Analysis of zz-www.sudokuoftheday.co.uk-20060908-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: 2....9..4.5.27...........1.......167....18.5...4.....2...1..38..3.78...16..3..... initial

Autosolve

position: 2....9.7445.271....7....21.......167.2..1845.1.4..78.2.4.1..38..3.78...16..3..7.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # I3: 5,6 => CTR => I3: 3,8,9
* DIS # D1: 5,6 => CTR => D1: 8
* PRF # E1: 5,6 => SOL
* DIS # E1: 3 => CTR => E1: 5,6
* DIS # G8: 5,6 => CTR => G8: 9
* DIS # I2: 6,9 => CTR => I2: 3,8
* DIS # I3: 6,9 => CTR => I3: 3,5,8
* DIS # C2: 6,9 => CTR => C2: 3,8
* DIS # G8: 5 => CTR => G8: 6,9
* PRF # I2: 3,9 => SOL
* PRF # C5: 3,7 => SOL
* DIS # C5: 6 => CTR => C5: 3,7
* PRF # D6: 6,9 => SOL
* PRF # D6: 6,9 => SOL
* PRF # I2: 3,9 => SOL
* PRF # C7: 5,9 => SOL
* DIS # C8: 5,9 => CTR => C8: 2
* DIS # G8: 6 => CTR => G8: 5,9
* PRF # B1: 1,8 => SOL
* DIS # B1: 6 => CTR => B1: 1,8
* DIS # C1: 1,8 => CTR => C1: 3,6
* PRF # C1: 3,6 => SOL
* DIS # F8: 2,4 => CTR => F8: 5,6
* DIS # E9: 2,4 => CTR => E9: 5,9
* DIS # I7: 5,9 => CTR => I7: 6
* DIS # E9: 2,4 => CTR => E9: 5,9
* DIS # I3: 5,9 => CTR => I3: 3,6,8
* CNT  27 HDP CHAINS /  53 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 # I3: 5,6 => CTR => I3: 3,8,9
* DIS I3: 3,8,9 # I2: 6,9 => CTR => I2: 3,8
* PRF I3: 3,8,9 + I2: 3,8 # I3: 8 => SOL
* STA I3: 3,8,9 + I2: 3,8 + I3: 8
* CNT   3 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

2....9..4.5.27...........1.......167....18.5...4.....2...1..38..3.78...16..3..... initial
2....9.7445.271....7....21.......167.2..1845.1.4..78.2.4.1..38..3.78...16..3..7.. autosolve
213869574458271693976543218895432167327618459164957832749125386532786941681394725 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
G1: 5,6
G2: 6,9
H2: 3,9
B4: 8,9
A5: 3,7
B6: 6,9
D4: 4,9
D5: 6,9
I5: 3,9
H6: 3,9
A8: 5,9
B9: 1,8
C9: 1,8
H8: 2,4
H9: 2,4
I9: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,C1: 1.. / B1 = 1  =>  0 pairs (*) / C1 = 1  =>  0 pairs (X)
B9,C9: 1.. / B9 = 1  =>  0 pairs (X) / C9 = 1  =>  0 pairs (_)
B1,B9: 1.. / B1 = 1  =>  0 pairs (*) / B9 = 1  =>  0 pairs (X)
C1,C9: 1.. / C1 = 1  =>  0 pairs (X) / C9 = 1  =>  0 pairs (_)
E4,F4: 2.. / E4 = 2  => 17 pairs (_) / F4 = 2  =>  0 pairs (*)
C7,C8: 2.. / C7 = 2  =>  0 pairs (X) / C8 = 2  => 16 pairs (_)
H8,H9: 2.. / H8 = 2  =>  0 pairs (X) / H9 = 2  => 15 pairs (_)
I5,H6: 3.. / I5 = 3  =>  0 pairs (X) / H6 = 3  =>  0 pairs (_)
C1,E1: 3.. / C1 = 3  =>  0 pairs (*) / E1 = 3  =>  0 pairs (X)
E6,H6: 3.. / E6 = 3  =>  0 pairs (X) / H6 = 3  =>  0 pairs (_)
F3,F4: 3.. / F3 = 3  =>  0 pairs (*) / F4 = 3  =>  0 pairs (X)
H2,H6: 3.. / H2 = 3  =>  0 pairs (X) / H6 = 3  =>  0 pairs (_)
H8,H9: 4.. / H8 = 4  => 15 pairs (_) / H9 = 4  =>  0 pairs (X)
F8,H8: 4.. / F8 = 4  =>  0 pairs (X) / H8 = 4  => 15 pairs (_)
D3,D4: 4.. / D3 = 4  =>  0 pairs (X) / D4 = 4  =>  0 pairs (_)
G1,I3: 5.. / G1 = 5  => 18 pairs (_) / I3 = 5  =>  0 pairs (X)
A4,C4: 5.. / A4 = 5  =>  0 pairs (X) / C4 = 5  => 18 pairs (_)
D6,E6: 5.. / D6 = 5  => 18 pairs (_) / E6 = 5  =>  0 pairs (*)
G1,G8: 5.. / G1 = 5  => 18 pairs (_) / G8 = 5  =>  0 pairs (X)
C5,B6: 6.. / C5 = 6  =>  0 pairs (X) / B6 = 6  =>  0 pairs (_)
I7,G8: 6.. / I7 = 6  => 17 pairs (_) / G8 = 6  =>  0 pairs (X)
C5,D5: 6.. / C5 = 6  =>  0 pairs (X) / D5 = 6  =>  0 pairs (_)
F8,G8: 6.. / F8 = 6  => 17 pairs (_) / G8 = 6  =>  0 pairs (X)
B1,B6: 6.. / B1 = 6  =>  0 pairs (X) / B6 = 6  =>  0 pairs (_)
A5,C5: 7.. / A5 = 7  => 19 pairs (_) / C5 = 7  =>  0 pairs (*)
A7,C7: 7.. / A7 = 7  =>  0 pairs (*) / C7 = 7  =>  0 pairs (X)
A5,A7: 7.. / A5 = 7  => 19 pairs (_) / A7 = 7  =>  0 pairs (*)
C5,C7: 7.. / C5 = 7  =>  0 pairs (*) / C7 = 7  =>  0 pairs (X)
D1,D3: 8.. / D1 = 8  => 17 pairs (_) / D3 = 8  =>  0 pairs (X)
I2,I3: 8.. / I2 = 8  => 16 pairs (_) / I3 = 8  =>  0 pairs (*)
B9,C9: 8.. / B9 = 8  =>  0 pairs (*) / C9 = 8  =>  0 pairs (X)
C2,I2: 8.. / C2 = 8  =>  0 pairs (*) / I2 = 8  =>  0 pairs (X)
A3,A4: 8.. / A3 = 8  => 21 pairs (_) / A4 = 8  =>  0 pairs (*)
B4,B6: 9.. / B4 = 9  =>  0 pairs (*) / B6 = 9  =>  0 pairs (X)
I5,H6: 9.. / I5 = 9  =>  0 pairs (*) / H6 = 9  =>  0 pairs (X)
E7,E9: 9.. / E7 = 9  =>  0 pairs (X) / E9 = 9  => 20 pairs (_)
B4,D4: 9.. / B4 = 9  =>  0 pairs (*) / D4 = 9  =>  0 pairs (X)
D5,I5: 9.. / D5 = 9  =>  0 pairs (X) / I5 = 9  =>  0 pairs (_)
E9,I9: 9.. / E9 = 9  => 20 pairs (_) / I9 = 9  =>  0 pairs (X)
G2,G8: 9.. / G2 = 9  =>  0 pairs (X) / G8 = 9  => 19 pairs (_)
H2,H6: 9.. / H2 = 9  =>  0 pairs (*) / H6 = 9  =>  0 pairs (X)
* DURATION: 0:00:57.203435  START: 02:28:28.148505  END: 02:29:25.351940 2019-05-01
* CP COUNT: (41)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B4,B6,B9,C9,D4,D5,G1,G2,H2,H6,H8,H9,I5,I9)
* 2....9.7445.271....7....21.......167.2..1845.1.4..78.2.4.1..38..3.78...16..3..7..
* PAIR G1: 5,6 BLK 3
I3: 5,6,3,8,9                            # reduction candidate for 5,6
I3: 5,6 => CTR
* 2.3..9.7445.271938.7...321.39....167.2..184531.4.37892.4.1..38..3.78...16..3..7..
I3: 3,8,9                                # 18 pairs
* PAIR G1: 5,6 ROW 1
D1: 5,6,8                                # reduction candidate for 5,6
D1: 5,6 => CTR
* 2..5.967445.271..8.7.8..21.8954..167.2.618459164957832.4.1..38..3.78.9.16..39.7.5
D1: 8                                    # 17 pairs
E1: 5,6,3                                # reduction candidate for 5,6
E1: 5,6 => SOLVED
* 213869574458271693976543218895432167327618459164957832749125386532786941681394725
E1: 3 => CTR
* 2...3957445.27169..7..4.21....423167.2.618459164957832.4.16.38..3.78.9.16..39.7.5
* PAIR G1: 5,6 COL G
G8: 5,6,9                                # reduction candidate for 5,6
G8: 5,6 => CTR
* 2.3..9.7445.27193..7...321.39....167.2..184531.4.37892.4.1..38..3.78...16..3..7..
G8: 9                                    # 19 pairs
* PAIR G2: 6,9 BLK 3
I2: 6,9,3,8                              # reduction candidate for 6,9
I2: 6,9 => CTR
* 2....9.74458271.3..7....2188954..167.2..18453164.378.2.4.1..38..3.78...16..3..7..
I2: 3,8                                  # 17 pairs
I3: 6,9,3,5,8                            # reduction candidate for 6,9
I3: 6,9 => CTR
* 2.3.6957445.271.38.7...321.39....167.2..184531.4.37892.4.1..38..3.78...16..3..7..
I3: 3,5,8                                # 16 pairs
* PAIR G2: 6,9 ROW 2
C2: 6,9,3,8                              # reduction candidate for 6,9
C2: 6,9 => CTR
* 2.3..9.7445.271.38.7...321.39....167.2..184531.4.37892.4.1..38..3.78...16..3..7..
C2: 3,8                                  # 20 pairs
* PAIR G2: 6,9 COL G
G8: 6,9,5                                # reduction candidate for 6,9
G8: 5 => CTR
* 2.3..9674456271938.7..6321539....167.2..184531.4.37892.4.1..386.3.7865416..3..729
G8: 6,9                                  # 18 pairs
* PAIR H2: 3,9 BLK 3
I2: 3,9,6,8                              # reduction candidate for 3,9
I2: 3,9 => SOLVED
* 213869574458271693976543218895432167327618459164957832749125386532786941681394725
I2: 6,8                                  # 17 pairs
I3: 3,9,5,6,8                            # reduction candidate for 3,9
I3: 3,9                                  # 21 pairs
* PAIR H2: 3,9 ROW 2
C2: 3,9,6,8                              # reduction candidate for 3,9
C2: 3,9                                  # 21 pairs
C2: 6,8                                  # 17 pairs
* PAIR A5: 3,7 BLK 4
C5: 3,7,6                                # reduction candidate for 3,7
C5: 3,7 => SOLVED
* 213869574458271693976543218895432167327618459164957832749125386532786941681394725
C5: 6 => CTR
* 2....9.7445.271....7....21.......167726918453194..78.2.4.1..38..3.78...16..3..7..
* PAIR B6: 6,9 ROW 6
D6: 6,9,5                                # reduction candidate for 6,9
D6: 6,9 => SOLVED
* 213869574458271693976543218895432167327618459164957832749125386532786941681394725
D6: 5                                    # 18 pairs
* PAIR D5: 6,9 BLK 5
D6: 6,9,5                                # reduction candidate for 6,9
D6: 6,9 => SOLVED
* 213869574458271693976543218895432167327618459164957832749125386532786941681394725
D6: 5                                    # 18 pairs
* PAIR I5: 3,9 COL I
I2: 3,9,6,8                              # reduction candidate for 3,9
I2: 3,9 => SOLVED
* 213869574458271693976543218895432167327618459164957832749125386532786941681394725
I2: 6,8                                  # 17 pairs
I3: 3,9,5,6,8                            # reduction candidate for 3,9
I3: 3,9                                  # 21 pairs
* PAIR A8: 5,9 BLK 7
A7: 5,9,7                                # reduction candidate for 5,9
A7: 5,9                                  # 19 pairs
C7: 5,9,2,7                              # reduction candidate for 5,9
C7: 5,9 => SOLVED
* 213869574458271693976543218895432167327618459164957832749125386532786941681394725
C7: 2,7                                  # 17 pairs
C8: 5,9,2                                # reduction candidate for 5,9
C8: 5,9 => CTR
* 2....9.7445.271....7....21.......167.2761845916495783274219.38..3.78.9.16..3..7.5
C8: 2                                    # 16 pairs
* PAIR A8: 5,9 ROW 8
G8: 5,9,6                                # reduction candidate for 5,9
G8: 6 => CTR
* 2.3.6957445.27193..7...321.39....167.2..184531.4.37892.4.1..38..3.78.6.16..3..7..
G8: 5,9                                  # 17 pairs
* PAIR B9: 1,8 COL B
B1: 1,8,6                                # reduction candidate for 1,8
B1: 1,8 => SOLVED
* 213869574458271693976543218895432167327618459164957832749125386532786941681394725
B1: 6 => CTR
* 26183957445.271....7....21......3167.2691845.1.4..78.2.4.1..38..3.78...16..3..7..
* PAIR C9: 1,8 COL C
C1: 1,8,3,6                              # reduction candidate for 1,8
C1: 1,8 => CTR
* 2...3957445.27169..7..4.21....423167.2.618459164957832.4.16.38..3.78.9.16..39.7.5
C1: 3,6 => SOLVED
* 213869574458271693976543218895432167327618459164957832749125386532786941681394725
* PAIR H8: 2,4 ROW 8
F8: 2,4,5,6                              # reduction candidate for 2,4
F8: 2,4 => CTR
* 2.3.6957445.27193..7...321.39....167.2..184531.4.37892.4.1..38..3.78.6.16..3..7..
F8: 5,6                                  # 16 pairs
* PAIR H9: 2,4 ROW 9
E9: 2,4,5,9                              # reduction candidate for 2,4
E9: 2,4 => CTR
* 2....9.7445.27193..7....21.......167.2.9184531.4.37892.4.19.38..3.78...16..3..7.9
E9: 5,9                                  # 19 pairs
F9: 2,4,5                                # reduction candidate for 2,4
F9: 2,4                                  # 19 pairs
* PAIR I9: 5,9 BLK 9
I7: 5,9,6                                # reduction candidate for 5,9
I7: 5,9 => CTR
* 2.3.6957445.27193..7...321.39....167.2..184531.4.37892.4.1..38..3.78.6.16..3..7..
I7: 6                                    # 17 pairs
G8: 5,9,6                                # reduction candidate for 5,9
G8: 5,9                                  # 17 pairs
* PAIR I9: 5,9 ROW 9
E9: 5,9,2,4                              # reduction candidate for 5,9
E9: 2,4 => CTR
* 2....9.7445.27193..7....21.......167.2.9184531.4.37892.4.19.38..3.78...16..3..7.9
E9: 5,9                                  # 19 pairs
* PAIR I9: 5,9 COL I
I3: 5,9,3,6,8                            # reduction candidate for 5,9
I3: 5,9 => CTR
* 2.3..9.7445.271.38.7...321.39....167.2..184531.4.37892.4.1..386.3.786.416..3..72.
I3: 3,6,8                                # 18 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060908-absurd-base-pr-000.dot
* REASONING
* DIS # I3: 5,6 => CTR => I3: 3,8,9
* DIS # D1: 5,6 => CTR => D1: 8
* PRF # E1: 5,6 => SOL
* DIS # E1: 3 => CTR => E1: 5,6
* DIS # G8: 5,6 => CTR => G8: 9
* DIS # I2: 6,9 => CTR => I2: 3,8
* DIS # I3: 6,9 => CTR => I3: 3,5,8
* DIS # C2: 6,9 => CTR => C2: 3,8
* DIS # G8: 5 => CTR => G8: 6,9
* PRF # I2: 3,9 => SOL
* PRF # C5: 3,7 => SOL
* DIS # C5: 6 => CTR => C5: 3,7
* PRF # D6: 6,9 => SOL
* PRF # D6: 6,9 => SOL
* PRF # I2: 3,9 => SOL
* PRF # C7: 5,9 => SOL
* DIS # C8: 5,9 => CTR => C8: 2
* DIS # G8: 6 => CTR => G8: 5,9
* PRF # B1: 1,8 => SOL
* DIS # B1: 6 => CTR => B1: 1,8
* DIS # C1: 1,8 => CTR => C1: 3,6
* PRF # C1: 3,6 => SOL
* DIS # F8: 2,4 => CTR => F8: 5,6
* DIS # E9: 2,4 => CTR => E9: 5,9
* DIS # I7: 5,9 => CTR => I7: 6
* DIS # E9: 2,4 => CTR => E9: 5,9
* DIS # I3: 5,9 => CTR => I3: 3,6,8
* CNT  27 HDP CHAINS /  53 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B4,B6,B9,C9,D4,D5,G1,G2,H2,H6,H8,H9,I5,I9)
* 2....9.7445.271....7....21.......167.2..1845.1.4..78.2.4.1..38..3.78...16..3..7..
* PAIR G1: 5,6 BLK 3
I3: 5,6,3,8,9                            # reduction candidate for 5,6
I3: 5,6 => CTR
* 2.3..9.7445.271938.7...321.39....167.2..184531.4.37892.4.1..38..3.78...16..3..7..
* PAIR G2: 6,9 BLK 3
I2: 6,9,3,8                              # reduction candidate for 6,9
I2: 6,9 => CTR
* 2....9574458271.3..7....2188954..167.2..18453164.378.2.4.1..38..3.78...16..3..7..
* PAIR H2: 3,9 BLK 3
I3: 3,9,8                                # reduction candidate for 3,9
I3: 8 => SOLVED
* 213869574458271693976543218895432167327618459164957832749125386532786941681394725
* DURATION: 0:00:05.797407  START: 02:30:05.939861  END: 02:30:11.737268 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060908-absurd-base-pr-001.dot
* REASONING
* DIS # I3: 5,6 => CTR => I3: 3,8,9
* DIS I3: 3,8,9 # I2: 6,9 => CTR => I2: 3,8
* PRF I3: 3,8,9 + I2: 3,8 # I3: 8 => SOL
* STA I3: 3,8,9 + I2: 3,8 + I3: 8
* CNT   3 HDP CHAINS /   4 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006, 20060908, absurd

Solution

position: 213869574458271693976543218895432167327618459164957832749125386532786941681394725 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 # I3: 5,6 => CTR => I3: 3,8,9
* INC # I3: 3,8,9 => UNS
* DIS # D1: 5,6 => CTR => D1: 8
* INC # D1: 8 => UNS
* PRF # E1: 5,6 => SOL
* DIS # E1: 3 => CTR => E1: 5,6
* DIS # G8: 5,6 => CTR => G8: 9
* INC # G8: 9 => UNS
* DIS # I2: 6,9 => CTR => I2: 3,8
* INC # I2: 3,8 => UNS
* DIS # I3: 6,9 => CTR => I3: 3,5,8
* INC # I3: 3,5,8 => UNS
* DIS # C2: 6,9 => CTR => C2: 3,8
* INC # C2: 3,8 => UNS
* INC # G8: 6,9 => UNS
* DIS # G8: 5 => CTR => G8: 6,9
* PRF # I2: 3,9 => SOL
* INC # I2: 6,8 => UNS
* INC # I3: 3,9 => UNS
* INC # C2: 3,9 => UNS
* INC # C2: 6,8 => UNS
* PRF # C5: 3,7 => SOL
* DIS # C5: 6 => CTR => C5: 3,7
* PRF # D6: 6,9 => SOL
* INC # D6: 5 => UNS
* PRF # D6: 6,9 => SOL
* INC # D6: 5 => UNS
* PRF # I2: 3,9 => SOL
* INC # I2: 6,8 => UNS
* INC # I3: 3,9 => UNS
* INC # A7: 5,9 => UNS
* PRF # C7: 5,9 => SOL
* INC # C7: 2,7 => UNS
* DIS # C8: 5,9 => CTR => C8: 2
* INC # C8: 2 => UNS
* INC # G8: 5,9 => UNS
* DIS # G8: 6 => CTR => G8: 5,9
* PRF # B1: 1,8 => SOL
* DIS # B1: 6 => CTR => B1: 1,8
* DIS # C1: 1,8 => CTR => C1: 3,6
* PRF # C1: 3,6 => SOL
* DIS # F8: 2,4 => CTR => F8: 5,6
* INC # F8: 5,6 => UNS
* DIS # E9: 2,4 => CTR => E9: 5,9
* INC # E9: 5,9 => UNS
* INC # F9: 2,4 => UNS
* DIS # I7: 5,9 => CTR => I7: 6
* INC # I7: 6 => UNS
* INC # G8: 5,9 => UNS
* INC # E9: 5,9 => UNS
* DIS # E9: 2,4 => CTR => E9: 5,9
* DIS # I3: 5,9 => CTR => I3: 3,6,8
* INC # I3: 3,6,8 => UNS
* CNT  53 HDP CHAINS /  53 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # I3: 5,6 => CTR => I3: 3,8,9
* DIS I3: 3,8,9 # I2: 6,9 => CTR => I2: 3,8
* INC I3: 3,8,9 + I2: 3,8 # I3: 3,9 => UNS
* PRF I3: 3,8,9 + I2: 3,8 # I3: 8 => SOL
* STA I3: 3,8,9 + I2: 3,8 + I3: 8
* CNT   4 HDP CHAINS /   4 HYP OPENED