Analysis of zz-www.sudokuoftheday.co.uk-20190127-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019

position: .2........38.7.6.914.8........1.....6.....1.34...95.7......8.91.81.2.7.5.....9..2 initial

Autosolve

position: 7269.....538.7.6.91498....78..1..9..69..8.1.341..95.7.2....8.91981.2.7.53...19..2 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # F2: 1 => CTR => F2: 2,4
* DIS # H2: 2,4 => CTR => H2: 1
* PRF # G1: 4,8 => SOL
* DIS # H1: 4,8 => CTR => H1: 1,3
* PRF # H1: 1,3 => SOL
* PRF # G3: 5 => SOL
* DIS # F3: 2,3 => CTR => F3: 6
* DIS # C4: 5,7 => CTR => C4: 2,3
* PRF # B7: 5,7 => SOL
* DIS # B7: 6 => CTR => B7: 5,7
* DIS # B9: 5,7 => CTR => B9: 6
* PRF # B9: 6 => SOL
* DIS # C4: 5,7 => CTR => C4: 2,3
* PRF # F4: 3,6 => SOL
* DIS # F4: 4,6 => CTR => F4: 2,3,7
* PRF # B7: 5,7 => SOL
* DIS # B7: 6 => CTR => B7: 5,7
* DIS # C7: 5,7 => CTR => C7: 4
* PRF # C7: 4 => SOL
* DIS # F8: 3,6 => CTR => F8: 4
* DIS # H8: 4 => CTR => H8: 3,6
* DIS # B9: 5,7 => CTR => B9: 6
* PRF # B9: 6 => SOL
* PRF # C9: 5,7 => SOL
* DIS # C9: 4 => CTR => C9: 5,7
* DIS # H8: 3,4 => CTR => H8: 6
* PRF # H8: 6 => SOL
* DIS # E7: 3,4 => CTR => E7: 6
* PRF # E7: 6 => SOL
* DIS # G1: 3,4 => CTR => G1: 5,8
* PRF # H9: 4,8 => SOL
* DIS # H9: 6 => CTR => H9: 4,8
* PRF # G1: 4,8 => SOL
* CNT  33 HDP CHAINS /  54 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 # F2: 1 => CTR => F2: 2,4
* PRF F2: 2,4 # G1: 4,8 => SOL
* STA F2: 2,4 + G1: 4,8
* CNT   2 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

.2........38.7.6.914.8........1.....6.....1.34...95.7......8.91.81.2.7.5.....9..2 initial
7269.....538.7.6.91498....78..1..9..69..8.1.341..95.7.2....8.91981.2.7.53...19..2 autosolve
726951834538472619149836527872143956695287143413695278254768391981324765367519482 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
D2: 2,4
I1: 4,8
H3: 2,3
B4: 5,7
C6: 2,3
D5: 2,4
D6: 3,6
I4: 4,6
G6: 2,8
I6: 6,8
D7: 5,7
D8: 3,6
D9: 5,7
G7: 3,4
G9: 4,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F1,F2: 1.. / F1 = 1  => 18 pairs (_) / F2 = 1  =>  0 pairs (X)
H1,H2: 1.. / H1 = 1  =>  0 pairs (X) / H2 = 1  => 18 pairs (_)
F1,H1: 1.. / F1 = 1  => 18 pairs (_) / H1 = 1  =>  0 pairs (X)
F2,H2: 1.. / F2 = 1  =>  0 pairs (X) / H2 = 1  => 18 pairs (_)
C6,G6: 2.. / C6 = 2  =>  0 pairs (X) / G6 = 2  =>  0 pairs (_)
D2,D5: 2.. / D2 = 2  => 20 pairs (_) / D5 = 2  => 21 pairs (_)
G3,G6: 2.. / G3 = 2  =>  0 pairs (X) / G6 = 2  =>  0 pairs (_)
C4,C6: 3.. / C4 = 3  =>  0 pairs (X) / C6 = 3  =>  0 pairs (_)
G7,H8: 3.. / G7 = 3  => 17 pairs (_) / H8 = 3  =>  0 pairs (X)
C6,D6: 3.. / C6 = 3  =>  0 pairs (*) / D6 = 3  =>  0 pairs (X)
E7,G7: 3.. / E7 = 3  =>  0 pairs (X) / G7 = 3  => 17 pairs (_)
D6,D8: 3.. / D6 = 3  =>  0 pairs (X) / D8 = 3  =>  0 pairs (_)
C7,C9: 4.. / C7 = 4  =>  0 pairs (*) / C9 = 4  =>  0 pairs (X)
E7,F8: 4.. / E7 = 4  =>  0 pairs (X) / F8 = 4  => 20 pairs (_)
F8,H8: 4.. / F8 = 4  => 20 pairs (_) / H8 = 4  =>  0 pairs (X)
D2,D5: 4.. / D2 = 4  => 21 pairs (_) / D5 = 4  => 20 pairs (_)
I1,I4: 4.. / I1 = 4  =>  0 pairs (*) / I4 = 4  =>  0 pairs (X)
E1,E3: 5.. / E1 = 5  =>  0 pairs (*) / E3 = 5  =>  0 pairs (X)
G1,G3: 5.. / G1 = 5  => 24 pairs (_) / G3 = 5  =>  0 pairs (*)
H4,H5: 5.. / H4 = 5  => 20 pairs (_) / H5 = 5  => 19 pairs (_)
D7,D9: 5.. / D7 = 5  => 17 pairs (_) / D9 = 5  => 17 pairs (_)
E1,G1: 5.. / E1 = 5  =>  0 pairs (*) / G1 = 5  =>  0 pairs (X)
E3,G3: 5.. / E3 = 5  => 24 pairs (_) / G3 = 5  =>  0 pairs (*)
C5,H5: 5.. / C5 = 5  => 20 pairs (_) / H5 = 5  => 19 pairs (_)
E3,F3: 6.. / E3 = 6  =>  0 pairs (X) / F3 = 6  => 18 pairs (_)
I4,I6: 6.. / I4 = 6  =>  0 pairs (*) / I6 = 6  =>  0 pairs (X)
B7,B9: 6.. / B7 = 6  =>  0 pairs (X) / B9 = 6  =>  0 pairs (_)
H8,H9: 6.. / H8 = 6  =>  0 pairs (*) / H9 = 6  =>  0 pairs (X)
D6,I6: 6.. / D6 = 6  =>  0 pairs (*) / I6 = 6  =>  0 pairs (X)
B7,E7: 6.. / B7 = 6  =>  0 pairs (X) / E7 = 6  =>  0 pairs (_)
B9,H9: 6.. / B9 = 6  =>  0 pairs (*) / H9 = 6  =>  0 pairs (X)
D6,D8: 6.. / D6 = 6  =>  0 pairs (*) / D8 = 6  =>  0 pairs (X)
F4,F5: 7.. / F4 = 7  => 22 pairs (_) / F5 = 7  => 16 pairs (_)
D7,D9: 7.. / D7 = 7  => 17 pairs (_) / D9 = 7  => 17 pairs (_)
C5,F5: 7.. / C5 = 7  => 22 pairs (_) / F5 = 7  => 16 pairs (_)
G6,I6: 8.. / G6 = 8  =>  0 pairs (X) / I6 = 8  =>  0 pairs (_)
G9,H9: 8.. / G9 = 8  =>  0 pairs (X) / H9 = 8  =>  0 pairs (_)
H1,H9: 8.. / H1 = 8  =>  0 pairs (X) / H9 = 8  =>  0 pairs (_)
I1,I6: 8.. / I1 = 8  =>  0 pairs (X) / I6 = 8  =>  0 pairs (_)
* DURATION: 0:00:48.549606  START: 03:15:00.188119  END: 03:15:48.737725 2019-05-01
* CP COUNT: (39)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C6,D2,D5,D6,D7,D8,D9,G6,G7,G9,H3,I1,I4,I6)
* 7269.....538.7.6.91498....78..1..9..69..8.1.341..95.7.2....8.91981.2.7.53...19..2
* PAIR D2: 2,4 BLK 2
F2: 2,4,1                                # reduction candidate for 2,4
F2: 1 => CTR
* 7269.381453847162914985..378..1..9..69..8.1.341.695.782.4.6839198132476536..19482
F2: 2,4                                  # 18 pairs
* PAIR D2: 2,4 ROW 2
H2: 2,4,1                                # reduction candidate for 2,4
H2: 2,4 => CTR
* 7269.381453847162914985..378..1..9..69..8.1.341.695.782.4.6839198132476536..19482
H2: 1                                    # 18 pairs
* PAIR I1: 4,8 BLK 3
G1: 4,8,3,5                              # reduction candidate for 4,8
G1: 4,8 => SOLVED
* 726951834538472619149836527872143956695287143413695278254768391981324765367519482
G1: 3,5                                  # 24 pairs
H1: 4,8,1,3                              # reduction candidate for 4,8
H1: 4,8 => CTR
* 7269.1...5384726191498....78..14.9.669.28714341.695.782...683919813247653...19..2
H1: 1,3 => SOLVED
* 726951834538472619149836527872143956695287143413695278254768391981324765367519482
* PAIR H3: 2,3 BLK 3
G3: 2,3,5                                # reduction candidate for 2,3
G3: 5 => SOLVED
* 726951834538472619149836527872143956695287143413695278254768391981324765367519482
G3: 2,3                                  # 24 pairs
* PAIR H3: 2,3 ROW 3
F3: 2,3,6                                # reduction candidate for 2,3
F3: 2,3 => CTR
* 72695..84538.7.61914986.5278..1..9.669..8.1.341369527826...8.919813267453.4.19862
F3: 6                                    # 18 pairs
* PAIR B4: 5,7 BLK 4
C4: 5,7,2,3                              # reduction candidate for 5,7
C4: 5,7 => CTR
* 7269....4538.7.6.91498....78..1.29.66924871534136952782...483919813267453...19..2
C4: 2,3                                  # 17 pairs
C5: 5,7,2                                # reduction candidate for 5,7
C5: 5,7                                  # 17 pairs
* PAIR B4: 5,7 COL B
B7: 5,7,6                                # reduction candidate for 5,7
B7: 5,7 => SOLVED
* 726951834538472619149836527872143956695287143413695278254768391981324765367519482
B7: 6 => CTR
* 7269...84538.7.6191498....78..1..9.669..8.1.341.695.7826...8.919813267453.4.19862
B9: 5,7,6                                # reduction candidate for 5,7
B9: 5,7 => CTR
* 7269...84538.7.6191498....78..1..9.669..8.1.341.695.7826...8.919813267453.4.19862
B9: 6 => SOLVED
* 726951834538472619149836527872143956695287143413695278254768391981324765367519482
* PAIR C6: 2,3 BLK 4
C4: 2,3,5,7                              # reduction candidate for 2,3
C4: 5,7 => CTR
* 7269....4538.7.6.91498....78..1.29.66924871534136952782...483919813267453...19..2
C4: 2,3                                  # 17 pairs
* PAIR D5: 2,4 BLK 5
F4: 2,4,3,6,7                            # reduction candidate for 2,4
F4: 2,4                                  # 18 pairs
F5: 2,4,7                                # reduction candidate for 2,4
F5: 2,4                                  # 22 pairs
* PAIR D5: 2,4 ROW 5
H5: 2,4,5                                # reduction candidate for 2,4
H5: 2,4                                  # 20 pairs
H5: 5                                    # 19 pairs
* PAIR D6: 3,6 BLK 5
E4: 3,6,4                                # reduction candidate for 3,6
E4: 3,6                                  # 16 pairs
F4: 3,6,2,4,7                            # reduction candidate for 3,6
F4: 3,6 => SOLVED
* 726951834538472619149836527872143956695287143413695278254768391981324765367519482
F4: 2,4,7                                # 16 pairs
* PAIR I4: 4,6 ROW 4
E4: 4,6,3                                # reduction candidate for 4,6
E4: 4,6                                  # 17 pairs
F4: 4,6,2,3,7                            # reduction candidate for 4,6
F4: 4,6 => CTR
* 7269.....538.7.6.91498....78..1..9..69.28714341..95.7.2....8.91981.247.53...19..2
F4: 2,3,7                                # 15 pairs
* PAIR D7: 5,7 ROW 7
B7: 5,7,6                                # reduction candidate for 5,7
B7: 5,7 => SOLVED
* 726951834538472619149836527872143956695287143413695278254768391981324765367519482
B7: 6 => CTR
* 7269...84538.7.6191498....78..1..9.669..8.1.341.695.7826...8.919813267453.4.19862
C7: 5,7,4                                # reduction candidate for 5,7
C7: 5,7 => CTR
* 7269...84538.7.6191498....78..1..9.669..8.1.341.69527826...849198132.7.53.4.19862
C7: 4 => SOLVED
* 726951834538472619149836527872143956695287143413695278254768391981324765367519482
* PAIR D8: 3,6 BLK 8
E7: 3,6,4                                # reduction candidate for 3,6
E7: 3,6                                  # 20 pairs
F8: 3,6,4                                # reduction candidate for 3,6
F8: 3,6 => CTR
* 7269..48.538.7.6.91498....78..1..9..69..8.1.341..95.7.2...48391981.2.7453.4.19862
F8: 4                                    # 20 pairs
* PAIR D8: 3,6 ROW 8
H8: 3,6,4                                # reduction candidate for 3,6
H8: 4 => CTR
* 7269..48.538.7.6.91498....78..1..9..69..8.1.341..95.7.2....8391981.2.7453.4.19862
H8: 3,6                                  # 20 pairs
* PAIR D9: 5,7 ROW 9
B9: 5,7,6                                # reduction candidate for 5,7
B9: 5,7 => CTR
* 7269...84538.7.6191498....78..1..9.669..8.1.341.695.7826...8.919813267453.4.19862
B9: 6 => SOLVED
* 726951834538472619149836527872143956695287143413695278254768391981324765367519482
C9: 5,7,4                                # reduction candidate for 5,7
C9: 5,7 => SOLVED
* 726951834538472619149836527872143956695287143413695278254768391981324765367519482
C9: 4 => CTR
* 7269...84538.7.6191498....78..1..9.669..8.1.341.69527826...849198132.7.53.4.19862
* PAIR G7: 3,4 BLK 9
H8: 3,4,6                                # reduction candidate for 3,4
H8: 3,4 => CTR
* 7269...84538.7.6191498....78..1..9.669..8.1.341.695.7826...8.919813267453.4.19862
H8: 6 => SOLVED
* 726951834538472619149836527872143956695287143413695278254768391981324765367519482
* PAIR G7: 3,4 ROW 7
E7: 3,4,6                                # reduction candidate for 3,4
E7: 3,4 => CTR
* 7269...84538.7.6191498....78..1..9.669..8.1.341.695.7826...8.919813267453.4.19862
E7: 6 => SOLVED
* 726951834538472619149836527872143956695287143413695278254768391981324765367519482
* PAIR G7: 3,4 COL G
G1: 3,4,5,8                              # reduction candidate for 3,4
G1: 3,4 => CTR
* 72695..84538.7.6191498..5278..1..9.669..8.1.34136952782....84919813247653...198.2
G1: 5,8                                  # 22 pairs
* PAIR G9: 4,8 BLK 9
H9: 4,8,6                                # reduction candidate for 4,8
H9: 4,8 => SOLVED
* 726951834538472619149836527872143956695287143413695278254768391981324765367519482
H9: 6 => CTR
* 7269...84538.7.6191498....78..1..9.669..8.1.341.695.782....8.9198132.7.53...19862
* PAIR G9: 4,8 COL G
G1: 4,8,3,5                              # reduction candidate for 4,8
G1: 4,8 => SOLVED
* 726951834538472619149836527872143956695287143413695278254768391981324765367519482
G1: 3,5                                  # 24 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190127-absurd-base-pr-000.dot
* REASONING
* DIS # F2: 1 => CTR => F2: 2,4
* DIS # H2: 2,4 => CTR => H2: 1
* PRF # G1: 4,8 => SOL
* DIS # H1: 4,8 => CTR => H1: 1,3
* PRF # H1: 1,3 => SOL
* PRF # G3: 5 => SOL
* DIS # F3: 2,3 => CTR => F3: 6
* DIS # C4: 5,7 => CTR => C4: 2,3
* PRF # B7: 5,7 => SOL
* DIS # B7: 6 => CTR => B7: 5,7
* DIS # B9: 5,7 => CTR => B9: 6
* PRF # B9: 6 => SOL
* DIS # C4: 5,7 => CTR => C4: 2,3
* PRF # F4: 3,6 => SOL
* DIS # F4: 4,6 => CTR => F4: 2,3,7
* PRF # B7: 5,7 => SOL
* DIS # B7: 6 => CTR => B7: 5,7
* DIS # C7: 5,7 => CTR => C7: 4
* PRF # C7: 4 => SOL
* DIS # F8: 3,6 => CTR => F8: 4
* DIS # H8: 4 => CTR => H8: 3,6
* DIS # B9: 5,7 => CTR => B9: 6
* PRF # B9: 6 => SOL
* PRF # C9: 5,7 => SOL
* DIS # C9: 4 => CTR => C9: 5,7
* DIS # H8: 3,4 => CTR => H8: 6
* PRF # H8: 6 => SOL
* DIS # E7: 3,4 => CTR => E7: 6
* PRF # E7: 6 => SOL
* DIS # G1: 3,4 => CTR => G1: 5,8
* PRF # H9: 4,8 => SOL
* DIS # H9: 6 => CTR => H9: 4,8
* PRF # G1: 4,8 => SOL
* CNT  33 HDP CHAINS /  54 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C6,D2,D5,D6,D7,D8,D9,G6,G7,G9,H3,I1,I4,I6)
* 7269.....538.7.6.91498....78..1..9..69..8.1.341..95.7.2....8.91981.2.7.53...19..2
* PAIR D2: 2,4 BLK 2
F2: 2,4,1                                # reduction candidate for 2,4
F2: 1 => CTR
* 7269.381453847162914985..378..1..9..69..8.1.341.695.782.4.6839198132476536..19482
* PAIR I1: 4,8 BLK 3
G1: 4,8,3,5                              # reduction candidate for 4,8
G1: 4,8 => SOLVED
* 726951834538472619149836527872143956695287143413695278254768391981324765367519482
* DURATION: 0:00:03.198857  START: 03:16:29.977772  END: 03:16:33.176629 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190127-absurd-base-pr-001.dot
* REASONING
* DIS # F2: 1 => CTR => F2: 2,4
* PRF F2: 2,4 # G1: 4,8 => SOL
* STA F2: 2,4 + G1: 4,8
* CNT   2 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190127, absurd

Solution

position: 726951834538472619149836527872143956695287143413695278254768391981324765367519482 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 # F2: 2,4 => UNS
* DIS # F2: 1 => CTR => F2: 2,4
* DIS # H2: 2,4 => CTR => H2: 1
* INC # H2: 1 => UNS
* PRF # G1: 4,8 => SOL
* INC # G1: 3,5 => UNS
* DIS # H1: 4,8 => CTR => H1: 1,3
* PRF # H1: 1,3 => SOL
* INC # G3: 2,3 => UNS
* PRF # G3: 5 => SOL
* DIS # F3: 2,3 => CTR => F3: 6
* INC # F3: 6 => UNS
* DIS # C4: 5,7 => CTR => C4: 2,3
* INC # C4: 2,3 => UNS
* INC # C5: 5,7 => UNS
* PRF # B7: 5,7 => SOL
* DIS # B7: 6 => CTR => B7: 5,7
* DIS # B9: 5,7 => CTR => B9: 6
* PRF # B9: 6 => SOL
* INC # C4: 2,3 => UNS
* DIS # C4: 5,7 => CTR => C4: 2,3
* INC # F4: 2,4 => UNS
* INC # F5: 2,4 => UNS
* INC # H5: 2,4 => UNS
* INC # H5: 5 => UNS
* INC # E4: 3,6 => UNS
* PRF # F4: 3,6 => SOL
* INC # F4: 2,4,7 => UNS
* INC # E4: 4,6 => UNS
* DIS # F4: 4,6 => CTR => F4: 2,3,7
* INC # F4: 2,3,7 => UNS
* PRF # B7: 5,7 => SOL
* DIS # B7: 6 => CTR => B7: 5,7
* DIS # C7: 5,7 => CTR => C7: 4
* PRF # C7: 4 => SOL
* INC # E7: 3,6 => UNS
* DIS # F8: 3,6 => CTR => F8: 4
* INC # F8: 4 => UNS
* INC # H8: 3,6 => UNS
* DIS # H8: 4 => CTR => H8: 3,6
* DIS # B9: 5,7 => CTR => B9: 6
* PRF # B9: 6 => SOL
* PRF # C9: 5,7 => SOL
* DIS # C9: 4 => CTR => C9: 5,7
* DIS # H8: 3,4 => CTR => H8: 6
* PRF # H8: 6 => SOL
* DIS # E7: 3,4 => CTR => E7: 6
* PRF # E7: 6 => SOL
* DIS # G1: 3,4 => CTR => G1: 5,8
* INC # G1: 5,8 => UNS
* PRF # H9: 4,8 => SOL
* DIS # H9: 6 => CTR => H9: 4,8
* PRF # G1: 4,8 => SOL
* INC # G1: 3,5 => UNS
* CNT  54 HDP CHAINS /  54 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F2: 2,4 => UNS
* DIS # F2: 1 => CTR => F2: 2,4
* PRF F2: 2,4 # G1: 4,8 => SOL
* STA F2: 2,4 + G1: 4,8
* CNT   3 HDP CHAINS /   3 HYP OPENED