Analysis of zz-www.sudokuwiki.org-0121-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=121

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=121

position: 5.........1.67..9...7.2.4.......1..9.3..6..2.1..7.......8.4.5...2..36.7....9....2 initial

Autosolve

position: 5.........1.67..9...7.2.4.......1..9.3..6..2.1..7....4..8.4.5..42..3697....9...42 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C6: 5,9 => CTR => C6: 2,6
* DIS # E6: 5,8 => CTR => E6: 9
* DIS # B4: 5,8 => CTR => B4: 4,6,7
* DIS # D8: 8 => CTR => D8: 1,5
* DIS # I1: 1,8 => CTR => I1: 3,6,7
* CNT   5 HDP CHAINS /  26 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 # C6: 5,9 => CTR => C6: 2,6
* DIS C6: 2,6 # E6: 5,8 => CTR => E6: 9
* DIS C6: 2,6 + E6: 9 # B4: 5,8 => CTR => B4: 4,6,7
* PRF C6: 2,6 + E6: 9 + B4: 4,6,7 # E9: 1 => SOL
* STA C6: 2,6 + E6: 9 + B4: 4,6,7 + E9: 1
* CNT   4 HDP CHAINS /  15 HYP OPENED

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

Details

Positions

5.........1.67..9...7.2.4.......1..9.3..6..2.1..7.......8.4.5...2..36.7....9....2 initial
5.........1.67..9...7.2.4.......1..9.3..6..2.1..7....4..8.4.5..42..3697....9...42 autosolve
563489217214675893987123456842351769739864125156792384698247531421536978375918642 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
C5: 5,9
D4: 2,3
E4: 5,8
F6: 2,3
C8: 1,5
D7: 1,2
F7: 2,7
I8: 1,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G5,I5: 1.. / G5 = 1  =>  8 pairs (_) / I5 = 1  => 11 pairs (_)
C8,C9: 1.. / C8 = 1  => 10 pairs (_) / C9 = 1  => 12 pairs (_)
E1,E9: 1.. / E1 = 1  =>  9 pairs (_) / E9 = 1  =>  9 pairs (_)
G1,G2: 2.. / G1 = 2  =>  9 pairs (_) / G2 = 2  => 11 pairs (_)
D4,F6: 2.. / D4 = 2  => 19 pairs (_) / F6 = 2  =>  8 pairs (_)
D7,F7: 2.. / D7 = 2  =>  8 pairs (_) / F7 = 2  => 19 pairs (_)
C1,G1: 2.. / C1 = 2  => 11 pairs (_) / G1 = 2  =>  9 pairs (_)
C6,F6: 2.. / C6 = 2  => 19 pairs (_) / F6 = 2  =>  8 pairs (_)
A2,A4: 2.. / A2 = 2  => 10 pairs (_) / A4 = 2  =>  9 pairs (_)
D4,D7: 2.. / D4 = 2  => 19 pairs (_) / D7 = 2  =>  8 pairs (_)
F6,F7: 2.. / F6 = 2  =>  8 pairs (_) / F7 = 2  => 19 pairs (_)
D4,F6: 3.. / D4 = 3  =>  8 pairs (_) / F6 = 3  => 19 pairs (_)
B4,C4: 4.. / B4 = 4  =>  9 pairs (_) / C4 = 4  =>  9 pairs (_)
D5,F5: 4.. / D5 = 4  =>  8 pairs (_) / F5 = 4  => 11 pairs (_)
C2,F2: 4.. / C2 = 4  =>  9 pairs (_) / F2 = 4  =>  9 pairs (_)
B1,B4: 4.. / B1 = 4  =>  9 pairs (_) / B4 = 4  =>  9 pairs (_)
D1,D5: 4.. / D1 = 4  => 11 pairs (_) / D5 = 4  =>  8 pairs (_)
F2,I2: 5.. / F2 = 5  => 11 pairs (_) / I2 = 5  =>  8 pairs (_)
C8,D8: 5.. / C8 = 5  => 12 pairs (_) / D8 = 5  => 10 pairs (_)
G1,I1: 7.. / G1 = 7  =>  0 pairs (X) / I1 = 7  =>  8 pairs (_)
F7,F9: 7.. / F7 = 7  =>  8 pairs (_) / F9 = 7  => 19 pairs (_)
I1,I5: 7.. / I1 = 7  =>  8 pairs (_) / I5 = 7  =>  0 pairs (X)
I8,G9: 8.. / I8 = 8  =>  9 pairs (_) / G9 = 8  =>  0 pairs (X)
D8,I8: 8.. / D8 = 8  =>  0 pairs (X) / I8 = 8  =>  9 pairs (_)
F5,E6: 9.. / F5 = 9  =>  0 pairs (X) / E6 = 9  =>  9 pairs (_)
A7,B7: 9.. / A7 = 9  => 10 pairs (_) / B7 = 9  =>  9 pairs (_)
E1,E6: 9.. / E1 = 9  =>  0 pairs (X) / E6 = 9  =>  9 pairs (_)
* DURATION: 0:00:34.639801  START: 05:42:49.701819  END: 05:43:24.341620 2017-05-01
* CP COUNT: (27)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,C8,D4,D7,E4,F6,F7,I8)
* 5.........1.67..9...7.2.4.......1..9.3..6..2.1..7....4..8.4.5..42..3697....9...42
* PAIR C5: 5,9 BLK 4
B6: 5,9,6,8                              # reduction candidate for 5,9
B6: 5,9                                  # 11 pairs
C6: 5,9,2,6                              # reduction candidate for 5,9
C6: 5,9 => CTR
* 54........1.6748959871254..2743.16.9835469.2.1697.23.4.982475..42153697875.918.42
C6: 2,6                                  #  9 pairs
* PAIR C5: 5,9 ROW 5
F5: 5,9,4,8                              # reduction candidate for 5,9
F5: 5,9                                  # 12 pairs
F5: 4,8                                  # 10 pairs
* PAIR E4: 5,8 BLK 5
D5: 5,8,4                                # reduction candidate for 5,8
D5: 5,8                                  # 11 pairs
F5: 5,8,4,9                              # reduction candidate for 5,8
F5: 5,8                                  # 10 pairs
E6: 5,8,9                                # reduction candidate for 5,8
E6: 5,8 => CTR
* 54..93....1.6748959871254..2743.16.9835469.2.1697.23.4.982475..42153697875.918.42
E6: 9                                    #  9 pairs
* PAIR E4: 5,8 ROW 4
B4: 5,8,4,6,7                            # reduction candidate for 5,8
B4: 5,8 => CTR
* 54......7813674295..7.2.4..254381769739465.2.186792354..82475..42..3697.37.958642
B4: 4,6,7                                #  8 pairs
H4: 5,8,3,6                              # reduction candidate for 5,8
H4: 5,8                                  #  9 pairs
* PAIR E4: 5,8 COL E
E9: 5,8,1                                # reduction candidate for 5,8
E9: 5,8                                  #  9 pairs
E9: 1                                    #  9 pairs
* PAIR C8: 1,5 BLK 7
C9: 1,5,3,6                              # reduction candidate for 1,5
C9: 1,5                                  # 13 pairs
C9: 3,6                                  # 11 pairs
* PAIR C8: 1,5 ROW 8
D8: 1,5,8                                # reduction candidate for 1,5
D8: 8 => CTR
* 5...1.2.721.67.39...732.41....281739739564128182793654978142563425836971361957842
D8: 1,5                                  #  9 pairs
* PAIR I8: 1,8 BLK 9
G9: 1,8,3,6                              # reduction candidate for 1,8
G9: 1,8                                  # 19 pairs
G9: 3,6                                  #  8 pairs
* PAIR I8: 1,8 ROW 8
D8: 1,8,5                                # reduction candidate for 1,8
D8: 1,8                                  # 12 pairs
D8: 5                                    # 10 pairs
* PAIR I8: 1,8 COL I
I1: 1,8,3,6,7                            # reduction candidate for 1,8
I1: 1,8 => CTR
* 542...76..13674295..7.2.4..2743.16.9.3.46.1271..7.2..439824751642..369787..9..342
I1: 3,6,7                                #  8 pairs
I3: 1,8,3,5,6                            # reduction candidate for 1,8
I3: 1,8                                  # 12 pairs
I5: 1,8,5,7                              # reduction candidate for 1,8
I5: 1,8                                  # 11 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0121-base-pr-000.dot
* REASONING
* DIS # C6: 5,9 => CTR => C6: 2,6
* DIS # E6: 5,8 => CTR => E6: 9
* DIS # B4: 5,8 => CTR => B4: 4,6,7
* DIS # D8: 8 => CTR => D8: 1,5
* DIS # I1: 1,8 => CTR => I1: 3,6,7
* CNT   5 HDP CHAINS /  26 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,C8,D4,D7,E4,F6,F7,I8)
* 5.........1.67..9...7.2.4.......1..9.3..6..2.1..7....4..8.4.5..42..3697....9...42
* PAIR C5: 5,9 BLK 4
B6: 5,9,6,8                              # reduction candidate for 5,9
B6: 5,9                                  # 11 pairs
C6: 5,9,2,6                              # reduction candidate for 5,9
C6: 5,9 => CTR
* 54........1.6748959871254..2743.16.9835469.2.1697.23.4.982475..42153697875.918.42
* RESTART
* PAIR C5: 5,9 BLK 4
B6: 5,9,6,8                              # reduction candidate for 5,9
B6: 6,8                                  # 11 pairs
B6: 5,9                                  # 11 pairs
* PAIR C5: 5,9 ROW 5
F5: 5,9,4,8                              # reduction candidate for 5,9
F5: 5,9                                  # 13 pairs
F5: 4,8                                  # 11 pairs
* PAIR E4: 5,8 BLK 5
D5: 5,8,4                                # reduction candidate for 5,8
D5: 5,8                                  # 12 pairs
F5: 5,8,4,9                              # reduction candidate for 5,8
F5: 5,8                                  # 11 pairs
E6: 5,8,9                                # reduction candidate for 5,8
E6: 5,8 => CTR
* 5...9.....1.67..9...7.2.4.......1..9.39.6..2.1..7....4..8.4.5..42..3697....91..42
* PAIR E4: 5,8 ROW 4
B4: 5,8,4,6,7                            # reduction candidate for 5,8
B4: 5,8 => CTR
* 54..19..7813674295..7523481254381769739465.2.1.6792354..82475..42..3697..7.958.42
H4: 5,8,3,6                              # reduction candidate for 5,8
H4: 5,8                                  # 16 pairs
* RESTART
* PAIR E4: 5,8 ROW 4
H4: 5,8,3,6                              # reduction candidate for 5,8
H4: 5,8                                  # 16 pairs
H4: 3,6                                  # 11 pairs
* PAIR E4: 5,8 COL E
E9: 5,8,1                                # reduction candidate for 5,8
E9: 1 => SOLVED
* 563489217214675893987123456842351769739864125156792384698247531421536978375918642
* DURATION: 0:00:12.531465  START: 05:43:43.237252  END: 05:43:55.768717 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0121-base-pr-001.dot
* REASONING
* DIS # C6: 5,9 => CTR => C6: 2,6
* DIS C6: 2,6 # E6: 5,8 => CTR => E6: 9
* DIS C6: 2,6 + E6: 9 # B4: 5,8 => CTR => B4: 4,6,7
* PRF C6: 2,6 + E6: 9 + B4: 4,6,7 # E9: 1 => SOL
* STA C6: 2,6 + E6: 9 + B4: 4,6,7 + E9: 1
* CNT   4 HDP CHAINS /  15 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=121

Solution

position: 563489217214675893987123456842351769739864125156792384698247531421536978375918642 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 # B6: 5,9 => UNS
* DIS # C6: 5,9 => CTR => C6: 2,6
* INC # C6: 2,6 => UNS
* INC # F5: 5,9 => UNS
* INC # F5: 4,8 => UNS
* INC # D5: 5,8 => UNS
* INC # F5: 5,8 => UNS
* DIS # E6: 5,8 => CTR => E6: 9
* INC # E6: 9 => UNS
* DIS # B4: 5,8 => CTR => B4: 4,6,7
* INC # B4: 4,6,7 => UNS
* INC # H4: 5,8 => UNS
* INC # E9: 5,8 => UNS
* INC # E9: 1 => UNS
* INC # C9: 1,5 => UNS
* INC # C9: 3,6 => UNS
* INC # D8: 1,5 => UNS
* DIS # D8: 8 => CTR => D8: 1,5
* INC # G9: 1,8 => UNS
* INC # G9: 3,6 => UNS
* INC # D8: 1,8 => UNS
* INC # D8: 5 => UNS
* DIS # I1: 1,8 => CTR => I1: 3,6,7
* INC # I1: 3,6,7 => UNS
* INC # I3: 1,8 => UNS
* INC # I5: 1,8 => UNS
* CNT  26 HDP CHAINS /  26 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B6: 5,9 => UNS
* DIS # C6: 5,9 => CTR => C6: 2,6
* INC C6: 2,6 # B6: 5,9 => UNS
* INC C6: 2,6 # B6: 6,8 => UNS
* INC C6: 2,6 # F5: 5,9 => UNS
* INC C6: 2,6 # F5: 4,8 => UNS
* INC C6: 2,6 # D5: 5,8 => UNS
* INC C6: 2,6 # F5: 5,8 => UNS
* DIS C6: 2,6 # E6: 5,8 => CTR => E6: 9
* DIS C6: 2,6 + E6: 9 # B4: 5,8 => CTR => B4: 4,6,7
* INC C6: 2,6 + E6: 9 + B4: 4,6,7 # H4: 5,8 => UNS
* INC C6: 2,6 + E6: 9 + B4: 4,6,7 # H4: 5,8 => UNS
* INC C6: 2,6 + E6: 9 + B4: 4,6,7 # H4: 3,6 => UNS
* INC C6: 2,6 + E6: 9 + B4: 4,6,7 # E9: 5,8 => UNS
* PRF C6: 2,6 + E6: 9 + B4: 4,6,7 # E9: 1 => SOL
* STA C6: 2,6 + E6: 9 + B4: 4,6,7 + E9: 1
* CNT  15 HDP CHAINS /  15 HYP OPENED