Analysis of zz-www.sudokuoftheday.co.uk-20060408-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
Autosolve
Pair Reduction Variants
- Pair Reduction Analysis
- Pair Reduction
Details
Solution
Appendix: Full HDP Chains
- A1. Pair Reduction Analysis
- A2. Pair Reduction

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

level: medium

position: ...2..4.32...39.8..83.4...97..4.39.......51....618....6......7.......5..8.5.....6 initial

Autosolve

position: ...2.84.32...39.8..83.4...97..4.39.......51....618....6.....87....8..5..8.5.....6 autosolve

Pair Reduction Variants

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A1: 1,5 => SOL
* DIS # B1: 1,5 => CTR => B1: 6,7,9
* DIS # H3: 1,5 => CTR => H3: 2
* DIS # H3: 1,5 => CTR => H3: 2
* PRF # A1: 1,5 => SOL
* DIS # B1: 1,5 => CTR => B1: 6,7,9
* DIS # G3: 2 => CTR => G3: 6,7
* PRF # B2: 6,7 => SOL
* DIS # B5: 3,4 => CTR => B5: 2
* PRF # B6: 3,4 => SOL
* DIS # H5: 2,6 => CTR => H5: 3,4
* PRF # A8: 3,4 => SOL
* DIS # H4: 5 => CTR => H4: 2,6
* DIS # E5: 2,7 => CTR => E5: 6,9
* DIS # I6: 2,7 => CTR => I6: 4,5
* DIS # F8: 2,7 => CTR => F8: 1,4,6
* DIS # H8: 2,3 => CTR => H8: 1,4,9
* DIS # H9: 2,3 => CTR => H9: 1,4,9
* DIS # G6: 7 => CTR => G6: 2,3
* CNT  19 HDP CHAINS /  51 HYP OPENED

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

Pair Reduction

The following important HDP chains were detected:

* PRF # A1: 1,5 => SOL
* STA A1: 1,5
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

`...2..4.32...39.8..83.4...97..4.39.......51....618....6......7.......5..8.5.....6`	initial
`...2.84.32...39.8..83.4...97..4.39.......51....618....6.....87....8..5..8.5.....6`	autosolve
`197268453264539781583741629751423968428695137936187245619354872372816594845972316`	solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
A3: 1,5
H1: 1,5
G2: 6,7
A5: 3,4
E4: 2,6
F6: 2,7
G9: 2,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E1,F3: 1.. / E1 = 1  => 15 pairs (_) / F3 = 1  => 13 pairs (_)
B4,C4: 1.. / B4 = 1  =>  0 pairs (X) / C4 = 1  => 10 pairs (_)
G3,H3: 2.. / G3 = 2  =>  0 pairs (X) / H3 = 2  => 11 pairs (_)
D7,D9: 3.. / D7 = 3  =>  8 pairs (_) / D9 = 3  =>  0 pairs (X)
B7,D7: 3.. / B7 = 3  =>  0 pairs (X) / D7 = 3  =>  8 pairs (_)
G6,G9: 3.. / G6 = 3  =>  0 pairs (X) / G9 = 3  =>  9 pairs (_)
B2,C2: 4.. / B2 = 4  =>  9 pairs (_) / C2 = 4  =>  8 pairs (_)
D7,E7: 5.. / D7 = 5  =>  0 pairs (X) / E7 = 5  =>  8 pairs (_)
E1,E7: 5.. / E1 = 5  =>  0 pairs (X) / E7 = 5  =>  8 pairs (_)
B1,B2: 6.. / B1 = 6  =>  7 pairs (_) / B2 = 6  =>  0 pairs (*)
G2,G3: 6.. / G2 = 6  =>  8 pairs (_) / G3 = 6  => 13 pairs (_)
H4,H5: 6.. / H4 = 6  => 14 pairs (_) / H5 = 6  =>  0 pairs (X)
E8,F8: 6.. / E8 = 6  =>  0 pairs (X) / F8 = 6  =>  8 pairs (_)
B1,E1: 6.. / B1 = 6  =>  7 pairs (_) / E1 = 6  =>  0 pairs (*)
E4,H4: 6.. / E4 = 6  =>  0 pairs (X) / H4 = 6  => 14 pairs (_)
F3,F8: 6.. / F3 = 6  =>  0 pairs (X) / F8 = 6  =>  8 pairs (_)
C4,C5: 8.. / C4 = 8  =>  0 pairs (X) / C5 = 8  =>  8 pairs (_)
I4,I5: 8.. / I4 = 8  =>  8 pairs (_) / I5 = 8  =>  0 pairs (X)
C4,I4: 8.. / C4 = 8  =>  0 pairs (X) / I4 = 8  =>  8 pairs (_)
C5,I5: 8.. / C5 = 8  =>  8 pairs (_) / I5 = 8  =>  0 pairs (X)
A6,B6: 9.. / A6 = 9  =>  0 pairs (*) / B6 = 9  =>  0 pairs (X)
D5,E5: 9.. / D5 = 9  => 10 pairs (_) / E5 = 9  => 10 pairs (_)
H8,H9: 9.. / H8 = 9  =>  8 pairs (_) / H9 = 9  =>  8 pairs (_)
* DURATION: 0:00:23.225937  START: 22:14:27.918543  END: 22:14:51.144480 2019-04-30
* CP COUNT: (23)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,E4,F6,G2,G9,H1)
* ...2.84.32...39.8..83.4...97..4.39.......51....618....6.....87....8..5..8.5.....6
* PAIR A3: 1,5 BLK 1
A1: 1,5,9                                # reduction candidate for 1,5
A1: 1,5 => SOLVED
* 197268453264539781583741629751423968428695137936187245619354872372816594845972316
A1: 9                                    #  8 pairs
B1: 1,5,6,7,9                            # reduction candidate for 1,5
B1: 1,5 => CTR
* 917268453264539781583741629751423968.286951.7.961872.56...5.87.1..8765..875.12346
B1: 6,7,9                                #  7 pairs
B2: 1,5,4,6,7                            # reduction candidate for 1,5
B2: 1,5                                  # 10 pairs
* PAIR A3: 1,5 ROW 3
H3: 1,5,2                                # reduction candidate for 1,5
H3: 1,5 => CTR
* 9672184532415396875836472197..46392....79516..961827356.9354871134876592875921346
H3: 2                                    # 11 pairs
* PAIR H1: 1,5 BLK 3
I2: 1,5,7                                # reduction candidate for 1,5
I2: 1,5                                  # 11 pairs
H3: 1,5,2                                # reduction candidate for 1,5
H3: 1,5 => CTR
* 9672184532415396875836472197..46392....79516..961827356.9354871134876592875921346
H3: 2                                    # 11 pairs
* PAIR H1: 1,5 ROW 1
A1: 1,5,9                                # reduction candidate for 1,5
A1: 1,5 => SOLVED
* 197268453264539781583741629751423968428695137936187245619354872372816594845972316
A1: 9                                    #  8 pairs
B1: 1,5,6,7,9                            # reduction candidate for 1,5
B1: 1,5 => CTR
* 917268453264539781583741629751423968.286951.7.961872.56...5.87.1..8765..875.12346
B1: 6,7,9                                #  7 pairs
E1: 1,5,6,7                              # reduction candidate for 1,5
E1: 1,5                                  #  9 pairs
* PAIR G2: 6,7 BLK 3
G3: 6,7,2                                # reduction candidate for 6,7
G3: 2 => CTR
* 9672184532..5396875836472197514639283.87951644961827356.935487113.8.65..875921346
G3: 6,7                                  # 11 pairs
* PAIR G2: 6,7 ROW 2
B2: 6,7,1,4,5                            # reduction candidate for 6,7
B2: 6,7 => SOLVED
* 197268453264539781583741629751423968428695137936187245619354872372816594845972316
B2: 1,4,5                                #  7 pairs
D2: 6,7,5                                # reduction candidate for 6,7
D2: 6,7                                  # 14 pairs
* PAIR A5: 3,4 BLK 4
B5: 3,4,2                                # reduction candidate for 3,4
B5: 3,4 => CTR
* ...2.84.32...39.8..83.4...97..4.39.......51....618....6.....87....8..5..8.5.....6
B5: 2                                    # 10 pairs
A6: 3,4,5,9                              # reduction candidate for 3,4
A6: 3,4                                  # 13 pairs
B6: 3,4,2,5,9                            # reduction candidate for 3,4
B6: 3,4 => SOLVED
* 197268453264539781583741629751423968428695137936187245619354872372816594845972316
B6: 2,5,9                                #  7 pairs
* PAIR A5: 3,4 ROW 5
H5: 3,4,2,6                              # reduction candidate for 3,4
H5: 2,6 => CTR
* 9672.84532..539687583.4.2197514.39.8328..516449618273564....87113.8..5..875...3.6
H5: 3,4                                  # 14 pairs
* PAIR A5: 3,4 COL A
A8: 3,4,1,9                              # reduction candidate for 3,4
A8: 3,4 => SOLVED
* 197268453264539781583741629751423968428695137936187245619354872372816594845972316
A8: 1,9                                  # 13 pairs
* PAIR E4: 2,6 BLK 5
E5: 2,6,7,9                              # reduction candidate for 2,6
E5: 2,6                                  # 18 pairs
E5: 7,9                                  #  8 pairs
* PAIR E4: 2,6 ROW 4
H4: 2,6,5                                # reduction candidate for 2,6
H4: 5 => CTR
* .6.2.84132...39.85583.41.297..46395......516.95618....6.....87.1..8.65..8.5.1...6
H4: 2,6                                  # 11 pairs
* PAIR E4: 2,6 COL E
E8: 2,6,1,7,9                            # reduction candidate for 2,6
E8: 2,6                                  #  9 pairs
E8: 1,7,9                                #  8 pairs
* PAIR F6: 2,7 BLK 5
E5: 2,7,6,9                              # reduction candidate for 2,7
E5: 2,7 => CTR
* 9672.84.32...39.8.583.4...97..4639..3..9.516.49618..356.....87113.8765..8753..2.6
E5: 6,9                                  #  8 pairs
* PAIR F6: 2,7 ROW 6
G6: 2,7,3                                # reduction candidate for 2,7
G6: 2,7                                  #  9 pairs
I6: 2,7,4,5                              # reduction candidate for 2,7
I6: 2,7 => CTR
* 9.72584132...39.85583.41.297514.396832896514749618735263.5.28711728965.48.531.296
I6: 4,5                                  #  8 pairs
* PAIR F6: 2,7 COL F
F8: 2,7,1,4,6                            # reduction candidate for 2,7
F8: 2,7 => CTR
* .6.2184532...396811835467297..423968..86951.7596187...6.295.874...8625..8.5.....6
F8: 1,4,6                                #  7 pairs
F9: 2,7,1,4                              # reduction candidate for 2,7
F9: 2,7                                  # 10 pairs
* PAIR G9: 2,3 BLK 9
H8: 2,3,1,4,9                            # reduction candidate for 2,3
H8: 2,3 => CTR
* 967258413214.39.85583.41.297514239683289651474961873526325948711.98..5348.53..296
H8: 1,4,9                                #  8 pairs
H9: 2,3,1,4,9                            # reduction candidate for 2,3
H9: 2,3 => CTR
* 9.72.84532..539.87583.4..197..4.39.......51...9618.7.56.935.87113.8..5948759....6
H9: 1,4,9                                #  7 pairs
* PAIR G9: 2,3 ROW 9
B9: 2,3,1,4,7,9                          # reduction candidate for 2,3
B9: 2,3                                  #  9 pairs
B9: 1,4,7,9                              #  7 pairs
* PAIR G9: 2,3 COL G
G6: 2,3,7                                # reduction candidate for 2,3
G6: 7 => CTR
* 9672184532..5396875836472197..46392.3..79516.4961827356.9354871134876592875921346
G6: 2,3                                  # 11 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060408-absurd-base-pr-000.dot
* REASONING
* PRF # A1: 1,5 => SOL
* DIS # B1: 1,5 => CTR => B1: 6,7,9
* DIS # H3: 1,5 => CTR => H3: 2
* DIS # H3: 1,5 => CTR => H3: 2
* PRF # A1: 1,5 => SOL
* DIS # B1: 1,5 => CTR => B1: 6,7,9
* DIS # G3: 2 => CTR => G3: 6,7
* PRF # B2: 6,7 => SOL
* DIS # B5: 3,4 => CTR => B5: 2
* PRF # B6: 3,4 => SOL
* DIS # H5: 2,6 => CTR => H5: 3,4
* PRF # A8: 3,4 => SOL
* DIS # H4: 5 => CTR => H4: 2,6
* DIS # E5: 2,7 => CTR => E5: 6,9
* DIS # I6: 2,7 => CTR => I6: 4,5
* DIS # F8: 2,7 => CTR => F8: 1,4,6
* DIS # H8: 2,3 => CTR => H8: 1,4,9
* DIS # H9: 2,3 => CTR => H9: 1,4,9
* DIS # G6: 7 => CTR => G6: 2,3
* CNT  19 HDP CHAINS /  51 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,E4,F6,G2,G9,H1)
* ...2.84.32...39.8..83.4...97..4.39.......51....618....6.....87....8..5..8.5.....6
* PAIR A3: 1,5 BLK 1
A1: 1,5,9                                # reduction candidate for 1,5
A1: 1,5 => SOLVED
* 197268453264539781583741629751423968428695137936187245619354872372816594845972316
* DURATION: 0:00:01.841279  START: 22:15:19.893642  END: 22:15:21.734921 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060408-absurd-base-pr-001.dot
* REASONING
* PRF # A1: 1,5 => SOL
* STA A1: 1,5
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060408, absurd

Solution

position: 197268453264539781583741629751423968428695137936187245619354872372816594845972316 solved

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:

* PRF # A1: 1,5 => SOL
* INC # A1: 9 => UNS
* DIS # B1: 1,5 => CTR => B1: 6,7,9
* INC # B1: 6,7,9 => UNS
* INC # B2: 1,5 => UNS
* DIS # H3: 1,5 => CTR => H3: 2
* INC # H3: 2 => UNS
* INC # I2: 1,5 => UNS
* DIS # H3: 1,5 => CTR => H3: 2
* INC # H3: 2 => UNS
* PRF # A1: 1,5 => SOL
* INC # A1: 9 => UNS
* DIS # B1: 1,5 => CTR => B1: 6,7,9
* INC # B1: 6,7,9 => UNS
* INC # E1: 1,5 => UNS
* INC # G3: 6,7 => UNS
* DIS # G3: 2 => CTR => G3: 6,7
* PRF # B2: 6,7 => SOL
* INC # B2: 1,4,5 => UNS
* INC # D2: 6,7 => UNS
* DIS # B5: 3,4 => CTR => B5: 2
* INC # B5: 2 => UNS
* INC # A6: 3,4 => UNS
* PRF # B6: 3,4 => SOL
* INC # B6: 2,5,9 => UNS
* INC # H5: 3,4 => UNS
* DIS # H5: 2,6 => CTR => H5: 3,4
* PRF # A8: 3,4 => SOL
* INC # A8: 1,9 => UNS
* INC # E5: 2,6 => UNS
* INC # E5: 7,9 => UNS
* INC # H4: 2,6 => UNS
* DIS # H4: 5 => CTR => H4: 2,6
* INC # E8: 2,6 => UNS
* INC # E8: 1,7,9 => UNS
* DIS # E5: 2,7 => CTR => E5: 6,9
* INC # E5: 6,9 => UNS
* INC # G6: 2,7 => UNS
* DIS # I6: 2,7 => CTR => I6: 4,5
* INC # I6: 4,5 => UNS
* DIS # F8: 2,7 => CTR => F8: 1,4,6
* INC # F8: 1,4,6 => UNS
* INC # F9: 2,7 => UNS
* DIS # H8: 2,3 => CTR => H8: 1,4,9
* INC # H8: 1,4,9 => UNS
* DIS # H9: 2,3 => CTR => H9: 1,4,9
* INC # H9: 1,4,9 => UNS
* INC # B9: 2,3 => UNS
* INC # B9: 1,4,7,9 => UNS
* INC # G6: 2,3 => UNS
* DIS # G6: 7 => CTR => G6: 2,3
* CNT  51 HDP CHAINS /  51 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # A1: 1,5 => SOL
* STA A1: 1,5
* CNT   1 HDP CHAINS /   1 HYP OPENED