Analysis of zz-www.sudokuwiki.org-0111-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=111

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=111

position: .2.....9...1.8...47.....6....3..6..8...2.1...6..5..3....9.....23...5.4.6.5.....8. initial

Autosolve

position: .2....89...1.8...47.....6....3..6..8...231.6.6..5.83....9.....23...5.4.6.5.....8. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A5: 4,5 => CTR => A5: 8,9
* DIS # A5: 5,9 => CTR => A5: 4,8
* DIS # H6: 2,7 => CTR => H6: 1,4
* PRF # C9: 2,7 => SOL
* DIS # H7: 1,7 => CTR => H7: 3,5
* DIS # I9: 1,7 => CTR => I9: 3,9
* DIS # D8: 1,7 => CTR => D8: 8,9
* DIS # H4: 1,7 => CTR => H4: 2,4,5
* DIS # H6: 1,7 => CTR => H6: 2,4
* CNT   9 HDP CHAINS /  29 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 # A5: 4,5 => CTR => A5: 8,9
* DIS A5: 8,9 # H6: 2,7 => CTR => H6: 1,4
* DIS A5: 8,9 + H6: 1,4 # H7: 1,7 => CTR => H7: 3,5
* DIS A5: 8,9 + H6: 1,4 + H7: 3,5 # I9: 1,7 => CTR => I9: 3,9
* DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 # B8: 8 => CTR => B8: 1,7
* DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 # H4: 1,7 => CTR => H4: 2,4,5
* DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 # G7: 1,7 => CTR => G7: 5
* DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 # F1: 5,7 => CTR => F1: 3,4
* PRF A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 + F1: 3,4 # I3: 1,5 => SOL
* STA A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 + F1: 3,4 + I3: 1,5
* CNT   9 HDP CHAINS /  27 HYP OPENED

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

Details

Positions

.2.....9...1.8...47.....6....3..6..8...2.1...6..5..3....9.....23...5.4.6.5.....8. initial
.2....89...1.8...47.....6....3..6..8...231.6.6..5.83....9.....23...5.4.6.5.....8. autosolve
526174893931685724784329615193746258845231967672598341469817532318952476257463189 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (4)
A1: 4,5
A2: 5,9
C6: 2,7
H8: 1,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A4,C6: 2.. / A4 = 2  =>  0 pairs (X) / C6 = 2  =>  6 pairs (_)
C6,H6: 2.. / C6 = 2  =>  6 pairs (_) / H6 = 2  =>  0 pairs (X)
C8,F8: 2.. / C8 = 2  =>  0 pairs (X) / F8 = 2  =>  7 pairs (_)
A4,A9: 2.. / A4 = 2  =>  0 pairs (X) / A9 = 2  =>  6 pairs (_)
E3,E9: 2.. / E3 = 2  =>  5 pairs (_) / E9 = 2  =>  0 pairs (X)
G2,G4: 2.. / G2 = 2  =>  6 pairs (_) / G4 = 2  =>  0 pairs (*)
B2,B3: 3.. / B2 = 3  =>  5 pairs (_) / B3 = 3  =>  9 pairs (_)
H7,I9: 3.. / H7 = 3  =>  7 pairs (_) / I9 = 3  =>  6 pairs (_)
H4,H6: 4.. / H4 = 4  =>  0 pairs (X) / H6 = 4  =>  7 pairs (_)
E6,H6: 4.. / E6 = 4  =>  0 pairs (X) / H6 = 4  =>  7 pairs (_)
G7,H7: 5.. / G7 = 5  =>  6 pairs (_) / H7 = 5  =>  7 pairs (_)
C1,B2: 6.. / C1 = 6  =>  6 pairs (_) / B2 = 6  => 14 pairs (_)
B7,C9: 6.. / B7 = 6  =>  6 pairs (_) / C9 = 6  => 14 pairs (_)
B2,D2: 6.. / B2 = 6  => 14 pairs (_) / D2 = 6  =>  6 pairs (_)
B2,B7: 6.. / B2 = 6  => 14 pairs (_) / B7 = 6  =>  6 pairs (_)
C1,C9: 6.. / C1 = 6  =>  6 pairs (_) / C9 = 6  => 14 pairs (_)
B3,C3: 8.. / B3 = 8  => 12 pairs (_) / C3 = 8  =>  7 pairs (_)
D7,D8: 8.. / D7 = 8  =>  5 pairs (_) / D8 = 8  =>  0 pairs (X)
A5,A7: 8.. / A5 = 8  =>  5 pairs (_) / A7 = 8  =>  0 pairs (X)
D8,F8: 9.. / D8 = 9  =>  7 pairs (_) / F8 = 9  =>  0 pairs (X)
G9,I9: 9.. / G9 = 9  =>  5 pairs (_) / I9 = 9  => 10 pairs (_)
* DURATION: 0:00:29.316827  START: 05:29:59.836891  END: 05:30:29.153718 2017-05-01
* CP COUNT: (21)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,C6,H8)
* .2....89...1.8...47.....6....3..6..8...231.6.6..5.83....9.....23...5.4.6.5.....8.
* PAIR A1: 4,5 BLK 1
C1: 4,5,6                                # reduction candidate for 4,5
C1: 4,5                                  # 14 pairs
C3: 4,5,8                                # reduction candidate for 4,5
C3: 4,5                                  # 12 pairs
* PAIR A1: 4,5 ROW 1
F1: 4,5,3,7                              # reduction candidate for 4,5
F1: 4,5                                  #  8 pairs
F1: 3,7                                  #  5 pairs
* PAIR A1: 4,5 COL A
A5: 4,5,8,9                              # reduction candidate for 4,5
A5: 4,5 => CTR
* .2....89.9.1.8.2.47.....6..2.3..6.48...231.6.6.754832.8.9.....237285941615.....8.
A5: 8,9                                  #  5 pairs
* PAIR A2: 5,9 ROW 2
F2: 5,9,2,3,7                            # reduction candidate for 5,9
F2: 5,9                                  #  7 pairs
F2: 2,3,7                                #  4 pairs
* PAIR A2: 5,9 COL A
A4: 5,9,1,2                              # reduction candidate for 5,9
A4: 5,9                                  # 21 pairs
A5: 5,9,4,8                              # reduction candidate for 5,9
A5: 5,9 => CTR
* 42....89...1.8.2.47.....6..2.3..6.48...231.6.6.754832.8.9.....237285941615.....8.
A5: 4,8                                  #  5 pairs
* PAIR C6: 2,7 ROW 6
H6: 2,7,1,4                              # reduction candidate for 2,7
H6: 2,7 => CTR
* 524613897961785234738...61521397654884523176969754832147986.152382159476156...983
H6: 1,4                                  #  7 pairs
* PAIR C6: 2,7 COL C
C8: 2,7,8                                # reduction candidate for 2,7
C8: 2,7                                  #  6 pairs
C9: 2,7,4,6                              # reduction candidate for 2,7
C9: 2,7 => SOLVED
* 526174893931685724784329615193746258845231967672598341469817532318952476257463189
C9: 4,6                                  #  5 pairs
* PAIR H8: 1,7 BLK 9
G7: 1,7,5                                # reduction candidate for 1,7
G7: 1,7                                  #  7 pairs
H7: 1,7,3,5                              # reduction candidate for 1,7
H7: 1,7 => CTR
* 42....8979.1.8.2.47...296.1573.96128894231765612578349149863572387952416256.47983
H7: 3,5                                  #  5 pairs
G9: 1,7,9                                # reduction candidate for 1,7
G9: 1,7                                  # 10 pairs
I9: 1,7,3,9                              # reduction candidate for 1,7
I9: 1,7 => CTR
* 42....89.9.1.8.2.47...296..573.96128894231765612578349149867532387952416256.43987
I9: 3,9                                  #  5 pairs
* PAIR H8: 1,7 ROW 8
B8: 1,7,8                                # reduction candidate for 1,7
B8: 1,7                                  # 10 pairs
D8: 1,7,8,9                              # reduction candidate for 1,7
D8: 1,7 => CTR
* 524613897961785234738...61521397654884523176969754832147986.152382159476156...983
D8: 8,9                                  #  5 pairs
* PAIR H8: 1,7 COL H
H4: 1,7,2,4,5                            # reduction candidate for 1,7
H4: 1,7 => CTR
* .2....89...1.8..247...2.6..5.3..62.8...231.6.6.25.834.1.9.....23..95241625.....8.
H4: 2,4,5                                #  4 pairs
H6: 1,7,2,4                              # reduction candidate for 1,7
H6: 1,7 => CTR
* .2....89...1.8..247...2.6..513796248...231.6.6.25483..1.98....23..95241625.....8.
H6: 2,4                                  #  5 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0111-base-pr-000.dot
* REASONING
* DIS # A5: 4,5 => CTR => A5: 8,9
* DIS # A5: 5,9 => CTR => A5: 4,8
* DIS # H6: 2,7 => CTR => H6: 1,4
* PRF # C9: 2,7 => SOL
* DIS # H7: 1,7 => CTR => H7: 3,5
* DIS # I9: 1,7 => CTR => I9: 3,9
* DIS # D8: 1,7 => CTR => D8: 8,9
* DIS # H4: 1,7 => CTR => H4: 2,4,5
* DIS # H6: 1,7 => CTR => H6: 2,4
* CNT   9 HDP CHAINS /  29 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,C6,H8)
* .2....89...1.8...47.....6....3..6..8...231.6.6..5.83....9.....23...5.4.6.5.....8.
* PAIR A1: 4,5 BLK 1
C1: 4,5,6                                # reduction candidate for 4,5
C1: 4,5                                  # 14 pairs
C3: 4,5,8                                # reduction candidate for 4,5
C3: 4,5                                  # 12 pairs
* PAIR A1: 4,5 ROW 1
F1: 4,5,3,7                              # reduction candidate for 4,5
F1: 4,5                                  #  8 pairs
F1: 3,7                                  #  5 pairs
* PAIR A1: 4,5 COL A
A5: 4,5,8,9                              # reduction candidate for 4,5
A5: 4,5 => CTR
* .2....89.9.1.8.2.47.....6..2.3..6.48...231.6.6.754832.8.9.....237285941615.....8.
* PAIR RESTART
* PAIR A1: 4,5 BLK 1
C1: 4,5,6                                # reduction candidate for 4,5
C1: 4,5                                  # 15 pairs
C3: 4,5,8                                # reduction candidate for 4,5
C3: 4,5                                  # 10 pairs
* PAIR A1: 4,5 ROW 1
F1: 4,5,3,7                              # reduction candidate for 4,5
F1: 4,5                                  #  9 pairs
F1: 3,7                                  #  6 pairs
* PAIR A2: 5,9 ROW 2
F2: 5,9,2,3,7                            # reduction candidate for 5,9
F2: 5,9                                  #  8 pairs
F2: 2,3,7                                #  5 pairs
* PAIR A2: 5,9 COL A
A4: 5,9,1,2                              # reduction candidate for 5,9
A4: 1,2                                  # 25 pairs
A4: 5,9                                  # 21 pairs
* PAIR C6: 2,7 ROW 6
H6: 2,7,1,4                              # reduction candidate for 2,7
H6: 2,7 => CTR
* 524613897961785234738...61521397654884523176969754832147986.152382159476156...983
* PAIR RESTART
* PAIR H8: 1,7 BLK 9
G7: 1,7,5                                # reduction candidate for 1,7
G7: 1,7                                  # 14 pairs
H7: 1,7,3,5                              # reduction candidate for 1,7
H7: 1,7 => CTR
* 42.3..897..1.8.2.47...2.6.15734.61288..2317656125783491.98.35723..95241625....983
G9: 1,7,9                                # reduction candidate for 1,7
G9: 1,7                                  # 14 pairs
I9: 1,7,3,9                              # reduction candidate for 1,7
I9: 1,7 => CTR
* 42....89...1.8.2747...2.65.5734961288942317656125783491498675323..95241625....987
* PAIR H8: 1,7 ROW 8
B8: 1,7,8                                # reduction candidate for 1,7
B8: 8 => CTR
* 4256..89.961385274738.296515.3..61288.4231.656125.834714986.5323879524162561...8.
* PAIR H8: 1,7 COL H
H4: 1,7,2,4,5                            # reduction candidate for 1,7
H4: 1,7 => CTR
* .26...89.93168..2478..296..5.3..62.8847231.6.6.25.834.1698....237895241625416..8.
* PAIR RESTART
* PAIR H8: 1,7 BLK 9
G7: 1,7,5                                # reduction candidate for 1,7
G7: 1,7 => CTR
* .2631.89.93168...478.429631..37.6..884.231.696.25.83.7.698731523.89524.625.16.983
* RESTART

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,A4,A7,B8,C3,C5,C9,D4,F2,F7,F9,G2,G9,H3,H6,H8,I5,I6)
* .26...89.93168...478..296....3..6..884.23196.6.25.83...698..5323.89524.625..6..89
* PAIR A1: 4,5 ROW 1
F1: 4,5,3,7                              # reduction candidate for 4,5
F1: 3,7                                  # 22 pairs
F1: 4,5                                  # 20 pairs
* PAIR F2: 5,7 BLK 2
F1: 5,7,3,4                              # reduction candidate for 5,7
F1: 5,7 => CTR
* 426.1.89.93168.27478542961...3..6..884.23196.6.25.83...698.45323.89524.6254163789
* PAIR H3: 1,5 BLK 3
I1: 1,5,3                                # reduction candidate for 1,5
I1: 1,5                                  # 22 pairs
I3: 1,5,3                                # reduction candidate for 1,5
I3: 1,5 => SOLVED
* 526174893931685724784329615193746258845231967672598341469817532318952476257463189
* DURATION: 0:00:28.661996  START: 05:30:50.299137  END: 05:31:18.961133 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0111-base-pr-001.dot
* REASONING
* DIS # A5: 4,5 => CTR => A5: 8,9
* DIS A5: 8,9 # H6: 2,7 => CTR => H6: 1,4
* DIS A5: 8,9 + H6: 1,4 # H7: 1,7 => CTR => H7: 3,5
* DIS A5: 8,9 + H6: 1,4 + H7: 3,5 # I9: 1,7 => CTR => I9: 3,9
* DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 # B8: 8 => CTR => B8: 1,7
* DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 # H4: 1,7 => CTR => H4: 2,4,5
* DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 # G7: 1,7 => CTR => G7: 5
* DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 # F1: 5,7 => CTR => F1: 3,4
* PRF A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 + F1: 3,4 # I3: 1,5 => SOL
* STA A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 + F1: 3,4 + I3: 1,5
* CNT   9 HDP CHAINS /  27 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=111

Solution

position: 526174893931685724784329615193746258845231967672598341469817532318952476257463189 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 # C1: 4,5 => UNS
* INC # C3: 4,5 => UNS
* INC # F1: 4,5 => UNS
* INC # F1: 3,7 => UNS
* DIS # A5: 4,5 => CTR => A5: 8,9
* INC # A5: 8,9 => UNS
* INC # F2: 5,9 => UNS
* INC # F2: 2,3,7 => UNS
* INC # A4: 5,9 => UNS
* DIS # A5: 5,9 => CTR => A5: 4,8
* INC # A5: 4,8 => UNS
* DIS # H6: 2,7 => CTR => H6: 1,4
* INC # H6: 1,4 => UNS
* INC # C8: 2,7 => UNS
* PRF # C9: 2,7 => SOL
* INC # C9: 4,6 => UNS
* INC # G7: 1,7 => UNS
* DIS # H7: 1,7 => CTR => H7: 3,5
* INC # H7: 3,5 => UNS
* INC # G9: 1,7 => UNS
* DIS # I9: 1,7 => CTR => I9: 3,9
* INC # I9: 3,9 => UNS
* INC # B8: 1,7 => UNS
* DIS # D8: 1,7 => CTR => D8: 8,9
* INC # D8: 8,9 => UNS
* DIS # H4: 1,7 => CTR => H4: 2,4,5
* INC # H4: 2,4,5 => UNS
* DIS # H6: 1,7 => CTR => H6: 2,4
* INC # H6: 2,4 => UNS
* CNT  29 HDP CHAINS /  29 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 4,5 => UNS
* INC # C3: 4,5 => UNS
* INC # F1: 4,5 => UNS
* INC # F1: 3,7 => UNS
* DIS # A5: 4,5 => CTR => A5: 8,9
* INC A5: 8,9 # C1: 4,5 => UNS
* INC A5: 8,9 # C3: 4,5 => UNS
* INC A5: 8,9 # F1: 4,5 => UNS
* INC A5: 8,9 # F1: 3,7 => UNS
* INC A5: 8,9 # F2: 5,9 => UNS
* INC A5: 8,9 # F2: 2,3,7 => UNS
* INC A5: 8,9 # A4: 5,9 => UNS
* INC A5: 8,9 # A4: 1,2 => UNS
* DIS A5: 8,9 # H6: 2,7 => CTR => H6: 1,4
* INC A5: 8,9 + H6: 1,4 # G7: 1,7 => UNS
* DIS A5: 8,9 + H6: 1,4 # H7: 1,7 => CTR => H7: 3,5
* INC A5: 8,9 + H6: 1,4 + H7: 3,5 # G9: 1,7 => UNS
* DIS A5: 8,9 + H6: 1,4 + H7: 3,5 # I9: 1,7 => CTR => I9: 3,9
* INC A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 # B8: 1,7 => UNS
* DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 # B8: 8 => CTR => B8: 1,7
* DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 # H4: 1,7 => CTR => H4: 2,4,5
* DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 # G7: 1,7 => CTR => G7: 5
* INC A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 # F1: 4,5 => UNS
* INC A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 # F1: 3,7 => UNS
* DIS A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 # F1: 5,7 => CTR => F1: 3,4
* INC A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 + F1: 3,4 # I1: 1,5 => UNS
* PRF A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 + F1: 3,4 # I3: 1,5 => SOL
* STA A5: 8,9 + H6: 1,4 + H7: 3,5 + I9: 3,9 + B8: 1,7 + H4: 2,4,5 + G7: 5 + F1: 3,4 + I3: 1,5
* CNT  27 HDP CHAINS /  27 HYP OPENED