Analysis of zz-www.sudokuoftheday.co.uk-20060807-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006

position: 1.9......7...6.......35...9.9.1....38..7....5.1...42...64...5....8..7.6........42 initial

Autosolve

position: 1.9.7....7...6.......35...9.9.1....38..7....5.1...42...64.1.5....8.47.61.71....42 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A3: 2,6 => CTR => A3: 4
* DIS # C4: 2,6 => CTR => C4: 5,7
* DIS # D1: 2,8 => CTR => D1: 4
* DIS # F3: 2,8 => CTR => F3: 1
* DIS # B1: 2,8 => CTR => B1: 3,5
* DIS # H1: 2,8 => CTR => H1: 3,5
* DIS # G4: 7,8 => CTR => G4: 4,6
* DIS # H6: 7,8 => CTR => H6: 9
* DIS # H3: 7,8 => CTR => H3: 1,2
* PRF # H7: 7,8 => SOL
* DIS # G5: 1,9 => CTR => G5: 4,6
* PRF # H7: 7,8 => SOL
* PRF # G9: 3,9 => SOL
* CNT  13 HDP CHAINS /  41 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 # A3: 2,6 => CTR => A3: 4
* DIS A3: 4 # D1: 2,8 => CTR => D1: 4
* DIS A3: 4 + D1: 4 # F3: 2,8 => CTR => F3: 1
* DIS A3: 4 + D1: 4 + F3: 1 # B1: 2,8 => CTR => B1: 3,5
* DIS A3: 4 + D1: 4 + F3: 1 + B1: 3,5 # H1: 2,8 => CTR => H1: 3,5
* DIS A3: 4 + D1: 4 + F3: 1 + B1: 3,5 + H1: 3,5 # H6: 7,8 => CTR => H6: 9
* PRF A3: 4 + D1: 4 + F3: 1 + B1: 3,5 + H1: 3,5 + H6: 9 => SOL
* STA A3: 4 + D1: 4 + F3: 1 + B1: 3,5 + H1: 3,5 + H6: 9
* CNT   7 HDP CHAINS /   8 HYP OPENED

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

Details

Positions

1.9......7...6.......35...9.9.1....38..7....5.1...42...64...5....8..7.6........42 initial
1.9.7....7...6.......35...9.9.1....38..7....5.1...42...64.1.5....8.47.61.71....42 autosolve
159472836723968154486351729697125483842739615315684297964213578238547961571896342 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
C3: 2,6
F1: 2,8
I2: 4,8
E4: 2,8
H4: 7,8
H5: 1,9
I7: 7,8
G8: 3,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F2,F3: 1.. / F2 = 1  =>  0 pairs (X) / F3 = 1  =>  9 pairs (_)
G5,H5: 1.. / G5 = 1  =>  0 pairs (X) / H5 = 1  =>  7 pairs (_)
E4,E5: 2.. / E4 = 2  =>  8 pairs (_) / E5 = 2  => 13 pairs (_)
A3,B3: 4.. / A3 = 4  =>  9 pairs (_) / B3 = 4  =>  0 pairs (X)
D1,D2: 4.. / D1 = 4  =>  8 pairs (_) / D2 = 4  =>  0 pairs (X)
I1,I2: 4.. / I1 = 4  =>  0 pairs (X) / I2 = 4  =>  8 pairs (_)
A4,B5: 4.. / A4 = 4  =>  0 pairs (X) / B5 = 4  =>  9 pairs (_)
G4,G5: 4.. / G4 = 4  =>  9 pairs (_) / G5 = 4  =>  0 pairs (X)
D1,I1: 4.. / D1 = 4  =>  8 pairs (_) / I1 = 4  =>  0 pairs (X)
D2,I2: 4.. / D2 = 4  =>  0 pairs (X) / I2 = 4  =>  8 pairs (_)
A4,G4: 4.. / A4 = 4  =>  0 pairs (X) / G4 = 4  =>  9 pairs (_)
B5,G5: 4.. / B5 = 4  =>  9 pairs (_) / G5 = 4  =>  0 pairs (X)
A3,A4: 4.. / A3 = 4  =>  9 pairs (_) / A4 = 4  =>  0 pairs (X)
B3,B5: 4.. / B3 = 4  =>  0 pairs (X) / B5 = 4  =>  9 pairs (_)
H1,H2: 5.. / H1 = 5  =>  8 pairs (_) / H2 = 5  => 14 pairs (_)
F4,D6: 5.. / F4 = 5  =>  8 pairs (_) / D6 = 5  => 12 pairs (_)
B1,H1: 5.. / B1 = 5  => 14 pairs (_) / H1 = 5  =>  8 pairs (_)
F4,F9: 5.. / F4 = 5  =>  8 pairs (_) / F9 = 5  => 12 pairs (_)
A3,C3: 6.. / A3 = 6  =>  0 pairs (X) / C3 = 6  =>  9 pairs (_)
G1,I1: 6.. / G1 = 6  => 20 pairs (_) / I1 = 6  => 12 pairs (_)
D9,F9: 6.. / D9 = 6  =>  8 pairs (_) / F9 = 6  => 19 pairs (_)
D6,D9: 6.. / D6 = 6  => 19 pairs (_) / D9 = 6  =>  8 pairs (_)
I1,I6: 6.. / I1 = 6  => 12 pairs (_) / I6 = 6  => 20 pairs (_)
G3,H3: 7.. / G3 = 7  =>  8 pairs (_) / H3 = 7  =>  0 pairs (X)
C4,C6: 7.. / C4 = 7  => 12 pairs (_) / C6 = 7  =>  9 pairs (_)
H7,I7: 7.. / H7 = 7  =>  0 pairs (*) / I7 = 7  =>  0 pairs (X)
G3,G4: 7.. / G3 = 7  =>  8 pairs (_) / G4 = 7  =>  0 pairs (X)
I6,I7: 7.. / I6 = 7  =>  0 pairs (*) / I7 = 7  =>  0 pairs (X)
D2,F2: 9.. / D2 = 9  => 12 pairs (_) / F2 = 9  => 10 pairs (_)
* DURATION: 0:00:29.852192  START: 01:37:29.299164  END: 01:37:59.151356 2019-05-01
* CP COUNT: (29)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,E4,F1,G8,H4,H5,I2,I7)
* 1.9.7....7...6.......35...9.9.1....38..7....5.1...42...64.1.5....8.47.61.71....42
* PAIR C3: 2,6 BLK 1
A3: 2,6,4                                # reduction candidate for 2,6
A3: 2,6 => CTR
* 1.9.7....7...6.....4.35...949.1....38.6793415317584296.64.1.537.38247961.71635842
A3: 4                                    #  9 pairs
* PAIR C3: 2,6 COL C
C4: 2,6,5,7                              # reduction candidate for 2,6
C4: 2,6 => CTR
* 1.9.7..567.5.6..34...35..29.921....38.37....5.17.34298.64.13587.58.47.61.71.8..42
C4: 5,7                                  #  9 pairs
C5: 2,6,3                                # reduction candidate for 2,6
C5: 2,6                                  # 11 pairs
* PAIR F1: 2,8 BLK 2
D1: 2,8,4                                # reduction candidate for 2,8
D1: 2,8 => CTR
* 159.7.63472346915848635172969.1.54.384273691531.9.42.6.64.1.5.7..8547.61571693842
D1: 4                                    #  8 pairs
D2: 2,8,4,9                              # reduction candidate for 2,8
D2: 2,8                                  # 11 pairs
F2: 2,8,1,9                              # reduction candidate for 2,8
F2: 2,8                                  # 14 pairs
F3: 2,8,1                                # reduction candidate for 2,8
F3: 2,8 => CTR
* 139472658785961324...358..9.9.1....38..7....5.1...42.6.64819537358247961971635842
F3: 1                                    #  9 pairs
* PAIR F1: 2,8 ROW 1
B1: 2,8,3,5                              # reduction candidate for 2,8
B1: 2,8 => CTR
* 1.947.3567...6.1.4...3517.9.9.18..738..729.15.17.34298.64.1.537..8.47961.71.93842
B1: 3,5                                  #  9 pairs
H1: 2,8,3,5                              # reduction candidate for 2,8
H1: 2,8 => CTR
* 15947.3.67...6.154...3517.9.9.18..738..729.15.17.34298.64.1.537..8.47961.71.93842
H1: 3,5                                  #  9 pairs
* PAIR F1: 2,8 COL F
F7: 2,8,3,9                              # reduction candidate for 2,8
F7: 2,8                                  # 14 pairs
F7: 3,9                                  # 10 pairs
* PAIR I2: 4,8 BLK 3
I1: 4,8,6                                # reduction candidate for 4,8
I1: 4,8                                  # 20 pairs
I1: 6                                    # 12 pairs
* PAIR I2: 4,8 ROW 2
D2: 4,8,2,9                              # reduction candidate for 4,8
D2: 4,8                                  # 12 pairs
D2: 2,9                                  # 10 pairs
* PAIR H4: 7,8 BLK 6
G4: 7,8,4,6                              # reduction candidate for 7,8
G4: 7,8 => CTR
* 139.7265878596132464235817949612578382.7..415.17..4296.6481.537..8.47961.716..842
G4: 4,6                                  #  9 pairs
H6: 7,8,9                                # reduction candidate for 7,8
H6: 7,8 => CTR
* 1.9.7.6..7...69...4.635172969.1.54.384.7.6..5315984276.64.1.537.38547961571693842
H6: 9                                    #  9 pairs
I6: 7,8,6                                # reduction candidate for 7,8
I6: 7,8                                  # 12 pairs
* PAIR H4: 7,8 COL H
H3: 7,8,1,2                              # reduction candidate for 7,8
H3: 7,8 => CTR
* 1.9.7....7...6.......35...9.9.1....38..793.15317584296.64.1.537.38247961.71635842
H3: 1,2                                  #  9 pairs
H7: 7,8,3,9                              # reduction candidate for 7,8
H7: 7,8 => SOLVED
* 159472836723968154486351729697125483842739615315684297964213578238547961571896342
H7: 3,9                                  # 14 pairs
* PAIR H5: 1,9 BLK 6
G5: 1,9,4,6                              # reduction candidate for 1,9
G5: 1,9 => CTR
* 1.9.7.6..7...69...48635172969.1.54.384.7.6..5315984276.64.1.537.38547961571693842
G5: 4,6                                  #  9 pairs
* PAIR I7: 7,8 BLK 9
H7: 7,8,3,9                              # reduction candidate for 7,8
H7: 7,8 => SOLVED
* 159472836723968154486351729697125483842739615315684297964213578238547961571896342
H7: 3,9                                  # 14 pairs
* PAIR I7: 7,8 COL I
I6: 7,8,6                                # reduction candidate for 7,8
I6: 6                                    # 20 pairs
I6: 7,8                                  # 12 pairs
* PAIR G8: 3,9 BLK 9
H7: 3,9,7,8                              # reduction candidate for 3,9
H7: 3,9                                  # 14 pairs
G9: 3,9,8                                # reduction candidate for 3,9
G9: 3,9 => SOLVED
* 159472836723968154486351729697125483842739615315684297964213578238547961571896342
G9: 8                                    # 14 pairs
* PAIR G8: 3,9 ROW 8
A8: 3,9,2,5                              # reduction candidate for 3,9
A8: 3,9                                  # 12 pairs
A8: 2,5                                  #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060807-absurd-base-pr-000.dot
* REASONING
* DIS # A3: 2,6 => CTR => A3: 4
* DIS # C4: 2,6 => CTR => C4: 5,7
* DIS # D1: 2,8 => CTR => D1: 4
* DIS # F3: 2,8 => CTR => F3: 1
* DIS # B1: 2,8 => CTR => B1: 3,5
* DIS # H1: 2,8 => CTR => H1: 3,5
* DIS # G4: 7,8 => CTR => G4: 4,6
* DIS # H6: 7,8 => CTR => H6: 9
* DIS # H3: 7,8 => CTR => H3: 1,2
* PRF # H7: 7,8 => SOL
* DIS # G5: 1,9 => CTR => G5: 4,6
* PRF # H7: 7,8 => SOL
* PRF # G9: 3,9 => SOL
* CNT  13 HDP CHAINS /  41 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,E4,F1,G8,H4,H5,I2,I7)
* 1.9.7....7...6.......35...9.9.1....38..7....5.1...42...64.1.5....8.47.61.71....42
* PAIR C3: 2,6 BLK 1
A3: 2,6,4                                # reduction candidate for 2,6
A3: 2,6 => CTR
* 1.9.7....7...6.....4.35...949.1....38.6793415317584296.64.1.537.38247961.71635842
* PAIR F1: 2,8 BLK 2
D1: 2,8,4                                # reduction candidate for 2,8
D1: 2,8 => CTR
* 159.7.63472346915848635172969.1.54.384273691531.9.42.6.64.1.5.7..8547.61571693842
D2: 2,8,9                                # reduction candidate for 2,8
D2: 2,8                                  # 12 pairs
F2: 2,8,1,9                              # reduction candidate for 2,8
F2: 2,8                                  # 15 pairs
F3: 2,8,1                                # reduction candidate for 2,8
F3: 2,8 => CTR
* 1.947.6.87..9613.44.635871969.1.54.384.7.6195.1.894276.64.1.5.7..8.47.61.716...42
* PAIR F1: 2,8 ROW 1
B1: 2,8,3,5                              # reduction candidate for 2,8
B1: 2,8 => CTR
* 1.947.3567...6.1.44.63517.9.9.18.47384.729615.17.34298.64.1.537..8.47961.71.93842
H1: 2,8,3,5                              # reduction candidate for 2,8
H1: 2,8 => CTR
* 15947.3.67...6.1544.63517.9.9518647384.729615617534298.64.1.537538247961.71...842
* PAIR RESTART
* PAIR H4: 7,8 BLK 6
H6: 7,8,9                                # reduction candidate for 7,8
H6: 7,8 => CTR
* 15947263872386915448635172969.1.54.384273691531.9.42.6.64.1.5.7..8547.61571693842
H6: 9 => SOLVED
* 159472836723968154486351729697125483842739615315684297964213578238547961571896342
* DURATION: 0:00:07.774291  START: 01:38:23.457071  END: 01:38:31.231362 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060807-absurd-base-pr-001.dot
* REASONING
* DIS # A3: 2,6 => CTR => A3: 4
* DIS A3: 4 # D1: 2,8 => CTR => D1: 4
* DIS A3: 4 + D1: 4 # F3: 2,8 => CTR => F3: 1
* DIS A3: 4 + D1: 4 + F3: 1 # B1: 2,8 => CTR => B1: 3,5
* DIS A3: 4 + D1: 4 + F3: 1 + B1: 3,5 # H1: 2,8 => CTR => H1: 3,5
* DIS A3: 4 + D1: 4 + F3: 1 + B1: 3,5 + H1: 3,5 # H6: 7,8 => CTR => H6: 9
* PRF A3: 4 + D1: 4 + F3: 1 + B1: 3,5 + H1: 3,5 + H6: 9 => SOL
* STA A3: 4 + D1: 4 + F3: 1 + B1: 3,5 + H1: 3,5 + H6: 9
* CNT   7 HDP CHAINS /   8 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060807, absurd

Solution

position: 159472836723968154486351729697125483842739615315684297964213578238547961571896342 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 # A3: 2,6 => CTR => A3: 4
* INC # A3: 4 => UNS
* DIS # C4: 2,6 => CTR => C4: 5,7
* INC # C4: 5,7 => UNS
* INC # C5: 2,6 => UNS
* DIS # D1: 2,8 => CTR => D1: 4
* INC # D1: 4 => UNS
* INC # D2: 2,8 => UNS
* INC # F2: 2,8 => UNS
* DIS # F3: 2,8 => CTR => F3: 1
* INC # F3: 1 => UNS
* DIS # B1: 2,8 => CTR => B1: 3,5
* INC # B1: 3,5 => UNS
* DIS # H1: 2,8 => CTR => H1: 3,5
* INC # H1: 3,5 => UNS
* INC # F7: 2,8 => UNS
* INC # F7: 3,9 => UNS
* INC # I1: 4,8 => UNS
* INC # I1: 6 => UNS
* INC # D2: 4,8 => UNS
* INC # D2: 2,9 => UNS
* DIS # G4: 7,8 => CTR => G4: 4,6
* INC # G4: 4,6 => UNS
* DIS # H6: 7,8 => CTR => H6: 9
* INC # H6: 9 => UNS
* INC # I6: 7,8 => UNS
* DIS # H3: 7,8 => CTR => H3: 1,2
* INC # H3: 1,2 => UNS
* PRF # H7: 7,8 => SOL
* INC # H7: 3,9 => UNS
* DIS # G5: 1,9 => CTR => G5: 4,6
* INC # G5: 4,6 => UNS
* PRF # H7: 7,8 => SOL
* INC # H7: 3,9 => UNS
* INC # I6: 7,8 => UNS
* INC # I6: 6 => UNS
* INC # H7: 3,9 => UNS
* PRF # G9: 3,9 => SOL
* INC # G9: 8 => UNS
* INC # A8: 3,9 => UNS
* INC # A8: 2,5 => UNS
* CNT  41 HDP CHAINS /  41 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A3: 2,6 => CTR => A3: 4
* DIS A3: 4 # D1: 2,8 => CTR => D1: 4
* INC A3: 4 + D1: 4 # D2: 2,8 => UNS
* INC A3: 4 + D1: 4 # F2: 2,8 => UNS
* DIS A3: 4 + D1: 4 # F3: 2,8 => CTR => F3: 1
* DIS A3: 4 + D1: 4 + F3: 1 # B1: 2,8 => CTR => B1: 3,5
* DIS A3: 4 + D1: 4 + F3: 1 + B1: 3,5 # H1: 2,8 => CTR => H1: 3,5
* DIS A3: 4 + D1: 4 + F3: 1 + B1: 3,5 + H1: 3,5 # H6: 7,8 => CTR => H6: 9
* PRF A3: 4 + D1: 4 + F3: 1 + B1: 3,5 + H1: 3,5 + H6: 9 => SOL
* STA A3: 4 + D1: 4 + F3: 1 + B1: 3,5 + H1: 3,5 + H6: 9
* CNT   9 HDP CHAINS /   8 HYP OPENED