Analysis of zz-www.sudokuoftheday.co.uk-20190422-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019

position: ..84..7..7......2..5..18.6.4.2....3....93......1..2....6..8917.......6......7...8 initial

Autosolve

position: ..842.7..7...9.82.25.718.6.4.2....3....93......1..2....6..8917.......6......7...8 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B4: 7,8 => CTR => B4: 9
* DIS # B8: 7,8 => CTR => B8: 1,2,3,4,9
* DIS # E6: 5,6 => CTR => E6: 4
* DIS # I4: 5,6 => CTR => I4: 1,7,9
* DIS # D4: 1 => CTR => D4: 5,8
* DIS # A6: 5,8 => CTR => A6: 3,6,9
* DIS # I4: 5,9 => CTR => I4: 1,6,7
* DIS # H6: 5,9 => CTR => H6: 4,8
* DIS # I6: 5,9 => CTR => I6: 4,6,7
* DIS # G9: 5,9 => CTR => G9: 2,3,4
* DIS # C7: 3,5 => CTR => C7: 4
* PRF # C7: 4 => SOL
* DIS # A8: 3,5 => CTR => A8: 1,8,9
* DIS # C8: 3,5 => CTR => C8: 4,7,9
* DIS # A9: 3,5 => CTR => A9: 1,9
* PRF # C9: 3,5 => SOL
* DIS # D7: 3,5 => CTR => D7: 2
* PRF # I7: 3,5 => SOL
* DIS # C8: 4,5 => CTR => C8: 3,7,9
* DIS # I8: 4,5 => CTR => I8: 2,3,9
* DIS # E6: 6 => CTR => E6: 4,5
* CNT  21 HDP CHAINS /  48 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 # B4: 7,8 => CTR => B4: 9
* DIS B4: 9 # B8: 7,8 => CTR => B8: 1,2,3,4
* PRF B4: 9 + B8: 1,2,3,4 # B9: 1,4 => SOL
* STA B4: 9 + B8: 1,2,3,4 + B9: 1,4
* CNT   3 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

..84..7..7......2..5..18.6.4.2....3....93......1..2....6..8917.......6......7...8 initial
..842.7..7...9.82.25.718.6.4.2....3....93......1..2....6..8917.......6......7...8 autosolve
138426795746395821259718364492861537685937412371542986564289173827153649913674258 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
B5: 7,8
E4: 5,6
D6: 5,8
G4: 5,9
A7: 3,5
E8: 4,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B2,I2: 1.. / B2 = 1  =>  0 pairs (X) / I2 = 1  =>  0 pairs (_)
H1,H5: 1.. / H1 = 1  =>  0 pairs (X) / H5 = 1  =>  0 pairs (_)
G5,I5: 2.. / G5 = 2  =>  6 pairs (_) / I5 = 2  =>  0 pairs (*)
B8,B9: 2.. / B8 = 2  => 11 pairs (_) / B9 = 2  =>  6 pairs (_)
D7,I7: 2.. / D7 = 2  =>  6 pairs (_) / I7 = 2  =>  0 pairs (X)
G5,G9: 2.. / G5 = 2  =>  6 pairs (_) / G9 = 2  =>  0 pairs (*)
A6,B6: 3.. / A6 = 3  => 16 pairs (_) / B6 = 3  =>  8 pairs (_)
G3,G9: 3.. / G3 = 3  =>  0 pairs (*) / G9 = 3  =>  0 pairs (X)
F5,E6: 4.. / F5 = 4  =>  0 pairs (X) / E6 = 4  => 16 pairs (_)
C7,I7: 4.. / C7 = 4  =>  0 pairs (*) / I7 = 4  =>  0 pairs (X)
E6,E8: 4.. / E6 = 4  => 16 pairs (_) / E8 = 4  =>  0 pairs (X)
A1,C2: 6.. / A1 = 6  =>  0 pairs (X) / C2 = 6  => 11 pairs (_)
E4,E6: 6.. / E4 = 6  => 16 pairs (_) / E6 = 6  =>  0 pairs (X)
D9,F9: 6.. / D9 = 6  =>  7 pairs (_) / F9 = 6  =>  0 pairs (X)
A1,F1: 6.. / A1 = 6  =>  0 pairs (X) / F1 = 6  => 11 pairs (_)
E4,I4: 6.. / E4 = 6  => 16 pairs (_) / I4 = 6  =>  0 pairs (X)
C2,C5: 6.. / C2 = 6  => 11 pairs (_) / C5 = 6  =>  0 pairs (X)
D2,D9: 6.. / D2 = 6  =>  0 pairs (X) / D9 = 6  =>  7 pairs (_)
F4,F5: 7.. / F4 = 7  =>  7 pairs (_) / F5 = 7  => 15 pairs (_)
B8,C8: 7.. / B8 = 7  =>  0 pairs (X) / C8 = 7  =>  7 pairs (_)
B6,I6: 7.. / B6 = 7  => 18 pairs (_) / I6 = 7  =>  6 pairs (_)
C5,C8: 7.. / C5 = 7  =>  0 pairs (X) / C8 = 7  =>  7 pairs (_)
D4,D6: 8.. / D4 = 8  => 16 pairs (_) / D6 = 8  =>  0 pairs (X)
H5,H6: 8.. / H5 = 8  =>  0 pairs (X) / H6 = 8  => 16 pairs (_)
A8,B8: 8.. / A8 = 8  =>  7 pairs (_) / B8 = 8  =>  0 pairs (X)
B4,D4: 8.. / B4 = 8  =>  0 pairs (X) / D4 = 8  => 16 pairs (_)
* DURATION: 0:00:26.747614  START: 05:31:08.347226  END: 05:31:35.094840 2019-05-01
* CP COUNT: (26)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B5,D6,E4,E8,G4)
* ..842.7..7...9.82.25.718.6.4.2....3....93......1..2....6..8917.......6......7...8
* PAIR B5: 7,8 BLK 4
B4: 7,8,9                                # reduction candidate for 7,8
B4: 7,8 => CTR
* ..842.71.71..9.82.25.718.6.482157936.7.934281..1862..7.6..8917.8.7.416..14.276..8
B4: 9                                    # 16 pairs
B6: 7,8,3,9                              # reduction candidate for 7,8
B6: 7,8                                  # 18 pairs
* PAIR B5: 7,8 COL B
B8: 7,8,1,2,3,4,9                        # reduction candidate for 7,8
B8: 7,8 => CTR
* .1842.7..74..9.82125.718.6.4.28.1.3....937214.31542987.64.8917...7.5.6...2..7...8
B8: 1,2,3,4,9                            # 10 pairs
* PAIR E4: 5,6 BLK 5
E6: 5,6,4                                # reduction candidate for 5,6
E6: 5,6 => CTR
* ..842.71.71..9.82.25.718.6.4821.7.36.7.934281..1862..7.6..8917.8.7.416..14.276..8
E6: 4                                    # 16 pairs
* PAIR E4: 5,6 ROW 4
I4: 5,6,1,7,9                            # reduction candidate for 5,6
I4: 5,6 => CTR
* ..842.71.71..9.82.25.718.6.482157936.7.934281..1862..7.6..8917.8.7.416..14.276..8
I4: 1,7,9                                # 16 pairs
* PAIR D6: 5,8 BLK 5
D4: 5,8,1                                # reduction candidate for 5,8
D4: 1 => CTR
* ..842.71.71..9.82.25.718.6.4821.7.36.7.93.281..1862..7.6..8917.8.7.416..14.276..8
D4: 5,8                                  # 16 pairs
* PAIR D6: 5,8 ROW 6
A6: 5,8,3,6,9                            # reduction candidate for 5,8
A6: 5,8 => CTR
* ..842.7..7...9.82.25.718.6.4928.7531...931..6.315.2..7.6..8917.......6......7...8
A6: 3,6,9                                #  7 pairs
H6: 5,8,4,9                              # reduction candidate for 5,8
H6: 5,8                                  # 10 pairs
* PAIR G4: 5,9 BLK 6
I4: 5,9,1,6,7                            # reduction candidate for 5,9
I4: 5,9 => CTR
* ..842.7..7...9.82.25.718.6.4.2.6..3....93......1..2....6..8917.......6......7...8
I4: 1,6,7                                #  6 pairs
G6: 5,9,4                                # reduction candidate for 5,9
G6: 5,9                                  # 10 pairs
H6: 5,9,4,8                              # reduction candidate for 5,9
H6: 5,9 => CTR
* ..842.71.71..9.82.25.718.6.4.2..7.3..7.93..8...1..2..7.6..8917...7...6......7...8
H6: 4,8                                  #  7 pairs
I6: 5,9,4,6,7                            # reduction candidate for 5,9
I6: 5,9 => CTR
* ..842.7..7...9.82.25.718.6.4.2....3..8.93....371.62.8.56..8917.8.7.4.6......7...8
I6: 4,6,7                                #  6 pairs
* PAIR G4: 5,9 COL G
G9: 5,9,2,3,4                            # reduction candidate for 5,9
G9: 5,9 => CTR
* ..842.7..74..9.8212597183644.28...3....93421...1..248..64.8917.....4.6......7..48
G9: 2,3,4                                #  6 pairs
* PAIR A7: 3,5 BLK 7
C7: 3,5,4                                # reduction candidate for 3,5
C7: 3,5 => CTR
* 69842.71.714.9682.2537184694.2.6.93...693.24.931.42....65289174.47.5.692.29.74358
C7: 4 => SOLVED
* 138426795746395821259718364492861537685937412371542986564289173827153649913674258
A8: 3,5,1,8,9                            # reduction candidate for 3,5
A8: 3,5 => CTR
* ..842.7..74..9.82125.718.6.4.28.1.3..7.93.21...15.2.87.6..8917..8715.6.2129.7...8
A8: 1,8,9                                #  6 pairs
C8: 3,5,4,7,9                            # reduction candidate for 3,5
C8: 3,5 => CTR
* ..842.7..746.9.82125.718.6.4.2..7.3..8793.21...1..2.87.6..8917.87....6..12967...8
C8: 4,7,9                                #  6 pairs
A9: 3,5,1,9                              # reduction candidate for 3,5
A9: 3,5 => CTR
* ..842.7..746.9.821253718.6.4.28.1.3...5937.1..31542987.64.8917...7.5.6....967.3.8
A9: 1,9                                  #  7 pairs
C9: 3,5,4,9                              # reduction candidate for 3,5
C9: 3,5 => SOLVED
* 138426795746395821259718364492861537685937412371542986564289173827153649913674258
C9: 4,9                                  #  7 pairs
* PAIR A7: 3,5 ROW 7
D7: 3,5,2                                # reduction candidate for 3,5
D7: 3,5 => CTR
* ..842.7..74..9.82125.718.6.4.28.1.3....937214..154298.564389172..7.54693....76.48
D7: 2                                    #  6 pairs
I7: 3,5,2,4                              # reduction candidate for 3,5
I7: 3,5 => SOLVED
* 138426795746395821259718364492861537685937412371542986564289173827153649913674258
I7: 2,4                                  #  7 pairs
* PAIR A7: 3,5 COL A
A6: 3,5,6,8,9                            # reduction candidate for 3,5
A6: 3,5                                  # 10 pairs
A6: 6,8,9                                #  9 pairs
* PAIR E8: 4,5 BLK 8
F8: 4,5,1,3                              # reduction candidate for 4,5
F8: 4,5                                  # 12 pairs
F9: 4,5,1,3,6                            # reduction candidate for 4,5
F9: 4,5                                  # 10 pairs
* PAIR E8: 4,5 ROW 8
C8: 4,5,3,7,9                            # reduction candidate for 4,5
C8: 4,5 => CTR
* ..842.7..746.9.82125.718.6.4.2..7.3..8793.21...1..2.87.6..8917.87....6..12967...8
C8: 3,7,9                                #  6 pairs
H8: 4,5,9                                # reduction candidate for 4,5
H8: 4,5                                  #  8 pairs
I8: 4,5,2,3,9                            # reduction candidate for 4,5
I8: 4,5 => CTR
* ..842.75.74..9.82125.718.6.4.28.1.3....93..1...1..2.8..64.8917.......69.....7..48
I8: 2,3,9                                #  6 pairs
* PAIR E8: 4,5 COL E
E6: 4,5,6                                # reduction candidate for 4,5
E6: 6 => CTR
* ..842.71.71..9.82.25.718.6.482157936.7.934281..1862..7.6..8917.8.7.416..14.276..8
E6: 4,5                                  # 16 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190422-absurd-base-pr-000.dot
* REASONING
* DIS # B4: 7,8 => CTR => B4: 9
* DIS # B8: 7,8 => CTR => B8: 1,2,3,4,9
* DIS # E6: 5,6 => CTR => E6: 4
* DIS # I4: 5,6 => CTR => I4: 1,7,9
* DIS # D4: 1 => CTR => D4: 5,8
* DIS # A6: 5,8 => CTR => A6: 3,6,9
* DIS # I4: 5,9 => CTR => I4: 1,6,7
* DIS # H6: 5,9 => CTR => H6: 4,8
* DIS # I6: 5,9 => CTR => I6: 4,6,7
* DIS # G9: 5,9 => CTR => G9: 2,3,4
* DIS # C7: 3,5 => CTR => C7: 4
* PRF # C7: 4 => SOL
* DIS # A8: 3,5 => CTR => A8: 1,8,9
* DIS # C8: 3,5 => CTR => C8: 4,7,9
* DIS # A9: 3,5 => CTR => A9: 1,9
* PRF # C9: 3,5 => SOL
* DIS # D7: 3,5 => CTR => D7: 2
* PRF # I7: 3,5 => SOL
* DIS # C8: 4,5 => CTR => C8: 3,7,9
* DIS # I8: 4,5 => CTR => I8: 2,3,9
* DIS # E6: 6 => CTR => E6: 4,5
* CNT  21 HDP CHAINS /  48 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B5,D6,E4,E8,G4)
* ..842.7..7...9.82.25.718.6.4.2....3....93......1..2....6..8917.......6......7...8
* PAIR B5: 7,8 BLK 4
B4: 7,8,9                                # reduction candidate for 7,8
B4: 7,8 => CTR
* ..842.71.71..9.82.25.718.6.482157936.7.934281..1862..7.6..8917.8.7.416..14.276..8
* RESTART
* PAIR B5: 7,8 COL B
B8: 7,8,1,2,3,4                          # reduction candidate for 7,8
B8: 7,8 => CTR
* ..842.7..74..9.82125.718.6.492861537...937214.71542986.64.8917..8..5.6...2..7...8
* PAIR RESTART

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,A9,B2,B8,C3,C7,F4,F5,F8,F9,G3,G5,H1,H5,H8,I2,I4,I7)
* .384267.57.639582.25.718.6.49286.53.68593....37154298656.28917.8.715.6.....67..58
* PAIR B2: 1,4 COL B
B9: 1,4,2                                # reduction candidate for 1,4
B9: 1,4 => SOLVED
* 138426795746395821259718364492861537685937412371542986564289173827153649913674258
* DURATION: 0:00:03.898761  START: 05:31:58.866610  END: 05:32:02.765371 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190422-absurd-base-pr-001.dot
* REASONING
* DIS # B4: 7,8 => CTR => B4: 9
* DIS B4: 9 # B8: 7,8 => CTR => B8: 1,2,3,4
* PRF B4: 9 + B8: 1,2,3,4 # B9: 1,4 => SOL
* STA B4: 9 + B8: 1,2,3,4 + B9: 1,4
* CNT   3 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190422, absurd

Solution

position: 138426795746395821259718364492861537685937412371542986564289173827153649913674258 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 # B4: 7,8 => CTR => B4: 9
* INC # B4: 9 => UNS
* INC # B6: 7,8 => UNS
* DIS # B8: 7,8 => CTR => B8: 1,2,3,4,9
* INC # B8: 1,2,3,4,9 => UNS
* DIS # E6: 5,6 => CTR => E6: 4
* INC # E6: 4 => UNS
* DIS # I4: 5,6 => CTR => I4: 1,7,9
* INC # I4: 1,7,9 => UNS
* INC # D4: 5,8 => UNS
* DIS # D4: 1 => CTR => D4: 5,8
* DIS # A6: 5,8 => CTR => A6: 3,6,9
* INC # A6: 3,6,9 => UNS
* INC # H6: 5,8 => UNS
* DIS # I4: 5,9 => CTR => I4: 1,6,7
* INC # I4: 1,6,7 => UNS
* INC # G6: 5,9 => UNS
* DIS # H6: 5,9 => CTR => H6: 4,8
* INC # H6: 4,8 => UNS
* DIS # I6: 5,9 => CTR => I6: 4,6,7
* INC # I6: 4,6,7 => UNS
* DIS # G9: 5,9 => CTR => G9: 2,3,4
* INC # G9: 2,3,4 => UNS
* DIS # C7: 3,5 => CTR => C7: 4
* PRF # C7: 4 => SOL
* DIS # A8: 3,5 => CTR => A8: 1,8,9
* INC # A8: 1,8,9 => UNS
* DIS # C8: 3,5 => CTR => C8: 4,7,9
* INC # C8: 4,7,9 => UNS
* DIS # A9: 3,5 => CTR => A9: 1,9
* INC # A9: 1,9 => UNS
* PRF # C9: 3,5 => SOL
* INC # C9: 4,9 => UNS
* DIS # D7: 3,5 => CTR => D7: 2
* INC # D7: 2 => UNS
* PRF # I7: 3,5 => SOL
* INC # I7: 2,4 => UNS
* INC # A6: 3,5 => UNS
* INC # A6: 6,8,9 => UNS
* INC # F8: 4,5 => UNS
* INC # F9: 4,5 => UNS
* DIS # C8: 4,5 => CTR => C8: 3,7,9
* INC # C8: 3,7,9 => UNS
* INC # H8: 4,5 => UNS
* DIS # I8: 4,5 => CTR => I8: 2,3,9
* INC # I8: 2,3,9 => UNS
* INC # E6: 4,5 => UNS
* DIS # E6: 6 => CTR => E6: 4,5
* CNT  48 HDP CHAINS /  48 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B4: 7,8 => CTR => B4: 9
* DIS B4: 9 # B8: 7,8 => CTR => B8: 1,2,3,4
* PRF B4: 9 + B8: 1,2,3,4 # B9: 1,4 => SOL
* STA B4: 9 + B8: 1,2,3,4 + B9: 1,4
* CNT   3 HDP CHAINS /   3 HYP OPENED