Analysis of zz-www.sudokuoftheday.co.uk-20190417-absurd-base.sdk

Contents

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

level: medium

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

position: ..4............5.7....39..4.3.......24.7....37..18..2.95...21.....8..2..8..56.... initial

Autosolve

position: ..4675..2...4185.7...239..4.38924..1241756..37..18342.95.3421.84..89.2..8..56..49 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # H1: 8,9 => CTR => H1: 1,3
* DIS # H1: 8,9 => CTR => H1: 1,3
* DIS # H2: 9 => CTR => H2: 3,6
* PRF # H3: 6,8 => SOL
* DIS # B3: 6,8 => CTR => B3: 7
* DIS # C6: 5,6 => CTR => C6: 9
* PRF # C6: 9 => SOL
* DIS # H4: 7 => CTR => H4: 5,6
* PRF # A3: 1 => SOL
* PRF # C6: 6,9 => SOL
* DIS # C6: 5 => CTR => C6: 6,9
* PRF # B2: 6,9 => SOL
* PRF # H4: 6,7 => SOL
* DIS # H4: 5 => CTR => H4: 6,7
* DIS # G1: 3 => CTR => G1: 8,9
* DIS # H1: 8,9 => CTR => H1: 1,3
* DIS # H4: 7 => CTR => H4: 5,6
* DIS # C6: 5,6 => CTR => C6: 9
* PRF # C6: 9 => SOL
* DIS # C8: 6,7 => CTR => C8: 3
* DIS # C3: 6,7 => CTR => C3: 5
* PRF # C3: 5 => SOL
* DIS # B8: 6 => CTR => B8: 1,7
* PRF # B9: 2 => SOL
* DIS # H8: 6,7 => CTR => H8: 3,5
* PRF # H4: 6,7 => SOL
* DIS # H4: 5 => CTR => H4: 6,7
* DIS # H8: 3,7 => CTR => H8: 5,6
* DIS # H8: 3,7 => CTR => H8: 5,6
* PRF # C9: 3,7 => SOL
* CNT  30 HDP CHAINS /  50 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 # H1: 8,9 => CTR => H1: 1,3
* DIS H1: 1,3 # C6: 5,6 => CTR => C6: 9
* PRF H1: 1,3 + C6: 9 => SOL
* STA H1: 1,3 + C6: 9
* CNT   3 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

..4............5.7....39..4.3.......24.7....37..18..2.95...21.....8..2..8..56.... initial
..4675..2...4185.7...239..4.38924..1241756..37..18342.95.3421.84..89.2..8..56..49 autosolve
384675912692418537175239684538924761241756893769183425956342178413897256827561349 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
A1: 1,3
B1: 8,9
A2: 3,6
G3: 6,8
A4: 5,6
B6: 6,9
G4: 6,7
G5: 8,9
H5: 8,9
I6: 5,6
C7: 6,7
F8: 1,7
F9: 1,7
H7: 6,7
I8: 5,6
G9: 3,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,A3: 1.. / A1 = 1  => 16 pairs (_) / A3 = 1  =>  0 pairs (*)
H1,H3: 1.. / H1 = 1  =>  0 pairs (*) / H3 = 1  =>  0 pairs (X)
B8,B9: 1.. / B8 = 1  => 19 pairs (_) / B9 = 1  => 21 pairs (_)
F8,F9: 1.. / F8 = 1  => 21 pairs (_) / F9 = 1  => 19 pairs (_)
A1,H1: 1.. / A1 = 1  => 16 pairs (_) / H1 = 1  =>  0 pairs (*)
A3,H3: 1.. / A3 = 1  =>  0 pairs (*) / H3 = 1  =>  0 pairs (X)
B8,F8: 1.. / B8 = 1  => 19 pairs (_) / F8 = 1  => 21 pairs (_)
B9,F9: 1.. / B9 = 1  => 21 pairs (_) / F9 = 1  => 19 pairs (_)
B2,C2: 2.. / B2 = 2  => 23 pairs (_) / C2 = 2  =>  0 pairs (*)
B9,C9: 2.. / B9 = 2  =>  0 pairs (*) / C9 = 2  =>  0 pairs (X)
B2,B9: 2.. / B2 = 2  => 23 pairs (_) / B9 = 2  =>  0 pairs (*)
C2,C9: 2.. / C2 = 2  =>  0 pairs (*) / C9 = 2  =>  0 pairs (X)
A1,A2: 3.. / A1 = 3  =>  0 pairs (*) / A2 = 3  =>  0 pairs (X)
C8,C9: 3.. / C8 = 3  => 22 pairs (_) / C9 = 3  =>  0 pairs (X)
H8,G9: 3.. / H8 = 3  =>  0 pairs (X) / G9 = 3  => 22 pairs (_)
A2,H2: 3.. / A2 = 3  => 16 pairs (_) / H2 = 3  =>  0 pairs (*)
C8,H8: 3.. / C8 = 3  => 22 pairs (_) / H8 = 3  =>  0 pairs (X)
C9,G9: 3.. / C9 = 3  =>  0 pairs (X) / G9 = 3  => 22 pairs (_)
G1,G9: 3.. / G1 = 3  =>  0 pairs (X) / G9 = 3  => 22 pairs (_)
A3,C3: 5.. / A3 = 5  =>  0 pairs (X) / C3 = 5  =>  0 pairs (_)
A4,C6: 5.. / A4 = 5  =>  0 pairs (*) / C6 = 5  =>  0 pairs (X)
H4,I6: 5.. / H4 = 5  =>  0 pairs (X) / I6 = 5  =>  0 pairs (_)
H8,I8: 5.. / H8 = 5  =>  0 pairs (*) / I8 = 5  =>  0 pairs (X)
A4,H4: 5.. / A4 = 5  =>  0 pairs (*) / H4 = 5  =>  0 pairs (X)
C6,I6: 5.. / C6 = 5  =>  0 pairs (X) / I6 = 5  =>  0 pairs (_)
A3,A4: 5.. / A3 = 5  =>  0 pairs (X) / A4 = 5  =>  0 pairs (_)
C3,C6: 5.. / C3 = 5  =>  0 pairs (*) / C6 = 5  =>  0 pairs (X)
H4,H8: 5.. / H4 = 5  =>  0 pairs (X) / H8 = 5  =>  0 pairs (_)
I6,I8: 5.. / I6 = 5  =>  0 pairs (*) / I8 = 5  =>  0 pairs (X)
C7,H7: 6.. / C7 = 6  => 24 pairs (_) / H7 = 6  =>  0 pairs (X)
G3,G4: 6.. / G3 = 6  => 22 pairs (_) / G4 = 6  =>  0 pairs (X)
I6,I8: 6.. / I6 = 6  =>  0 pairs (X) / I8 = 6  =>  0 pairs (_)
B3,C3: 7.. / B3 = 7  => 24 pairs (_) / C3 = 7  =>  0 pairs (X)
G4,H4: 7.. / G4 = 7  => 22 pairs (_) / H4 = 7  =>  0 pairs (X)
F8,F9: 7.. / F8 = 7  => 19 pairs (_) / F9 = 7  => 21 pairs (_)
C7,H7: 7.. / C7 = 7  =>  0 pairs (X) / H7 = 7  => 24 pairs (_)
G4,G9: 7.. / G4 = 7  => 22 pairs (_) / G9 = 7  =>  0 pairs (X)
B1,B3: 8.. / B1 = 8  => 22 pairs (_) / B3 = 8  =>  0 pairs (X)
G5,H5: 8.. / G5 = 8  =>  0 pairs (*) / H5 = 8  =>  0 pairs (X)
B6,C6: 9.. / B6 = 9  =>  0 pairs (X) / C6 = 9  =>  0 pairs (_)
G5,H5: 9.. / G5 = 9  => 16 pairs (_) / H5 = 9  =>  0 pairs (*)
C2,C6: 9.. / C2 = 9  =>  0 pairs (X) / C6 = 9  =>  0 pairs (_)
G1,G5: 9.. / G1 = 9  =>  0 pairs (*) / G5 = 9  =>  0 pairs (X)
* DURATION: 0:00:50.977164  START: 05:21:56.699364  END: 05:22:47.676528 2019-05-01
* CP COUNT: (43)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A4,B1,B6,C7,F8,F9,G3,G4,G5,G9,H5,H7,I6,I8)
* ..4675..2...4185.7...239..4.38924..1241756..37..18342.95.3421.84..89.2..8..56..49
* PAIR A1: 1,3 ROW 1
H1: 1,3,8,9                              # reduction candidate for 1,3
H1: 8,9 => CTR
* 1.46753.23..4185.7...239.14.38924..12417569837..18342.95.3421.84..89.2358.356.749
H1: 1,3                                  # 22 pairs
* PAIR B1: 8,9 ROW 1
G1: 8,9,3                                # reduction candidate for 8,9
G1: 8,9                                  # 22 pairs
H1: 8,9,1,3                              # reduction candidate for 8,9
H1: 8,9 => CTR
* 1.46753.23..4185.7...239.14.38924..12417569837..18342.95.3421.84..89.2358.356.749
H1: 1,3                                  # 22 pairs
* PAIR A2: 3,6 ROW 2
H2: 3,6,9                                # reduction candidate for 3,6
H2: 9 => CTR
* 1946758323..418597.8.239..4.38924..12417569837.918342595.3421.84..89.2568..56.349
H2: 3,6                                  # 22 pairs
* PAIR G3: 6,8 BLK 3
H3: 6,8,1                                # reduction candidate for 6,8
H3: 6,8 => SOLVED
* 384675912692418537175239684538924761241756893769183425956342178413897256827561349
H3: 1                                    # 16 pairs
* PAIR G3: 6,8 ROW 3
B3: 6,8,7                                # reduction candidate for 6,8
B3: 6,8 => CTR
* ..4675..2.29418537567239..4.38924..1241756..37.51834269563421784.389.2658.256.349
B3: 7                                    # 24 pairs
* PAIR A4: 5,6 BLK 4
C6: 5,6,9                                # reduction candidate for 5,6
C6: 5,6 => CTR
* .846759.2.294185.7...239684.389247.124175689379.18342.95.3421.8463891275812567349
C6: 9 => SOLVED
* 384675912692418537175239684538924761241756893769183425956342178413897256827561349
* PAIR A4: 5,6 ROW 4
H4: 5,6,7                                # reduction candidate for 5,6
H4: 7 => CTR
* ..4675..2...4185.7...239..4538924671241756..37..1834259573421684..89.2..8..56..49
H4: 5,6                                  # 22 pairs
* PAIR A4: 5,6 COL A
A3: 5,6,1                                # reduction candidate for 5,6
A3: 1 => SOLVED
* 384675912692418537175239684538924761241756893769183425956342178413897256827561349
A3: 5,6                                  # 16 pairs
* PAIR B6: 6,9 BLK 4
C6: 6,9,5                                # reduction candidate for 6,9
C6: 6,9 => SOLVED
* 384675912692418537175239684538924761241756893769183425956342178413897256827561349
C6: 5 => CTR
* .846759.2.294185.75..2396.4.38924..1241756..379518342695.3421.84..89.2.58.256.349
* PAIR B6: 6,9 COL B
B2: 6,9,2                                # reduction candidate for 6,9
B2: 6,9 => SOLVED
* 384675912692418537175239684538924761241756893769183425956342178413897256827561349
B2: 2                                    # 23 pairs
* PAIR G4: 6,7 BLK 6
H4: 6,7,5                                # reduction candidate for 6,7
H4: 6,7 => SOLVED
* 384675912692418537175239684538924761241756893769183425956342178413897256827561349
H4: 5 => CTR
* ..4675..2..94185.75..239614638924751241756..379518342695.3421.84..89.2.58..56.349
* PAIR G5: 8,9 COL G
G1: 8,9,3                                # reduction candidate for 8,9
G1: 3 => CTR
* ..46753.23..4185.7...239..4.38924..12417569837..18342.95.3421.84..89.2358.356.749
G1: 8,9                                  # 22 pairs
* PAIR H5: 8,9 COL H
H1: 8,9,1,3                              # reduction candidate for 8,9
H1: 8,9 => CTR
* 1.46753.23..4185.7...239.14.38924..12417569837..18342.95.3421.84..89.2358.356.749
H1: 1,3                                  # 22 pairs
* PAIR I6: 5,6 BLK 6
H4: 5,6,7                                # reduction candidate for 5,6
H4: 7 => CTR
* ..4675..2...4185.7...239..4538924671241756..37..1834259573421684..89.2..8..56..49
H4: 5,6                                  # 22 pairs
* PAIR I6: 5,6 ROW 6
C6: 5,6,9                                # reduction candidate for 5,6
C6: 5,6 => CTR
* .846759.2.294185.7...239684.389247.124175689379.18342.95.3421.8463891275812567349
C6: 9 => SOLVED
* 384675912692418537175239684538924761241756893769183425956342178413897256827561349
* PAIR C7: 6,7 BLK 7
B8: 6,7,1                                # reduction candidate for 6,7
B8: 6,7                                  # 21 pairs
C8: 6,7,3                                # reduction candidate for 6,7
C8: 6,7 => CTR
* ..4675..2...4185.7...239..4.38924..1241756..37..18342.95.3421.84..89.2358.356.749
C8: 3                                    # 22 pairs
* PAIR C7: 6,7 COL C
C3: 6,7,5                                # reduction candidate for 6,7
C3: 6,7 => CTR
* 1846759.2...4185.75..239.14638924751241756..379518342695.3421.84..89.2.58..56.349
C3: 5 => SOLVED
* 384675912692418537175239684538924761241756893769183425956342178413897256827561349
* PAIR F8: 1,7 ROW 8
B8: 1,7,6                                # reduction candidate for 1,7
B8: 6 => CTR
* .846759.2.29418537576239..4.38924751241756..3795183426957342168463891275812567349
B8: 1,7                                  # 21 pairs
* PAIR F9: 1,7 ROW 9
B9: 1,7,2                                # reduction candidate for 1,7
B9: 2 => SOLVED
* 384675912692418537175239684538924761241756893769183425956342178413897256827561349
B9: 1,7                                  # 23 pairs
* PAIR H7: 6,7 BLK 9
H8: 6,7,3,5                              # reduction candidate for 6,7
H8: 6,7 => CTR
* ..4675..2..94185.75..239614638924751241756..379518342695.3421.84.389.2.58..56.349
H8: 3,5                                  # 17 pairs
* PAIR H7: 6,7 COL H
H4: 6,7,5                                # reduction candidate for 6,7
H4: 6,7 => SOLVED
* 384675912692418537175239684538924761241756893769183425956342178413897256827561349
H4: 5 => CTR
* ..4675..2..94185.75..239614638924751241756..379518342695.3421.84..89.2.58..56.349
* PAIR I8: 5,6 BLK 9
H8: 5,6,3,7                              # reduction candidate for 5,6
H8: 3,7 => CTR
* ..4675..2..941853757.239..4.38924.51241756..37.518342695.3421684..89.2758..567349
H8: 5,6                                  # 24 pairs
* PAIR G9: 3,7 BLK 9
H8: 3,7,5,6                              # reduction candidate for 3,7
H8: 3,7 => CTR
* ..4675..2..941853757.239..4.38924.51241756..37.518342695.3421684..89.2758..567349
H8: 5,6                                  # 24 pairs
* PAIR G9: 3,7 ROW 9
C9: 3,7,2                                # reduction candidate for 3,7
C9: 3,7 => SOLVED
* 384675912692418537175239684538924761241756893769183425956342178413897256827561349
C9: 2                                    # 23 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190417-absurd-base-pr-000.dot
* REASONING
* DIS # H1: 8,9 => CTR => H1: 1,3
* DIS # H1: 8,9 => CTR => H1: 1,3
* DIS # H2: 9 => CTR => H2: 3,6
* PRF # H3: 6,8 => SOL
* DIS # B3: 6,8 => CTR => B3: 7
* DIS # C6: 5,6 => CTR => C6: 9
* PRF # C6: 9 => SOL
* DIS # H4: 7 => CTR => H4: 5,6
* PRF # A3: 1 => SOL
* PRF # C6: 6,9 => SOL
* DIS # C6: 5 => CTR => C6: 6,9
* PRF # B2: 6,9 => SOL
* PRF # H4: 6,7 => SOL
* DIS # H4: 5 => CTR => H4: 6,7
* DIS # G1: 3 => CTR => G1: 8,9
* DIS # H1: 8,9 => CTR => H1: 1,3
* DIS # H4: 7 => CTR => H4: 5,6
* DIS # C6: 5,6 => CTR => C6: 9
* PRF # C6: 9 => SOL
* DIS # C8: 6,7 => CTR => C8: 3
* DIS # C3: 6,7 => CTR => C3: 5
* PRF # C3: 5 => SOL
* DIS # B8: 6 => CTR => B8: 1,7
* PRF # B9: 2 => SOL
* DIS # H8: 6,7 => CTR => H8: 3,5
* PRF # H4: 6,7 => SOL
* DIS # H4: 5 => CTR => H4: 6,7
* DIS # H8: 3,7 => CTR => H8: 5,6
* DIS # H8: 3,7 => CTR => H8: 5,6
* PRF # C9: 3,7 => SOL
* CNT  30 HDP CHAINS /  50 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A4,B1,B6,C7,F8,F9,G3,G4,G5,G9,H5,H7,I6,I8)
* ..4675..2...4185.7...239..4.38924..1241756..37..18342.95.3421.84..89.2..8..56..49
* PAIR A1: 1,3 ROW 1
H1: 1,3,8,9                              # reduction candidate for 1,3
H1: 8,9 => CTR
* 1.46753.23..4185.7...239.14.38924..12417569837..18342.95.3421.84..89.2358.356.749
* PAIR RESTART
* PAIR A4: 5,6 BLK 4
C6: 5,6,9                                # reduction candidate for 5,6
C6: 5,6 => CTR
* 38467591262941853717523968453892476124175689379618342.95.3421.84.389.2..8.256.349
C6: 9 => SOLVED
* 384675912692418537175239684538924761241756893769183425956342178413897256827561349
* DURATION: 0:00:03.846094  START: 05:23:22.555789  END: 05:23:26.401883 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190417-absurd-base-pr-001.dot
* REASONING
* DIS # H1: 8,9 => CTR => H1: 1,3
* DIS H1: 1,3 # C6: 5,6 => CTR => C6: 9
* PRF H1: 1,3 + C6: 9 => SOL
* STA H1: 1,3 + C6: 9
* CNT   3 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190417, absurd

Solution

position: 384675912692418537175239684538924761241756893769183425956342178413897256827561349 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 # H1: 1,3 => UNS
* DIS # H1: 8,9 => CTR => H1: 1,3
* INC # G1: 8,9 => UNS
* DIS # H1: 8,9 => CTR => H1: 1,3
* INC # H1: 1,3 => UNS
* INC # H2: 3,6 => UNS
* DIS # H2: 9 => CTR => H2: 3,6
* PRF # H3: 6,8 => SOL
* INC # H3: 1 => UNS
* DIS # B3: 6,8 => CTR => B3: 7
* INC # B3: 7 => UNS
* DIS # C6: 5,6 => CTR => C6: 9
* PRF # C6: 9 => SOL
* INC # H4: 5,6 => UNS
* DIS # H4: 7 => CTR => H4: 5,6
* INC # A3: 5,6 => UNS
* PRF # A3: 1 => SOL
* PRF # C6: 6,9 => SOL
* DIS # C6: 5 => CTR => C6: 6,9
* PRF # B2: 6,9 => SOL
* INC # B2: 2 => UNS
* PRF # H4: 6,7 => SOL
* DIS # H4: 5 => CTR => H4: 6,7
* INC # G1: 8,9 => UNS
* DIS # G1: 3 => CTR => G1: 8,9
* DIS # H1: 8,9 => CTR => H1: 1,3
* INC # H1: 1,3 => UNS
* INC # H4: 5,6 => UNS
* DIS # H4: 7 => CTR => H4: 5,6
* DIS # C6: 5,6 => CTR => C6: 9
* PRF # C6: 9 => SOL
* INC # B8: 6,7 => UNS
* DIS # C8: 6,7 => CTR => C8: 3
* INC # C8: 3 => UNS
* DIS # C3: 6,7 => CTR => C3: 5
* PRF # C3: 5 => SOL
* INC # B8: 1,7 => UNS
* DIS # B8: 6 => CTR => B8: 1,7
* INC # B9: 1,7 => UNS
* PRF # B9: 2 => SOL
* DIS # H8: 6,7 => CTR => H8: 3,5
* INC # H8: 3,5 => UNS
* PRF # H4: 6,7 => SOL
* DIS # H4: 5 => CTR => H4: 6,7
* INC # H8: 5,6 => UNS
* DIS # H8: 3,7 => CTR => H8: 5,6
* DIS # H8: 3,7 => CTR => H8: 5,6
* INC # H8: 5,6 => UNS
* PRF # C9: 3,7 => SOL
* INC # C9: 2 => UNS
* CNT  50 HDP CHAINS /  50 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # H1: 1,3 => UNS
* DIS # H1: 8,9 => CTR => H1: 1,3
* DIS H1: 1,3 # C6: 5,6 => CTR => C6: 9
* PRF H1: 1,3 + C6: 9 => SOL
* STA H1: 1,3 + C6: 9
* CNT   4 HDP CHAINS /   3 HYP OPENED