Analysis of zz-www.sudokuwiki.org-0017-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=17

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=17

position: ..6...7...1.8...6...2.46.9..8......6...954...5......4..4.18.2.......9.1...7...5.. initial

Autosolve

position: 4.6...7...1.8..46.8.2.46.9..84....56.6.9548..5....8.4.64.18.2....8..961.1.7...5.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B8: 2,3 => CTR => B8: 5
* DIS # D9: 2,3 => CTR => D9: 4,6
* DIS # E9: 2,3 => CTR => E9: 6
* DIS # F1: 2,3 => CTR => F1: 1,5
* DIS # I8: 3,7 => CTR => I8: 4
* DIS # F7: 3,7 => CTR => F7: 5
* CNT   6 HDP CHAINS /  38 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 # B8: 2,3 => CTR => B8: 5
* DIS B8: 5 # D9: 2,3 => CTR => D9: 4,6
* DIS B8: 5 + D9: 4,6 # E9: 2,3 => CTR => E9: 6
* PRF B8: 5 + D9: 4,6 + E9: 6 # B9: 9 => SOL
* STA B8: 5 + D9: 4,6 + E9: 6 + B9: 9
* CNT   4 HDP CHAINS /  22 HYP OPENED

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

Details

Positions

..6...7...1.8...6...2.46.9..8......6...954...5......4..4.18.2.......9.1...7...5.. initial
4.6...7...1.8..46.8.2.46.9..84....56.6.9548..5....8.4.64.18.2....8..961.1.7...5.. autosolve
436591782915827463872346195784213956361954827529678341643185279258739614197462538 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
G3: 1,3
C5: 1,3
A8: 2,3
F9: 2,3
H7: 3,7
H9: 3,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E1,F1: 1.. / E1 = 1  =>  0 pairs (X) / F1 = 1  =>  6 pairs (_)
G3,I3: 1.. / G3 = 1  => 10 pairs (_) / I3 = 1  => 11 pairs (_)
C5,C6: 1.. / C5 = 1  =>  6 pairs (_) / C6 = 1  => 12 pairs (_)
C5,I5: 1.. / C5 = 1  =>  6 pairs (_) / I5 = 1  => 12 pairs (_)
F1,F4: 1.. / F1 = 1  =>  6 pairs (_) / F4 = 1  =>  0 pairs (X)
H1,H5: 2.. / H1 = 2  =>  8 pairs (_) / H5 = 2  => 10 pairs (_)
D8,D9: 4.. / D8 = 4  =>  0 pairs (X) / D9 = 4  =>  7 pairs (_)
I8,I9: 4.. / I8 = 4  =>  7 pairs (_) / I9 = 4  =>  0 pairs (X)
D8,I8: 4.. / D8 = 4  =>  0 pairs (X) / I8 = 4  =>  7 pairs (_)
D9,I9: 4.. / D9 = 4  =>  7 pairs (_) / I9 = 4  =>  0 pairs (X)
C7,B8: 5.. / C7 = 5  =>  0 pairs (X) / B8 = 5  => 11 pairs (_)
F7,D8: 5.. / F7 = 5  => 11 pairs (_) / D8 = 5  =>  0 pairs (X)
C7,F7: 5.. / C7 = 5  =>  0 pairs (X) / F7 = 5  => 11 pairs (_)
B8,D8: 5.. / B8 = 5  => 11 pairs (_) / D8 = 5  =>  0 pairs (X)
C2,C7: 5.. / C2 = 5  => 11 pairs (_) / C7 = 5  =>  0 pairs (X)
D6,E6: 6.. / D6 = 6  =>  6 pairs (_) / E6 = 6  =>  0 pairs (X)
D9,E9: 6.. / D9 = 6  =>  0 pairs (X) / E9 = 6  =>  6 pairs (_)
D6,D9: 6.. / D6 = 6  =>  6 pairs (_) / D9 = 6  =>  0 pairs (X)
E6,E9: 6.. / E6 = 6  =>  0 pairs (X) / E9 = 6  =>  6 pairs (_)
A2,B3: 7.. / A2 = 7  => 18 pairs (_) / B3 = 7  =>  8 pairs (_)
B3,D3: 7.. / B3 = 7  =>  8 pairs (_) / D3 = 7  => 18 pairs (_)
B3,B6: 7.. / B3 = 7  =>  8 pairs (_) / B6 = 7  => 18 pairs (_)
H5,H7: 7.. / H5 = 7  => 14 pairs (_) / H7 = 7  =>  9 pairs (_)
H1,I1: 8.. / H1 = 8  =>  9 pairs (_) / I1 = 8  =>  6 pairs (_)
H9,I9: 8.. / H9 = 8  =>  6 pairs (_) / I9 = 8  =>  9 pairs (_)
H1,H9: 8.. / H1 = 8  =>  9 pairs (_) / H9 = 8  =>  6 pairs (_)
I1,I9: 8.. / I1 = 8  =>  6 pairs (_) / I9 = 8  =>  9 pairs (_)
E1,E2: 9.. / E1 = 9  =>  7 pairs (_) / E2 = 9  => 17 pairs (_)
G4,G6: 9.. / G4 = 9  => 10 pairs (_) / G6 = 9  => 15 pairs (_)
C7,B9: 9.. / C7 = 9  => 15 pairs (_) / B9 = 9  =>  9 pairs (_)
I7,I9: 9.. / I7 = 9  =>  9 pairs (_) / I9 = 9  => 15 pairs (_)
B1,E1: 9.. / B1 = 9  => 17 pairs (_) / E1 = 9  =>  7 pairs (_)
A4,G4: 9.. / A4 = 9  => 15 pairs (_) / G4 = 9  => 10 pairs (_)
C7,I7: 9.. / C7 = 9  => 15 pairs (_) / I7 = 9  =>  9 pairs (_)
B9,I9: 9.. / B9 = 9  =>  9 pairs (_) / I9 = 9  => 15 pairs (_)
A2,A4: 9.. / A2 = 9  => 10 pairs (_) / A4 = 9  => 15 pairs (_)
* DURATION: 0:00:50.906673  START: 03:42:21.400827  END: 03:43:12.307500 2017-05-01
* CP COUNT: (36)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C5,F9,G3,H7,H9)
* 4.6...7...1.8..46.8.2.46.9..84....56.6.9548..5....8.4.64.18.2....8..961.1.7...5..
* PAIR G3: 1,3 BLK 3
I3: 1,3,5                                # reduction candidate for 1,3
I3: 5                                    # 12 pairs
I3: 1,3                                  # 11 pairs
* PAIR G3: 1,3 COL G
G4: 1,3,9                                # reduction candidate for 1,3
G4: 1,3                                  # 15 pairs
G6: 1,3,9                                # reduction candidate for 1,3
G6: 1,3                                  # 10 pairs
* PAIR C5: 1,3 BLK 4
C6: 1,3,9                                # reduction candidate for 1,3
C6: 9                                    # 12 pairs
C6: 1,3                                  # 10 pairs
* PAIR C5: 1,3 ROW 5
I5: 1,3,2,7                              # reduction candidate for 1,3
I5: 1,3                                  # 10 pairs
I5: 2,7                                  #  7 pairs
* PAIR A8: 2,3 BLK 7
B8: 2,3,5                                # reduction candidate for 2,3
B8: 2,3 => CTR
* 4.6.917..7198.546.8.2746.9.984..7.562619548375736.8942645183279328579614197462583
B8: 5                                    # 11 pairs
B9: 2,3,9                                # reduction candidate for 2,3
B9: 2,3                                  # 15 pairs
* PAIR A8: 2,3 ROW 8
D8: 2,3,4,5,7                            # reduction candidate for 2,3
D8: 2,3                                  # 11 pairs
E8: 2,3,7                                # reduction candidate for 2,3
E8: 2,3                                  # 13 pairs
* PAIR A8: 2,3 COL A
A4: 2,3,7,9                              # reduction candidate for 2,3
A4: 2,3                                  # 14 pairs
A5: 2,3,7                                # reduction candidate for 2,3
A5: 2,3                                  #  9 pairs
* PAIR F9: 2,3 BLK 8
D8: 2,3,4,5,7                            # reduction candidate for 2,3
D8: 2,3                                  # 11 pairs
E8: 2,3,7                                # reduction candidate for 2,3
E8: 2,3                                  # 13 pairs
D9: 2,3,4,6                              # reduction candidate for 2,3
D9: 2,3 => CTR
* 436591728.158..46.8.2.46.9..84....56.6.9548..5..6.8.4.64.1852.9.58479613197.6.584
D9: 4,6                                  #  7 pairs
E9: 2,3,6                                # reduction candidate for 2,3
E9: 2,3 => CTR
* 436591728.158..46.8.2.46.9..84.1..56.6.9548..5...68.4.64.185279.584796131976..584
E9: 6                                    #  6 pairs
* PAIR F9: 2,3 ROW 9
B9: 2,3,9                                # reduction candidate for 2,3
B9: 2,3                                  # 15 pairs
B9: 9                                    #  9 pairs
* PAIR F9: 2,3 COL F
F1: 2,3,1,5                              # reduction candidate for 2,3
F1: 2,3 => CTR
* 496.1.7.8.15897462872.46195984..1356763954821521..8947649185273258..9614137462589
F1: 1,5                                  #  7 pairs
F2: 2,3,5,7                              # reduction candidate for 2,3
F2: 2,3                                  # 10 pairs
F4: 2,3,1,7                              # reduction candidate for 2,3
F4: 2,3                                  #  9 pairs
* PAIR H7: 3,7 BLK 9
I7: 3,7,9                                # reduction candidate for 3,7
I7: 3,7                                  # 15 pairs
I8: 3,7,4                                # reduction candidate for 3,7
I8: 3,7 => CTR
* 436591728.158..46.8.2.46.9..84....56.6.9548..5....8.4.64.1852.9.58479613197...584
I8: 4                                    #  7 pairs
* PAIR H7: 3,7 ROW 7
F7: 3,7,5                                # reduction candidate for 3,7
F7: 3,7 => CTR
* 4.6.917..7198.546.8.2746.9.984..7.562619548375736.8942645183279328579614197462583
F7: 5                                    # 11 pairs
* PAIR H7: 3,7 COL H
H5: 3,7,2                                # reduction candidate for 3,7
H5: 2                                    # 10 pairs
H5: 3,7                                  #  8 pairs
* PAIR H9: 3,8 BLK 9
I9: 3,8,4,9                              # reduction candidate for 3,8
I9: 3,8                                  # 11 pairs
I9: 4,9                                  #  7 pairs
* PAIR H9: 3,8 COL H
H1: 3,8,2                                # reduction candidate for 3,8
H1: 3,8                                  # 10 pairs
H1: 2                                    #  8 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0017-base-pr-000.dot
* REASONING
* DIS # B8: 2,3 => CTR => B8: 5
* DIS # D9: 2,3 => CTR => D9: 4,6
* DIS # E9: 2,3 => CTR => E9: 6
* DIS # F1: 2,3 => CTR => F1: 1,5
* DIS # I8: 3,7 => CTR => I8: 4
* DIS # F7: 3,7 => CTR => F7: 5
* CNT   6 HDP CHAINS /  38 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C5,F9,G3,H7,H9)
* 4.6...7...1.8..46.8.2.46.9..84....56.6.9548..5....8.4.64.18.2....8..961.1.7...5..
* PAIR G3: 1,3 BLK 3
I3: 1,3,5                                # reduction candidate for 1,3
I3: 5                                    # 12 pairs
I3: 1,3                                  # 11 pairs
* PAIR G3: 1,3 COL G
G4: 1,3,9                                # reduction candidate for 1,3
G4: 1,3                                  # 15 pairs
G6: 1,3,9                                # reduction candidate for 1,3
G6: 1,3                                  # 10 pairs
* PAIR C5: 1,3 BLK 4
C6: 1,3,9                                # reduction candidate for 1,3
C6: 9                                    # 12 pairs
C6: 1,3                                  # 10 pairs
* PAIR C5: 1,3 ROW 5
I5: 1,3,2,7                              # reduction candidate for 1,3
I5: 1,3                                  # 10 pairs
I5: 2,7                                  #  7 pairs
* PAIR A8: 2,3 BLK 7
B8: 2,3,5                                # reduction candidate for 2,3
B8: 2,3 => CTR
* 4.6.917..7198.546.8.2746.9.984..7.562619548375736.8942645183279328579614197462583
B9: 2,3,9                                # reduction candidate for 2,3
B9: 2,3                                  # 15 pairs
* RESTART
* PAIR A8: 2,3 BLK 7
B9: 2,3,9                                # reduction candidate for 2,3
B9: 2,3                                  # 15 pairs
B9: 9                                    # 13 pairs
* PAIR A8: 2,3 ROW 8
D8: 2,3,4,7                              # reduction candidate for 2,3
D8: 2,3                                  # 11 pairs
E8: 2,3,7                                # reduction candidate for 2,3
E8: 2,3                                  # 13 pairs
* PAIR A8: 2,3 COL A
A4: 2,3,7,9                              # reduction candidate for 2,3
A4: 2,3                                  # 17 pairs
A5: 2,3,7                                # reduction candidate for 2,3
A5: 2,3                                  # 15 pairs
* PAIR F9: 2,3 BLK 8
D8: 2,3,4,7                              # reduction candidate for 2,3
D8: 2,3                                  # 11 pairs
E8: 2,3,7                                # reduction candidate for 2,3
E8: 2,3                                  # 13 pairs
D9: 2,3,4,6                              # reduction candidate for 2,3
D9: 2,3 => CTR
* 4.6...7.8.158..4628.2.46.95.84....56.6.95482.5..6.8.4.643185279258479613197.6.584
E9: 2,3,6                                # reduction candidate for 2,3
E9: 2,3 => CTR
* 436591728.158..46.8.2.46.95.84....56.6.9548..5...68.4.64.1852.9.584796131976..584
* PAIR F9: 2,3 ROW 9
B9: 2,3,9                                # reduction candidate for 2,3
B9: 9 => SOLVED
* 436591782915827463872346195784213956361954827529678341643185279258739614197462538
* DURATION: 0:00:19.465958  START: 03:43:41.193608  END: 03:44:00.659566 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0017-base-pr-001.dot
* REASONING
* DIS # B8: 2,3 => CTR => B8: 5
* DIS B8: 5 # D9: 2,3 => CTR => D9: 4,6
* DIS B8: 5 + D9: 4,6 # E9: 2,3 => CTR => E9: 6
* PRF B8: 5 + D9: 4,6 + E9: 6 # B9: 9 => SOL
* STA B8: 5 + D9: 4,6 + E9: 6 + B9: 9
* CNT   4 HDP CHAINS /  22 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=17

Solution

position: 436591782915827463872346195784213956361954827529678341643185279258739614197462538 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 # I3: 1,3 => UNS
* INC # I3: 5 => UNS
* INC # G4: 1,3 => UNS
* INC # G6: 1,3 => UNS
* INC # C6: 1,3 => UNS
* INC # C6: 9 => UNS
* INC # I5: 1,3 => UNS
* INC # I5: 2,7 => UNS
* DIS # B8: 2,3 => CTR => B8: 5
* INC # B8: 5 => UNS
* INC # B9: 2,3 => UNS
* INC # D8: 2,3 => UNS
* INC # E8: 2,3 => UNS
* INC # A4: 2,3 => UNS
* INC # A5: 2,3 => UNS
* INC # D8: 2,3 => UNS
* INC # E8: 2,3 => UNS
* DIS # D9: 2,3 => CTR => D9: 4,6
* INC # D9: 4,6 => UNS
* DIS # E9: 2,3 => CTR => E9: 6
* INC # E9: 6 => UNS
* INC # B9: 2,3 => UNS
* INC # B9: 9 => UNS
* DIS # F1: 2,3 => CTR => F1: 1,5
* INC # F1: 1,5 => UNS
* INC # F2: 2,3 => UNS
* INC # F4: 2,3 => UNS
* INC # I7: 3,7 => UNS
* DIS # I8: 3,7 => CTR => I8: 4
* INC # I8: 4 => UNS
* DIS # F7: 3,7 => CTR => F7: 5
* INC # F7: 5 => UNS
* INC # H5: 3,7 => UNS
* INC # H5: 2 => UNS
* INC # I9: 3,8 => UNS
* INC # I9: 4,9 => UNS
* INC # H1: 3,8 => UNS
* INC # H1: 2 => UNS
* CNT  38 HDP CHAINS /  38 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # I3: 1,3 => UNS
* INC # I3: 5 => UNS
* INC # G4: 1,3 => UNS
* INC # G6: 1,3 => UNS
* INC # C6: 1,3 => UNS
* INC # C6: 9 => UNS
* INC # I5: 1,3 => UNS
* INC # I5: 2,7 => UNS
* DIS # B8: 2,3 => CTR => B8: 5
* INC B8: 5 # B9: 2,3 => UNS
* INC B8: 5 # B9: 2,3 => UNS
* INC B8: 5 # B9: 9 => UNS
* INC B8: 5 # D8: 2,3 => UNS
* INC B8: 5 # E8: 2,3 => UNS
* INC B8: 5 # A4: 2,3 => UNS
* INC B8: 5 # A5: 2,3 => UNS
* INC B8: 5 # D8: 2,3 => UNS
* INC B8: 5 # E8: 2,3 => UNS
* DIS B8: 5 # D9: 2,3 => CTR => D9: 4,6
* DIS B8: 5 + D9: 4,6 # E9: 2,3 => CTR => E9: 6
* INC B8: 5 + D9: 4,6 + E9: 6 # B9: 2,3 => UNS
* PRF B8: 5 + D9: 4,6 + E9: 6 # B9: 9 => SOL
* STA B8: 5 + D9: 4,6 + E9: 6 + B9: 9
* CNT  22 HDP CHAINS /  22 HYP OPENED