Analysis of zz-www.sudokuwiki.org-0096-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=96

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=96

position: ....43..95.........7...8.5..5.7..8...9..2..6...2..5.3..3.6...9.........41..85.... initial

Autosolve

position: ...543..95.........7...8.5..5.7..8...9.321.6...248593..3.6...9.....3...41..85.... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C4: 3,4 => CTR => C4: 1
* DIS # H4: 1,2 => CTR => H4: 4
* DIS # I2: 1,2 => CTR => I2: 3,6,8
* DIS # I3: 1,2 => CTR => I3: 3,6
* DIS # I7: 1,2 => CTR => I7: 5,7,8
* DIS # G5: 4 => CTR => G5: 5,7
* DIS # I7: 5,7 => CTR => I7: 1,2,8
* DIS # H8: 2,7 => CTR => H8: 1,8
* DIS # F9: 2,7 => CTR => F9: 4,9
* CNT   9 HDP CHAINS /  41 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 # C4: 3,4 => CTR => C4: 1
* DIS C4: 1 # E2: 6,9 => CTR => E2: 1,7
* DIS C4: 1 + E2: 1,7 # F2: 6,9 => CTR => F2: 2,7
* DIS C4: 1 + E2: 1,7 + F2: 2,7 # I7: 5,7 => CTR => I7: 8
* PRF C4: 1 + E2: 1,7 + F2: 2,7 + I7: 8 => SOL
* STA C4: 1 + E2: 1,7 + F2: 2,7 + I7: 8
* CNT   5 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

....43..95.........7...8.5..5.7..8...9..2..6...2..5.3..3.6...9.........41..85.... initial
...543..95.........7...8.5..5.7..8...9.321.6...248593..3.6...9.....3...41..85.... autosolve
628543179513972486479168253351796842894321765762485931237614598985237614146859327 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
A4: 3,4
A6: 6,7
B6: 1,6
E4: 6,9
F4: 6,9
I4: 1,2
I5: 5,7
I6: 1,7
E7: 1,7
H9: 2,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C4,B6: 1.. / C4 = 1  => 14 pairs (_) / B6 = 1  =>  0 pairs (X)
E7,D8: 1.. / E7 = 1  => 11 pairs (_) / D8 = 1  => 13 pairs (_)
B6,I6: 1.. / B6 = 1  =>  0 pairs (X) / I6 = 1  => 14 pairs (_)
H4,I4: 2.. / H4 = 2  =>  0 pairs (X) / I4 = 2  => 10 pairs (_)
A4,C4: 3.. / A4 = 3  => 10 pairs (_) / C4 = 3  =>  0 pairs (X)
G9,I9: 3.. / G9 = 3  => 10 pairs (_) / I9 = 3  => 10 pairs (_)
A3,A4: 3.. / A3 = 3  =>  0 pairs (X) / A4 = 3  => 10 pairs (_)
H4,G5: 4.. / H4 = 4  => 14 pairs (_) / G5 = 4  =>  0 pairs (X)
F7,F9: 4.. / F7 = 4  => 10 pairs (_) / F9 = 4  =>  0 pairs (X)
B2,B9: 4.. / B2 = 4  =>  0 pairs (X) / B9 = 4  => 10 pairs (_)
H2,H4: 4.. / H2 = 4  =>  0 pairs (X) / H4 = 4  => 14 pairs (_)
G5,I5: 5.. / G5 = 5  =>  0 pairs (X) / I5 = 5  => 10 pairs (_)
C7,C8: 5.. / C7 = 5  => 13 pairs (_) / C8 = 5  => 10 pairs (_)
C8,G8: 5.. / C8 = 5  => 10 pairs (_) / G8 = 5  => 13 pairs (_)
I5,I7: 5.. / I5 = 5  => 10 pairs (_) / I7 = 5  =>  0 pairs (X)
A6,B6: 6.. / A6 = 6  =>  0 pairs (X) / B6 = 6  => 14 pairs (_)
E4,F4: 6.. / E4 = 6  =>  0 pairs (X) / F4 = 6  =>  9 pairs (_)
F2,F4: 6.. / F2 = 6  =>  0 pairs (X) / F4 = 6  =>  9 pairs (_)
E2,F2: 7.. / E2 = 7  => 11 pairs (_) / F2 = 7  => 13 pairs (_)
G1,H1: 7.. / G1 = 7  => 11 pairs (_) / H1 = 7  => 11 pairs (_)
A6,I6: 7.. / A6 = 7  => 14 pairs (_) / I6 = 7  =>  0 pairs (X)
E2,E7: 7.. / E2 = 7  => 11 pairs (_) / E7 = 7  => 13 pairs (_)
A5,C5: 8.. / A5 = 8  => 12 pairs (_) / C5 = 8  => 12 pairs (_)
I7,H8: 8.. / I7 = 8  => 10 pairs (_) / H8 = 8  => 15 pairs (_)
I2,I7: 8.. / I2 = 8  => 15 pairs (_) / I7 = 8  => 10 pairs (_)
E4,F4: 9.. / E4 = 9  =>  9 pairs (_) / F4 = 9  =>  0 pairs (X)
C9,F9: 9.. / C9 = 9  => 12 pairs (_) / F9 = 9  => 13 pairs (_)
A3,A8: 9.. / A3 = 9  => 12 pairs (_) / A8 = 9  => 13 pairs (_)
* DURATION: 0:00:36.943553  START: 05:12:36.715349  END: 05:13:13.658902 2017-05-01
* CP COUNT: (28)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B6,E4,E7,F4,H9,I4,I5,I6)
* ...543..95.........7...8.5..5.7..8...9.321.6...248593..3.6...9.....3...41..85....
* PAIR A4: 3,4 BLK 4
C4: 3,4,1                                # reduction candidate for 3,4
C4: 3,4 => CTR
* 8.1543..95......48.7...8.5..5.7968..79832146561248593723.6.4.9198.132.74147859.2.
C4: 1                                    # 14 pairs
* PAIR A4: 3,4 COL A
A3: 3,4,2,6,9                            # reduction candidate for 3,4
A3: 3,4                                  # 15 pairs
A3: 2,6,9                                # 10 pairs
* PAIR A6: 6,7 COL A
A8: 6,7,2,8,9                            # reduction candidate for 6,7
A8: 6,7                                  # 15 pairs
A8: 2,8,9                                # 10 pairs
* PAIR B6: 1,6 COL B
B1: 1,6,2,8                              # reduction candidate for 1,6
B1: 1,6                                  # 13 pairs
B2: 1,6,2,4,8                            # reduction candidate for 1,6
B2: 1,6                                  # 14 pairs
* PAIR E4: 6,9 COL E
E2: 6,9,1,7                              # reduction candidate for 6,9
E2: 6,9                                  # 11 pairs
E3: 6,9,1                                # reduction candidate for 6,9
E3: 6,9                                  # 12 pairs
* PAIR F4: 6,9 COL F
F2: 6,9,2,7                              # reduction candidate for 6,9
F2: 2,7                                  # 11 pairs
F2: 6,9                                  # 10 pairs
* PAIR I4: 1,2 BLK 6
H4: 1,2,4                                # reduction candidate for 1,2
H4: 1,2 => CTR
* 8.1543..95......48.7...8.5..5.7968..79832146561248593723.6.4.9198.132.74147859.2.
H4: 4                                    # 14 pairs
* PAIR I4: 1,2 COL I
I2: 1,2,3,6,8                            # reduction candidate for 1,2
I2: 1,2 => CTR
* 26154378958.....4..7...8.5..5.7..8...9.321465612485937735614298.2.937514149852.7.
I2: 3,6,8                                # 10 pairs
I3: 1,2,3,6                              # reduction candidate for 1,2
I3: 1,2 => CTR
* 26154378958.....4..7...8.5..5.7..8...9.321465612485937735614298.2.937514149852.7.
I3: 3,6                                  # 11 pairs
I7: 1,2,5,7,8                            # reduction candidate for 1,2
I7: 1,2 => CTR
* 28.543..956.....48.7..68.533547968...9.321465612485937.3.6.4.9..2..3..8414.852376
I7: 5,7,8                                # 10 pairs
* PAIR I5: 5,7 BLK 6
G5: 5,7,4                                # reduction candidate for 5,7
G5: 4 => CTR
* 8.1543..95......48.7...8.5..5.7968..79832146561248593723.6.4.9198.132.74147859.2.
G5: 5,7                                  # 14 pairs
* PAIR I5: 5,7 COL I
I7: 5,7,1,2,8                            # reduction candidate for 5,7
I7: 5,7 => CTR
* .8654371951.....28.7...8.5..517..842.9.321.6.76248593183.6.429..2..3.18414.852.7.
I7: 1,2,8                                # 10 pairs
* PAIR I6: 1,7 COL I
I7: 1,7,2,5,8                            # reduction candidate for 1,7
I7: 1,7                                  # 18 pairs
I7: 2,5,8                                # 10 pairs
* PAIR E7: 1,7 ROW 7
G7: 1,7,2,5                              # reduction candidate for 1,7
G7: 1,7                                  # 12 pairs
I7: 1,7,2,5,8                            # reduction candidate for 1,7
I7: 1,7                                  # 18 pairs
* PAIR E7: 1,7 COL E
E2: 1,7,6,9                              # reduction candidate for 1,7
E2: 1,7                                  # 12 pairs
E2: 6,9                                  # 11 pairs
* PAIR H9: 2,7 BLK 9
G7: 2,7,1,5                              # reduction candidate for 2,7
G7: 2,7                                  # 17 pairs
I7: 2,7,1,5,8                            # reduction candidate for 2,7
I7: 2,7                                  # 23 pairs
G8: 2,7,1,5,6                            # reduction candidate for 2,7
G8: 2,7                                  # 18 pairs
H8: 2,7,1,8                              # reduction candidate for 2,7
H8: 2,7 => CTR
* 26154378958.....4..7...8.5..5.7..812.9.321465612485937735614.98....3...414.85....
H8: 1,8                                  # 11 pairs
G9: 2,7,3,6                              # reduction candidate for 2,7
G9: 2,7                                  # 17 pairs
I9: 2,7,3,6                              # reduction candidate for 2,7
I9: 2,7                                  # 21 pairs
* PAIR H9: 2,7 ROW 9
F9: 2,7,4,9                              # reduction candidate for 2,7
F9: 2,7 => CTR
* ..6543..95.......897.218.5.3517..842498321.6.76248593183.674.9.6...3...414985....
F9: 4,9                                  # 11 pairs
* PAIR H9: 2,7 COL H
H1: 2,7,1,8                              # reduction candidate for 2,7
H1: 2,7                                  # 12 pairs
H1: 1,8                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0096-base-pr-000.dot
* REASONING
* DIS # C4: 3,4 => CTR => C4: 1
* DIS # H4: 1,2 => CTR => H4: 4
* DIS # I2: 1,2 => CTR => I2: 3,6,8
* DIS # I3: 1,2 => CTR => I3: 3,6
* DIS # I7: 1,2 => CTR => I7: 5,7,8
* DIS # G5: 4 => CTR => G5: 5,7
* DIS # I7: 5,7 => CTR => I7: 1,2,8
* DIS # H8: 2,7 => CTR => H8: 1,8
* DIS # F9: 2,7 => CTR => F9: 4,9
* CNT   9 HDP CHAINS /  41 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B6,E4,E7,F4,H9,I4,I5,I6)
* ...543..95.........7...8.5..5.7..8...9.321.6...248593..3.6...9.....3...41..85....
* PAIR A4: 3,4 BLK 4
C4: 3,4,1                                # reduction candidate for 3,4
C4: 3,4 => CTR
* 8.1543..95......48.7...8.5..5.7968..79832146561248593723.6.4.9198.132.74147859.2.
* PAIR E4: 6,9 COL E
E2: 6,9,1,7                              # reduction candidate for 6,9
E2: 6,9 => CTR
* ...543..95...67..3.73.18.56351796842.9.32176.762485931.3567.198.8.13.5.41..85....
* RESTART
* PAIR RESTART
* PAIR F4: 6,9 COL F
F2: 6,9,2,7                              # reduction candidate for 6,9
F2: 6,9 => CTR
* ...543..95.3.796.8974.68.53351796842498321.6.76248593183.61429.62.937.84149852376
* PAIR RESTART
* PAIR I5: 5,7 COL I
I7: 5,7,8                                # reduction candidate for 5,7
I7: 5,7 => CTR
* ...543..95.39....8.7..68.53351796842.9.321.6.76248593183.6.429..2.13..8414.852376
I7: 8 => SOLVED
* 628543179513972486479168253351796842894321765762485931237614598985237614146859327
* DURATION: 0:00:08.987418  START: 05:13:44.071125  END: 05:13:53.058543 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0096-base-pr-001.dot
* REASONING
* DIS # C4: 3,4 => CTR => C4: 1
* DIS C4: 1 # E2: 6,9 => CTR => E2: 1,7
* DIS C4: 1 + E2: 1,7 # F2: 6,9 => CTR => F2: 2,7
* DIS C4: 1 + E2: 1,7 + F2: 2,7 # I7: 5,7 => CTR => I7: 8
* PRF C4: 1 + E2: 1,7 + F2: 2,7 + I7: 8 => SOL
* STA C4: 1 + E2: 1,7 + F2: 2,7 + I7: 8
* CNT   5 HDP CHAINS /   4 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=96

Solution

position: 628543179513972486479168253351796842894321765762485931237614598985237614146859327 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:

* DIS # C4: 3,4 => CTR => C4: 1
* INC # C4: 1 => UNS
* INC # A3: 3,4 => UNS
* INC # A3: 2,6,9 => UNS
* INC # A8: 6,7 => UNS
* INC # A8: 2,8,9 => UNS
* INC # B1: 1,6 => UNS
* INC # B2: 1,6 => UNS
* INC # E2: 6,9 => UNS
* INC # E3: 6,9 => UNS
* INC # F2: 6,9 => UNS
* INC # F2: 2,7 => UNS
* DIS # H4: 1,2 => CTR => H4: 4
* INC # H4: 4 => UNS
* DIS # I2: 1,2 => CTR => I2: 3,6,8
* INC # I2: 3,6,8 => UNS
* DIS # I3: 1,2 => CTR => I3: 3,6
* INC # I3: 3,6 => UNS
* DIS # I7: 1,2 => CTR => I7: 5,7,8
* INC # I7: 5,7,8 => UNS
* INC # G5: 5,7 => UNS
* DIS # G5: 4 => CTR => G5: 5,7
* DIS # I7: 5,7 => CTR => I7: 1,2,8
* INC # I7: 1,2,8 => UNS
* INC # I7: 1,7 => UNS
* INC # I7: 2,5,8 => UNS
* INC # G7: 1,7 => UNS
* INC # I7: 1,7 => UNS
* INC # E2: 1,7 => UNS
* INC # E2: 6,9 => UNS
* INC # G7: 2,7 => UNS
* INC # I7: 2,7 => UNS
* INC # G8: 2,7 => UNS
* DIS # H8: 2,7 => CTR => H8: 1,8
* INC # H8: 1,8 => UNS
* INC # G9: 2,7 => UNS
* INC # I9: 2,7 => UNS
* DIS # F9: 2,7 => CTR => F9: 4,9
* INC # F9: 4,9 => UNS
* INC # H1: 2,7 => UNS
* INC # H1: 1,8 => UNS
* CNT  41 HDP CHAINS /  41 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # C4: 3,4 => CTR => C4: 1
* DIS C4: 1 # E2: 6,9 => CTR => E2: 1,7
* DIS C4: 1 + E2: 1,7 # F2: 6,9 => CTR => F2: 2,7
* DIS C4: 1 + E2: 1,7 + F2: 2,7 # I7: 5,7 => CTR => I7: 8
* PRF C4: 1 + E2: 1,7 + F2: 2,7 + I7: 8 => SOL
* STA C4: 1 + E2: 1,7 + F2: 2,7 + I7: 8
* CNT   5 HDP CHAINS /   4 HYP OPENED