Analysis of zz-www.sudokuoftheday.co.uk-20060906-absurd-base.sdk

Contents

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

level: medium

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

position: ............534...658.1.........8.61....75.923......4.5..4.......2..67.9.6.2..... initial

Autosolve

position: ...86...5...534...65871........48.61....75.923...21.475..4.......21.67.9.6.2..... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 2,9 => CTR => A1: 1,4,7
* DIS # B1: 2,9 => CTR => B1: 1,3,4,7
* DIS # G3: 2,9 => CTR => G3: 4
* DIS # I7: 3 => CTR => I7: 6,8
* DIS # H7: 2,3 => CTR => H7: 1,8
* DIS # I9: 8 => CTR => I9: 3,4
* PRF # C6: 6,9 => SOL
* DIS # C6: 5 => CTR => C6: 6,9
* DIS # B8: 3 => CTR => B8: 4,8
* DIS # E9: 5 => CTR => E9: 8,9
* DIS # H8: 5,8 => CTR => H8: 3
* CNT  11 HDP CHAINS /  33 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 # A1: 2,9 => CTR => A1: 1,4,7
* DIS A1: 1,4,7 # B1: 2,9 => CTR => B1: 1,3,4,7
* DIS A1: 1,4,7 + B1: 1,3,4,7 # G1: 1 => CTR => G1: 2,9
* DIS A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 # G3: 2,9 => CTR => G3: 4
* DIS A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 + G3: 4 # B7: 8,9 => CTR => B7: 1,3,7
* PRF A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 + G3: 4 + B7: 1,3,7 # C6: 6,9 => SOL
* STA A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 + G3: 4 + B7: 1,3,7 + C6: 6,9
* CNT   6 HDP CHAINS /   8 HYP OPENED

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

Details

Positions

............534...658.1.........8.61....75.923......4.5..4.......2..67.9.6.2..... initial
...86...5...534...65871........48.61....75.923...21.475..4.......21.67.9.6.2..... autosolve
134862975297534618658719423725948361416375892389621547571493286842156739963287154 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (18)
F1: 2,9
F3: 2,9
I2: 6,8
H3: 2,3
I3: 3,4
B6: 8,9
D4: 3,9
D5: 3,6
D6: 6,9
G4: 3,5
G5: 3,8
G6: 5,8
A8: 4,8
E7: 8,9
F7: 3,7
E8: 5,8
F9: 3,7
G9: 1,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F1,F3: 2.. / F1 = 2  => 19 pairs (_) / F3 = 2  =>  0 pairs (X)
A4,B4: 2.. / A4 = 2  => 19 pairs (_) / B4 = 2  => 19 pairs (_)
G7,H7: 2.. / G7 = 2  => 20 pairs (_) / H7 = 2  =>  0 pairs (X)
B1,C1: 3.. / B1 = 3  => 15 pairs (_) / C1 = 3  =>  0 pairs (X)
H3,I3: 3.. / H3 = 3  =>  0 pairs (X) / I3 = 3  => 15 pairs (_)
D4,D5: 3.. / D4 = 3  =>  0 pairs (X) / D5 = 3  =>  0 pairs (_)
G4,G5: 3.. / G4 = 3  =>  0 pairs (*) / G5 = 3  =>  0 pairs (X)
F7,F9: 3.. / F7 = 3  => 18 pairs (_) / F9 = 3  => 17 pairs (_)
D4,G4: 3.. / D4 = 3  =>  0 pairs (X) / G4 = 3  =>  0 pairs (_)
D5,G5: 3.. / D5 = 3  =>  0 pairs (*) / G5 = 3  =>  0 pairs (X)
B8,H8: 3.. / B8 = 3  =>  0 pairs (X) / H8 = 3  => 14 pairs (_)
G3,I3: 4.. / G3 = 4  => 15 pairs (_) / I3 = 4  =>  0 pairs (X)
A8,B8: 4.. / A8 = 4  => 21 pairs (_) / B8 = 4  => 14 pairs (_)
G9,I9: 4.. / G9 = 4  =>  0 pairs (X) / I9 = 4  => 15 pairs (_)
C1,C5: 4.. / C1 = 4  => 19 pairs (_) / C5 = 4  =>  0 pairs (X)
G3,G9: 4.. / G3 = 4  => 15 pairs (_) / G9 = 4  =>  0 pairs (X)
I3,I9: 4.. / I3 = 4  =>  0 pairs (X) / I9 = 4  => 15 pairs (_)
C4,C6: 5.. / C4 = 5  =>  0 pairs (*) / C6 = 5  =>  0 pairs (X)
G4,G6: 5.. / G4 = 5  =>  0 pairs (X) / G6 = 5  =>  0 pairs (_)
E8,E9: 5.. / E8 = 5  => 19 pairs (_) / E9 = 5  =>  0 pairs (X)
H8,H9: 5.. / H8 = 5  =>  0 pairs (X) / H9 = 5  => 19 pairs (_)
C4,G4: 5.. / C4 = 5  =>  0 pairs (*) / G4 = 5  =>  0 pairs (X)
C6,G6: 5.. / C6 = 5  =>  0 pairs (X) / G6 = 5  =>  0 pairs (_)
E8,H8: 5.. / E8 = 5  => 19 pairs (_) / H8 = 5  =>  0 pairs (X)
E9,H9: 5.. / E9 = 5  =>  0 pairs (X) / H9 = 5  => 19 pairs (_)
G2,I2: 6.. / G2 = 6  => 19 pairs (_) / I2 = 6  =>  0 pairs (X)
C5,C6: 6.. / C5 = 6  =>  0 pairs (*) / C6 = 6  =>  0 pairs (X)
D5,D6: 6.. / D5 = 6  =>  0 pairs (X) / D6 = 6  =>  0 pairs (_)
G7,I7: 6.. / G7 = 6  =>  0 pairs (X) / I7 = 6  => 19 pairs (_)
C5,D5: 6.. / C5 = 6  =>  0 pairs (*) / D5 = 6  =>  0 pairs (X)
C6,D6: 6.. / C6 = 6  =>  0 pairs (X) / D6 = 6  =>  0 pairs (_)
G2,G7: 6.. / G2 = 6  => 19 pairs (_) / G7 = 6  =>  0 pairs (X)
I2,I7: 6.. / I2 = 6  =>  0 pairs (X) / I7 = 6  => 19 pairs (_)
H1,H2: 7.. / H1 = 7  => 18 pairs (_) / H2 = 7  => 22 pairs (_)
F7,F9: 7.. / F7 = 7  => 17 pairs (_) / F9 = 7  => 18 pairs (_)
H2,I2: 8.. / H2 = 8  =>  0 pairs (X) / I2 = 8  => 19 pairs (_)
G5,G6: 8.. / G5 = 8  =>  0 pairs (*) / G6 = 8  =>  0 pairs (X)
B6,G6: 8.. / B6 = 8  =>  0 pairs (*) / G6 = 8  =>  0 pairs (X)
F1,F3: 9.. / F1 = 9  =>  0 pairs (X) / F3 = 9  => 19 pairs (_)
D4,D6: 9.. / D4 = 9  =>  0 pairs (*) / D6 = 9  =>  0 pairs (X)
E7,E9: 9.. / E7 = 9  => 18 pairs (_) / E9 = 9  => 18 pairs (_)
F3,G3: 9.. / F3 = 9  => 19 pairs (_) / G3 = 9  =>  0 pairs (X)
* DURATION: 0:00:57.396888  START: 02:24:03.955667  END: 02:25:01.352555 2019-05-01
* CP COUNT: (42)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B6,D4,D5,D6,E7,E8,F1,F3,F7,F9,G4,G5,G6,G9,H3,I2,I3)
* ...86...5...534...65871........48.61....75.923...21.475..4.......21.67.9.6.2.....
* PAIR F1: 2,9 ROW 1
A1: 2,9,1,4,7                            # reduction candidate for 2,9
A1: 2,9 => CTR
* .4386.175...534...65871..34....48.61..46753923.6921.475..4......321.67.9.6.2..4..
A1: 1,4,7                                # 18 pairs
B1: 2,9,1,3,4,7                          # reduction candidate for 2,9
B1: 2,9 => CTR
* ..386...5...534...65871........48.61..46753923.6921.475..4.......21.67.9.6.2.....
B1: 1,3,4,7                              # 18 pairs
G1: 2,9,1                                # reduction candidate for 2,9
G1: 2,9                                  # 21 pairs
* PAIR F3: 2,9 ROW 3
G3: 2,9,4                                # reduction candidate for 2,9
G3: 2,9 => CTR
* ..386...5...534...65871..34....48.61..46753923.6921.475..4......321.67.9.6.2..4..
G3: 4                                    # 15 pairs
* PAIR I2: 6,8 COL I
I7: 6,8,3                                # reduction candidate for 6,8
I7: 3 => CTR
* ..386...5...534.8665871..34....48.61..46753923.6921.475..4..623.321.67.9.6.2.3..8
I7: 6,8                                  # 20 pairs
* PAIR H3: 2,3 COL H
H7: 2,3,1,8                              # reduction candidate for 2,3
H7: 2,3 => CTR
* ..386...5...534...65871........48.61..46753923.6921.475..4......321.67.9.6.2.....
H7: 1,8                                  # 21 pairs
* PAIR I3: 3,4 COL I
I9: 3,4,8                                # reduction candidate for 3,4
I9: 8 => CTR
* ..386...5...534.8665871..34....48.61..46753923.6921.475..4....3.321.67.9.6.2.34.8
I9: 3,4                                  # 20 pairs
* PAIR B6: 8,9 COL B
B7: 8,9,1,3,7                            # reduction candidate for 8,9
B7: 8,9                                  # 23 pairs
B7: 1,3,7                                # 18 pairs
* PAIR D6: 6,9 ROW 6
C6: 6,9,5                                # reduction candidate for 6,9
C6: 6,9 => SOLVED
* 134862975297534618658719423725948361416375892389621547571493286842156739963287154
C6: 5 => CTR
* ...86...5...534...65871........48.61..6375892385.21.475..4.......21.67.9.6.2.....
* PAIR A8: 4,8 BLK 7
B8: 4,8,3                                # reduction candidate for 4,8
B8: 3 => CTR
* ..386...5...534...65871........48.61..46753923.6921.475..4.....4321.67.9.6.2.....
B8: 4,8                                  # 14 pairs
* PAIR A8: 4,8 COL A
A5: 4,8,1                                # reduction candidate for 4,8
A5: 4,8                                  # 21 pairs
A5: 1                                    # 21 pairs
* PAIR E7: 8,9 BLK 8
E9: 8,9,5                                # reduction candidate for 8,9
E9: 5 => CTR
* ..386...5...534...65871........48.61..46753923.6921.475..49....432186759.6.25....
E9: 8,9                                  # 19 pairs
* PAIR E7: 8,9 ROW 7
B7: 8,9,1,3,7                            # reduction candidate for 8,9
B7: 8,9                                  # 23 pairs
B7: 1,3,7                                # 18 pairs
* PAIR F7: 3,7 ROW 7
B7: 3,7,1,8,9                            # reduction candidate for 3,7
B7: 3,7                                  # 22 pairs
C7: 3,7,1,9                              # reduction candidate for 3,7
C7: 3,7                                  # 21 pairs
* PAIR E8: 5,8 BLK 8
E9: 5,8,9                                # reduction candidate for 5,8
E9: 9                                    # 18 pairs
E9: 5,8                                  # 18 pairs
* PAIR E8: 5,8 ROW 8
H8: 5,8,3                                # reduction candidate for 5,8
H8: 5,8 => CTR
* ..386...5...534...65871........48.61..46753923.6921.475..4......321.67.9.6.2.....
H8: 3                                    # 14 pairs
* PAIR F9: 3,7 ROW 9
C9: 3,7,1,9                              # reduction candidate for 3,7
C9: 3,7                                  # 20 pairs
C9: 1,9                                  # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060906-absurd-base-pr-000.dot
* REASONING
* DIS # A1: 2,9 => CTR => A1: 1,4,7
* DIS # B1: 2,9 => CTR => B1: 1,3,4,7
* DIS # G3: 2,9 => CTR => G3: 4
* DIS # I7: 3 => CTR => I7: 6,8
* DIS # H7: 2,3 => CTR => H7: 1,8
* DIS # I9: 8 => CTR => I9: 3,4
* PRF # C6: 6,9 => SOL
* DIS # C6: 5 => CTR => C6: 6,9
* DIS # B8: 3 => CTR => B8: 4,8
* DIS # E9: 5 => CTR => E9: 8,9
* DIS # H8: 5,8 => CTR => H8: 3
* CNT  11 HDP CHAINS /  33 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B6,D4,D5,D6,E7,E8,F1,F3,F7,F9,G4,G5,G6,G9,H3,I2,I3)
* ...86...5...534...65871........48.61....75.923...21.475..4.......21.67.9.6.2.....
* PAIR F1: 2,9 ROW 1
A1: 2,9,1,4,7                            # reduction candidate for 2,9
A1: 2,9 => CTR
* .4386.175...534...65871..34....48.61..46753923.6921.475..4......321.67.9.6.2..4..
B1: 2,9,1,3,4,7                          # reduction candidate for 2,9
B1: 2,9 => CTR
* ..386...5...534...65871........48.61..46753923.6921.475..4.......21.67.9.6.2.....
G1: 2,9,1                                # reduction candidate for 2,9
G1: 2,9                                  # 21 pairs
* RESTART
* PAIR F1: 2,9 ROW 1
G1: 2,9,1                                # reduction candidate for 2,9
G1: 1 => CTR
* ..3869125...534.78658712934....48.61..46753923.6921.475..4......321.67.9.6.2..4..
* PAIR RESTART
* PAIR F3: 2,9 ROW 3
G3: 2,9,4                                # reduction candidate for 2,9
G3: 2,9 => CTR
* ..386...5...534...65871..34....48.61..46753923.6921.475..4...2..321.67.9.6.2..4..
* PAIR RESTART
* PAIR B6: 8,9 COL B
B7: 8,9,1,3,7                            # reduction candidate for 8,9
B7: 8,9 => CTR
* ..38629.5...5346.8658719423....48.61..46753923.6921.475.14.7236.321.67.9.6.2.31.4
* PAIR RESTART
* PAIR D6: 6,9 ROW 6
C6: 6,9,5                                # reduction candidate for 6,9
C6: 6,9 => SOLVED
* 134862975297534618658719423725948361416375892389621547571493286842156739963287154
* DURATION: 0:00:09.786917  START: 02:25:25.173634  END: 02:25:34.960551 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060906-absurd-base-pr-001.dot
* REASONING
* DIS # A1: 2,9 => CTR => A1: 1,4,7
* DIS A1: 1,4,7 # B1: 2,9 => CTR => B1: 1,3,4,7
* DIS A1: 1,4,7 + B1: 1,3,4,7 # G1: 1 => CTR => G1: 2,9
* DIS A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 # G3: 2,9 => CTR => G3: 4
* DIS A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 + G3: 4 # B7: 8,9 => CTR => B7: 1,3,7
* PRF A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 + G3: 4 + B7: 1,3,7 # C6: 6,9 => SOL
* STA A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 + G3: 4 + B7: 1,3,7 + C6: 6,9
* CNT   6 HDP CHAINS /   8 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006, 20060906, absurd

Solution

position: 134862975297534618658719423725948361416375892389621547571493286842156739963287154 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 # A1: 2,9 => CTR => A1: 1,4,7
* INC # A1: 1,4,7 => UNS
* DIS # B1: 2,9 => CTR => B1: 1,3,4,7
* INC # B1: 1,3,4,7 => UNS
* INC # G1: 2,9 => UNS
* DIS # G3: 2,9 => CTR => G3: 4
* INC # G3: 4 => UNS
* INC # I7: 6,8 => UNS
* DIS # I7: 3 => CTR => I7: 6,8
* DIS # H7: 2,3 => CTR => H7: 1,8
* INC # H7: 1,8 => UNS
* INC # I9: 3,4 => UNS
* DIS # I9: 8 => CTR => I9: 3,4
* INC # B7: 8,9 => UNS
* INC # B7: 1,3,7 => UNS
* PRF # C6: 6,9 => SOL
* DIS # C6: 5 => CTR => C6: 6,9
* INC # B8: 4,8 => UNS
* DIS # B8: 3 => CTR => B8: 4,8
* INC # A5: 4,8 => UNS
* INC # A5: 1 => UNS
* INC # E9: 8,9 => UNS
* DIS # E9: 5 => CTR => E9: 8,9
* INC # B7: 8,9 => UNS
* INC # B7: 1,3,7 => UNS
* INC # B7: 3,7 => UNS
* INC # C7: 3,7 => UNS
* INC # E9: 5,8 => UNS
* INC # E9: 9 => UNS
* DIS # H8: 5,8 => CTR => H8: 3
* INC # H8: 3 => UNS
* INC # C9: 3,7 => UNS
* INC # C9: 1,9 => UNS
* CNT  33 HDP CHAINS /  33 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 2,9 => CTR => A1: 1,4,7
* DIS A1: 1,4,7 # B1: 2,9 => CTR => B1: 1,3,4,7
* INC A1: 1,4,7 + B1: 1,3,4,7 # G1: 2,9 => UNS
* INC A1: 1,4,7 + B1: 1,3,4,7 # G1: 2,9 => UNS
* DIS A1: 1,4,7 + B1: 1,3,4,7 # G1: 1 => CTR => G1: 2,9
* DIS A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 # G3: 2,9 => CTR => G3: 4
* DIS A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 + G3: 4 # B7: 8,9 => CTR => B7: 1,3,7
* PRF A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 + G3: 4 + B7: 1,3,7 # C6: 6,9 => SOL
* STA A1: 1,4,7 + B1: 1,3,4,7 + G1: 2,9 + G3: 4 + B7: 1,3,7 + C6: 6,9
* CNT   8 HDP CHAINS /   8 HYP OPENED