Analysis of zz-www.sudokuwiki.org-0003-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=3

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=3

position: .3...5.4.5...1.6.3..6......8....1.5.....6.....9.7....8......4..1.4.8...2.5..7..9. initial

Autosolve

position: .3.6.5.4.5...1.6.3..6......8....1.5.....6.....9.7....8......4..1.4.8...2.5..7..9. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C1: 2,9 => CTR => C1: 1,7,8
* DIS # G1: 2,9 => CTR => G1: 1,7,8
* DIS # B7: 6,7 => CTR => B7: 2,8
* DIS # B4: 2,4 => CTR => B4: 6,7
* PRF # I7: 1,6 => SOL
* CNT   5 HDP CHAINS /  22 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 # C1: 2,9 => CTR => C1: 1,7,8
* DIS C1: 1,7,8 # G1: 2,9 => CTR => G1: 1,7,8
* DIS C1: 1,7,8 + G1: 1,7,8 # B7: 6,7 => CTR => B7: 2,8
* DIS C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 # B4: 2,4 => CTR => B4: 6,7
* PRF C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 # I7: 1,6 => SOL
* STA C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 + I7: 1,6
* CNT   5 HDP CHAINS /  35 HYP OPENED

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

Details

Positions

.3...5.4.5...1.6.3..6......8....1.5.....6.....9.7....8......4..1.4.8...2.5..7..9. initial
.3.6.5.4.5...1.6.3..6......8....1.5.....6.....9.7....8......4..1.4.8...2.5..7..9. autosolve
938625147547819623216347985863291754725468319491753268689532471174986532352174896 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (3)
E1: 2,9
B8: 6,7
I9: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C1,B3: 1.. / C1 = 1  =>  6 pairs (_) / B3 = 1  =>  5 pairs (_)
D7,D9: 1.. / D7 = 1  =>  3 pairs (_) / D9 = 1  => 18 pairs (_)
B3,B5: 1.. / B3 = 1  =>  5 pairs (_) / B5 = 1  =>  6 pairs (_)
I4,I5: 4.. / I4 = 4  =>  7 pairs (_) / I5 = 4  =>  5 pairs (_)
D9,F9: 4.. / D9 = 4  =>  3 pairs (_) / F9 = 4  =>  4 pairs (_)
G3,I3: 5.. / G3 = 5  =>  6 pairs (_) / I3 = 5  =>  4 pairs (_)
C5,C6: 5.. / C5 = 5  =>  4 pairs (_) / C6 = 5  =>  4 pairs (_)
D5,E6: 5.. / D5 = 5  =>  4 pairs (_) / E6 = 5  =>  4 pairs (_)
I7,G8: 5.. / I7 = 5  =>  6 pairs (_) / G8 = 5  =>  4 pairs (_)
C5,D5: 5.. / C5 = 5  =>  4 pairs (_) / D5 = 5  =>  4 pairs (_)
C6,E6: 5.. / C6 = 5  =>  4 pairs (_) / E6 = 5  =>  4 pairs (_)
D8,G8: 5.. / D8 = 5  =>  6 pairs (_) / G8 = 5  =>  4 pairs (_)
E6,E7: 5.. / E6 = 5  =>  4 pairs (_) / E7 = 5  =>  4 pairs (_)
G3,G8: 5.. / G3 = 5  =>  6 pairs (_) / G8 = 5  =>  4 pairs (_)
I3,I7: 5.. / I3 = 5  =>  4 pairs (_) / I7 = 5  =>  6 pairs (_)
B4,A6: 6.. / B4 = 6  =>  6 pairs (_) / A6 = 6  =>  0 pairs (X)
I4,H6: 6.. / I4 = 6  =>  0 pairs (X) / H6 = 6  =>  6 pairs (_)
B4,I4: 6.. / B4 = 6  =>  6 pairs (_) / I4 = 6  =>  0 pairs (X)
A6,H6: 6.. / A6 = 6  =>  0 pairs (X) / H6 = 6  =>  6 pairs (_)
F2,F3: 7.. / F2 = 7  =>  4 pairs (_) / F3 = 7  =>  3 pairs (_)
D5,F5: 8.. / D5 = 8  =>  6 pairs (_) / F5 = 8  =>  3 pairs (_)
H7,G9: 8.. / H7 = 8  =>  5 pairs (_) / G9 = 8  =>  6 pairs (_)
C1,G1: 8.. / C1 = 8  =>  6 pairs (_) / G1 = 8  =>  5 pairs (_)
C9,G9: 8.. / C9 = 8  =>  5 pairs (_) / G9 = 8  =>  6 pairs (_)
A7,C7: 9.. / A7 = 9  =>  4 pairs (_) / C7 = 9  =>  5 pairs (_)
D8,F8: 9.. / D8 = 9  =>  5 pairs (_) / F8 = 9  =>  4 pairs (_)
* DURATION: 0:00:29.287567  START: 03:23:18.985309  END: 03:23:48.272876 2017-05-01
* CP COUNT: (26)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,E1,I9)
* .3.6.5.4.5...1.6.3..6......8....1.5.....6.....9.7....8......4..1.4.8...2.5..7..9.
* PAIR E1: 2,9 BLK 2
D2: 2,9,4,8                              # reduction candidate for 2,9
D2: 2,9                                  #  5 pairs
F2: 2,9,4,7,8                            # reduction candidate for 2,9
F2: 2,9                                  #  6 pairs
D3: 2,9,3,4,8                            # reduction candidate for 2,9
D3: 2,9                                  #  7 pairs
E3: 2,9,3,4                              # reduction candidate for 2,9
E3: 2,9                                  #  9 pairs
F3: 2,9,3,4,7,8                          # reduction candidate for 2,9
F3: 2,9                                  #  8 pairs
* PAIR E1: 2,9 ROW 1
A1: 2,9,7                                # reduction candidate for 2,9
A1: 2,9                                  #  7 pairs
C1: 2,9,1,7,8                            # reduction candidate for 2,9
C1: 2,9 => CTR
* 73.6.584158..1.6.3416......86...1.5..4..6.....9.7...68......48.1.4.8...2.58.7.196
C1: 1,7,8                                #  3 pairs
G1: 2,9,1,7,8                            # reduction candidate for 2,9
G1: 2,9 => CTR
* 7386.5.415.2.1.6.3916.....586...1.5..2..6..7..9.7...68689...417174986532253174896
G1: 1,7,8                                #  3 pairs
* PAIR E1: 2,9 COL E
E4: 2,9,3,4                              # reduction candidate for 2,9
E4: 2,9                                  #  6 pairs
E4: 3,4                                  #  5 pairs
* PAIR B8: 6,7 BLK 7
A7: 6,7,2,3,9                            # reduction candidate for 6,7
A7: 6,7                                  #  9 pairs
B7: 6,7,2,8                              # reduction candidate for 6,7
B7: 6,7 => CTR
* 731625849529814673486..7..584.2.1.56.1.5689.469574...8963152487174.89562258476391
B7: 2,8                                  #  4 pairs
* PAIR B8: 6,7 ROW 8
H8: 6,7,3                                # reduction candidate for 6,7
H8: 3                                    #  7 pairs
H8: 6,7                                  #  6 pairs
* PAIR B8: 6,7 COL B
B4: 6,7,2,4                              # reduction candidate for 6,7
B4: 2,4 => CTR
* .3.625.49529814673486..7..584.291756.1.5689.4695743..896.152487174389562.58476391
B4: 6,7                                  #  5 pairs
* PAIR I9: 1,6 BLK 9
H7: 1,6,3,7,8                            # reduction candidate for 1,6
H7: 1,6                                  # 11 pairs
I7: 1,6,5,7                              # reduction candidate for 1,6
I7: 1,6 => SOLVED
* 938625147547819623216347985863291754725468319491753268689532471174986532352174896
I7: 5,7                                  #  4 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0003-base-pr-000.dot
* REASONING
* DIS # C1: 2,9 => CTR => C1: 1,7,8
* DIS # G1: 2,9 => CTR => G1: 1,7,8
* DIS # B7: 6,7 => CTR => B7: 2,8
* DIS # B4: 2,4 => CTR => B4: 6,7
* PRF # I7: 1,6 => SOL
* CNT   5 HDP CHAINS /  22 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,E1,I9)
* .3.6.5.4.5...1.6.3..6......8....1.5.....6.....9.7....8......4..1.4.8...2.5..7..9.
* PAIR E1: 2,9 BLK 2
D2: 2,9,4,8                              # reduction candidate for 2,9
D2: 2,9                                  #  5 pairs
F2: 2,9,4,7,8                            # reduction candidate for 2,9
F2: 2,9                                  #  6 pairs
D3: 2,9,3,4,8                            # reduction candidate for 2,9
D3: 2,9                                  #  7 pairs
E3: 2,9,3,4                              # reduction candidate for 2,9
E3: 2,9                                  #  9 pairs
F3: 2,9,3,4,7,8                          # reduction candidate for 2,9
F3: 2,9                                  #  8 pairs
* PAIR E1: 2,9 ROW 1
A1: 2,9,7                                # reduction candidate for 2,9
A1: 2,9                                  #  7 pairs
C1: 2,9,1,7,8                            # reduction candidate for 2,9
C1: 2,9 => CTR
* 73.6.584158..1.6.3416......86...1.5..4..6.....9.7...68......48.1.4.8...2.58.7.196
G1: 2,9,1,7,8                            # reduction candidate for 2,9
G1: 2,9 => CTR
* 7386.5.415.2.1.6.3916.....586...1.5..2..6..7..9.7...68689...417174986532253174896
* RESTART
* PAIR E1: 2,9 ROW 1
A1: 2,9,7                                # reduction candidate for 2,9
A1: 2,9                                  #  7 pairs
A1: 7                                    #  5 pairs
* PAIR E1: 2,9 COL E
E4: 2,9,3,4                              # reduction candidate for 2,9
E4: 2,9                                  #  6 pairs
E4: 3,4                                  #  5 pairs
* PAIR RESTART
* PAIR E1: 2,9 BLK 2
D2: 2,9,4,8                              # reduction candidate for 2,9
D2: 2,9                                  #  5 pairs
F2: 2,9,4,7,8                            # reduction candidate for 2,9
F2: 2,9                                  #  6 pairs
D3: 2,9,3,4,8                            # reduction candidate for 2,9
D3: 2,9                                  #  7 pairs
E3: 2,9,3,4                              # reduction candidate for 2,9
E3: 2,9                                  #  9 pairs
F3: 2,9,3,4,7,8                          # reduction candidate for 2,9
F3: 2,9                                  #  8 pairs
* PAIR E1: 2,9 ROW 1
A1: 2,9,7                                # reduction candidate for 2,9
A1: 2,9                                  #  7 pairs
A1: 7                                    #  5 pairs
* PAIR E1: 2,9 COL E
E4: 2,9,3,4                              # reduction candidate for 2,9
E4: 2,9                                  #  6 pairs
E4: 3,4                                  #  5 pairs
* PAIR B8: 6,7 BLK 7
A7: 6,7,2,3,9                            # reduction candidate for 6,7
A7: 6,7                                  #  9 pairs
B7: 6,7,2,8                              # reduction candidate for 6,7
B7: 6,7 => CTR
* 731625849529814673486..7..584.2.1.56.1.5689.469574...8963152487174.89562258476391
* RESTART
* PAIR B8: 6,7 BLK 7
A7: 6,7,2,3,9                            # reduction candidate for 6,7
A7: 6,7                                  #  9 pairs
A7: 2,3,9                                #  4 pairs
* PAIR B8: 6,7 ROW 8
H8: 6,7,3                                # reduction candidate for 6,7
H8: 3                                    #  8 pairs
H8: 6,7                                  #  7 pairs
* PAIR B8: 6,7 COL B
B4: 6,7,2,4                              # reduction candidate for 6,7
B4: 2,4 => CTR
* .3.6.5.4.5...1.6.34.6......84...1.56....6...469.74...8...15.467164.8.532.5.476891
* PAIR RESTART
* PAIR B8: 6,7 BLK 7
A7: 6,7,2,3,9                            # reduction candidate for 6,7
A7: 6,7                                  # 10 pairs
A7: 2,3,9                                #  5 pairs
* PAIR B8: 6,7 ROW 8
H8: 6,7,3                                # reduction candidate for 6,7
H8: 3                                    #  9 pairs
H8: 6,7                                  #  8 pairs
* PAIR I9: 1,6 BLK 9
H7: 1,6,3,7,8                            # reduction candidate for 1,6
H7: 1,6                                  # 15 pairs
I7: 1,6,5,7                              # reduction candidate for 1,6
I7: 1,6 => SOLVED
* 938625147547819623216347985863291754725468319491753268689532471174986532352174896
* DURATION: 0:00:23.940118  START: 03:24:03.174129  END: 03:24:27.114247 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0003-base-pr-001.dot
* REASONING
* DIS # C1: 2,9 => CTR => C1: 1,7,8
* DIS C1: 1,7,8 # G1: 2,9 => CTR => G1: 1,7,8
* DIS C1: 1,7,8 + G1: 1,7,8 # B7: 6,7 => CTR => B7: 2,8
* DIS C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 # B4: 2,4 => CTR => B4: 6,7
* PRF C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 # I7: 1,6 => SOL
* STA C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 + I7: 1,6
* CNT   5 HDP CHAINS /  35 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=3

Solution

position: 938625147547819623216347985863291754725468319491753268689532471174986532352174896 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 # D2: 2,9 => UNS
* INC # F2: 2,9 => UNS
* INC # D3: 2,9 => UNS
* INC # E3: 2,9 => UNS
* INC # F3: 2,9 => UNS
* INC # A1: 2,9 => UNS
* DIS # C1: 2,9 => CTR => C1: 1,7,8
* INC # C1: 1,7,8 => UNS
* DIS # G1: 2,9 => CTR => G1: 1,7,8
* INC # G1: 1,7,8 => UNS
* INC # E4: 2,9 => UNS
* INC # E4: 3,4 => UNS
* INC # A7: 6,7 => UNS
* DIS # B7: 6,7 => CTR => B7: 2,8
* INC # B7: 2,8 => UNS
* INC # H8: 6,7 => UNS
* INC # H8: 3 => UNS
* INC # B4: 6,7 => UNS
* DIS # B4: 2,4 => CTR => B4: 6,7
* INC # H7: 1,6 => UNS
* PRF # I7: 1,6 => SOL
* INC # I7: 5,7 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D2: 2,9 => UNS
* INC # F2: 2,9 => UNS
* INC # D3: 2,9 => UNS
* INC # E3: 2,9 => UNS
* INC # F3: 2,9 => UNS
* INC # A1: 2,9 => UNS
* DIS # C1: 2,9 => CTR => C1: 1,7,8
* DIS C1: 1,7,8 # G1: 2,9 => CTR => G1: 1,7,8
* INC C1: 1,7,8 + G1: 1,7,8 # A1: 2,9 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 # A1: 7 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 # E4: 2,9 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 # E4: 3,4 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 # D2: 2,9 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 # F2: 2,9 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 # D3: 2,9 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 # E3: 2,9 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 # F3: 2,9 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 # A1: 2,9 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 # A1: 7 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 # E4: 2,9 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 # E4: 3,4 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 # A7: 6,7 => UNS
* DIS C1: 1,7,8 + G1: 1,7,8 # B7: 6,7 => CTR => B7: 2,8
* INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 # A7: 6,7 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 # A7: 2,3,9 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 # H8: 6,7 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 # H8: 3 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 # B4: 6,7 => UNS
* DIS C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 # B4: 2,4 => CTR => B4: 6,7
* INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 # A7: 6,7 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 # A7: 2,3,9 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 # H8: 6,7 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 # H8: 3 => UNS
* INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 # H7: 1,6 => UNS
* PRF C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 # I7: 1,6 => SOL
* STA C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 + I7: 1,6
* CNT  35 HDP CHAINS /  35 HYP OPENED