Analysis of zz-www.sudokuwiki.org-0147-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=147

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=147

position: ...3..4..1...5.7.8.8.......5....8...4.6.2.5.9...4....2.......6.2.9.1...7..5..23.. initial

Autosolve

position: .5.38.4.61...5.7.8.8....9..5....8...4.6.2.589...4.5..2......26.2.9.1.8.7..5..239. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # D3: 1,7 => SOL
* DIS # H4: 7 => CTR => H4: 3,4
* DIS # B6: 3,7 => CTR => B6: 1,9
* PRF # I7: 1 => SOL
* CNT   4 HDP CHAINS /  39 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 # D3: 1,7 => SOL
* STA D3: 1,7
* CNT   1 HDP CHAINS /  21 HYP OPENED

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

Details

Positions

...3..4..1...5.7.8.8.......5....8...4.6.2.5.9...4....2.......6.2.9.1...7..5..23.. initial
.5.38.4.61...5.7.8.8....9..5....8...4.6.2.589...4.5..2......26.2.9.1.8.7..5..239. autosolve
952387416164259738783146925527968143436721589891435672378594261249613857615872394 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
A1: 7,9
C1: 2,7
H1: 1,2
H2: 2,3
I3: 3,5
D5: 1,7
G4: 1,6
I4: 3,4
G6: 1,6
H6: 3,7
D8: 5,6
H8: 4,5
I9: 1,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H3: 1.. / H1 = 1  => 13 pairs (_) / H3 = 1  => 19 pairs (_)
G4,G6: 1.. / G4 = 1  => 14 pairs (_) / G6 = 1  => 15 pairs (_)
I7,I9: 1.. / I7 = 1  =>  0 pairs (*) / I9 = 1  =>  0 pairs (X)
F1,H1: 1.. / F1 = 1  => 19 pairs (_) / H1 = 1  => 13 pairs (_)
B9,I9: 1.. / B9 = 1  =>  0 pairs (*) / I9 = 1  =>  0 pairs (X)
D2,D3: 2.. / D2 = 2  =>  0 pairs (*) / D3 = 2  =>  0 pairs (X)
B4,C4: 2.. / B4 = 2  => 13 pairs (_) / C4 = 2  =>  0 pairs (X)
C1,H1: 2.. / C1 = 2  => 13 pairs (_) / H1 = 2  => 19 pairs (_)
B2,B4: 2.. / B2 = 2  =>  0 pairs (X) / B4 = 2  => 13 pairs (_)
B5,F5: 3.. / B5 = 3  => 18 pairs (_) / F5 = 3  => 18 pairs (_)
B8,F8: 3.. / B8 = 3  => 18 pairs (_) / F8 = 3  => 18 pairs (_)
I3,I4: 3.. / I3 = 3  => 14 pairs (_) / I4 = 3  => 17 pairs (_)
H4,I4: 4.. / H4 = 4  => 17 pairs (_) / I4 = 4  => 14 pairs (_)
H4,H8: 4.. / H4 = 4  => 17 pairs (_) / H8 = 4  => 14 pairs (_)
H3,I3: 5.. / H3 = 5  => 14 pairs (_) / I3 = 5  => 17 pairs (_)
D7,D8: 5.. / D7 = 5  => 17 pairs (_) / D8 = 5  => 14 pairs (_)
I7,H8: 5.. / I7 = 5  => 14 pairs (_) / H8 = 5  => 17 pairs (_)
D7,I7: 5.. / D7 = 5  => 17 pairs (_) / I7 = 5  => 14 pairs (_)
D8,H8: 5.. / D8 = 5  => 14 pairs (_) / H8 = 5  => 17 pairs (_)
H3,H8: 5.. / H3 = 5  => 14 pairs (_) / H8 = 5  => 17 pairs (_)
I3,I7: 5.. / I3 = 5  => 17 pairs (_) / I7 = 5  => 14 pairs (_)
B2,A3: 6.. / B2 = 6  => 18 pairs (_) / A3 = 6  => 15 pairs (_)
G4,G6: 6.. / G4 = 6  => 15 pairs (_) / G6 = 6  => 14 pairs (_)
E6,G6: 6.. / E6 = 6  => 15 pairs (_) / G6 = 6  => 14 pairs (_)
A3,A9: 6.. / A3 = 6  => 15 pairs (_) / A9 = 6  => 18 pairs (_)
H4,H6: 7.. / H4 = 7  =>  0 pairs (X) / H6 = 7  => 13 pairs (_)
A6,C6: 8.. / A6 = 8  => 16 pairs (_) / C6 = 8  => 13 pairs (_)
D7,D9: 8.. / D7 = 8  => 16 pairs (_) / D9 = 8  => 14 pairs (_)
A9,D9: 8.. / A9 = 8  => 16 pairs (_) / D9 = 8  => 14 pairs (_)
C6,C7: 8.. / C6 = 8  => 13 pairs (_) / C7 = 8  => 16 pairs (_)
A1,B2: 9.. / A1 = 9  => 13 pairs (_) / B2 = 9  =>  0 pairs (X)
A1,F1: 9.. / A1 = 9  => 13 pairs (_) / F1 = 9  =>  0 pairs (X)
A1,A6: 9.. / A1 = 9  => 13 pairs (_) / A6 = 9  =>  0 pairs (X)
* DURATION: 0:00:46.566191  START: 06:10:29.570190  END: 06:11:16.136381 2017-05-01
* CP COUNT: (33)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C1,D5,D8,G4,G6,H1,H2,H6,H8,I3,I4,I9)
* .5.38.4.61...5.7.8.8....9..5....8...4.6.2.589...4.5..2......26.2.9.1.8.7..5..239.
* PAIR A1: 7,9 ROW 1
F1: 7,9,1                                # reduction candidate for 7,9
F1: 1                                    # 19 pairs
F1: 7,9                                  # 13 pairs
* PAIR A1: 7,9 COL A
A6: 7,9,3,8                              # reduction candidate for 7,9
A6: 7,9                                  # 17 pairs
A6: 3,8                                  # 14 pairs
* PAIR C1: 2,7 BLK 1
C3: 2,7,3,4                              # reduction candidate for 2,7
C3: 2,7                                  # 18 pairs
C3: 3,4                                  # 14 pairs
* PAIR C1: 2,7 COL C
C4: 2,7,1,3                              # reduction candidate for 2,7
C4: 2,7                                  # 19 pairs
C4: 1,3                                  # 14 pairs
* PAIR H1: 1,2 BLK 3
H3: 1,2,3,5                              # reduction candidate for 1,2
H3: 1,2                                  # 18 pairs
H3: 3,5                                  # 17 pairs
* PAIR H2: 2,3 BLK 3
H3: 2,3,1,5                              # reduction candidate for 2,3
H3: 2,3                                  # 20 pairs
H3: 1,5                                  # 14 pairs
* PAIR H2: 2,3 ROW 2
B2: 2,3,4,6,9                            # reduction candidate for 2,3
B2: 2,3                                  # 20 pairs
C2: 2,3,4                                # reduction candidate for 2,3
C2: 2,3                                  # 16 pairs
* PAIR I3: 3,5 BLK 3
H3: 3,5,1,2                              # reduction candidate for 3,5
H3: 1,2                                  # 18 pairs
H3: 3,5                                  # 17 pairs
* PAIR D5: 1,7 BLK 5
D4: 1,7,6,9                              # reduction candidate for 1,7
D4: 1,7                                  # 24 pairs
F5: 1,7,3                                # reduction candidate for 1,7
F5: 1,7                                  # 18 pairs
* PAIR D5: 1,7 ROW 5
B5: 1,7,3                                # reduction candidate for 1,7
B5: 3                                    # 18 pairs
B5: 1,7                                  # 18 pairs
* PAIR D5: 1,7 COL D
D3: 1,7,2,6                              # reduction candidate for 1,7
D3: 1,7 => SOLVED
* 952387416164259738783146925527968143436721589891435672378594261249613857615872394
D3: 2,6                                  # 15 pairs
* PAIR G4: 1,6 ROW 4
D4: 1,6,7,9                              # reduction candidate for 1,6
D4: 7,9                                  # 18 pairs
D4: 1,6                                  # 16 pairs
* PAIR I4: 3,4 BLK 6
H4: 3,4,7                                # reduction candidate for 3,4
H4: 7 => CTR
* 75238941619365.72868.2.195352..38.74436127589...4.5.323.....265269513847..5..2391
H4: 3,4                                  # 13 pairs
* PAIR H6: 3,7 BLK 6
H4: 3,7,4                                # reduction candidate for 3,7
H4: 4                                    # 17 pairs
H4: 3,7                                  # 14 pairs
* PAIR H6: 3,7 ROW 6
A6: 3,7,8,9                              # reduction candidate for 3,7
A6: 3,7                                  # 16 pairs
B6: 3,7,1,9                              # reduction candidate for 3,7
B6: 3,7 => CTR
* .5.38.4.61...567.868....9..5...38..4436.2.589.7.4.5.323.....26.2.9.13847..5..2391
B6: 1,9                                  # 14 pairs
C6: 3,7,1,8                              # reduction candidate for 3,7
C6: 3,7                                  # 22 pairs
E6: 3,7,6,9                              # reduction candidate for 3,7
E6: 3,7                                  # 19 pairs
* PAIR H8: 4,5 BLK 9
I7: 4,5,1                                # reduction candidate for 4,5
I7: 1 => SOLVED
* 952387416164259738783146925527968143436721589891435672378594261249613857615872394
I7: 4,5                                  # 13 pairs
* PAIR I9: 1,4 BLK 9
I7: 1,4,5                                # reduction candidate for 1,4
I7: 1,4                                  # 17 pairs
I7: 5                                    # 14 pairs
* PAIR I9: 1,4 ROW 9
B9: 1,4,6,7                              # reduction candidate for 1,4
B9: 6,7                                  # 16 pairs
B9: 1,4                                  # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0147-base-pr-000.dot
* REASONING
* PRF # D3: 1,7 => SOL
* DIS # H4: 7 => CTR => H4: 3,4
* DIS # B6: 3,7 => CTR => B6: 1,9
* PRF # I7: 1 => SOL
* CNT   4 HDP CHAINS /  39 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C1,D5,D8,G4,G6,H1,H2,H6,H8,I3,I4,I9)
* .5.38.4.61...5.7.8.8....9..5....8...4.6.2.589...4.5..2......26.2.9.1.8.7..5..239.
* PAIR A1: 7,9 ROW 1
F1: 7,9,1                                # reduction candidate for 7,9
F1: 1                                    # 19 pairs
F1: 7,9                                  # 13 pairs
* PAIR A1: 7,9 COL A
A6: 7,9,3,8                              # reduction candidate for 7,9
A6: 7,9                                  # 17 pairs
A6: 3,8                                  # 14 pairs
* PAIR C1: 2,7 BLK 1
C3: 2,7,3,4                              # reduction candidate for 2,7
C3: 2,7                                  # 18 pairs
C3: 3,4                                  # 14 pairs
* PAIR C1: 2,7 COL C
C4: 2,7,1,3                              # reduction candidate for 2,7
C4: 2,7                                  # 19 pairs
C4: 1,3                                  # 14 pairs
* PAIR H1: 1,2 BLK 3
H3: 1,2,3,5                              # reduction candidate for 1,2
H3: 1,2                                  # 18 pairs
H3: 3,5                                  # 17 pairs
* PAIR H2: 2,3 BLK 3
H3: 2,3,1,5                              # reduction candidate for 2,3
H3: 2,3                                  # 20 pairs
H3: 1,5                                  # 14 pairs
* PAIR H2: 2,3 ROW 2
B2: 2,3,4,6,9                            # reduction candidate for 2,3
B2: 2,3                                  # 20 pairs
C2: 2,3,4                                # reduction candidate for 2,3
C2: 2,3                                  # 16 pairs
* PAIR I3: 3,5 BLK 3
H3: 3,5,1,2                              # reduction candidate for 3,5
H3: 1,2                                  # 18 pairs
H3: 3,5                                  # 17 pairs
* PAIR D5: 1,7 BLK 5
D4: 1,7,6,9                              # reduction candidate for 1,7
D4: 1,7                                  # 24 pairs
F5: 1,7,3                                # reduction candidate for 1,7
F5: 1,7                                  # 18 pairs
* PAIR D5: 1,7 ROW 5
B5: 1,7,3                                # reduction candidate for 1,7
B5: 3                                    # 18 pairs
B5: 1,7                                  # 18 pairs
* PAIR D5: 1,7 COL D
D3: 1,7,2,6                              # reduction candidate for 1,7
D3: 1,7 => SOLVED
* 952387416164259738783146925527968143436721589891435672378594261249613857615872394
* DURATION: 0:00:16.378859  START: 06:11:45.801690  END: 06:12:02.180549 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0147-base-pr-001.dot
* REASONING
* PRF # D3: 1,7 => SOL
* STA D3: 1,7
* CNT   1 HDP CHAINS /  21 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=147

Solution

position: 952387416164259738783146925527968143436721589891435672378594261249613857615872394 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 # F1: 7,9 => UNS
* INC # F1: 1 => UNS
* INC # A6: 7,9 => UNS
* INC # A6: 3,8 => UNS
* INC # C3: 2,7 => UNS
* INC # C3: 3,4 => UNS
* INC # C4: 2,7 => UNS
* INC # C4: 1,3 => UNS
* INC # H3: 1,2 => UNS
* INC # H3: 3,5 => UNS
* INC # H3: 2,3 => UNS
* INC # H3: 1,5 => UNS
* INC # B2: 2,3 => UNS
* INC # C2: 2,3 => UNS
* INC # H3: 3,5 => UNS
* INC # H3: 1,2 => UNS
* INC # D4: 1,7 => UNS
* INC # F5: 1,7 => UNS
* INC # B5: 1,7 => UNS
* INC # B5: 3 => UNS
* PRF # D3: 1,7 => SOL
* INC # D3: 2,6 => UNS
* INC # D4: 1,6 => UNS
* INC # D4: 7,9 => UNS
* INC # H4: 3,4 => UNS
* DIS # H4: 7 => CTR => H4: 3,4
* INC # H4: 3,7 => UNS
* INC # H4: 4 => UNS
* INC # A6: 3,7 => UNS
* DIS # B6: 3,7 => CTR => B6: 1,9
* INC # B6: 1,9 => UNS
* INC # C6: 3,7 => UNS
* INC # E6: 3,7 => UNS
* INC # I7: 4,5 => UNS
* PRF # I7: 1 => SOL
* INC # I7: 1,4 => UNS
* INC # I7: 5 => UNS
* INC # B9: 1,4 => UNS
* INC # B9: 6,7 => UNS
* CNT  39 HDP CHAINS /  39 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F1: 7,9 => UNS
* INC # F1: 1 => UNS
* INC # A6: 7,9 => UNS
* INC # A6: 3,8 => UNS
* INC # C3: 2,7 => UNS
* INC # C3: 3,4 => UNS
* INC # C4: 2,7 => UNS
* INC # C4: 1,3 => UNS
* INC # H3: 1,2 => UNS
* INC # H3: 3,5 => UNS
* INC # H3: 2,3 => UNS
* INC # H3: 1,5 => UNS
* INC # B2: 2,3 => UNS
* INC # C2: 2,3 => UNS
* INC # H3: 3,5 => UNS
* INC # H3: 1,2 => UNS
* INC # D4: 1,7 => UNS
* INC # F5: 1,7 => UNS
* INC # B5: 1,7 => UNS
* INC # B5: 3 => UNS
* PRF # D3: 1,7 => SOL
* STA D3: 1,7
* CNT  21 HDP CHAINS /  21 HYP OPENED