Analysis of zz-www.sudokuwiki.org-0129-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=129

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=129

position: 39..1......2.5..3.5..2....8.......9..3..9...7...4.26...1..3.......9..72.94....... initial

Autosolve

position: 39..1...2..2.59.3.5..2.39.8.2.3...9..3..9.2.7..94.26.321..3...9..39..72.94..2.3.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A2: 6,7 => CTR => A2: 1,4,8
* PRF # H3: 6,7 => SOL
* PRF # H1: 4,5 => SOL
* DIS # I2: 1,4 => CTR => I2: 6
* DIS # A2: 6,7,8 => CTR => A2: 1,4
* DIS # A6: 7,8 => CTR => A6: 1
* DIS # B8: 6,8 => CTR => B8: 5
* PRF # E8: 6,8 => SOL
* DIS # F8: 6,8 => CTR => F8: 1,4,5
* DIS # A2: 6,8 => CTR => A2: 1,4,7
* CNT  10 HDP CHAINS /  34 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 # A2: 6,7 => CTR => A2: 1,4,8
* DIS A2: 1,4,8 # B2: 8 => CTR => B2: 6,7
* DIS A2: 1,4,8 + B2: 6,7 # E3: 6,7 => CTR => E3: 4
* PRF A2: 1,4,8 + B2: 6,7 + E3: 4 => SOL
* STA A2: 1,4,8 + B2: 6,7 + E3: 4
* CNT   4 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

39..1......2.5..3.5..2....8.......9..3..9...7...4.26...1..3.......9..72.94....... initial
39..1...2..2.59.3.5..2.39.8.2.3...9..3..9.2.7..94.26.321..3...9..39..72.94..2.3.. autosolve
398617542472859136561243978725386491634195287189472653217534869853961724946728315 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
B3: 6,7
G1: 4,5
G2: 1,4
E6: 7,8
A8: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A2,C3: 1.. / A2 = 1  =>  0 pairs (X) / C3 = 1  =>  5 pairs (_)
C3,H3: 1.. / C3 = 1  =>  5 pairs (_) / H3 = 1  =>  0 pairs (X)
A6,H6: 1.. / A6 = 1  =>  6 pairs (_) / H6 = 1  =>  0 pairs (X)
F8,I8: 1.. / F8 = 1  =>  5 pairs (_) / I8 = 1  =>  8 pairs (_)
D5,D9: 1.. / D5 = 1  =>  5 pairs (_) / D9 = 1  =>  8 pairs (_)
G2,G4: 1.. / G2 = 1  =>  5 pairs (_) / G4 = 1  =>  0 pairs (X)
F1,E3: 4.. / F1 = 4  => 18 pairs (_) / E3 = 4  =>  0 pairs (*)
E3,E8: 4.. / E3 = 4  =>  0 pairs (*) / E8 = 4  =>  0 pairs (X)
G1,H1: 5.. / G1 = 5  =>  5 pairs (_) / H1 = 5  =>  0 pairs (X)
B6,H6: 5.. / B6 = 5  =>  0 pairs (X) / H6 = 5  =>  8 pairs (_)
B6,B8: 5.. / B6 = 5  =>  0 pairs (X) / B8 = 5  =>  8 pairs (_)
H1,H3: 7.. / H1 = 7  =>  6 pairs (_) / H3 = 7  =>  0 pairs (*)
C7,C9: 7.. / C7 = 7  =>  5 pairs (_) / C9 = 7  =>  5 pairs (_)
G4,G7: 8.. / G4 = 8  =>  8 pairs (_) / G7 = 8  =>  5 pairs (_)
* DURATION: 0:00:20.538206  START: 05:55:42.696993  END: 05:56:03.235199 2017-05-01
* CP COUNT: (14)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B3,E6,G1,G2)
* 39..1...2..2.59.3.5..2.39.8.2.3...9..3..9.2.7..94.26.321..3...9..39..72.94..2.3..
* PAIR B3: 6,7 BLK 1
A2: 6,7,1,4,8                            # reduction candidate for 6,7
A2: 6,7 => CTR
* 394.1.5.2.82.59.3.561243978.2.3...95.3..9.2.7..94.26.321..3...9..39..72.94..2.3..
A2: 1,4,8                                #  6 pairs
B2: 6,7,8                                # reduction candidate for 6,7
B2: 6,7                                  # 10 pairs
* PAIR B3: 6,7 ROW 3
E3: 6,7,4                                # reduction candidate for 6,7
E3: 6,7                                  # 18 pairs
H3: 6,7,1,4                              # reduction candidate for 6,7
H3: 6,7 => SOLVED
* 398617542472859136561243978725386491634195287189472653217534869853961724946728315
H3: 1,4                                  # 12 pairs
* PAIR G1: 4,5 BLK 3
H1: 4,5,6,7                              # reduction candidate for 4,5
H1: 4,5 => SOLVED
* 398617542472859136561243978725386491634195287189472653217534869853961724946728315
H1: 6,7                                  #  6 pairs
* PAIR G1: 4,5 COL G
G4: 4,5,1,8                              # reduction candidate for 4,5
G4: 4,5                                  #  6 pairs
G7: 4,5,8                                # reduction candidate for 4,5
G7: 4,5                                  #  8 pairs
* PAIR G2: 1,4 BLK 3
I2: 1,4,6                                # reduction candidate for 1,4
I2: 1,4 => CTR
* 394.1.5.2..2.59.3.5.12439.8.2.3...95.3..9.2.7.594.26.321..3...9..39..72.94..2.3..
I2: 6                                    # 10 pairs
H3: 1,4,6,7                              # reduction candidate for 1,4
H3: 1,4                                  # 12 pairs
* PAIR G2: 1,4 ROW 2
A2: 1,4,6,7,8                            # reduction candidate for 1,4
A2: 6,7,8 => CTR
* 394.1.5.2..2.59.3.5.12439.8.2.3...95.3..9.2.7.594.26.321..3...9..39..72.94..2.3..
A2: 1,4                                  # 10 pairs
* PAIR G2: 1,4 COL G
G4: 1,4,5,8                              # reduction candidate for 1,4
G4: 5,8                                  #  6 pairs
G4: 1,4                                  #  5 pairs
* PAIR E6: 7,8 BLK 5
E4: 7,8,6                                # reduction candidate for 7,8
E4: 7,8                                  #  8 pairs
F4: 7,8,1,5,6                            # reduction candidate for 7,8
F4: 7,8                                  # 11 pairs
* PAIR E6: 7,8 ROW 6
A6: 7,8,1                                # reduction candidate for 7,8
A6: 7,8 => CTR
* 398614572472859136561273948.2.3.5894.34.9.257.5948261321..3.4.9..394172594..2.3.1
A6: 1                                    #  6 pairs
B6: 7,8,5                                # reduction candidate for 7,8
B6: 7,8                                  #  8 pairs
* PAIR A8: 6,8 BLK 7
C7: 6,8,5,7                              # reduction candidate for 6,8
C7: 6,8                                  # 12 pairs
B8: 6,8,5                                # reduction candidate for 6,8
B8: 6,8 => CTR
* 39681457218275943657.2639.862.375.94.3.19625775948261321..3...986394172594..2.3.1
B8: 5                                    #  8 pairs
C9: 6,8,5,7                              # reduction candidate for 6,8
C9: 6,8                                  #  9 pairs
* PAIR A8: 6,8 ROW 8
E8: 6,8,4                                # reduction candidate for 6,8
E8: 6,8 => SOLVED
* 398617542472859136561243978725386491634195287189472653217534869853961724946728315
E8: 4                                    # 18 pairs
F8: 6,8,1,4,5                            # reduction candidate for 6,8
F8: 6,8 => CTR
* 39..145.2..2.59.3656.2739.8.2.367.94.3..9.2.717948265321..3...9.5394.72194..2.3.5
F8: 1,4,5                                #  5 pairs
* PAIR A8: 6,8 COL A
A2: 6,8,1,4,7                            # reduction candidate for 6,8
A2: 6,8 => CTR
* 394.1.5.2..2.59.3.5.12439.8.2.3...95.3..9.2.7.594.26.321..3...9..39..72.94..2.3..
A2: 1,4,7                                #  5 pairs
A4: 6,8,1,4,7                            # reduction candidate for 6,8
A4: 6,8                                  # 11 pairs
A5: 6,8,1,4                              # reduction candidate for 6,8
A5: 6,8                                  #  7 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0129-base-pr-000.dot
* REASONING
* DIS # A2: 6,7 => CTR => A2: 1,4,8
* PRF # H3: 6,7 => SOL
* PRF # H1: 4,5 => SOL
* DIS # I2: 1,4 => CTR => I2: 6
* DIS # A2: 6,7,8 => CTR => A2: 1,4
* DIS # A6: 7,8 => CTR => A6: 1
* DIS # B8: 6,8 => CTR => B8: 5
* PRF # E8: 6,8 => SOL
* DIS # F8: 6,8 => CTR => F8: 1,4,5
* DIS # A2: 6,8 => CTR => A2: 1,4,7
* CNT  10 HDP CHAINS /  34 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B3,E6,G1,G2)
* 39..1...2..2.59.3.5..2.39.8.2.3...9..3..9.2.7..94.26.321..3...9..39..72.94..2.3..
* PAIR B3: 6,7 BLK 1
A2: 6,7,1,4,8                            # reduction candidate for 6,7
A2: 6,7 => CTR
* 394.1.5.2.82.59.3.561243978.2.3...95.3..9.2.7..94.26.321..3...9..39..72.94..2.3..
B2: 6,7,8                                # reduction candidate for 6,7
B2: 6,7                                  # 10 pairs
* RESTART
* PAIR B3: 6,7 BLK 1
B2: 6,7,8                                # reduction candidate for 6,7
B2: 8 => CTR
* 39681457218275943657.2639.862.375.94.3.19625775948261321..3...986394172594..2.3.1
* PAIR B3: 6,7 ROW 3
E3: 6,7,4                                # reduction candidate for 6,7
E3: 6,7 => CTR
* 398614572.72859136561273948125367.94.3..9.2.77.948261321..3...9.8394.72.94..2.3..
E3: 4 => SOLVED
* 398617542472859136561243978725386491634195287189472653217534869853961724946728315
* DURATION: 0:00:05.271339  START: 05:56:30.893138  END: 05:56:36.164477 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0129-base-pr-001.dot
* REASONING
* DIS # A2: 6,7 => CTR => A2: 1,4,8
* DIS A2: 1,4,8 # B2: 8 => CTR => B2: 6,7
* DIS A2: 1,4,8 + B2: 6,7 # E3: 6,7 => CTR => E3: 4
* PRF A2: 1,4,8 + B2: 6,7 + E3: 4 => SOL
* STA A2: 1,4,8 + B2: 6,7 + E3: 4
* CNT   4 HDP CHAINS /   5 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=129

Solution

position: 398617542472859136561243978725386491634195287189472653217534869853961724946728315 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 # A2: 6,7 => CTR => A2: 1,4,8
* INC # A2: 1,4,8 => UNS
* INC # B2: 6,7 => UNS
* INC # E3: 6,7 => UNS
* PRF # H3: 6,7 => SOL
* INC # H3: 1,4 => UNS
* PRF # H1: 4,5 => SOL
* INC # H1: 6,7 => UNS
* INC # G4: 4,5 => UNS
* INC # G7: 4,5 => UNS
* DIS # I2: 1,4 => CTR => I2: 6
* INC # I2: 6 => UNS
* INC # H3: 1,4 => UNS
* INC # A2: 1,4 => UNS
* DIS # A2: 6,7,8 => CTR => A2: 1,4
* INC # G4: 1,4 => UNS
* INC # G4: 5,8 => UNS
* INC # E4: 7,8 => UNS
* INC # F4: 7,8 => UNS
* DIS # A6: 7,8 => CTR => A6: 1
* INC # A6: 1 => UNS
* INC # B6: 7,8 => UNS
* INC # C7: 6,8 => UNS
* DIS # B8: 6,8 => CTR => B8: 5
* INC # B8: 5 => UNS
* INC # C9: 6,8 => UNS
* PRF # E8: 6,8 => SOL
* INC # E8: 4 => UNS
* DIS # F8: 6,8 => CTR => F8: 1,4,5
* INC # F8: 1,4,5 => UNS
* DIS # A2: 6,8 => CTR => A2: 1,4,7
* INC # A2: 1,4,7 => UNS
* INC # A4: 6,8 => UNS
* INC # A5: 6,8 => UNS
* CNT  34 HDP CHAINS /  34 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A2: 6,7 => CTR => A2: 1,4,8
* INC A2: 1,4,8 # B2: 6,7 => UNS
* INC A2: 1,4,8 # B2: 6,7 => UNS
* DIS A2: 1,4,8 # B2: 8 => CTR => B2: 6,7
* DIS A2: 1,4,8 + B2: 6,7 # E3: 6,7 => CTR => E3: 4
* PRF A2: 1,4,8 + B2: 6,7 + E3: 4 => SOL
* STA A2: 1,4,8 + B2: 6,7 + E3: 4
* CNT   6 HDP CHAINS /   5 HYP OPENED