Analysis of zz-www.sudokuwiki.org-0107-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=107

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=107

position: .8...9.........2.69...5..3...24..17.3...2...5..7..3....3..9...12.4.........6...5. initial

Autosolve

position: .8.2.951.......29692..5..3..924..1733...2...5..7..3....3..9...12.4........96...5. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # F5: 6,8 => CTR => F5: 1,7
* DIS # E6: 6,8 => CTR => E6: 1
* DIS # B8: 1,7 => CTR => B8: 5,6
* DIS # E9: 1,7 => CTR => E9: 3,4,8
* DIS # F9: 1,7 => CTR => F9: 2,4,8
* CNT   5 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:

* DIS # F5: 6,8 => CTR => F5: 1,7
* DIS F5: 1,7 # E6: 6,8 => CTR => E6: 1
* DIS F5: 1,7 + E6: 1 # F4: 5 => CTR => F4: 6,8
* DIS F5: 1,7 + E6: 1 + F4: 6,8 # B8: 1,7 => CTR => B8: 5,6
* PRF F5: 1,7 + E6: 1 + F4: 6,8 + B8: 5,6 # A9: 1,7 => SOL
* STA F5: 1,7 + E6: 1 + F4: 6,8 + B8: 5,6 + A9: 1,7
* CNT   5 HDP CHAINS /  25 HYP OPENED

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

Details

Positions

.8...9.........2.69...5..3...24..17.3...2...5..7..3....3..9...12.4.........6...5. initial
.8.2.951.......29692..5..3..924..1733...2...5..7..3....3..9...12.4........96...5. autosolve
783269514415378296926154837592486173341927685867513942638795421254831769179642358 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
C1: 3,6
C3: 1,6
D3: 1,7
I1: 4,7
E4: 6,8
B9: 1,7
H8: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H6,I6: 2.. / H6 = 2  =>  7 pairs (_) / I6 = 2  =>  7 pairs (_)
F7,F9: 2.. / F7 = 2  =>  7 pairs (_) / F9 = 2  =>  7 pairs (_)
H7,I9: 2.. / H7 = 2  =>  7 pairs (_) / I9 = 2  =>  7 pairs (_)
F7,H7: 2.. / F7 = 2  =>  7 pairs (_) / H7 = 2  =>  7 pairs (_)
F9,I9: 2.. / F9 = 2  =>  7 pairs (_) / I9 = 2  =>  7 pairs (_)
H6,H7: 2.. / H6 = 2  =>  7 pairs (_) / H7 = 2  =>  7 pairs (_)
I6,I9: 2.. / I6 = 2  =>  7 pairs (_) / I9 = 2  =>  7 pairs (_)
C1,C2: 3.. / C1 = 3  =>  7 pairs (_) / C2 = 3  =>  0 pairs (X)
G8,G9: 3.. / G8 = 3  => 15 pairs (_) / G9 = 3  =>  7 pairs (_)
C1,E1: 3.. / C1 = 3  =>  7 pairs (_) / E1 = 3  =>  0 pairs (X)
E9,G9: 3.. / E9 = 3  => 15 pairs (_) / G9 = 3  =>  7 pairs (_)
D2,D8: 3.. / D2 = 3  =>  7 pairs (_) / D8 = 3  =>  7 pairs (_)
F4,D6: 5.. / F4 = 5  =>  8 pairs (_) / D6 = 5  => 10 pairs (_)
A4,F4: 5.. / A4 = 5  => 10 pairs (_) / F4 = 5  =>  8 pairs (_)
C2,C7: 5.. / C2 = 5  =>  7 pairs (_) / C7 = 5  => 14 pairs (_)
E1,F3: 6.. / E1 = 6  => 14 pairs (_) / F3 = 6  => 13 pairs (_)
C3,F3: 6.. / C3 = 6  => 14 pairs (_) / F3 = 6  => 13 pairs (_)
D5,F5: 7.. / D5 = 7  =>  0 pairs (X) / F5 = 7  =>  7 pairs (_)
G3,I3: 8.. / G3 = 8  => 10 pairs (_) / I3 = 8  =>  9 pairs (_)
C5,C7: 8.. / C5 = 8  => 11 pairs (_) / C7 = 8  => 11 pairs (_)
D5,D6: 9.. / D5 = 9  =>  7 pairs (_) / D6 = 9  =>  8 pairs (_)
G8,I8: 9.. / G8 = 9  =>  9 pairs (_) / I8 = 9  =>  7 pairs (_)
D5,G5: 9.. / D5 = 9  =>  7 pairs (_) / G5 = 9  =>  8 pairs (_)
I6,I8: 9.. / I6 = 9  =>  9 pairs (_) / I8 = 9  =>  7 pairs (_)
* DURATION: 0:00:27.582277  START: 05:23:18.758277  END: 05:23:46.340554 2017-05-01
* CP COUNT: (24)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,C1,C3,D3,E4,H8,I1)
* .8.2.951.......29692..5..3..924..1733...2...5..7..3....3..9...12.4........96...5.
* PAIR C1: 3,6 ROW 1
E1: 3,6,4,7                              # reduction candidate for 3,6
E1: 4,7                                  # 16 pairs
E1: 3,6                                  # 11 pairs
* PAIR C3: 1,6 ROW 3
F3: 1,6,4,7                              # reduction candidate for 1,6
F3: 4,7                                  # 14 pairs
F3: 1,6                                  # 11 pairs
* PAIR C3: 1,6 COL C
C5: 1,6,8                                # reduction candidate for 1,6
C5: 8                                    # 11 pairs
C5: 1,6                                  # 11 pairs
* PAIR D3: 1,7 BLK 2
D2: 1,7,3,8                              # reduction candidate for 1,7
D2: 1,7                                  # 17 pairs
E2: 1,7,3,4,8                            # reduction candidate for 1,7
E2: 1,7                                  # 11 pairs
F2: 1,7,4,8                              # reduction candidate for 1,7
F2: 1,7                                  # 11 pairs
F3: 1,7,4,6                              # reduction candidate for 1,7
F3: 1,7                                  # 22 pairs
* PAIR D3: 1,7 COL D
D5: 1,7,8,9                              # reduction candidate for 1,7
D5: 1,7                                  # 11 pairs
D8: 1,7,3,5,8                            # reduction candidate for 1,7
D8: 1,7                                  # 11 pairs
* PAIR I1: 4,7 BLK 3
G3: 4,7,8                                # reduction candidate for 4,7
G3: 4,7                                  #  9 pairs
I3: 4,7,8                                # reduction candidate for 4,7
I3: 4,7                                  # 10 pairs
* PAIR I1: 4,7 ROW 1
A1: 4,7,6                                # reduction candidate for 4,7
A1: 4,7                                  # 11 pairs
E1: 4,7,3,6                              # reduction candidate for 4,7
E1: 4,7                                  # 16 pairs
* PAIR I1: 4,7 COL I
I9: 4,7,2,8                              # reduction candidate for 4,7
I9: 4,7                                  #  9 pairs
I9: 2,8                                  #  8 pairs
* PAIR E4: 6,8 BLK 5
F4: 6,8,5                                # reduction candidate for 6,8
F4: 6,8                                  # 10 pairs
F5: 6,8,1,7                              # reduction candidate for 6,8
F5: 6,8 => CTR
* .8326951....3.829692615..3.6924851733.8726945..7913....3589...12645.1.898196...5.
F5: 1,7                                  #  8 pairs
E6: 6,8,1                                # reduction candidate for 6,8
E6: 6,8 => CTR
* .8.2.9517...3.8296921756.3..924.51733...27..5..7..3....3.89...12645.1.898196...5.
E6: 1                                    #  7 pairs
* PAIR E4: 6,8 ROW 4
A4: 6,8,5                                # reduction candidate for 6,8
A4: 5                                    # 10 pairs
A4: 6,8                                  #  8 pairs
* PAIR B9: 1,7 BLK 7
B8: 1,7,5,6                              # reduction candidate for 1,7
B8: 1,7 => CTR
* .8.2.951.......29692..5..3..924..1733.8.2...51.7.83...635.9...12.4......8.96...5.
B8: 5,6                                  #  8 pairs
A9: 1,7,8                                # reduction candidate for 1,7
A9: 1,7                                  # 10 pairs
* PAIR B9: 1,7 ROW 9
E9: 1,7,3,4,8                            # reduction candidate for 1,7
E9: 1,7 => CTR
* .8.2.9517......29692..56.3.692485173348.27.65157963....3..9...126453178981967.35.
E9: 3,4,8                                #  7 pairs
F9: 1,7,2,4,8                            # reduction candidate for 1,7
F9: 1,7 => CTR
* .8.2.951.......29692..56.3.692485173348.2..65157963.2..3..92.41264531.89819647352
F9: 2,4,8                                #  7 pairs
* PAIR B9: 1,7 COL B
B2: 1,7,4,5                              # reduction candidate for 1,7
B2: 1,7                                  # 10 pairs
B2: 4,5                                  #  9 pairs
* PAIR H8: 6,8 BLK 9
G7: 6,8,4,7                              # reduction candidate for 6,8
G7: 6,8                                  # 11 pairs
H7: 6,8,2,4                              # reduction candidate for 6,8
H7: 6,8                                  # 13 pairs
G8: 6,8,3,7,9                            # reduction candidate for 6,8
G8: 6,8                                  # 13 pairs
* PAIR H8: 6,8 COL H
H5: 6,8,4                                # reduction candidate for 6,8
H5: 6,8                                  # 10 pairs
H6: 6,8,2,4                              # reduction candidate for 6,8
H6: 6,8                                  #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0107-base-pr-000.dot
* REASONING
* DIS # F5: 6,8 => CTR => F5: 1,7
* DIS # E6: 6,8 => CTR => E6: 1
* DIS # B8: 1,7 => CTR => B8: 5,6
* DIS # E9: 1,7 => CTR => E9: 3,4,8
* DIS # F9: 1,7 => CTR => F9: 2,4,8
* CNT   5 HDP CHAINS /  39 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,C1,C3,D3,E4,H8,I1)
* .8.2.951.......29692..5..3..924..1733...2...5..7..3....3..9...12.4........96...5.
* PAIR C1: 3,6 ROW 1
E1: 3,6,4,7                              # reduction candidate for 3,6
E1: 4,7                                  # 16 pairs
E1: 3,6                                  # 11 pairs
* PAIR C3: 1,6 ROW 3
F3: 1,6,4,7                              # reduction candidate for 1,6
F3: 4,7                                  # 14 pairs
F3: 1,6                                  # 11 pairs
* PAIR C3: 1,6 COL C
C5: 1,6,8                                # reduction candidate for 1,6
C5: 8                                    # 11 pairs
C5: 1,6                                  # 11 pairs
* PAIR D3: 1,7 BLK 2
D2: 1,7,3,8                              # reduction candidate for 1,7
D2: 1,7                                  # 17 pairs
E2: 1,7,3,4,8                            # reduction candidate for 1,7
E2: 1,7                                  # 11 pairs
F2: 1,7,4,8                              # reduction candidate for 1,7
F2: 1,7                                  # 11 pairs
F3: 1,7,4,6                              # reduction candidate for 1,7
F3: 1,7                                  # 22 pairs
* PAIR D3: 1,7 COL D
D5: 1,7,8,9                              # reduction candidate for 1,7
D5: 1,7                                  # 11 pairs
D8: 1,7,3,5,8                            # reduction candidate for 1,7
D8: 1,7                                  # 11 pairs
* PAIR I1: 4,7 BLK 3
G3: 4,7,8                                # reduction candidate for 4,7
G3: 4,7                                  #  9 pairs
I3: 4,7,8                                # reduction candidate for 4,7
I3: 4,7                                  # 10 pairs
* PAIR I1: 4,7 ROW 1
A1: 4,7,6                                # reduction candidate for 4,7
A1: 4,7                                  # 11 pairs
E1: 4,7,3,6                              # reduction candidate for 4,7
E1: 4,7                                  # 16 pairs
* PAIR I1: 4,7 COL I
I9: 4,7,2,8                              # reduction candidate for 4,7
I9: 4,7                                  #  9 pairs
I9: 2,8                                  #  8 pairs
* PAIR E4: 6,8 BLK 5
F4: 6,8,5                                # reduction candidate for 6,8
F4: 6,8                                  # 10 pairs
F5: 6,8,1,7                              # reduction candidate for 6,8
F5: 6,8 => CTR
* .8326951....3.829692615..3.6924851733.8726945..7913....3589...12645.1.898196...5.
E6: 6,8,1                                # reduction candidate for 6,8
E6: 6,8 => CTR
* .8.2.9517...3.8296921756.3..924.51733...27..5..7..3....3.89...12645.1.898196...5.
* RESTART
* PAIR E4: 6,8 BLK 5
F4: 6,8,5                                # reduction candidate for 6,8
F4: 5 => CTR
* .8.2.951.......296921756.3.892465173316.27..5..7.13....3859...12.4........96...5.
* PAIR B9: 1,7 BLK 7
B8: 1,7,5,6                              # reduction candidate for 1,7
B8: 1,7 => CTR
* .8.2.951.153...29692..5..3.5924..1733.8927..5..7513...635.9...12.4..5...8.96...5.
A9: 1,7,8                                # reduction candidate for 1,7
A9: 1,7 => SOLVED
* 783269514415378296926154837592486173341927685867513942638795421254831769179642358
* DURATION: 0:00:18.419982  START: 05:24:11.626500  END: 05:24:30.046482 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0107-base-pr-001.dot
* REASONING
* DIS # F5: 6,8 => CTR => F5: 1,7
* DIS F5: 1,7 # E6: 6,8 => CTR => E6: 1
* DIS F5: 1,7 + E6: 1 # F4: 5 => CTR => F4: 6,8
* DIS F5: 1,7 + E6: 1 + F4: 6,8 # B8: 1,7 => CTR => B8: 5,6
* PRF F5: 1,7 + E6: 1 + F4: 6,8 + B8: 5,6 # A9: 1,7 => SOL
* STA F5: 1,7 + E6: 1 + F4: 6,8 + B8: 5,6 + A9: 1,7
* CNT   5 HDP CHAINS /  25 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=107

Solution

position: 783269514415378296926154837592486173341927685867513942638795421254831769179642358 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 # E1: 3,6 => UNS
* INC # E1: 4,7 => UNS
* INC # F3: 1,6 => UNS
* INC # F3: 4,7 => UNS
* INC # C5: 1,6 => UNS
* INC # C5: 8 => UNS
* INC # D2: 1,7 => UNS
* INC # E2: 1,7 => UNS
* INC # F2: 1,7 => UNS
* INC # F3: 1,7 => UNS
* INC # D5: 1,7 => UNS
* INC # D8: 1,7 => UNS
* INC # G3: 4,7 => UNS
* INC # I3: 4,7 => UNS
* INC # A1: 4,7 => UNS
* INC # E1: 4,7 => UNS
* INC # I9: 4,7 => UNS
* INC # I9: 2,8 => UNS
* INC # F4: 6,8 => UNS
* DIS # F5: 6,8 => CTR => F5: 1,7
* INC # F5: 1,7 => UNS
* DIS # E6: 6,8 => CTR => E6: 1
* INC # E6: 1 => UNS
* INC # A4: 6,8 => UNS
* INC # A4: 5 => UNS
* DIS # B8: 1,7 => CTR => B8: 5,6
* INC # B8: 5,6 => UNS
* INC # A9: 1,7 => UNS
* DIS # E9: 1,7 => CTR => E9: 3,4,8
* INC # E9: 3,4,8 => UNS
* DIS # F9: 1,7 => CTR => F9: 2,4,8
* INC # F9: 2,4,8 => UNS
* INC # B2: 1,7 => UNS
* INC # B2: 4,5 => UNS
* INC # G7: 6,8 => UNS
* INC # H7: 6,8 => UNS
* INC # G8: 6,8 => UNS
* INC # H5: 6,8 => UNS
* INC # H6: 6,8 => UNS
* CNT  39 HDP CHAINS /  39 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E1: 3,6 => UNS
* INC # E1: 4,7 => UNS
* INC # F3: 1,6 => UNS
* INC # F3: 4,7 => UNS
* INC # C5: 1,6 => UNS
* INC # C5: 8 => UNS
* INC # D2: 1,7 => UNS
* INC # E2: 1,7 => UNS
* INC # F2: 1,7 => UNS
* INC # F3: 1,7 => UNS
* INC # D5: 1,7 => UNS
* INC # D8: 1,7 => UNS
* INC # G3: 4,7 => UNS
* INC # I3: 4,7 => UNS
* INC # A1: 4,7 => UNS
* INC # E1: 4,7 => UNS
* INC # I9: 4,7 => UNS
* INC # I9: 2,8 => UNS
* INC # F4: 6,8 => UNS
* DIS # F5: 6,8 => CTR => F5: 1,7
* DIS F5: 1,7 # E6: 6,8 => CTR => E6: 1
* INC F5: 1,7 + E6: 1 # F4: 6,8 => UNS
* DIS F5: 1,7 + E6: 1 # F4: 5 => CTR => F4: 6,8
* DIS F5: 1,7 + E6: 1 + F4: 6,8 # B8: 1,7 => CTR => B8: 5,6
* PRF F5: 1,7 + E6: 1 + F4: 6,8 + B8: 5,6 # A9: 1,7 => SOL
* STA F5: 1,7 + E6: 1 + F4: 6,8 + B8: 5,6 + A9: 1,7
* CNT  25 HDP CHAINS /  25 HYP OPENED