS
* INC # G3: 2,7 => UNS
* INC # G3: 1,5 => UNS
* INC # D1: 4,6 => UNS
* INC # D1: 7,9 => UNS
* INC # F2: 2,6 => UNS
* INC # F2: 4,7,9 => UNS
* INC # G3: 1,2 => UNS
* INC # G3: 5,7 => UNS
* INC # A6: 4,5 => UNS
* INC # C6: 4,5 => UNS
* INC # A9: 4,5 => UNS
* INC # A9: 3,7 => UNS
* INC # D6: 1,4 => UNS
* DIS # E6: 1,4 => CTR => E6: 2,9
* INC # E6: 2,9 => UNS
* INC # E7: 1,4 => UNS
* INC # E9: 1,4 => UNS
* INC # B4: 1,5 => UNS
* INC # D4: 1,5 => UNS
* CNT  31 HDP CHAINS /  31 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 7,9 => UNS
* INC # C1: 7,9 => UNS
* INC # D2: 7,9 => UNS
* INC # F2: 7,9 => UNS
* INC # A1: 5,7 => UNS
* INC # C1: 5,7 => UNS
* INC # G3: 5,7 => UNS
* INC # G3: 1,2 => UNS
* INC # C8: 5,7 => UNS
* INC # C9: 5,7 => UNS
* INC # F2: 2,7 => UNS
* INC # F2: 4,6,9 => UNS
* INC # G3: 2,7 => UNS
* INC # G3: 1,5 => UNS
* INC # D1: 4,6 => UNS
* INC # D1: 7,9 => UNS
* INC # F2: 2,6 => UNS
* INC # F2: 4,7,9 => UNS
* INC # G3: 1,2 => UNS
* INC # G3: 5,7 => UNS
* INC # A6: 4,5 => UNS
* INC # C6: 4,5 => UNS
* INC # A9: 4,5 => UNS
* INC # A9: 3,7 => UNS
* INC # D6: 1,4 => UNS
* DIS # E6: 1,4 => CTR => E6: 2,9
* INC E6: 2,9 # D6: 1,4 => UNS
* INC E6: 2,9 # D6: 5,9 => UNS
* INC E6: 2,9 # E7: 1,4 => UNS
* INC E6: 2,9 # E9: 1,4 => UNS
* INC E6: 2,9 # B4: 1,5 => UNS
* INC E6: 2,9 # D4: 1,5 => UNS
* INC E6: 2,9 # A1: 7,9 => UNS
* INC E6: 2,9 # C1: 7,9 => UNS
* INC E6: 2,9 # D2: 7,9 => UNS
* INC E6: 2,9 # F2: 7,9 => UNS
* INC E6: 2,9 # A1: 5,7 => UNS
* INC E6: 2,9 # C1: 5,7 => UNS
* INC E6: 2,9 # G3: 5,7 => UNS
* PRF E6: 2,9 # G3: 1,2 => SOL
* STA E6: 2,9 + G3: 1,2
* CNT  40 HDP CHAINS /  40 HYP OPENED