Analysis of zz-www.sudokuwiki.org-0018-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=18

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=18

position: .3.96..1.9..........74.8..5..4.5.68...........69.4.3..4..3.57..........4.7..94.2. initial

Autosolve

position: .3.96.41.94.5.......74.8..5..4.5.68........4..69.4.3..4..3.57..........4.7..94.2. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A3: 1,2 => SOL
* DIS # F4: 2,7 => CTR => F4: 1,3,9
* DIS # I2: 2,8 => CTR => I2: 3,6,7
* DIS # F4: 1,2 => CTR => F4: 3,7,9
* PRF # B8: 9 => SOL
* PRF # I7: 6,9 => SOL
* CNT   6 HDP CHAINS /  45 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 # A3: 1,2 => SOL
* STA A3: 1,2
* CNT   1 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

.3.96..1.9..........74.8..5..4.5.68...........69.4.3..4..3.57..........4.7..94.2. initial
.3.96.41.94.5.......74.8..5..4.5.68........4..69.4.3..4..3.57..........4.7..94.2. autosolve
835967412946512873127438965714253689358679241269841357481325796592786134673194528 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
B3: 1,2
F1: 2,7
G2: 2,8
G3: 2,9
B4: 1,2
B5: 5,8
H6: 5,7
B7: 8,9
H7: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B3,B4: 1.. / B3 = 1  => 10 pairs (_) / B4 = 1  => 19 pairs (_)
C7,E7: 2.. / C7 = 2  => 11 pairs (_) / E7 = 2  => 11 pairs (_)
B3,B4: 2.. / B3 = 2  => 19 pairs (_) / B4 = 2  => 10 pairs (_)
H8,I9: 3.. / H8 = 3  =>  0 pairs (*) / I9 = 3  =>  0 pairs (X)
E3,H3: 3.. / E3 = 3  => 15 pairs (_) / H3 = 3  => 10 pairs (_)
A4,F4: 3.. / A4 = 3  =>  9 pairs (_) / F4 = 3  => 10 pairs (_)
I2,I9: 3.. / I2 = 3  =>  0 pairs (*) / I9 = 3  =>  0 pairs (X)
A1,C1: 5.. / A1 = 5  => 12 pairs (_) / C1 = 5  => 10 pairs (_)
G5,H6: 5.. / G5 = 5  =>  0 pairs (X) / H6 = 5  => 11 pairs (_)
A6,H6: 5.. / A6 = 5  =>  0 pairs (X) / H6 = 5  => 11 pairs (_)
B5,B8: 5.. / B5 = 5  => 11 pairs (_) / B8 = 5  => 12 pairs (_)
H6,H8: 5.. / H6 = 5  => 11 pairs (_) / H8 = 5  =>  0 pairs (X)
C2,A3: 6.. / C2 = 6  =>  0 pairs (*) / A3 = 6  =>  0 pairs (X)
D5,F5: 6.. / D5 = 6  => 10 pairs (_) / F5 = 6  => 12 pairs (_)
A3,H3: 6.. / A3 = 6  => 10 pairs (_) / H3 = 6  =>  0 pairs (*)
F5,F8: 6.. / F5 = 6  => 12 pairs (_) / F8 = 6  => 10 pairs (_)
F1,I1: 7.. / F1 = 7  => 10 pairs (_) / I1 = 7  =>  0 pairs (X)
H2,H6: 7.. / H2 = 7  => 11 pairs (_) / H6 = 7  =>  0 pairs (X)
A6,D6: 8.. / A6 = 8  => 15 pairs (_) / D6 = 8  => 10 pairs (_)
G3,H3: 9.. / G3 = 9  =>  9 pairs (_) / H3 = 9  =>  0 pairs (X)
F4,F5: 9.. / F4 = 9  =>  9 pairs (_) / F5 = 9  => 10 pairs (_)
B7,B8: 9.. / B7 = 9  => 12 pairs (_) / B8 = 9  =>  0 pairs (*)
F4,I4: 9.. / F4 = 9  =>  9 pairs (_) / I4 = 9  => 10 pairs (_)
* DURATION: 0:00:31.256819  START: 03:44:16.312221  END: 03:44:47.569040 2017-05-01
* CP COUNT: (23)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B4,B5,B7,F1,G2,G3,H6,H7)
* .3.96.41.94.5.......74.8..5..4.5.68........4..69.4.3..4..3.57..........4.7..94.2.
* PAIR B3: 1,2 BLK 1
C2: 1,2,6,8                              # reduction candidate for 1,2
C2: 1,2                                  # 19 pairs
A3: 1,2,6                                # reduction candidate for 1,2
A3: 1,2 => SOLVED
* 835967412946512873127438965714253689358679241269841357481325796592786134673194528
A3: 6                                    # 10 pairs
* PAIR B3: 1,2 ROW 3
E3: 1,2,3                                # reduction candidate for 1,2
E3: 3                                    # 15 pairs
E3: 1,2                                  # 10 pairs
* PAIR F1: 2,7 BLK 2
E2: 2,7,1,3                              # reduction candidate for 2,7
E2: 2,7                                  # 12 pairs
F2: 2,7,1,3                              # reduction candidate for 2,7
F2: 2,7                                  # 18 pairs
* PAIR F1: 2,7 ROW 1
I1: 2,7,8                                # reduction candidate for 2,7
I1: 8                                    # 18 pairs
I1: 2,7                                  # 17 pairs
* PAIR F1: 2,7 COL F
F4: 2,7,1,3,9                            # reduction candidate for 2,7
F4: 2,7 => CTR
* .3.96.41.9415.327.627418935314.5.689...63914..6984135.4.23857.11.3..6.94.76194.23
F4: 1,3,9                                #  9 pairs
F5: 2,7,1,3,6,9                          # reduction candidate for 2,7
F5: 2,7                                  # 20 pairs
F6: 2,7,1                                # reduction candidate for 2,7
F6: 2,7                                  # 12 pairs
F8: 2,7,1,6                              # reduction candidate for 2,7
F8: 2,7                                  # 16 pairs
* PAIR G2: 2,8 BLK 3
I1: 2,8,7                                # reduction candidate for 2,8
I1: 2,8                                  # 10 pairs
I2: 2,8,3,6,7                            # reduction candidate for 2,8
I2: 2,8 => CTR
* .3.96.41.94.5.......74.89.5..4.5.68..5.....4..69.4.37.48.3.5796.9.....54.7..94.23
I2: 3,6,7                                #  9 pairs
* PAIR G2: 2,8 ROW 2
C2: 2,8,1,6                              # reduction candidate for 2,8
C2: 1,6                                  # 19 pairs
C2: 2,8                                  # 11 pairs
* PAIR G3: 2,9 COL G
G5: 2,9,1,5                              # reduction candidate for 2,9
G5: 2,9                                  # 24 pairs
G5: 1,5                                  # 11 pairs
* PAIR B4: 1,2 BLK 4
A4: 1,2,3,7                              # reduction candidate for 1,2
A4: 1,2                                  # 12 pairs
A5: 1,2,3,5,7,8                          # reduction candidate for 1,2
A5: 1,2                                  # 11 pairs
C5: 1,2,3,5,8                            # reduction candidate for 1,2
C5: 1,2                                  # 11 pairs
A6: 1,2,5,7,8                            # reduction candidate for 1,2
A6: 1,2                                  # 14 pairs
* PAIR B4: 1,2 ROW 4
D4: 1,2,7                                # reduction candidate for 1,2
D4: 1,2                                  # 12 pairs
F4: 1,2,3,7,9                            # reduction candidate for 1,2
F4: 1,2 => CTR
* .3.96741894.5.3..66.74.89353.475.689...63914..6984135.4923857611.3276.94.76194.23
F4: 3,7,9                                #  9 pairs
I4: 1,2,7,9                              # reduction candidate for 1,2
I4: 1,2                                  # 11 pairs
* PAIR B5: 5,8 BLK 4
A5: 5,8,1,2,3,7                          # reduction candidate for 5,8
A5: 5,8                                  # 13 pairs
C5: 5,8,1,2,3                            # reduction candidate for 5,8
C5: 5,8                                  # 13 pairs
A6: 5,8,1,2,7                            # reduction candidate for 5,8
A6: 5,8                                  # 10 pairs
* PAIR B5: 5,8 COL B
B8: 5,8,9                                # reduction candidate for 5,8
B8: 9 => SOLVED
* 835967412946512873127438965714253689358679241269841357481325796592786134673194528
B8: 5,8                                  # 12 pairs
* PAIR H6: 5,7 ROW 6
A6: 5,7,1,2,8                            # reduction candidate for 5,7
A6: 5,7                                  # 13 pairs
A6: 1,2,8                                # 11 pairs
* PAIR B7: 8,9 BLK 7
B8: 8,9,5                                # reduction candidate for 8,9
B8: 5                                    # 12 pairs
B8: 8,9                                  # 11 pairs
* PAIR B7: 8,9 ROW 7
I7: 8,9,1,6                              # reduction candidate for 8,9
I7: 8,9                                  # 14 pairs
I7: 1,6                                  # 10 pairs
* PAIR H7: 6,9 BLK 9
I7: 6,9,1,8                              # reduction candidate for 6,9
I7: 6,9 => SOLVED
* 835967412946512873127438965714253689358679241269841357481325796592786134673194528
I7: 1,8                                  # 12 pairs
H8: 6,9,3,5                              # reduction candidate for 6,9
H8: 6,9                                  # 12 pairs
* PAIR H7: 6,9 COL H
H3: 6,9,3                                # reduction candidate for 6,9
H3: 6,9                                  # 15 pairs
H3: 3                                    # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0018-base-pr-000.dot
* REASONING
* PRF # A3: 1,2 => SOL
* DIS # F4: 2,7 => CTR => F4: 1,3,9
* DIS # I2: 2,8 => CTR => I2: 3,6,7
* DIS # F4: 1,2 => CTR => F4: 3,7,9
* PRF # B8: 9 => SOL
* PRF # I7: 6,9 => SOL
* CNT   6 HDP CHAINS /  45 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B4,B5,B7,F1,G2,G3,H6,H7)
* .3.96.41.94.5.......74.8..5..4.5.68........4..69.4.3..4..3.57..........4.7..94.2.
* PAIR B3: 1,2 BLK 1
C2: 1,2,6,8                              # reduction candidate for 1,2
C2: 1,2                                  # 19 pairs
A3: 1,2,6                                # reduction candidate for 1,2
A3: 1,2 => SOLVED
* 835967412946512873127438965714253689358679241269841357481325796592786134673194528
* DURATION: 0:00:03.377931  START: 03:45:23.098702  END: 03:45:26.476633 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0018-base-pr-001.dot
* REASONING
* PRF # A3: 1,2 => SOL
* STA A3: 1,2
* CNT   1 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=18

Solution

position: 835967412946512873127438965714253689358679241269841357481325796592786134673194528 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 # C2: 1,2 => UNS
* PRF # A3: 1,2 => SOL
* INC # A3: 6 => UNS
* INC # E3: 1,2 => UNS
* INC # E3: 3 => UNS
* INC # E2: 2,7 => UNS
* INC # F2: 2,7 => UNS
* INC # I1: 2,7 => UNS
* INC # I1: 8 => UNS
* DIS # F4: 2,7 => CTR => F4: 1,3,9
* INC # F4: 1,3,9 => UNS
* INC # F5: 2,7 => UNS
* INC # F6: 2,7 => UNS
* INC # F8: 2,7 => UNS
* INC # I1: 2,8 => UNS
* DIS # I2: 2,8 => CTR => I2: 3,6,7
* INC # I2: 3,6,7 => UNS
* INC # C2: 2,8 => UNS
* INC # C2: 1,6 => UNS
* INC # G5: 2,9 => UNS
* INC # G5: 1,5 => UNS
* INC # A4: 1,2 => UNS
* INC # A5: 1,2 => UNS
* INC # C5: 1,2 => UNS
* INC # A6: 1,2 => UNS
* INC # D4: 1,2 => UNS
* DIS # F4: 1,2 => CTR => F4: 3,7,9
* INC # F4: 3,7,9 => UNS
* INC # I4: 1,2 => UNS
* INC # A5: 5,8 => UNS
* INC # C5: 5,8 => UNS
* INC # A6: 5,8 => UNS
* INC # B8: 5,8 => UNS
* PRF # B8: 9 => SOL
* INC # A6: 5,7 => UNS
* INC # A6: 1,2,8 => UNS
* INC # B8: 8,9 => UNS
* INC # B8: 5 => UNS
* INC # I7: 8,9 => UNS
* INC # I7: 1,6 => UNS
* PRF # I7: 6,9 => SOL
* INC # I7: 1,8 => UNS
* INC # H8: 6,9 => UNS
* INC # H3: 6,9 => UNS
* INC # H3: 3 => UNS
* CNT  45 HDP CHAINS /  45 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C2: 1,2 => UNS
* PRF # A3: 1,2 => SOL
* STA A3: 1,2
* CNT   2 HDP CHAINS /   2 HYP OPENED