Analysis of zz-www.sudokuoftheday.co.uk-20060821-absurd-base.sdk

Contents

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

level: medium

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

position: .894...5.3..69..2....3..............5..7.4.3.2.3....97.68...1..7.......5.2.1..96. initial

Autosolve

position: .894..35.3..69..2...23....98........5967.4.3.2.3....97968...17.731.....54251..96. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B2: 4,7 => CTR => B2: 5
* DIS # G2: 8 => CTR => G2: 4,7
* PRF # I4: 1,6 => SOL
* DIS # I4: 2,4 => CTR => I4: 1,6
* PRF # B4: 4,7 => SOL
* DIS # B4: 1 => CTR => B4: 4,7
* PRF # B4: 1,4 => SOL
* DIS # B4: 7 => CTR => B4: 1,4
* DIS # G6: 5,8 => CTR => G6: 4,6
* DIS # I4: 1,4 => CTR => I4: 2,6
* PRF # B4: 1,4 => SOL
* DIS # B4: 7 => CTR => B4: 1,4
* DIS # H3: 8 => CTR => H3: 1,4
* PRF # I5: 2,8 => SOL
* DIS # I5: 1 => CTR => I5: 2,8
* DIS # E5: 2,8 => CTR => E5: 1
* PRF # E5: 1 => SOL
* DIS # G8: 4 => CTR => G8: 2,8
* PRF # E7: 2,5 => SOL
* DIS # D4: 9 => CTR => D4: 2,5
* DIS # G8: 4,8 => CTR => G8: 2
* PRF # E8: 4,8 => SOL
* PRF # H3: 4,8 => SOL
* DIS # H3: 1 => CTR => H3: 4,8
* DIS # F9: 3,8 => CTR => F9: 7
* CNT  25 HDP CHAINS /  41 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 # B2: 4,7 => CTR => B2: 5
* DIS B2: 5 # G2: 8 => CTR => G2: 4,7
* PRF B2: 5 + G2: 4,7 # I4: 1,6 => SOL
* STA B2: 5 + G2: 4,7 + I4: 1,6
* CNT   3 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

.894...5.3..69..2....3..............5..7.4.3.2.3....97.68...1..7.......5.2.1..96. initial
.894..35.3..69..2...23....98........5967.4.3.2.3....97968...17.731.....54251..96. autosolve
689472351354691728172358649847239516596714832213865497968523174731946285425187963 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
A1: 1,6
C2: 4,7
A3: 1,6
E1: 2,7
F1: 2,7
I1: 1,6
C4: 4,7
B6: 1,4
D6: 5,8
H4: 1,4
G5: 2,8
D7: 2,5
H8: 4,8
I9: 3,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,A3: 1.. / A1 = 1  =>  0 pairs (X) / A3 = 1  =>  0 pairs (_)
B4,B6: 1.. / B4 = 1  =>  0 pairs (X) / B6 = 1  =>  0 pairs (_)
A1,I1: 1.. / A1 = 1  =>  0 pairs (X) / I1 = 1  =>  0 pairs (_)
F2,I2: 1.. / F2 = 1  => 23 pairs (_) / I2 = 1  =>  0 pairs (X)
E5,I5: 1.. / E5 = 1  =>  0 pairs (*) / I5 = 1  =>  0 pairs (X)
H3,H4: 1.. / H3 = 1  =>  0 pairs (X) / H4 = 1  =>  0 pairs (_)
E1,F1: 2.. / E1 = 2  =>  0 pairs (X) / F1 = 2  => 14 pairs (_)
I7,G8: 2.. / I7 = 2  =>  0 pairs (X) / G8 = 2  => 21 pairs (_)
E4,F4: 3.. / E4 = 3  => 16 pairs (_) / F4 = 3  =>  0 pairs (X)
I7,I9: 3.. / I7 = 3  =>  0 pairs (X) / I9 = 3  => 17 pairs (_)
E7,E8: 4.. / E7 = 4  => 15 pairs (_) / E8 = 4  =>  0 pairs (*)
B6,G6: 4.. / B6 = 4  =>  0 pairs (X) / G6 = 4  =>  0 pairs (_)
E7,I7: 4.. / E7 = 4  => 15 pairs (_) / I7 = 4  =>  0 pairs (*)
C2,C4: 4.. / C2 = 4  =>  0 pairs (*) / C4 = 4  =>  0 pairs (X)
B2,B3: 5.. / B2 = 5  => 16 pairs (_) / B3 = 5  =>  0 pairs (X)
G4,G6: 5.. / G4 = 5  => 16 pairs (_) / G6 = 5  =>  0 pairs (X)
B2,F2: 5.. / B2 = 5  => 16 pairs (_) / F2 = 5  =>  0 pairs (X)
A1,A3: 6.. / A1 = 6  =>  0 pairs (*) / A3 = 6  =>  0 pairs (X)
I1,G3: 6.. / I1 = 6  =>  0 pairs (X) / G3 = 6  =>  0 pairs (_)
E8,F8: 6.. / E8 = 6  => 15 pairs (_) / F8 = 6  => 22 pairs (_)
A1,I1: 6.. / A1 = 6  =>  0 pairs (*) / I1 = 6  =>  0 pairs (X)
A3,G3: 6.. / A3 = 6  =>  0 pairs (X) / G3 = 6  =>  0 pairs (_)
I1,I4: 6.. / I1 = 6  =>  0 pairs (X) / I4 = 6  =>  0 pairs (_)
E1,F1: 7.. / E1 = 7  => 14 pairs (_) / F1 = 7  =>  0 pairs (X)
G2,G3: 7.. / G2 = 7  =>  0 pairs (*) / G3 = 7  =>  0 pairs (X)
B4,C4: 7.. / B4 = 7  =>  0 pairs (X) / C4 = 7  =>  0 pairs (_)
E9,F9: 7.. / E9 = 7  =>  0 pairs (X) / F9 = 7  => 14 pairs (_)
B3,G3: 7.. / B3 = 7  =>  0 pairs (*) / G3 = 7  =>  0 pairs (X)
C2,C4: 7.. / C2 = 7  =>  0 pairs (X) / C4 = 7  =>  0 pairs (_)
E1,E9: 7.. / E1 = 7  => 14 pairs (_) / E9 = 7  =>  0 pairs (X)
F1,F9: 7.. / F1 = 7  =>  0 pairs (X) / F9 = 7  => 14 pairs (_)
D6,D8: 8.. / D6 = 8  => 15 pairs (_) / D8 = 8  =>  0 pairs (X)
H3,H8: 8.. / H3 = 8  =>  0 pairs (X) / H8 = 8  => 18 pairs (_)
D4,F4: 9.. / D4 = 9  =>  0 pairs (X) / F4 = 9  => 18 pairs (_)
D8,F8: 9.. / D8 = 9  => 18 pairs (_) / F8 = 9  =>  0 pairs (X)
D4,D8: 9.. / D4 = 9  =>  0 pairs (X) / D8 = 9  => 18 pairs (_)
F4,F8: 9.. / F4 = 9  => 18 pairs (_) / F8 = 9  =>  0 pairs (X)
* DURATION: 0:00:46.723585  START: 01:57:38.738692  END: 01:58:25.462277 2019-05-01
* CP COUNT: (37)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B6,C2,C4,D6,D7,E1,F1,G5,H4,H8,I1,I9)
* .894..35.3..69..2...23....98........5967.4.3.2.3....97968...17.731.....54251..96.
* PAIR C2: 4,7 BLK 1
B2: 4,7,5                                # reduction candidate for 4,7
B2: 4,7 => CTR
* .894..35.3..695.21.523..7498......1.596714.3.213...497968...174731.462.54251..96.
B2: 5                                    # 16 pairs
B3: 4,7,5                                # reduction candidate for 4,7
B3: 4,7                                  # 16 pairs
* PAIR C2: 4,7 ROW 2
G2: 4,7,8                                # reduction candidate for 4,7
G2: 8 => CTR
* .894..3563..69.82.6.23..7.98........5967142382.3....97968...172731...4854251..963
G2: 4,7                                  # 18 pairs
* PAIR I1: 1,6 COL I
I4: 1,6,2,4                              # reduction candidate for 1,6
I4: 1,6 => SOLVED
* 689472351354691728172358649847239516596714832213865497968523174731946285425187963
I4: 2,4 => CTR
* 1894723563.46917286723..419817..9.42596724831243815.97968...174731.462854251..963
* PAIR C4: 4,7 BLK 4
B4: 4,7,1                                # reduction candidate for 4,7
B4: 4,7 => SOLVED
* 689472351354691728172358649847239516596714832213865497968523174731946285425187963
B4: 1 => CTR
* 1894723563546917286723..419817.6..4259672483124381..97968...174731.462854251..963
* PAIR B6: 1,4 BLK 4
B4: 1,4,7                                # reduction candidate for 1,4
B4: 1,4 => SOLVED
* 689472351354691728172358649847239516596714832213865497968523174731946285425187963
B4: 7 => CTR
* .894..35.3.769.82...23..749874....1.596714.3.213...497968...17.731.....54251..96.
* PAIR D6: 5,8 BLK 5
E6: 5,8,1,6                              # reduction candidate for 5,8
E6: 5,8                                  # 20 pairs
F6: 5,8,1,6                              # reduction candidate for 5,8
F6: 5,8                                  # 26 pairs
* PAIR D6: 5,8 ROW 6
G6: 5,8,4,6                              # reduction candidate for 5,8
G6: 5,8 => CTR
* 1894..3563.4691.286.23..419817..9.4.5967.4.31243....97968...174731.462854251..963
G6: 4,6                                  # 18 pairs
* PAIR H4: 1,4 BLK 6
I4: 1,4,2,6                              # reduction candidate for 1,4
I4: 1,4 => CTR
* 1894..3563..69..2.6.23....98........5967.4.3.2.3....97968...17.731.....54251..96.
I4: 2,6                                  # 15 pairs
* PAIR H4: 1,4 ROW 4
B4: 1,4,7                                # reduction candidate for 1,4
B4: 1,4 => SOLVED
* 689472351354691728172358649847239516596714832213865497968523174731946285425187963
B4: 7 => CTR
* .894..35.3.769.82...23..749874....1.596714.3.213...497968...17.731.....54251..96.
* PAIR H4: 1,4 COL H
H3: 1,4,8                                # reduction candidate for 1,4
H3: 8 => CTR
* .894..35.3..69872...23...898......1.596714.3.213...497968...17.731....454251..96.
H3: 1,4                                  # 18 pairs
* PAIR G5: 2,8 BLK 6
I5: 2,8,1                                # reduction candidate for 2,8
I5: 2,8 => SOLVED
* 689472351354691728172358649847239516596714832213865497968523174731946285425187963
I5: 1 => CTR
* 1894723563546917286723..419817....4259672483124381..979682..174731946285425187963
* PAIR G5: 2,8 ROW 5
E5: 2,8,1                                # reduction candidate for 2,8
E5: 2,8 => CTR
* 1894723563546917286723..419817....4259672483124381..979682..174731946285425187963
E5: 1 => SOLVED
* 689472351354691728172358649847239516596714832213865497968523174731946285425187963
* PAIR G5: 2,8 COL G
G8: 2,8,4                                # reduction candidate for 2,8
G8: 4 => CTR
* .894..35.3.469..2...23...4981.......5967.4.3.2438...97968543172731...4854251..963
G8: 2,8                                  # 20 pairs
* PAIR D7: 2,5 BLK 8
E7: 2,5,3,4                              # reduction candidate for 2,5
E7: 2,5 => SOLVED
* 689472351354691728172358649847239516596714832213865497968523174731946285425187963
E7: 3,4                                  # 15 pairs
F7: 2,5,3                                # reduction candidate for 2,5
F7: 2,5                                  # 23 pairs
* PAIR D7: 2,5 COL D
D4: 2,5,9                                # reduction candidate for 2,5
D4: 9 => CTR
* .894..35.3..69..24.423..7.98.49...1.596714.3.213...497968.4.17.731.69.454251..96.
D4: 2,5                                  # 18 pairs
* PAIR H8: 4,8 BLK 9
G8: 4,8,2                                # reduction candidate for 4,8
G8: 4,8 => CTR
* .894..35.3..69..24.423..7.98.4.3..1.5967.4.3.2.38...97968543172731.....54251..963
G8: 2                                    # 21 pairs
* PAIR H8: 4,8 ROW 8
E8: 4,8,2,6                              # reduction candidate for 4,8
E8: 4,8 => SOLVED
* 689472351354691728172358649847239516596714832213865497968523174731946285425187963
E8: 2,6                                  # 16 pairs
* PAIR H8: 4,8 COL H
H3: 4,8,1                                # reduction candidate for 4,8
H3: 4,8 => SOLVED
* 689472351354691728172358649847239516596714832213865497968523174731946285425187963
H3: 1 => CTR
* 1894723563546917286723..419817.6..4259672483124381..97968...174731.462854251..963
* PAIR I9: 3,8 ROW 9
E9: 3,8,7                                # reduction candidate for 3,8
E9: 3,8                                  # 14 pairs
F9: 3,8,7                                # reduction candidate for 3,8
F9: 3,8 => CTR
* 68942735135.6917281723..649847.3.516596714832213...497968...174731.46285425178963
F9: 7                                    # 14 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060821-absurd-base-pr-000.dot
* REASONING
* DIS # B2: 4,7 => CTR => B2: 5
* DIS # G2: 8 => CTR => G2: 4,7
* PRF # I4: 1,6 => SOL
* DIS # I4: 2,4 => CTR => I4: 1,6
* PRF # B4: 4,7 => SOL
* DIS # B4: 1 => CTR => B4: 4,7
* PRF # B4: 1,4 => SOL
* DIS # B4: 7 => CTR => B4: 1,4
* DIS # G6: 5,8 => CTR => G6: 4,6
* DIS # I4: 1,4 => CTR => I4: 2,6
* PRF # B4: 1,4 => SOL
* DIS # B4: 7 => CTR => B4: 1,4
* DIS # H3: 8 => CTR => H3: 1,4
* PRF # I5: 2,8 => SOL
* DIS # I5: 1 => CTR => I5: 2,8
* DIS # E5: 2,8 => CTR => E5: 1
* PRF # E5: 1 => SOL
* DIS # G8: 4 => CTR => G8: 2,8
* PRF # E7: 2,5 => SOL
* DIS # D4: 9 => CTR => D4: 2,5
* DIS # G8: 4,8 => CTR => G8: 2
* PRF # E8: 4,8 => SOL
* PRF # H3: 4,8 => SOL
* DIS # H3: 1 => CTR => H3: 4,8
* DIS # F9: 3,8 => CTR => F9: 7
* CNT  25 HDP CHAINS /  41 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B6,C2,C4,D6,D7,E1,F1,G5,H4,H8,I1,I9)
* .894..35.3..69..2...23....98........5967.4.3.2.3....97968...17.731.....54251..96.
* PAIR C2: 4,7 BLK 1
B2: 4,7,5                                # reduction candidate for 4,7
B2: 4,7 => CTR
* .894..35.3..695.21.523..7498......1.596714.3.213...497968...174731.462.54251..96.
* RESTART
* PAIR C2: 4,7 ROW 2
G2: 4,7,8                                # reduction candidate for 4,7
G2: 8 => CTR
* .894..35.35769.824.423..719874......5967.4.3.2.3....97968...17.731.....54251..96.
* PAIR RESTART
* PAIR I1: 1,6 COL I
I4: 1,6,2,4                              # reduction candidate for 1,6
I4: 1,6 => SOLVED
* 689472351354691728172358649847239516596714832213865497968523174731946285425187963
* DURATION: 0:00:03.740850  START: 01:58:55.322031  END: 01:58:59.062881 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060821-absurd-base-pr-001.dot
* REASONING
* DIS # B2: 4,7 => CTR => B2: 5
* DIS B2: 5 # G2: 8 => CTR => G2: 4,7
* PRF B2: 5 + G2: 4,7 # I4: 1,6 => SOL
* STA B2: 5 + G2: 4,7 + I4: 1,6
* CNT   3 HDP CHAINS /   4 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060821, absurd

Solution

position: 689472351354691728172358649847239516596714832213865497968523174731946285425187963 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 # B2: 4,7 => CTR => B2: 5
* INC # B2: 5 => UNS
* INC # B3: 4,7 => UNS
* INC # G2: 4,7 => UNS
* DIS # G2: 8 => CTR => G2: 4,7
* PRF # I4: 1,6 => SOL
* DIS # I4: 2,4 => CTR => I4: 1,6
* PRF # B4: 4,7 => SOL
* DIS # B4: 1 => CTR => B4: 4,7
* PRF # B4: 1,4 => SOL
* DIS # B4: 7 => CTR => B4: 1,4
* INC # E6: 5,8 => UNS
* INC # F6: 5,8 => UNS
* DIS # G6: 5,8 => CTR => G6: 4,6
* INC # G6: 4,6 => UNS
* DIS # I4: 1,4 => CTR => I4: 2,6
* INC # I4: 2,6 => UNS
* PRF # B4: 1,4 => SOL
* DIS # B4: 7 => CTR => B4: 1,4
* INC # H3: 1,4 => UNS
* DIS # H3: 8 => CTR => H3: 1,4
* PRF # I5: 2,8 => SOL
* DIS # I5: 1 => CTR => I5: 2,8
* DIS # E5: 2,8 => CTR => E5: 1
* PRF # E5: 1 => SOL
* INC # G8: 2,8 => UNS
* DIS # G8: 4 => CTR => G8: 2,8
* PRF # E7: 2,5 => SOL
* INC # E7: 3,4 => UNS
* INC # F7: 2,5 => UNS
* INC # D4: 2,5 => UNS
* DIS # D4: 9 => CTR => D4: 2,5
* DIS # G8: 4,8 => CTR => G8: 2
* INC # G8: 2 => UNS
* PRF # E8: 4,8 => SOL
* INC # E8: 2,6 => UNS
* PRF # H3: 4,8 => SOL
* DIS # H3: 1 => CTR => H3: 4,8
* INC # E9: 3,8 => UNS
* DIS # F9: 3,8 => CTR => F9: 7
* INC # F9: 7 => UNS
* CNT  41 HDP CHAINS /  41 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B2: 4,7 => CTR => B2: 5
* INC B2: 5 # G2: 4,7 => UNS
* DIS B2: 5 # G2: 8 => CTR => G2: 4,7
* PRF B2: 5 + G2: 4,7 # I4: 1,6 => SOL
* STA B2: 5 + G2: 4,7 + I4: 1,6
* CNT   4 HDP CHAINS /   4 HYP OPENED