Analysis of zz-www.sudokuwiki.org-0001-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=1

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=1

position: ......9...7.2.65...8...9.4....5..4.2.1.....7.4.6..2....2.8...9...83.7.2...1...... initial

Autosolve

position: ......9...7.2.65...8...924....5..4.2.1.....7.4.6..2....2.8...9...83.7.2...1.2.... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B1: 3,5 => CTR => B1: 4,6
* DIS # A3: 3,5 => CTR => A3: 1,6
* DIS # E3: 1,7 => CTR => E3: 3,5
* DIS # C5: 3,5 => CTR => C5: 2,9
* PRF # D1: 1,7 => SOL
* DIS # D1: 4 => CTR => D1: 1,7
* DIS # E1: 1,7 => CTR => E1: 3,4,5,8
* DIS # E3: 1,7 => CTR => E3: 3,5
* DIS # D6: 1,7 => CTR => D6: 9
* PRF # D6: 9 => SOL
* DIS # A4: 3,9 => CTR => A4: 7,8
* DIS # C4: 3,9 => CTR => C4: 7
* DIS # A5: 3,9 => CTR => A5: 2,5,8
* DIS # C5: 3,9 => CTR => C5: 2,5
* PRF # B6: 3,9 => SOL
* DIS # B6: 5 => CTR => B6: 3,9
* DIS # B9: 3,9 => CTR => B9: 4,5,6
* DIS # E8: 4,5 => CTR => E8: 1,6,9
* PRF # B9: 4,5 => SOL
* DIS # I9: 4,5 => CTR => I9: 3,6,8
* DIS # E8: 1,6 => CTR => E8: 4,5,9
* CNT  21 HDP CHAINS /  50 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 # B1: 3,5 => CTR => B1: 4,6
* DIS B1: 4,6 # A3: 3,5 => CTR => A3: 1,6
* DIS B1: 4,6 + A3: 1,6 # E3: 1,7 => CTR => E3: 3,5
* DIS B1: 4,6 + A3: 1,6 + E3: 3,5 # C5: 3,5 => CTR => C5: 2,9
* DIS B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 # A1: 3,5 => CTR => A1: 1,2,6
* PRF B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 + A1: 1,2,6 # C1: 2,4 => SOL
* STA B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 + A1: 1,2,6 + C1: 2,4
* CNT   6 HDP CHAINS /  14 HYP OPENED

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

Details

Positions

......9...7.2.65...8...9.4....5..4.2.1.....7.4.6..2....2.8...9...83.7.2...1...... initial
......9...7.2.65...8...924....5..4.2.1.....7.4.6..2....2.8...9...83.7.2...1.2.... autosolve
264185937379246518185739246897513462512468379436972851723851694648397125951624783 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
C3: 3,5
D3: 1,7
B4: 3,9
F9: 4,5
G8: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,C1: 2.. / A1 = 2  =>  5 pairs (_) / C1 = 2  =>  6 pairs (_)
A5,C5: 2.. / A5 = 2  =>  6 pairs (_) / C5 = 2  =>  5 pairs (_)
A1,A5: 2.. / A1 = 2  =>  5 pairs (_) / A5 = 2  =>  6 pairs (_)
C1,C5: 2.. / C1 = 2  =>  6 pairs (_) / C5 = 2  =>  5 pairs (_)
C2,E2: 4.. / C2 = 4  =>  0 pairs (X) / E2 = 4  =>  0 pairs (_)
H6,H9: 5.. / H6 = 5  =>  0 pairs (*) / H9 = 5  =>  0 pairs (X)
A3,I3: 6.. / A3 = 6  =>  6 pairs (_) / I3 = 6  =>  6 pairs (_)
E4,H4: 6.. / E4 = 6  =>  8 pairs (_) / H4 = 6  =>  9 pairs (_)
D5,D9: 6.. / D5 = 6  => 10 pairs (_) / D9 = 6  =>  8 pairs (_)
I1,I3: 7.. / I1 = 7  =>  6 pairs (_) / I3 = 7  =>  8 pairs (_)
A4,C4: 7.. / A4 = 7  =>  0 pairs (X) / C4 = 7  =>  5 pairs (_)
D6,E6: 7.. / D6 = 7  =>  0 pairs (X) / E6 = 7  =>  7 pairs (_)
G7,G9: 7.. / G7 = 7  =>  5 pairs (_) / G9 = 7  =>  5 pairs (_)
A9,G9: 7.. / A9 = 7  =>  5 pairs (_) / G9 = 7  =>  5 pairs (_)
C4,C7: 7.. / C4 = 7  =>  5 pairs (_) / C7 = 7  =>  0 pairs (X)
A4,A5: 8.. / A4 = 8  =>  6 pairs (_) / A5 = 8  =>  0 pairs (X)
A2,C2: 9.. / A2 = 9  =>  0 pairs (X) / C2 = 9  =>  0 pairs (_)
I5,I6: 9.. / I5 = 9  =>  0 pairs (*) / I6 = 9  =>  0 pairs (X)
E8,D9: 9.. / E8 = 9  =>  8 pairs (_) / D9 = 9  =>  0 pairs (X)
* DURATION: 0:00:24.329093  START: 03:20:16.875435  END: 03:20:41.204528 2017-05-01
* CP COUNT: (19)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C3,D3,F9,G8)
* ......9...7.2.65...8...924....5..4.2.1.....7.4.6..2....2.8...9...83.7.2...1.2....
* PAIR C3: 3,5 BLK 1
A1: 3,5,1,2,6                            # reduction candidate for 3,5
A1: 3,5                                  # 11 pairs
B1: 3,5,4,6                              # reduction candidate for 3,5
B1: 3,5 => CTR
* 2.4...9..1792465..68...924..9.5..4.2.12....794.6972....2.8...9.5.8397.2.9.1.2.7..
B1: 4,6                                  #  6 pairs
C1: 3,5,2,4                              # reduction candidate for 3,5
C1: 3,5                                  # 12 pairs
A3: 3,5,1,6                              # reduction candidate for 3,5
A3: 3,5 => CTR
* 1624..9.79742.65...8...92468375914622196...754567.2..9.2.8...9..983.7.2..4192..5.
A3: 1,6                                  #  6 pairs
* PAIR C3: 3,5 ROW 3
E3: 3,5,1,7                              # reduction candidate for 3,5
E3: 1,7 => CTR
* 1.24..9.79742.65...8...924.8375914622196...754567.2..9.2.8...9..983.7.2..4192..5.
E3: 3,5                                  #  7 pairs
* PAIR C3: 3,5 COL C
C5: 3,5,2,9                              # reduction candidate for 3,5
C5: 3,5 => CTR
* .42...9...792465...8...924.8975..4.221.....794.6972...7248...9.568397124931.2.7..
C5: 2,9                                  #  6 pairs
C7: 3,5,4,7                              # reduction candidate for 3,5
C7: 3,5                                  #  9 pairs
* PAIR D3: 1,7 BLK 2
D1: 1,7,4                                # reduction candidate for 1,7
D1: 1,7 => SOLVED
* 264185937379246518185739246897513462512468379436972851723851694648397125951624783
D1: 4 => CTR
* .6.4..9.79742.65...8...9246.3.5..462.1..4..75456..2..9.2.8...94.48397.21.91624.5.
E1: 1,7,3,4,5,8                          # reduction candidate for 1,7
E1: 1,7 => CTR
* .6.4..9..9742.65..18.7.9246.3.5..462.1.....75456172..9.2.8.1.9...83.7124.41.2..5.
E1: 3,4,5,8                              #  5 pairs
E3: 1,7,3,5                              # reduction candidate for 1,7
E3: 1,7 => CTR
* 1.24..9.79742.65...8...924.8375914622196...754567.2..9.2.8...9..983.7.2..4192..5.
E3: 3,5                                  #  7 pairs
* PAIR D3: 1,7 ROW 3
I3: 1,7,3,6                              # reduction candidate for 1,7
I3: 1,7                                  #  8 pairs
I3: 3,6                                  #  7 pairs
* PAIR D3: 1,7 COL D
D6: 1,7,9                                # reduction candidate for 1,7
D6: 1,7 => CTR
* .6.4..9.79742.65...8...9246.3.5..462.1..4..75456..2..9.2.8...94.48397.21.91624.5.
D6: 9 => SOLVED
* 264185937379246518185739246897513462512468379436972851723851694648397125951624783
* PAIR B4: 3,9 BLK 4
A4: 3,9,7,8                              # reduction candidate for 3,9
A4: 3,9 => CTR
* 2.....9...792465...8...924...75..4.2812493675456..2..9.2.8...9...83.712...1.24.5.
A4: 7,8                                  #  6 pairs
C4: 3,9,7                                # reduction candidate for 3,9
C4: 3,9 => CTR
* 26....9...7.2.65...8...924.7..568412812943675456..28396278..394548397126..1624758
C4: 7                                    #  5 pairs
A5: 3,9,2,5,8                            # reduction candidate for 3,9
A5: 3,9 => CTR
* 2.....9...792465...8...924.8.75..4.2.124...75456..2..9.2.8...9...83.7.2...1.24.5.
A5: 2,5,8                                #  5 pairs
C5: 3,9,2,5                              # reduction candidate for 3,9
C5: 3,9 => CTR
* ..24..9...742.65...8...924.8.75..4.221964..75456..2..9.2.8...94.483.7.2..91.24.5.
C5: 2,5                                  #  6 pairs
B6: 3,9,5                                # reduction candidate for 3,9
B6: 3,9 => SOLVED
* 264185937379246518185739246897513462512468379436972851723851694648397125951624783
B6: 5 => CTR
* .6.4..9..9742.65...8...9246.3956.4.2.1294.675456..2..962.8...94.48397.2..91624.5.
* PAIR B4: 3,9 ROW 4
E4: 3,9,1,6,8                            # reduction candidate for 3,9
E4: 3,9                                  # 18 pairs
E4: 1,6,8                                #  6 pairs
* PAIR B4: 3,9 COL B
B9: 3,9,4,5,6                            # reduction candidate for 3,9
B9: 3,9 => CTR
* .6.4..9..9742.65...8...9246...5..462.1.64..75456..2..9.2.861.945483.7.2...1.24.5.
B9: 4,5,6                                #  5 pairs
* PAIR F9: 4,5 BLK 8
E7: 4,5,1,6                              # reduction candidate for 4,5
E7: 4,5                                  # 12 pairs
F7: 4,5,1                                # reduction candidate for 4,5
F7: 4,5                                  #  9 pairs
E8: 4,5,1,6,9                            # reduction candidate for 4,5
E8: 4,5 => CTR
* .6.4..9..9742.65...8.1.9246.395184628126.4375456732..9.27861.94.98347.2..41925...
E8: 1,6,9                                #  5 pairs
* PAIR F9: 4,5 ROW 9
B9: 4,5,3,6,9                            # reduction candidate for 4,5
B9: 4,5 => SOLVED
* 264185937379246518185739246897513462512468379436972851723851694648397125951624783
B9: 3,6,9                                #  5 pairs
I9: 4,5,3,6,8                            # reduction candidate for 4,5
I9: 4,5 => CTR
* ......9...792465...8...924.8.75..4.2.1.4...7.4.6..2.5..2.8...9...83.7.2..6192....
I9: 3,6,8                                #  5 pairs
* PAIR F9: 4,5 COL F
F1: 4,5,1,3,8                            # reduction candidate for 4,5
F1: 4,5                                  # 12 pairs
F1: 1,3,8                                #  5 pairs
* PAIR G8: 1,6 BLK 9
G7: 1,6,3,7                              # reduction candidate for 1,6
G7: 1,6                                  # 11 pairs
I7: 1,6,3,4,5                            # reduction candidate for 1,6
I7: 1,6                                  #  8 pairs
I8: 1,6,4,5                              # reduction candidate for 1,6
I8: 1,6                                  #  8 pairs
* PAIR G8: 1,6 ROW 8
E8: 1,6,4,5,9                            # reduction candidate for 1,6
E8: 1,6 => CTR
* .6.4..9..9742.65...8...9246.3.5..462.1.6...7.456..2....2.8...955983.7.24.41925...
E8: 4,5,9                                #  5 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0001-base-pr-000.dot
* REASONING
* DIS # B1: 3,5 => CTR => B1: 4,6
* DIS # A3: 3,5 => CTR => A3: 1,6
* DIS # E3: 1,7 => CTR => E3: 3,5
* DIS # C5: 3,5 => CTR => C5: 2,9
* PRF # D1: 1,7 => SOL
* DIS # D1: 4 => CTR => D1: 1,7
* DIS # E1: 1,7 => CTR => E1: 3,4,5,8
* DIS # E3: 1,7 => CTR => E3: 3,5
* DIS # D6: 1,7 => CTR => D6: 9
* PRF # D6: 9 => SOL
* DIS # A4: 3,9 => CTR => A4: 7,8
* DIS # C4: 3,9 => CTR => C4: 7
* DIS # A5: 3,9 => CTR => A5: 2,5,8
* DIS # C5: 3,9 => CTR => C5: 2,5
* PRF # B6: 3,9 => SOL
* DIS # B6: 5 => CTR => B6: 3,9
* DIS # B9: 3,9 => CTR => B9: 4,5,6
* DIS # E8: 4,5 => CTR => E8: 1,6,9
* PRF # B9: 4,5 => SOL
* DIS # I9: 4,5 => CTR => I9: 3,6,8
* DIS # E8: 1,6 => CTR => E8: 4,5,9
* CNT  21 HDP CHAINS /  50 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C3,D3,F9,G8)
* ......9...7.2.65...8...924....5..4.2.1.....7.4.6..2....2.8...9...83.7.2...1.2....
* PAIR C3: 3,5 BLK 1
A1: 3,5,1,2,6                            # reduction candidate for 3,5
A1: 3,5                                  # 11 pairs
B1: 3,5,4,6                              # reduction candidate for 3,5
B1: 3,5 => CTR
* 2.4...9..1792465..68...924..9.5..4.2.12....794.6972....2.8...9.5.8397.2.9.1.2.7..
C1: 3,5,2,4                              # reduction candidate for 3,5
C1: 3,5                                  # 12 pairs
A3: 3,5,1,6                              # reduction candidate for 3,5
A3: 3,5 => CTR
* 1624..9.79742.65...8...92468375914622196...754567.2..9.2.8...9..983.7.2..4192..5.
* PAIR C3: 3,5 ROW 3
E3: 3,5,1,7                              # reduction candidate for 3,5
E3: 1,7 => CTR
* .4.1..9671792.65..685..9243...5..4.2.1.....7.4.6..2....2.8...9...83.7.2...1.2....
* PAIR C3: 3,5 COL C
C5: 3,5,2,9                              # reduction candidate for 3,5
C5: 3,5 => CTR
* .42...9...792465...8...924.8975..4.221.....794.6972...7248...9.568397124931.2.7..
C7: 3,5,4,7                              # reduction candidate for 3,5
C7: 3,5                                  # 13 pairs
* RESTART
* PAIR C3: 3,5 COL C
C7: 3,5,4,7                              # reduction candidate for 3,5
C7: 3,5                                  # 13 pairs
C7: 4,7                                  # 10 pairs
* PAIR RESTART
* PAIR C3: 3,5 BLK 1
A1: 3,5,1,2,6                            # reduction candidate for 3,5
A1: 3,5 => CTR
* ..2...9..97.2.65..18.7.92468375914.2219....75456..2..9.2.8...9...83.7.2...192..5.
C1: 3,5,2,4                              # reduction candidate for 3,5
C1: 3,5                                  # 13 pairs
* RESTART
* PAIR C3: 3,5 BLK 1
C1: 3,5,2,4                              # reduction candidate for 3,5
C1: 2,4 => SOLVED
* 264185937379246518185739246897513462512468379436972851723851694648397125951624783
* DURATION: 0:00:12.353030  START: 03:21:16.432863  END: 03:21:28.785893 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0001-base-pr-001.dot
* REASONING
* DIS # B1: 3,5 => CTR => B1: 4,6
* DIS B1: 4,6 # A3: 3,5 => CTR => A3: 1,6
* DIS B1: 4,6 + A3: 1,6 # E3: 1,7 => CTR => E3: 3,5
* DIS B1: 4,6 + A3: 1,6 + E3: 3,5 # C5: 3,5 => CTR => C5: 2,9
* DIS B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 # A1: 3,5 => CTR => A1: 1,2,6
* PRF B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 + A1: 1,2,6 # C1: 2,4 => SOL
* STA B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 + A1: 1,2,6 + C1: 2,4
* CNT   6 HDP CHAINS /  14 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=1

Solution

position: 264185937379246518185739246897513462512468379436972851723851694648397125951624783 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 # A1: 3,5 => UNS
* DIS # B1: 3,5 => CTR => B1: 4,6
* INC # B1: 4,6 => UNS
* INC # C1: 3,5 => UNS
* DIS # A3: 3,5 => CTR => A3: 1,6
* INC # A3: 1,6 => UNS
* INC # E3: 3,5 => UNS
* DIS # E3: 1,7 => CTR => E3: 3,5
* DIS # C5: 3,5 => CTR => C5: 2,9
* INC # C5: 2,9 => UNS
* INC # C7: 3,5 => UNS
* PRF # D1: 1,7 => SOL
* DIS # D1: 4 => CTR => D1: 1,7
* DIS # E1: 1,7 => CTR => E1: 3,4,5,8
* INC # E1: 3,4,5,8 => UNS
* DIS # E3: 1,7 => CTR => E3: 3,5
* INC # E3: 3,5 => UNS
* INC # I3: 1,7 => UNS
* INC # I3: 3,6 => UNS
* DIS # D6: 1,7 => CTR => D6: 9
* PRF # D6: 9 => SOL
* DIS # A4: 3,9 => CTR => A4: 7,8
* INC # A4: 7,8 => UNS
* DIS # C4: 3,9 => CTR => C4: 7
* INC # C4: 7 => UNS
* DIS # A5: 3,9 => CTR => A5: 2,5,8
* INC # A5: 2,5,8 => UNS
* DIS # C5: 3,9 => CTR => C5: 2,5
* INC # C5: 2,5 => UNS
* PRF # B6: 3,9 => SOL
* DIS # B6: 5 => CTR => B6: 3,9
* INC # E4: 3,9 => UNS
* INC # E4: 1,6,8 => UNS
* DIS # B9: 3,9 => CTR => B9: 4,5,6
* INC # B9: 4,5,6 => UNS
* INC # E7: 4,5 => UNS
* INC # F7: 4,5 => UNS
* DIS # E8: 4,5 => CTR => E8: 1,6,9
* INC # E8: 1,6,9 => UNS
* PRF # B9: 4,5 => SOL
* INC # B9: 3,6,9 => UNS
* DIS # I9: 4,5 => CTR => I9: 3,6,8
* INC # I9: 3,6,8 => UNS
* INC # F1: 4,5 => UNS
* INC # F1: 1,3,8 => UNS
* INC # G7: 1,6 => UNS
* INC # I7: 1,6 => UNS
* INC # I8: 1,6 => UNS
* DIS # E8: 1,6 => CTR => E8: 4,5,9
* INC # E8: 4,5,9 => UNS
* CNT  50 HDP CHAINS /  50 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 3,5 => UNS
* DIS # B1: 3,5 => CTR => B1: 4,6
* INC B1: 4,6 # C1: 3,5 => UNS
* DIS B1: 4,6 # A3: 3,5 => CTR => A3: 1,6
* INC B1: 4,6 + A3: 1,6 # E3: 3,5 => UNS
* DIS B1: 4,6 + A3: 1,6 # E3: 1,7 => CTR => E3: 3,5
* DIS B1: 4,6 + A3: 1,6 + E3: 3,5 # C5: 3,5 => CTR => C5: 2,9
* INC B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 # C7: 3,5 => UNS
* INC B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 # C7: 3,5 => UNS
* INC B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 # C7: 4,7 => UNS
* DIS B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 # A1: 3,5 => CTR => A1: 1,2,6
* INC B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 + A1: 1,2,6 # C1: 3,5 => UNS
* INC B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 + A1: 1,2,6 # C1: 3,5 => UNS
* PRF B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 + A1: 1,2,6 # C1: 2,4 => SOL
* STA B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 + A1: 1,2,6 + C1: 2,4
* CNT  14 HDP CHAINS /  14 HYP OPENED