Analysis of zz-www.sudokuoftheday.co.uk-20060708-absurd-base.sdk

Contents

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

level: medium

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

position: 6.....8....39.6.14492..1.......9...3.......6..46..3.......19..8.1587.3..7.....1.. initial

Autosolve

position: 6.1.3.8....39.6.14492.8163.1..69.4.3....4..6..46..3....64.19..8.1587.3.67...6.1.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # B2: 8 => SOL
* DIS # D1: 5,7 => CTR => D1: 2,4
* DIS # H1: 5,7 => CTR => H1: 2,9
* DIS # I1: 5,7 => CTR => I1: 2,9
* PRF # B2: 5,8 => SOL
* DIS # D1: 2,5 => CTR => D1: 4,7
* PRF # G2: 7 => SOL
* DIS # D1: 5,7 => CTR => D1: 2,4
* DIS # H1: 5,7 => CTR => H1: 2,9
* DIS # I1: 5,7 => CTR => I1: 2,9
* DIS # H4: 7,8 => CTR => H4: 2,5
* DIS # F4: 2,5 => CTR => F4: 7,8
* DIS # F5: 2,5 => CTR => F5: 7,8
* DIS # D6: 2,5 => CTR => D6: 1,7
* DIS # H6: 2,5 => CTR => H6: 7,8
* DIS # I6: 2,5 => CTR => I6: 1,7
* PRF # D7: 5 => SOL
* PRF # F9: 2,4 => SOL
* CNT  18 HDP CHAINS /  67 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # B2: 8 => SOL
* STA B2: 8
* CNT   1 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

6.....8....39.6.14492..1.......9...3.......6..46..3.......19..8.1587.3..7.....1.. initial
6.1.3.8....39.6.14492.8163.1..69.4.3....4..6..46..3....64.19..8.1587.3.67...6.1.. autosolve
671435892583926714492781635157698423839247561246153987364519278915872346728364159 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
B1: 5,7
A2: 5,8
E2: 2,5
D3: 5,7
I3: 5,7
C4: 7,8
E6: 2,5
A7: 2,3
A8: 2,9
C9: 8,9
F8: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D5,D6: 1.. / D5 = 1  => 11 pairs (_) / D6 = 1  => 11 pairs (_)
I5,I6: 1.. / I5 = 1  => 11 pairs (_) / I6 = 1  => 11 pairs (_)
D5,I5: 1.. / D5 = 1  => 11 pairs (_) / I5 = 1  => 11 pairs (_)
D6,I6: 1.. / D6 = 1  => 11 pairs (_) / I6 = 1  => 11 pairs (_)
E2,G2: 2.. / E2 = 2  => 12 pairs (_) / G2 = 2  =>  0 pairs (X)
E2,E6: 2.. / E2 = 2  => 12 pairs (_) / E6 = 2  =>  0 pairs (X)
A5,B5: 3.. / A5 = 3  => 12 pairs (_) / B5 = 3  => 12 pairs (_)
A7,B9: 3.. / A7 = 3  => 12 pairs (_) / B9 = 3  => 12 pairs (_)
D7,D9: 3.. / D7 = 3  => 12 pairs (_) / D9 = 3  => 12 pairs (_)
A7,D7: 3.. / A7 = 3  => 12 pairs (_) / D7 = 3  => 12 pairs (_)
B9,D9: 3.. / B9 = 3  => 12 pairs (_) / D9 = 3  => 12 pairs (_)
A5,A7: 3.. / A5 = 3  => 12 pairs (_) / A7 = 3  => 12 pairs (_)
B5,B9: 3.. / B5 = 3  => 12 pairs (_) / B9 = 3  => 12 pairs (_)
D1,F1: 4.. / D1 = 4  => 11 pairs (_) / F1 = 4  =>  0 pairs (X)
H8,H9: 4.. / H8 = 4  => 11 pairs (_) / H9 = 4  => 12 pairs (_)
F8,H8: 4.. / F8 = 4  => 12 pairs (_) / H8 = 4  => 11 pairs (_)
D1,D9: 4.. / D1 = 4  => 11 pairs (_) / D9 = 4  =>  0 pairs (X)
D3,I3: 5.. / D3 = 5  =>  0 pairs (X) / I3 = 5  => 16 pairs (_)
E2,E6: 5.. / E2 = 5  =>  0 pairs (X) / E6 = 5  => 12 pairs (_)
B1,B2: 7.. / B1 = 7  =>  0 pairs (*) / B2 = 7  =>  0 pairs (X)
C4,C5: 7.. / C4 = 7  => 11 pairs (_) / C5 = 7  => 13 pairs (_)
G7,H7: 7.. / G7 = 7  => 14 pairs (_) / H7 = 7  => 12 pairs (_)
B2,G2: 7.. / B2 = 7  => 11 pairs (_) / G2 = 7  =>  0 pairs (*)
D3,I3: 7.. / D3 = 7  => 16 pairs (_) / I3 = 7  =>  0 pairs (X)
A2,B2: 8.. / A2 = 8  => 12 pairs (_) / B2 = 8  =>  0 pairs (*)
F4,F5: 8.. / F4 = 8  => 13 pairs (_) / F5 = 8  => 12 pairs (_)
H4,H6: 8.. / H4 = 8  =>  0 pairs (X) / H6 = 8  => 11 pairs (_)
B9,C9: 8.. / B9 = 8  => 14 pairs (_) / C9 = 8  => 10 pairs (_)
A6,H6: 8.. / A6 = 8  =>  0 pairs (X) / H6 = 8  => 11 pairs (_)
H1,I1: 9.. / H1 = 9  => 10 pairs (_) / I1 = 9  => 14 pairs (_)
G5,G6: 9.. / G5 = 9  => 12 pairs (_) / G6 = 9  => 11 pairs (_)
A8,C9: 9.. / A8 = 9  => 10 pairs (_) / C9 = 9  => 14 pairs (_)
A6,G6: 9.. / A6 = 9  => 12 pairs (_) / G6 = 9  => 11 pairs (_)
A8,H8: 9.. / A8 = 9  => 10 pairs (_) / H8 = 9  => 14 pairs (_)
C5,C9: 9.. / C5 = 9  => 10 pairs (_) / C9 = 9  => 14 pairs (_)
I1,I9: 9.. / I1 = 9  => 14 pairs (_) / I9 = 9  => 10 pairs (_)
* DURATION: 0:00:39.416843  START: 00:29:03.478841  END: 00:29:42.895684 2019-05-01
* CP COUNT: (36)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,A8,B1,C4,C9,D3,E2,E6,F8,I3)
* 6.1.3.8....39.6.14492.8163.1..69.4.3....4..6..46..3....64.19..8.1587.3.67...6.1..
* PAIR B1: 5,7 BLK 1
B2: 5,7,8                                # reduction candidate for 5,7
B2: 8 => SOLVED
* 671435892583926714492781635157698423839247561246153987364519278915872346728364159
B2: 5,7                                  # 12 pairs
* PAIR B1: 5,7 ROW 1
D1: 5,7,2,4                              # reduction candidate for 5,7
D1: 5,7 => CTR
* 6.1.348....3926.14492.8163.1.76984.3389.4..6..46.53....64319..89158723467384651..
D1: 2,4                                  # 12 pairs
F1: 5,7,2,4                              # reduction candidate for 5,7
F1: 5,7                                  # 13 pairs
H1: 5,7,2,9                              # reduction candidate for 5,7
H1: 5,7 => CTR
* 651.3.879873956214492781635187695423.2..4..6..46.23.8..64.19758.1587.3.6738.6.192
H1: 2,9                                  # 12 pairs
I1: 5,7,2,9                              # reduction candidate for 5,7
I1: 5,7 => CTR
* 6.1.3.89..739562144927816351.769.4.3..9.47562546123....64.19..891587.3.67.8.6.1.9
I1: 2,9                                  # 12 pairs
* PAIR A2: 5,8 BLK 1
B2: 5,8,7                                # reduction candidate for 5,8
B2: 5,8 => SOLVED
* 671435892583926714492781635157698423839247561246153987364519278915872346728364159
B2: 7                                    # 11 pairs
* PAIR A2: 5,8 COL A
A5: 5,8,2,3,9                            # reduction candidate for 5,8
A5: 5,8                                  # 14 pairs
A6: 5,8,2,9                              # reduction candidate for 5,8
A6: 5,8                                  # 12 pairs
* PAIR E2: 2,5 BLK 2
D1: 2,5,4,7                              # reduction candidate for 2,5
D1: 2,5 => CTR
* 6.1.348..8.39.6.14492781635127698453389547261546123987264319..89158723467384651..
D1: 4,7                                  # 12 pairs
F1: 2,5,4,7                              # reduction candidate for 2,5
F1: 2,5                                  # 17 pairs
* PAIR E2: 2,5 ROW 2
G2: 2,5,7                                # reduction candidate for 2,5
G2: 7 => SOLVED
* 671435892583926714492781635157698423839247561246153987364519278915872346728364159
G2: 2,5                                  # 11 pairs
* PAIR D3: 5,7 BLK 2
D1: 5,7,2,4                              # reduction candidate for 5,7
D1: 5,7 => CTR
* 6.1.348....3926.14492.8163.1.76984.3389.4..6..46.53....64319..89158723467384651..
D1: 2,4                                  # 12 pairs
F1: 5,7,2,4                              # reduction candidate for 5,7
F1: 5,7                                  # 13 pairs
* PAIR D3: 5,7 COL D
D5: 5,7,1,2                              # reduction candidate for 5,7
D5: 5,7                                  # 17 pairs
D6: 5,7,1,2                              # reduction candidate for 5,7
D6: 5,7                                  # 17 pairs
* PAIR I3: 5,7 BLK 3
H1: 5,7,2,9                              # reduction candidate for 5,7
H1: 5,7 => CTR
* 651.3.879873956214492781635187695423.2..4..6..46.23.8..64.19758.1587.3.6738.6.192
H1: 2,9                                  # 12 pairs
I1: 5,7,2,9                              # reduction candidate for 5,7
I1: 5,7 => CTR
* 6.1.3.89..739562144927816351.769.4.3..9.47562546123....64.19..891587.3.67.8.6.1.9
I1: 2,9                                  # 12 pairs
G2: 5,7,2                                # reduction candidate for 5,7
G2: 5,7                                  # 12 pairs
* PAIR I3: 5,7 COL I
I5: 5,7,1,2                              # reduction candidate for 5,7
I5: 5,7                                  # 14 pairs
I6: 5,7,1,2                              # reduction candidate for 5,7
I6: 5,7                                  # 14 pairs
* PAIR C4: 7,8 BLK 4
C5: 7,8,9                                # reduction candidate for 7,8
C5: 7,8                                  # 14 pairs
C5: 9                                    # 10 pairs
* PAIR C4: 7,8 ROW 4
F4: 7,8,2,5                              # reduction candidate for 7,8
F4: 7,8                                  # 14 pairs
H4: 7,8,2,5                              # reduction candidate for 7,8
H4: 7,8 => CTR
* 65143782987392651449258163712.69.4.3....48.6..46.53....64.19..8.1587.3.6789365142
H4: 2,5                                  # 12 pairs
* PAIR E6: 2,5 BLK 5
F4: 2,5,7,8                              # reduction candidate for 2,5
F4: 2,5 => CTR
* 6514378..8739265144925816371..69245353..48.6.246.539813642197.8.1587.3.67...651..
F4: 7,8                                  # 14 pairs
D5: 2,5,1,7                              # reduction candidate for 2,5
D5: 2,5                                  # 16 pairs
F5: 2,5,7,8                              # reduction candidate for 2,5
F5: 2,5 => CTR
* 6514378..873926514492581637127698453538.42961946153782364219.78.1587.3.67...651..
F5: 7,8                                  # 12 pairs
D6: 2,5,1,7                              # reduction candidate for 2,5
D6: 2,5 => CTR
* 651.3.8..8739.6.14492.8163.1..69.4.3...14.96.946..3781.64.19.782158743967.9.6.14.
D6: 1,7                                  # 12 pairs
* PAIR E6: 2,5 ROW 6
A6: 2,5,8,9                              # reduction candidate for 2,5
A6: 2,5                                  # 14 pairs
G6: 2,5,7,9                              # reduction candidate for 2,5
G6: 2,5                                  # 15 pairs
H6: 2,5,7,8                              # reduction candidate for 2,5
H6: 2,5 => CTR
* 6.1.3.8..5839267144927816351.769.483..9.48.67846.53921.64.19..8.1587.3.67.8.6.1..
H6: 7,8                                  # 12 pairs
I6: 2,5,1,7                              # reduction candidate for 2,5
I6: 2,5 => CTR
* 65143.8298739265144925816371..69.45353.742961946153782364219.782158743967.9.6.14.
I6: 1,7                                  # 12 pairs
* PAIR A7: 2,3 BLK 7
B9: 2,3,8                                # reduction candidate for 2,3
B9: 8                                    # 14 pairs
B9: 2,3                                  # 10 pairs
* PAIR A7: 2,3 ROW 7
D7: 2,3,5                                # reduction candidate for 2,3
D7: 5 => SOLVED
* 671435892583926714492781635157698423839247561246153987364519278915872346728364159
D7: 2,3                                  # 15 pairs
* PAIR A7: 2,3 COL A
A5: 2,3,5,8,9                            # reduction candidate for 2,3
A5: 5,8,9                                # 12 pairs
A5: 2,3                                  # 12 pairs
* PAIR A8: 2,9 ROW 8
H8: 2,9,4                                # reduction candidate for 2,9
H8: 2,9                                  # 12 pairs
H8: 4                                    # 11 pairs
* PAIR A8: 2,9 COL A
A5: 2,9,3,5,8                            # reduction candidate for 2,9
A5: 2,9                                  # 14 pairs
A6: 2,9,5,8                              # reduction candidate for 2,9
A6: 2,9                                  # 14 pairs
* PAIR C9: 8,9 COL C
C5: 8,9,7                                # reduction candidate for 8,9
C5: 7                                    # 13 pairs
C5: 8,9                                  # 11 pairs
* PAIR F8: 2,4 BLK 8
D9: 2,4,3,5                              # reduction candidate for 2,4
D9: 2,4                                  # 14 pairs
F9: 2,4,5                                # reduction candidate for 2,4
F9: 2,4 => SOLVED
* 671435892583926714492781635157698423839247561246153987364519278915872346728364159
F9: 5                                    # 15 pairs
* PAIR F8: 2,4 ROW 8
H8: 2,4,9                                # reduction candidate for 2,4
H8: 9                                    # 14 pairs
H8: 2,4                                  # 10 pairs
* PAIR F8: 2,4 COL F
F1: 2,4,5,7                              # reduction candidate for 2,4
F1: 2,4                                  # 20 pairs
F1: 5,7                                  # 13 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060708-absurd-base-pr-000.dot
* REASONING
* PRF # B2: 8 => SOL
* DIS # D1: 5,7 => CTR => D1: 2,4
* DIS # H1: 5,7 => CTR => H1: 2,9
* DIS # I1: 5,7 => CTR => I1: 2,9
* PRF # B2: 5,8 => SOL
* DIS # D1: 2,5 => CTR => D1: 4,7
* PRF # G2: 7 => SOL
* DIS # D1: 5,7 => CTR => D1: 2,4
* DIS # H1: 5,7 => CTR => H1: 2,9
* DIS # I1: 5,7 => CTR => I1: 2,9
* DIS # H4: 7,8 => CTR => H4: 2,5
* DIS # F4: 2,5 => CTR => F4: 7,8
* DIS # F5: 2,5 => CTR => F5: 7,8
* DIS # D6: 2,5 => CTR => D6: 1,7
* DIS # H6: 2,5 => CTR => H6: 7,8
* DIS # I6: 2,5 => CTR => I6: 1,7
* PRF # D7: 5 => SOL
* PRF # F9: 2,4 => SOL
* CNT  18 HDP CHAINS /  67 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,A8,B1,C4,C9,D3,E2,E6,F8,I3)
* 6.1.3.8....39.6.14492.8163.1..69.4.3....4..6..46..3....64.19..8.1587.3.67...6.1..
* PAIR B1: 5,7 BLK 1
B2: 5,7,8                                # reduction candidate for 5,7
B2: 8 => SOLVED
* 671435892583926714492781635157698423839247561246153987364519278915872346728364159
* DURATION: 0:00:02.146662  START: 00:30:24.609181  END: 00:30:26.755843 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060708-absurd-base-pr-001.dot
* REASONING
* PRF # B2: 8 => SOL
* STA B2: 8
* CNT   1 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060708, absurd

Solution

position: 671435892583926714492781635157698423839247561246153987364519278915872346728364159 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 # B2: 5,7 => UNS
* PRF # B2: 8 => SOL
* DIS # D1: 5,7 => CTR => D1: 2,4
* INC # D1: 2,4 => UNS
* INC # F1: 5,7 => UNS
* DIS # H1: 5,7 => CTR => H1: 2,9
* INC # H1: 2,9 => UNS
* DIS # I1: 5,7 => CTR => I1: 2,9
* INC # I1: 2,9 => UNS
* PRF # B2: 5,8 => SOL
* INC # B2: 7 => UNS
* INC # A5: 5,8 => UNS
* INC # A6: 5,8 => UNS
* DIS # D1: 2,5 => CTR => D1: 4,7
* INC # D1: 4,7 => UNS
* INC # F1: 2,5 => UNS
* INC # G2: 2,5 => UNS
* PRF # G2: 7 => SOL
* DIS # D1: 5,7 => CTR => D1: 2,4
* INC # D1: 2,4 => UNS
* INC # F1: 5,7 => UNS
* INC # D5: 5,7 => UNS
* INC # D6: 5,7 => UNS
* DIS # H1: 5,7 => CTR => H1: 2,9
* INC # H1: 2,9 => UNS
* DIS # I1: 5,7 => CTR => I1: 2,9
* INC # I1: 2,9 => UNS
* INC # G2: 5,7 => UNS
* INC # I5: 5,7 => UNS
* INC # I6: 5,7 => UNS
* INC # C5: 7,8 => UNS
* INC # C5: 9 => UNS
* INC # F4: 7,8 => UNS
* DIS # H4: 7,8 => CTR => H4: 2,5
* INC # H4: 2,5 => UNS
* DIS # F4: 2,5 => CTR => F4: 7,8
* INC # F4: 7,8 => UNS
* INC # D5: 2,5 => UNS
* DIS # F5: 2,5 => CTR => F5: 7,8
* INC # F5: 7,8 => UNS
* DIS # D6: 2,5 => CTR => D6: 1,7
* INC # D6: 1,7 => UNS
* INC # A6: 2,5 => UNS
* INC # G6: 2,5 => UNS
* DIS # H6: 2,5 => CTR => H6: 7,8
* INC # H6: 7,8 => UNS
* DIS # I6: 2,5 => CTR => I6: 1,7
* INC # I6: 1,7 => UNS
* INC # B9: 2,3 => UNS
* INC # B9: 8 => UNS
* INC # D7: 2,3 => UNS
* PRF # D7: 5 => SOL
* INC # A5: 2,3 => UNS
* INC # A5: 5,8,9 => UNS
* INC # H8: 2,9 => UNS
* INC # H8: 4 => UNS
* INC # A5: 2,9 => UNS
* INC # A6: 2,9 => UNS
* INC # C5: 8,9 => UNS
* INC # C5: 7 => UNS
* INC # D9: 2,4 => UNS
* PRF # F9: 2,4 => SOL
* INC # F9: 5 => UNS
* INC # H8: 2,4 => UNS
* INC # H8: 9 => UNS
* INC # F1: 2,4 => UNS
* INC # F1: 5,7 => UNS
* CNT  67 HDP CHAINS /  67 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 5,7 => UNS
* PRF # B2: 8 => SOL
* STA B2: 8
* CNT   2 HDP CHAINS /   2 HYP OPENED