Analysis of zz-www.sudokuoftheday.co.uk-20060722-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: ..6.9...8.4.6...1.5.3...4.....357....2...6.75.....2....8.2.....4.9......35....9.4 initial

Autosolve

position: ..6.94.38.4.6...1.5.3...4.....357....2...6375735..2....8.249.534.9......352...9.4 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B3: 1,7 => CTR => B3: 9
* DIS # D1: 1,7 => CTR => D1: 5
* DIS # B8: 6 => CTR => B8: 1,7
* DIS # E2: 3 => CTR => E2: 2,7
* DIS # D3: 7 => CTR => D3: 1,8
* DIS # H6: 6,8 => CTR => H6: 4,9
* DIS # B8: 7 => CTR => B8: 1,6
* DIS # G7: 7 => CTR => G7: 1,6
* DIS # B8: 6 => CTR => B8: 1,7
* DIS # G7: 6 => CTR => G7: 1,7
* DIS # D9: 1,8 => CTR => D9: 7
* DIS # H8: 6,8 => CTR => H8: 2
* DIS # H6: 6,8 => CTR => H6: 4,9
* CNT  13 HDP CHAINS /  35 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 # B3: 1,7 => CTR => B3: 9
* DIS B3: 9 # B8: 6 => CTR => B8: 1,7
* DIS B3: 9 + B8: 1,7 # E2: 3 => CTR => E2: 2,7
* DIS B3: 9 + B8: 1,7 + E2: 2,7 # I3: 6 => CTR => I3: 2,7
* PRF B3: 9 + B8: 1,7 + E2: 2,7 + I3: 2,7 # G6: 6 => SOL
* STA B3: 9 + B8: 1,7 + E2: 2,7 + I3: 2,7 + G6: 6
* CNT   5 HDP CHAINS /  11 HYP OPENED

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

Details

Positions

..6.9...8.4.6...1.5.3...4.....357....2...6.75.....2....8.2.....4.9......35....9.4 initial
..6.94.38.4.6...1.5.3...4.....357....2...6375735..2....8.249.534.9......352...9.4 autosolve
176594238248673519593128467961357842824916375735482691687249153419835726352761984 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (18)
A1: 1,2
B1: 1,7
C2: 7,8
F2: 3,5
E3: 2,7
F3: 1,8
D5: 4,9
E5: 1,8
D6: 4,9
E6: 1,8
A7: 1,6
C7: 1,7
D8: 5,8
E8: 3,6
F8: 3,5
E9: 6,7
F9: 1,8
H9: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E5,E6: 1.. / E5 = 1  => 22 pairs (_) / E6 = 1  => 23 pairs (_)
D9,F9: 1.. / D9 = 1  =>  0 pairs (X) / F9 = 1  => 18 pairs (_)
F3,F9: 1.. / F3 = 1  =>  0 pairs (X) / F9 = 1  => 18 pairs (_)
A1,A2: 2.. / A1 = 2  => 22 pairs (_) / A2 = 2  =>  0 pairs (*)
E2,E3: 2.. / E2 = 2  =>  0 pairs (X) / E3 = 2  => 19 pairs (_)
A1,G1: 2.. / A1 = 2  => 22 pairs (_) / G1 = 2  =>  0 pairs (*)
E2,F2: 3.. / E2 = 3  =>  0 pairs (X) / F2 = 3  => 14 pairs (_)
E8,F8: 3.. / E8 = 3  => 14 pairs (_) / F8 = 3  =>  0 pairs (X)
E2,E8: 3.. / E2 = 3  =>  0 pairs (X) / E8 = 3  => 14 pairs (_)
F2,F8: 3.. / F2 = 3  => 14 pairs (_) / F8 = 3  =>  0 pairs (X)
C4,C5: 4.. / C4 = 4  => 24 pairs (_) / C5 = 4  => 21 pairs (_)
D5,D6: 4.. / D5 = 4  => 24 pairs (_) / D6 = 4  => 21 pairs (_)
H4,H6: 4.. / H4 = 4  => 21 pairs (_) / H6 = 4  => 24 pairs (_)
C4,H4: 4.. / C4 = 4  => 24 pairs (_) / H4 = 4  => 21 pairs (_)
C5,D5: 4.. / C5 = 4  => 21 pairs (_) / D5 = 4  => 24 pairs (_)
D6,H6: 4.. / D6 = 4  => 21 pairs (_) / H6 = 4  => 24 pairs (_)
D1,F2: 5.. / D1 = 5  => 14 pairs (_) / F2 = 5  =>  0 pairs (X)
G1,G2: 5.. / G1 = 5  =>  0 pairs (X) / G2 = 5  => 14 pairs (_)
D8,F8: 5.. / D8 = 5  =>  0 pairs (X) / F8 = 5  => 14 pairs (_)
D1,G1: 5.. / D1 = 5  => 14 pairs (_) / G1 = 5  =>  0 pairs (X)
F2,G2: 5.. / F2 = 5  =>  0 pairs (X) / G2 = 5  => 14 pairs (_)
D1,D8: 5.. / D1 = 5  => 14 pairs (_) / D8 = 5  =>  0 pairs (X)
F2,F8: 5.. / F2 = 5  =>  0 pairs (X) / F8 = 5  => 14 pairs (_)
H3,I3: 6.. / H3 = 6  => 17 pairs (_) / I3 = 6  => 20 pairs (_)
A4,B4: 6.. / A4 = 6  =>  0 pairs (X) / B4 = 6  => 27 pairs (_)
A7,B8: 6.. / A7 = 6  => 27 pairs (_) / B8 = 6  =>  0 pairs (X)
E8,E9: 6.. / E8 = 6  =>  0 pairs (X) / E9 = 6  => 14 pairs (_)
A7,G7: 6.. / A7 = 6  => 27 pairs (_) / G7 = 6  =>  0 pairs (X)
E9,H9: 6.. / E9 = 6  => 14 pairs (_) / H9 = 6  =>  0 pairs (X)
A4,A7: 6.. / A4 = 6  =>  0 pairs (X) / A7 = 6  => 27 pairs (_)
B4,B8: 6.. / B4 = 6  => 27 pairs (_) / B8 = 6  =>  0 pairs (X)
C7,B8: 7.. / C7 = 7  => 23 pairs (_) / B8 = 7  =>  0 pairs (X)
D9,E9: 7.. / D9 = 7  => 14 pairs (_) / E9 = 7  =>  0 pairs (X)
C7,G7: 7.. / C7 = 7  => 23 pairs (_) / G7 = 7  =>  0 pairs (X)
C2,C7: 7.. / C2 = 7  =>  0 pairs (X) / C7 = 7  => 23 pairs (_)
A2,C2: 8.. / A2 = 8  =>  0 pairs (X) / C2 = 8  => 23 pairs (_)
D3,F3: 8.. / D3 = 8  =>  0 pairs (X) / F3 = 8  => 18 pairs (_)
E5,E6: 8.. / E5 = 8  => 23 pairs (_) / E6 = 8  => 22 pairs (_)
F3,F9: 8.. / F3 = 8  => 18 pairs (_) / F9 = 8  =>  0 pairs (X)
A2,B3: 9.. / A2 = 9  =>  0 pairs (X) / B3 = 9  => 27 pairs (_)
D5,D6: 9.. / D5 = 9  => 21 pairs (_) / D6 = 9  => 24 pairs (_)
A2,I2: 9.. / A2 = 9  =>  0 pairs (X) / I2 = 9  => 27 pairs (_)
A5,D5: 9.. / A5 = 9  => 24 pairs (_) / D5 = 9  => 21 pairs (_)
B3,B4: 9.. / B3 = 9  => 27 pairs (_) / B4 = 9  =>  0 pairs (X)
* DURATION: 0:00:59.453287  START: 00:53:22.741350  END: 00:54:22.194637 2019-05-01
* CP COUNT: (44)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A7,B1,C2,C7,D5,D6,D8,E3,E5,E6,E8,E9,F2,F3,F8,F9,H9)
* ..6.94.38.4.6...1.5.3...4.....357....2...6375735..2....8.249.534.9......352...9.4
* PAIR B1: 1,7 BLK 1
B3: 1,7,9                                # reduction candidate for 1,7
B3: 1,7 => CTR
* 2.6594738948673512573.284..69.3578...2.9.63757354.2....87249.53469.35...352.6.984
B3: 9                                    # 27 pairs
* PAIR B1: 1,7 ROW 1
D1: 1,7,5                                # reduction candidate for 1,7
D1: 1,7 => CTR
* 2.6.94538.4.635.1.5.3.2.496...357....2...6375735..2....8.249.534.9563...352.7.964
D1: 5                                    # 14 pairs
* PAIR B1: 1,7 COL B
B8: 1,7,6                                # reduction candidate for 1,7
B8: 6 => CTR
* 2165947389486735125731284..6913578..82.916375735482...187249653469835.2.352761984
B8: 1,7                                  # 27 pairs
* PAIR E3: 2,7 BLK 2
E2: 2,7,3                                # reduction candidate for 2,7
E2: 3 => CTR
* ..6.94538.4.635.1.5.3.2.496...357....2...6375735..2....8.249.534.9563...352.7.964
E2: 2,7                                  # 14 pairs
* PAIR E3: 2,7 ROW 3
I3: 2,7,6,9                              # reduction candidate for 2,7
I3: 6,9                                  # 19 pairs
I3: 2,7                                  # 19 pairs
* PAIR F3: 1,8 BLK 2
D3: 1,8,7                                # reduction candidate for 1,8
D3: 7 => CTR
* ..6194538.4.635.1.513728496.9.357....2.9.63757354.2689681249753479......352.71964
D3: 1,8                                  # 21 pairs
* PAIR E5: 1,8 ROW 5
A5: 1,8,9                                # reduction candidate for 1,8
A5: 1,8                                  # 21 pairs
C5: 1,8,4                                # reduction candidate for 1,8
C5: 1,8                                  # 24 pairs
* PAIR D6: 4,9 ROW 6
H6: 4,9,6,8                              # reduction candidate for 4,9
H6: 6,8 => CTR
* 2.65947389486...1.5.3...496.91357.42824916375735482169187249653469.35.21352.6.984
H6: 4,9                                  # 20 pairs
* PAIR E6: 1,8 ROW 6
G6: 1,8,6                                # reduction candidate for 1,8
G6: 6                                    # 29 pairs
G6: 1,8                                  # 19 pairs
* PAIR A7: 1,6 BLK 7
B8: 1,6,7                                # reduction candidate for 1,6
B8: 7 => CTR
* .16794538.476.5219593.2.467.6.357....2...6375735..2...6812497534795.....352...9.4
B8: 1,6                                  # 23 pairs
* PAIR A7: 1,6 ROW 7
G7: 1,6,7                                # reduction candidate for 1,6
G7: 7 => CTR
* .16794538.476.5219593.2.467.6.357....2...6375735..2...6812497534795.....352...9.4
G7: 1,6                                  # 23 pairs
* PAIR A7: 1,6 COL A
A4: 1,6,8,9                              # reduction candidate for 1,6
A4: 8,9                                  # 28 pairs
A4: 1,6                                  # 24 pairs
* PAIR C7: 1,7 BLK 7
B8: 1,7,6                                # reduction candidate for 1,7
B8: 6 => CTR
* 2165947389486735125731284..6913578..82.916375735482...187249653469835.2.352761984
B8: 1,7                                  # 27 pairs
* PAIR C7: 1,7 ROW 7
G7: 1,7,6                                # reduction candidate for 1,7
G7: 6 => CTR
* 216594738.486.351.5.3..84..6..3578..82.9163757354821..187249653469835.21352761984
G7: 1,7                                  # 27 pairs
* PAIR F9: 1,8 BLK 8
D9: 1,8,7                                # reduction candidate for 1,8
D9: 1,8 => CTR
* ..6.94.38.4.6...1.5.3.2.496.9.357....2.9.63757354.268968.249.534.9.6382.352.7.964
D9: 7                                    # 14 pairs
* PAIR H9: 6,8 BLK 9
G8: 6,8,1,2,7                            # reduction candidate for 6,8
G8: 6,8                                  # 20 pairs
H8: 6,8,2                                # reduction candidate for 6,8
H8: 6,8 => CTR
* 2.6.94.38.4.6...1.593...426.6.3578.2.2..16375735.826.168.249.534.9...2.7352...9.4
H8: 2                                    # 19 pairs
* PAIR H9: 6,8 COL H
H6: 6,8,4,9                              # reduction candidate for 6,8
H6: 6,8 => CTR
* 2.65947389486...1.5.3...496.91357.42824916375735482169187249653469.35.21352.6.984
H6: 4,9                                  # 20 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060722-absurd-base-pr-000.dot
* REASONING
* DIS # B3: 1,7 => CTR => B3: 9
* DIS # D1: 1,7 => CTR => D1: 5
* DIS # B8: 6 => CTR => B8: 1,7
* DIS # E2: 3 => CTR => E2: 2,7
* DIS # D3: 7 => CTR => D3: 1,8
* DIS # H6: 6,8 => CTR => H6: 4,9
* DIS # B8: 7 => CTR => B8: 1,6
* DIS # G7: 7 => CTR => G7: 1,6
* DIS # B8: 6 => CTR => B8: 1,7
* DIS # G7: 6 => CTR => G7: 1,7
* DIS # D9: 1,8 => CTR => D9: 7
* DIS # H8: 6,8 => CTR => H8: 2
* DIS # H6: 6,8 => CTR => H6: 4,9
* CNT  13 HDP CHAINS /  35 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A7,B1,C2,C7,D5,D6,D8,E3,E5,E6,E8,E9,F2,F3,F8,F9,H9)
* ..6.94.38.4.6...1.5.3...4.....357....2...6375735..2....8.249.534.9......352...9.4
* PAIR B1: 1,7 BLK 1
B3: 1,7,9                                # reduction candidate for 1,7
B3: 1,7 => CTR
* 2.6594738948673512573.284..69.3578...2.9.63757354.2....87249.53469.35...352.6.984
* PAIR B1: 1,7 COL B
B8: 1,7,6                                # reduction candidate for 1,7
B8: 6 => CTR
* .765942382486.3519593.2.467.14357....2...6375735..2....8.249.534.9......352...9.4
* PAIR RESTART
* PAIR E3: 2,7 BLK 2
E2: 2,7,3                                # reduction candidate for 2,7
E2: 3 => CTR
* ..6.94.38.4.635.19593.2.467.6.357....2...6375735..2...68.249.534.95.....352...9.4
* PAIR E3: 2,7 ROW 3
I3: 2,7,6                                # reduction candidate for 2,7
I3: 6 => CTR
* ..6594738.47623519593178426.6.357....2...6375735..26.1681249.534.9835...352761984
* PAIR RESTART
* PAIR E5: 1,8 ROW 5
A5: 1,8,9                                # reduction candidate for 1,8
A5: 1,8                                  # 17 pairs
C5: 1,8,4                                # reduction candidate for 1,8
C5: 1,8                                  # 17 pairs
* PAIR E6: 1,8 ROW 6
G6: 1,8,6                                # reduction candidate for 1,8
G6: 6 => SOLVED
* 176594238248673519593128467961357842824916375735482691687249153419835726352761984
* DURATION: 0:00:11.645927  START: 00:54:48.532605  END: 00:55:00.178532 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060722-absurd-base-pr-001.dot
* REASONING
* DIS # B3: 1,7 => CTR => B3: 9
* DIS B3: 9 # B8: 6 => CTR => B8: 1,7
* DIS B3: 9 + B8: 1,7 # E2: 3 => CTR => E2: 2,7
* DIS B3: 9 + B8: 1,7 + E2: 2,7 # I3: 6 => CTR => I3: 2,7
* PRF B3: 9 + B8: 1,7 + E2: 2,7 + I3: 2,7 # G6: 6 => SOL
* STA B3: 9 + B8: 1,7 + E2: 2,7 + I3: 2,7 + G6: 6
* CNT   5 HDP CHAINS /  11 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060722, absurd

Solution

position: 176594238248673519593128467961357842824916375735482691687249153419835726352761984 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 # B3: 1,7 => CTR => B3: 9
* INC # B3: 9 => UNS
* DIS # D1: 1,7 => CTR => D1: 5
* INC # D1: 5 => UNS
* INC # B8: 1,7 => UNS
* DIS # B8: 6 => CTR => B8: 1,7
* INC # E2: 2,7 => UNS
* DIS # E2: 3 => CTR => E2: 2,7
* INC # I3: 2,7 => UNS
* INC # I3: 6,9 => UNS
* INC # D3: 1,8 => UNS
* DIS # D3: 7 => CTR => D3: 1,8
* INC # A5: 1,8 => UNS
* INC # C5: 1,8 => UNS
* INC # H6: 4,9 => UNS
* DIS # H6: 6,8 => CTR => H6: 4,9
* INC # G6: 1,8 => UNS
* INC # G6: 6 => UNS
* INC # B8: 1,6 => UNS
* DIS # B8: 7 => CTR => B8: 1,6
* INC # G7: 1,6 => UNS
* DIS # G7: 7 => CTR => G7: 1,6
* INC # A4: 1,6 => UNS
* INC # A4: 8,9 => UNS
* INC # B8: 1,7 => UNS
* DIS # B8: 6 => CTR => B8: 1,7
* INC # G7: 1,7 => UNS
* DIS # G7: 6 => CTR => G7: 1,7
* DIS # D9: 1,8 => CTR => D9: 7
* INC # D9: 7 => UNS
* INC # G8: 6,8 => UNS
* DIS # H8: 6,8 => CTR => H8: 2
* INC # H8: 2 => UNS
* DIS # H6: 6,8 => CTR => H6: 4,9
* INC # H6: 4,9 => UNS
* CNT  35 HDP CHAINS /  35 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B3: 1,7 => CTR => B3: 9
* INC B3: 9 # B8: 1,7 => UNS
* DIS B3: 9 # B8: 6 => CTR => B8: 1,7
* INC B3: 9 + B8: 1,7 # E2: 2,7 => UNS
* DIS B3: 9 + B8: 1,7 # E2: 3 => CTR => E2: 2,7
* INC B3: 9 + B8: 1,7 + E2: 2,7 # I3: 2,7 => UNS
* DIS B3: 9 + B8: 1,7 + E2: 2,7 # I3: 6 => CTR => I3: 2,7
* INC B3: 9 + B8: 1,7 + E2: 2,7 + I3: 2,7 # A5: 1,8 => UNS
* INC B3: 9 + B8: 1,7 + E2: 2,7 + I3: 2,7 # C5: 1,8 => UNS
* INC B3: 9 + B8: 1,7 + E2: 2,7 + I3: 2,7 # G6: 1,8 => UNS
* PRF B3: 9 + B8: 1,7 + E2: 2,7 + I3: 2,7 # G6: 6 => SOL
* STA B3: 9 + B8: 1,7 + E2: 2,7 + I3: 2,7 + G6: 6
* CNT  11 HDP CHAINS /  11 HYP OPENED