Analysis of zz-www.sudokuwiki.org-0106-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=106

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=106

position: .1..3..5.7..62.........47.2.6..7...4..3...6..5...8..1.3.98.........47..8.8..5..9. initial

Autosolve

position: .1.73..5.7..62.........47.2.6..7...4..3...6..5...86.1.3.986.......947..8.8..5..9. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 8,9 => CTR => A1: 2,4,6
* DIS # A1: 6,9 => CTR => A1: 2,4,8
* PRF # A5: 1,9 => SOL
* DIS # B7: 2,5 => CTR => B7: 4,7
* DIS # G8: 2,5 => CTR => G8: 1,3
* CNT   5 HDP CHAINS /  24 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 # A1: 8,9 => CTR => A1: 2,4,6
* PRF A1: 2,4,6 # A5: 1,9 => SOL
* STA A1: 2,4,6 + A5: 1,9
* CNT   2 HDP CHAINS /  15 HYP OPENED

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

Details

Positions

.1..3..5.7..62.........47.2.6..7...4..3...6..5...8..1.3.98.........47..8.8..5..9. initial
.1.73..5.7..62.........47.2.6..7...4..3...6..5...86.1.3.986.......947..8.8..5..9. autosolve
412739856735628149896514732968173524123495687574286913349861275251947368687352491 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
F1: 8,9
D3: 1,5
E3: 1,9
I1: 6,9
E5: 1,9
B8: 2,5
F7: 1,2

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D3,E3: 1.. / D3 = 1  =>  9 pairs (_) / E3 = 1  =>  8 pairs (_)
G2,I2: 1.. / G2 = 1  =>  9 pairs (_) / I2 = 1  => 12 pairs (_)
E3,E5: 1.. / E3 = 1  =>  8 pairs (_) / E5 = 1  =>  9 pairs (_)
A1,C1: 2.. / A1 = 2  =>  8 pairs (_) / C1 = 2  =>  9 pairs (_)
B2,B3: 3.. / B2 = 3  => 20 pairs (_) / B3 = 3  =>  8 pairs (_)
D9,F9: 3.. / D9 = 3  => 12 pairs (_) / F9 = 3  =>  8 pairs (_)
G8,H8: 3.. / G8 = 3  =>  9 pairs (_) / H8 = 3  =>  0 pairs (X)
B3,H3: 3.. / B3 = 3  =>  8 pairs (_) / H3 = 3  => 20 pairs (_)
F4,F9: 3.. / F4 = 3  => 12 pairs (_) / F9 = 3  =>  8 pairs (_)
I2,I6: 3.. / I2 = 3  => 17 pairs (_) / I6 = 3  => 11 pairs (_)
D5,D6: 4.. / D5 = 4  =>  8 pairs (_) / D6 = 4  =>  9 pairs (_)
H2,H7: 4.. / H2 = 4  => 17 pairs (_) / H7 = 4  => 15 pairs (_)
F2,D3: 5.. / F2 = 5  =>  9 pairs (_) / D3 = 5  =>  8 pairs (_)
G4,I5: 5.. / G4 = 5  => 11 pairs (_) / I5 = 5  =>  8 pairs (_)
I5,I7: 5.. / I5 = 5  =>  8 pairs (_) / I7 = 5  => 11 pairs (_)
I1,H3: 6.. / I1 = 6  => 12 pairs (_) / H3 = 6  =>  0 pairs (X)
H8,I9: 6.. / H8 = 6  => 12 pairs (_) / I9 = 6  =>  0 pairs (X)
H3,H8: 6.. / H3 = 6  =>  0 pairs (X) / H8 = 6  => 12 pairs (_)
I1,I9: 6.. / I1 = 6  => 12 pairs (_) / I9 = 6  =>  0 pairs (X)
B7,C9: 7.. / B7 = 7  => 18 pairs (_) / C9 = 7  =>  9 pairs (_)
C9,I9: 7.. / C9 = 7  =>  9 pairs (_) / I9 = 7  => 18 pairs (_)
C6,C9: 7.. / C6 = 7  => 18 pairs (_) / C9 = 7  =>  9 pairs (_)
H5,H7: 7.. / H5 = 7  => 12 pairs (_) / H7 = 7  =>  0 pairs (*)
F1,F2: 8.. / F1 = 8  =>  8 pairs (_) / F2 = 8  => 18 pairs (_)
A5,H5: 8.. / A5 = 8  => 10 pairs (_) / H5 = 8  =>  0 pairs (*)
E3,E5: 9.. / E3 = 9  =>  9 pairs (_) / E5 = 9  =>  8 pairs (_)
* DURATION: 0:00:31.504502  START: 05:22:03.415931  END: 05:22:34.920433 2017-05-01
* CP COUNT: (26)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,D3,E3,E5,F1,F7,I1)
* .1.73..5.7..62.........47.2.6..7...4..3...6..5...86.1.3.986.......947..8.8..5..9.
* PAIR F1: 8,9 BLK 2
F2: 8,9,5                                # reduction candidate for 8,9
F2: 5                                    #  9 pairs
F2: 8,9                                  #  8 pairs
* PAIR F1: 8,9 ROW 1
A1: 8,9,2,4,6                            # reduction candidate for 8,9
A1: 8,9 => CTR
* 9127384567..62...96...947.216..7..248.3...67.5...869133.986..4....947368486.5..97
A1: 2,4,6                                #  7 pairs
G1: 8,9,4                                # reduction candidate for 8,9
G1: 8,9                                  # 16 pairs
* PAIR D3: 1,5 COL D
D4: 1,5,2,3                              # reduction candidate for 1,5
D4: 1,5                                  # 10 pairs
D5: 1,5,2,4                              # reduction candidate for 1,5
D5: 1,5                                  # 12 pairs
* PAIR I1: 6,9 ROW 1
A1: 6,9,2,4,8                            # reduction candidate for 6,9
A1: 6,9 => CTR
* 6127384597..62...19...14762261.7.9848.3192675597.8621.3.986..4.1..947.2848..5.196
A1: 2,4,8                                #  7 pairs
* PAIR E5: 1,9 BLK 5
F4: 1,9,2,3,5                            # reduction candidate for 1,9
F4: 1,9                                  # 10 pairs
F5: 1,9,2,5                              # reduction candidate for 1,9
F5: 1,9                                  #  9 pairs
* PAIR E5: 1,9 ROW 5
A5: 1,9,2,4,8                            # reduction candidate for 1,9
A5: 1,9 => SOLVED
* 412739856735628149896514732968173524123495687574286913349861275251947368687352491
A5: 2,4,8                                #  7 pairs
* PAIR B8: 2,5 BLK 7
B7: 2,5,4,7                              # reduction candidate for 2,5
B7: 2,5 => CTR
* .1.7384597..62...1938514762.6..7...48.3...67557..869133.986..47...947..8487.5..96
B7: 4,7                                  #  8 pairs
C8: 2,5,1,6                              # reduction candidate for 2,5
C8: 2,5                                  # 12 pairs
* PAIR B8: 2,5 ROW 8
G8: 2,5,1,3                              # reduction candidate for 2,5
G8: 2,5 => CTR
* .1.7384597..62.38193851476216..7.8248.3...67557..869133.986..47...947.38487.5..96
G8: 1,3                                  #  8 pairs
* PAIR F7: 1,2 BLK 8
D9: 1,2,3                                # reduction candidate for 1,2
D9: 1,2                                  #  8 pairs
F9: 1,2,3                                # reduction candidate for 1,2
F9: 1,2                                  # 12 pairs
* PAIR F7: 1,2 ROW 7
G7: 1,2,4,5                              # reduction candidate for 1,2
G7: 1,2                                  # 10 pairs
G7: 4,5                                  #  8 pairs
* PAIR F7: 1,2 COL F
F4: 1,2,3,5,9                            # reduction candidate for 1,2
F4: 1,2                                  # 11 pairs
F5: 1,2,5,9                              # reduction candidate for 1,2
F5: 1,2                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0106-base-pr-000.dot
* REASONING
* DIS # A1: 8,9 => CTR => A1: 2,4,6
* DIS # A1: 6,9 => CTR => A1: 2,4,8
* PRF # A5: 1,9 => SOL
* DIS # B7: 2,5 => CTR => B7: 4,7
* DIS # G8: 2,5 => CTR => G8: 1,3
* CNT   5 HDP CHAINS /  24 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,D3,E3,E5,F1,F7,I1)
* .1.73..5.7..62.........47.2.6..7...4..3...6..5...86.1.3.986.......947..8.8..5..9.
* PAIR F1: 8,9 BLK 2
F2: 8,9,5                                # reduction candidate for 8,9
F2: 5                                    #  9 pairs
F2: 8,9                                  #  8 pairs
* PAIR F1: 8,9 ROW 1
A1: 8,9,2,4,6                            # reduction candidate for 8,9
A1: 8,9 => CTR
* 9127384567..62...96...947.216..7..248.3...67.5...869133.986..4....947368486.5..97
G1: 8,9,4                                # reduction candidate for 8,9
G1: 8,9                                  # 16 pairs
* RESTART
* PAIR F1: 8,9 ROW 1
G1: 8,9,4                                # reduction candidate for 8,9
G1: 8,9                                  # 16 pairs
G1: 4                                    # 16 pairs
* PAIR RESTART
* PAIR F1: 8,9 BLK 2
F2: 8,9,5                                # reduction candidate for 8,9
F2: 5                                    # 13 pairs
F2: 8,9                                  #  8 pairs
* PAIR F1: 8,9 ROW 1
G1: 8,9,4                                # reduction candidate for 8,9
G1: 8,9                                  # 16 pairs
G1: 4                                    # 16 pairs
* PAIR D3: 1,5 COL D
D4: 1,5,2,3                              # reduction candidate for 1,5
D4: 1,5                                  # 10 pairs
D5: 1,5,2,4                              # reduction candidate for 1,5
D5: 1,5                                  # 12 pairs
* PAIR E5: 1,9 BLK 5
F4: 1,9,2,3,5                            # reduction candidate for 1,9
F4: 1,9                                  # 10 pairs
F5: 1,9,2,5                              # reduction candidate for 1,9
F5: 1,9                                  #  9 pairs
* PAIR E5: 1,9 ROW 5
A5: 1,9,2,4,8                            # reduction candidate for 1,9
A5: 1,9 => SOLVED
* 412739856735628149896514732968173524123495687574286913349861275251947368687352491
* DURATION: 0:00:12.187849  START: 05:22:51.377259  END: 05:23:03.565108 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0106-base-pr-001.dot
* REASONING
* DIS # A1: 8,9 => CTR => A1: 2,4,6
* PRF A1: 2,4,6 # A5: 1,9 => SOL
* STA A1: 2,4,6 + A5: 1,9
* CNT   2 HDP CHAINS /  15 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=106

Solution

position: 412739856735628149896514732968173524123495687574286913349861275251947368687352491 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 # F2: 8,9 => UNS
* INC # F2: 5 => UNS
* DIS # A1: 8,9 => CTR => A1: 2,4,6
* INC # A1: 2,4,6 => UNS
* INC # G1: 8,9 => UNS
* INC # D4: 1,5 => UNS
* INC # D5: 1,5 => UNS
* DIS # A1: 6,9 => CTR => A1: 2,4,8
* INC # A1: 2,4,8 => UNS
* INC # F4: 1,9 => UNS
* INC # F5: 1,9 => UNS
* PRF # A5: 1,9 => SOL
* INC # A5: 2,4,8 => UNS
* DIS # B7: 2,5 => CTR => B7: 4,7
* INC # B7: 4,7 => UNS
* INC # C8: 2,5 => UNS
* DIS # G8: 2,5 => CTR => G8: 1,3
* INC # G8: 1,3 => UNS
* INC # D9: 1,2 => UNS
* INC # F9: 1,2 => UNS
* INC # G7: 1,2 => UNS
* INC # G7: 4,5 => UNS
* INC # F4: 1,2 => UNS
* INC # F5: 1,2 => UNS
* CNT  24 HDP CHAINS /  24 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F2: 8,9 => UNS
* INC # F2: 5 => UNS
* DIS # A1: 8,9 => CTR => A1: 2,4,6
* INC A1: 2,4,6 # G1: 8,9 => UNS
* INC A1: 2,4,6 # G1: 8,9 => UNS
* INC A1: 2,4,6 # G1: 4 => UNS
* INC A1: 2,4,6 # F2: 8,9 => UNS
* INC A1: 2,4,6 # F2: 5 => UNS
* INC A1: 2,4,6 # G1: 8,9 => UNS
* INC A1: 2,4,6 # G1: 4 => UNS
* INC A1: 2,4,6 # D4: 1,5 => UNS
* INC A1: 2,4,6 # D5: 1,5 => UNS
* INC A1: 2,4,6 # F4: 1,9 => UNS
* INC A1: 2,4,6 # F5: 1,9 => UNS
* PRF A1: 2,4,6 # A5: 1,9 => SOL
* STA A1: 2,4,6 + A5: 1,9
* CNT  15 HDP CHAINS /  15 HYP OPENED