Analysis of zz-www.sudokuoftheday.co.uk-20190108-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: ..49...6.....2..7.9......3....536.9............74....1..2...9...78..2...4..75...2 initial

Autosolve

position: 7.491..6.....2..799....7.3.2.153679....271.....7489.21..2...9.7.78.92...4..75...2 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A2: 5,6 => CTR => A2: 1,3,8
* DIS # B2: 5,6 => CTR => B2: 1,3,8
* DIS # C5: 5,6 => CTR => C5: 3,9
* PRF # D2: 6,8 => SOL
* DIS # D2: 3 => CTR => D2: 6,8
* DIS # D7: 6,8 => CTR => D7: 1,3
* DIS # B1: 2,8 => CTR => B1: 3,5
* PRF # B1: 3,5 => SOL
* PRF # I3: 5,8 => SOL
* DIS # I3: 4 => CTR => I3: 5,8
* DIS # B1: 5,8 => CTR => B1: 2,3
* PRF # F1: 5,8 => SOL
* DIS # F1: 3 => CTR => F1: 5,8
* DIS # B5: 3,5,6,9 => CTR => B5: 4,8
* DIS # I3: 4,8 => CTR => I3: 5
* PRF # I3: 5 => SOL
* DIS # B5: 3,6 => CTR => B5: 4,5,8,9
* DIS # C5: 3,6 => CTR => C5: 5,9
* PRF # D7: 3,8 => SOL
* DIS # F7: 3,8 => CTR => F7: 4
* PRF # F7: 4 => SOL
* DIS # F1: 3,8 => CTR => F1: 5
* PRF # F1: 5 => SOL
* PRF # F2: 3,8 => SOL
* DIS # G8: 3,6 => CTR => G8: 4,5
* DIS # H7: 5 => CTR => H7: 1,8
* CNT  26 HDP CHAINS /  49 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 # A2: 5,6 => CTR => A2: 1,3,8
* DIS A2: 1,3,8 # B2: 5,6 => CTR => B2: 1,3,8
* DIS A2: 1,3,8 + B2: 1,3,8 # C2: 3 => CTR => C2: 5,6
* PRF A2: 1,3,8 + B2: 1,3,8 + C2: 5,6 # D2: 6,8 => SOL
* STA A2: 1,3,8 + B2: 1,3,8 + C2: 5,6 + D2: 6,8
* CNT   4 HDP CHAINS /   6 HYP OPENED

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

Details

Positions

..49...6.....2..7.9......3....536.9............74....1..2...9...78..2...4..75...2 initial
7.491..6.....2..799....7.3.2.153679....271.....7489.21..2...9.7.78.92...4..75...2 autosolve
734915268815623479926847135281536794349271856567489321152364987678192543493758612 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
B3: 1,2
C3: 5,6
D3: 6,8
E3: 4,6
G1: 2,8
I1: 5,8
G3: 1,2
B4: 4,8
I4: 4,8
I5: 3,6
E7: 4,6
F9: 3,8
I8: 3,6
H9: 1,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,G3: 1.. / G2 = 1  =>  0 pairs (X) / G3 = 1  => 12 pairs (_)
D7,D8: 1.. / D7 = 1  => 21 pairs (_) / D8 = 1  => 15 pairs (_)
B3,G3: 1.. / B3 = 1  =>  0 pairs (X) / G3 = 1  => 12 pairs (_)
B9,H9: 1.. / B9 = 1  =>  0 pairs (X) / H9 = 1  => 15 pairs (_)
B1,B3: 2.. / B1 = 2  =>  0 pairs (X) / B3 = 2  => 12 pairs (_)
G1,G3: 2.. / G1 = 2  => 12 pairs (_) / G3 = 2  =>  0 pairs (X)
B1,G1: 2.. / B1 = 2  =>  0 pairs (X) / G1 = 2  => 12 pairs (_)
B3,G3: 2.. / B3 = 2  => 12 pairs (_) / G3 = 2  =>  0 pairs (X)
B1,F1: 3.. / B1 = 3  =>  0 pairs (*) / F1 = 3  =>  0 pairs (X)
I5,I8: 3.. / I5 = 3  =>  0 pairs (X) / I8 = 3  => 15 pairs (_)
F2,E3: 4.. / F2 = 4  =>  0 pairs (X) / E3 = 4  =>  0 pairs (_)
G2,I3: 4.. / G2 = 4  =>  0 pairs (*) / I3 = 4  =>  0 pairs (X)
B4,B5: 4.. / B4 = 4  =>  0 pairs (X) / B5 = 4  =>  0 pairs (_)
E7,F7: 4.. / E7 = 4  =>  0 pairs (X) / F7 = 4  =>  0 pairs (_)
G8,H8: 4.. / G8 = 4  =>  0 pairs (X) / H8 = 4  => 15 pairs (_)
F2,G2: 4.. / F2 = 4  =>  0 pairs (X) / G2 = 4  =>  0 pairs (_)
E3,I3: 4.. / E3 = 4  =>  0 pairs (*) / I3 = 4  =>  0 pairs (X)
B4,I4: 4.. / B4 = 4  =>  0 pairs (X) / I4 = 4  =>  0 pairs (_)
E3,E7: 4.. / E3 = 4  =>  0 pairs (*) / E7 = 4  =>  0 pairs (X)
F2,F7: 4.. / F2 = 4  =>  0 pairs (X) / F7 = 4  =>  0 pairs (_)
H5,H8: 4.. / H5 = 4  =>  0 pairs (X) / H8 = 4  => 15 pairs (_)
I3,I4: 4.. / I3 = 4  =>  0 pairs (X) / I4 = 4  =>  0 pairs (_)
F1,F2: 5.. / F1 = 5  =>  0 pairs (*) / F2 = 5  =>  0 pairs (X)
I1,I3: 5.. / I1 = 5  =>  0 pairs (X) / I3 = 5  =>  0 pairs (_)
C3,I3: 5.. / C3 = 5  =>  0 pairs (X) / I3 = 5  =>  0 pairs (_)
E3,E7: 6.. / E3 = 6  =>  0 pairs (X) / E7 = 6  =>  0 pairs (_)
I5,I8: 6.. / I5 = 6  => 15 pairs (_) / I8 = 6  =>  0 pairs (X)
D3,I3: 8.. / D3 = 8  => 16 pairs (_) / I3 = 8  =>  0 pairs (X)
B4,I4: 8.. / B4 = 8  =>  0 pairs (*) / I4 = 8  =>  0 pairs (X)
A2,A5: 8.. / A2 = 8  => 20 pairs (_) / A5 = 8  =>  0 pairs (X)
B5,C5: 9.. / B5 = 9  =>  0 pairs (X) / C5 = 9  => 16 pairs (_)
B9,C9: 9.. / B9 = 9  => 16 pairs (_) / C9 = 9  =>  0 pairs (X)
B5,B9: 9.. / B5 = 9  =>  0 pairs (X) / B9 = 9  => 16 pairs (_)
C5,C9: 9.. / C5 = 9  => 16 pairs (_) / C9 = 9  =>  0 pairs (X)
* DURATION: 0:00:41.301949  START: 02:47:52.303601  END: 02:48:33.605550 2019-05-01
* CP COUNT: (34)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B4,C3,D3,E3,E7,F9,G1,G3,H9,I1,I4,I5,I8)
* 7.491..6.....2..799....7.3.2.153679....271.....7489.21..2...9.7.78.92...4..75...2
* PAIR C3: 5,6 BLK 1
A2: 5,6,1,3,8                            # reduction candidate for 5,6
A2: 5,6 => CTR
* 7.491..65....254799....7.3.2415367988..271.....7489.21..2...9.7.78.92...4..75...2
A2: 1,3,8                                # 14 pairs
B2: 5,6,1,3,8                            # reduction candidate for 5,6
B2: 5,6 => CTR
* 7.4913.65..3.254799.5.47138281536794.49271.....7489.21..2.649.7.78.92.4.496758312
B2: 1,3,8                                # 14 pairs
C2: 5,6,3                                # reduction candidate for 5,6
C2: 5,6                                  # 17 pairs
* PAIR C3: 5,6 COL C
C5: 5,6,3,9                              # reduction candidate for 5,6
C5: 5,6 => CTR
* 7.4913.65..3.254799....7.3.24153679889.271.....7489.21..2...9.7.78.92...4.975...2
C5: 3,9                                  # 15 pairs
* PAIR D3: 6,8 BLK 2
D2: 6,8,3                                # reduction candidate for 6,8
D2: 6,8 => SOLVED
* 734915268815623479926847135281536794349271856567489321152364987678192543493758612
D2: 3 => CTR
* 73491.26....32.479925.47138281536794.49271.....7489.21..28649.7.78192.4.49375...2
* PAIR D3: 6,8 COL D
D7: 6,8,1,3                              # reduction candidate for 6,8
D7: 6,8 => CTR
* 73491.26....32.479925.47138281536794.49271.....7489.21..28649.7.78192.4.49375...2
D7: 1,3                                  # 16 pairs
* PAIR G1: 2,8 ROW 1
B1: 2,8,3,5                              # reduction candidate for 2,8
B1: 2,8 => CTR
* 7.4913.65....254799.5.47138281536794.49271.....7489.21..2.649.7.78.92.4.49.758.12
B1: 3,5 => SOLVED
* 734915268815623479926847135281536794349271856567489321152364987678192543493758612
* PAIR I1: 5,8 BLK 3
I3: 5,8,4                                # reduction candidate for 5,8
I3: 5,8 => SOLVED
* 734915268815623479926847135281536794349271856567489321152364987678192543493758612
I3: 4 => CTR
* 7.491..65....254799....7.3.2.153679....271.....7489.21..2...9.7.78.92...4..75...2
* PAIR I1: 5,8 ROW 1
B1: 5,8,2,3                              # reduction candidate for 5,8
B1: 5,8 => CTR
* 7.491326.....25479925647138281536794.49271.....7489.21..2.649.7.78.92.4.49.758.12
B1: 2,3                                  # 17 pairs
F1: 5,8,3                                # reduction candidate for 5,8
F1: 5,8 => SOLVED
* 734915268815623479926847135281536794349271856567489321152364987678192543493758612
F1: 3 => CTR
* 7.491326.....25479925647138281536794.49271.....7489.21..2.649.7.78.92.4.49.758.12
* PAIR B4: 4,8 BLK 4
B5: 4,8,3,5,6,9                          # reduction candidate for 4,8
B5: 3,5,6,9 => CTR
* 7.491..65....254799....7.3.2415367988..271.....7489.21..2...9.7.78.92...4..75...2
B5: 4,8                                  # 20 pairs
* PAIR I4: 4,8 BLK 6
G5: 4,8,3,5,6                            # reduction candidate for 4,8
G5: 4,8                                  # 18 pairs
H5: 4,8,5                                # reduction candidate for 4,8
H5: 4,8                                  # 15 pairs
* PAIR I4: 4,8 COL I
I3: 4,8,5                                # reduction candidate for 4,8
I3: 4,8 => CTR
* 7.4918265816325479925647138281536794.49271....67489.21.528649.7.78.92.4.49.75..12
I3: 5 => SOLVED
* 734915268815623479926847135281536794349271856567489321152364987678192543493758612
* PAIR I5: 3,6 BLK 6
G5: 3,6,4,5,8                            # reduction candidate for 3,6
G5: 3,6                                  # 20 pairs
G6: 3,6,5                                # reduction candidate for 3,6
G6: 3,6                                  # 15 pairs
* PAIR I5: 3,6 ROW 5
A5: 3,6,5,8                              # reduction candidate for 3,6
A5: 3,6                                  # 22 pairs
B5: 3,6,4,5,8,9                          # reduction candidate for 3,6
B5: 3,6 => CTR
* 7.491..65....254799....7.3.2415367988.9271.....7489.21..2...9.7.78.92...49.75..12
B5: 4,5,8,9                              # 14 pairs
C5: 3,6,5,9                              # reduction candidate for 3,6
C5: 3,6 => CTR
* 7.491..65....254799....7.3.24153679889.271.....7489.21..2...9.7.78.92...4.975...2
C5: 5,9                                  # 15 pairs
* PAIR F9: 3,8 BLK 8
D7: 3,8,1,6                              # reduction candidate for 3,8
D7: 3,8 => SOLVED
* 734915268815623479926847135281536794349271856567489321152364987678192543493758612
D7: 1,6                                  # 16 pairs
F7: 3,8,4                                # reduction candidate for 3,8
F7: 3,8 => CTR
* 7.4915.6.....24.799...67.34241536798...271.....7489.21..2.4.9.7.78.92...4..75...2
F7: 4 => SOLVED
* 734915268815623479926847135281536794349271856567489321152364987678192543493758612
* PAIR F9: 3,8 ROW 9
G9: 3,8,6                                # reduction candidate for 3,8
G9: 3,8                                  # 19 pairs
G9: 6                                    # 17 pairs
* PAIR F9: 3,8 COL F
F1: 3,8,5                                # reduction candidate for 3,8
F1: 3,8 => CTR
* 734918265816325479925647138281536794.49271....67489.213.2.649.7.78.92.4.49.75..12
F1: 5 => SOLVED
* 734915268815623479926847135281536794349271856567489321152364987678192543493758612
F2: 3,8,4,5                              # reduction candidate for 3,8
F2: 3,8 => SOLVED
* 734915268815623479926847135281536794349271856567489321152364987678192543493758612
F2: 4,5                                  # 15 pairs
* PAIR I8: 3,6 BLK 9
G8: 3,6,4,5                              # reduction candidate for 3,6
G8: 3,6 => CTR
* 7.491.26.8...2..7992...713.281536794.4927158..57489.211.2...957578192.4.496753812
G8: 4,5                                  # 17 pairs
G9: 3,6,8                                # reduction candidate for 3,6
G9: 3,6                                  # 17 pairs
* PAIR I8: 3,6 ROW 8
A8: 3,6,1,5                              # reduction candidate for 3,6
A8: 3,6                                  # 20 pairs
D8: 3,6,1                                # reduction candidate for 3,6
D8: 3,6                                  # 21 pairs
* PAIR H9: 1,8 BLK 9
H7: 1,8,5                                # reduction candidate for 1,8
H7: 5 => CTR
* 73491.26.186325479925.471382.153679...3271..66574893213.2...957578.92..34.9753..2
H7: 1,8                                  # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190108-absurd-base-pr-000.dot
* REASONING
* DIS # A2: 5,6 => CTR => A2: 1,3,8
* DIS # B2: 5,6 => CTR => B2: 1,3,8
* DIS # C5: 5,6 => CTR => C5: 3,9
* PRF # D2: 6,8 => SOL
* DIS # D2: 3 => CTR => D2: 6,8
* DIS # D7: 6,8 => CTR => D7: 1,3
* DIS # B1: 2,8 => CTR => B1: 3,5
* PRF # B1: 3,5 => SOL
* PRF # I3: 5,8 => SOL
* DIS # I3: 4 => CTR => I3: 5,8
* DIS # B1: 5,8 => CTR => B1: 2,3
* PRF # F1: 5,8 => SOL
* DIS # F1: 3 => CTR => F1: 5,8
* DIS # B5: 3,5,6,9 => CTR => B5: 4,8
* DIS # I3: 4,8 => CTR => I3: 5
* PRF # I3: 5 => SOL
* DIS # B5: 3,6 => CTR => B5: 4,5,8,9
* DIS # C5: 3,6 => CTR => C5: 5,9
* PRF # D7: 3,8 => SOL
* DIS # F7: 3,8 => CTR => F7: 4
* PRF # F7: 4 => SOL
* DIS # F1: 3,8 => CTR => F1: 5
* PRF # F1: 5 => SOL
* PRF # F2: 3,8 => SOL
* DIS # G8: 3,6 => CTR => G8: 4,5
* DIS # H7: 5 => CTR => H7: 1,8
* CNT  26 HDP CHAINS /  49 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B4,C3,D3,E3,E7,F9,G1,G3,H9,I1,I4,I5,I8)
* 7.491..6.....2..799....7.3.2.153679....271.....7489.21..2...9.7.78.92...4..75...2
* PAIR C3: 5,6 BLK 1
A2: 5,6,1,3,8                            # reduction candidate for 5,6
A2: 5,6 => CTR
* 7.491..65....254799....7.3.2415367988..271.....7489.21..2...9.7.78.92...4..75...2
B2: 5,6,1,3,8                            # reduction candidate for 5,6
B2: 5,6 => CTR
* 7.4913.65..3.254799.5.47138281536794.49271.....7489.21..2.649.7.78.92.4.496758312
C2: 5,6,3                                # reduction candidate for 5,6
C2: 5,6                                  # 17 pairs
* RESTART
* PAIR C3: 5,6 BLK 1
C2: 5,6,3                                # reduction candidate for 5,6
C2: 3 => CTR
* 7.491..6...36254799.68471352.1536794.4.271.....7489.21..2...9.7.78.92...4..75...2
* PAIR D3: 6,8 BLK 2
D2: 6,8,3                                # reduction candidate for 6,8
D2: 6,8 => SOLVED
* 734915268815623479926847135281536794349271856567489321152364987678192543493758612
* DURATION: 0:00:05.406682  START: 02:49:08.228080  END: 02:49:13.634762 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190108-absurd-base-pr-001.dot
* REASONING
* DIS # A2: 5,6 => CTR => A2: 1,3,8
* DIS A2: 1,3,8 # B2: 5,6 => CTR => B2: 1,3,8
* DIS A2: 1,3,8 + B2: 1,3,8 # C2: 3 => CTR => C2: 5,6
* PRF A2: 1,3,8 + B2: 1,3,8 + C2: 5,6 # D2: 6,8 => SOL
* STA A2: 1,3,8 + B2: 1,3,8 + C2: 5,6 + D2: 6,8
* CNT   4 HDP CHAINS /   6 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190108, absurd

Solution

position: 734915268815623479926847135281536794349271856567489321152364987678192543493758612 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 # A2: 5,6 => CTR => A2: 1,3,8
* INC # A2: 1,3,8 => UNS
* DIS # B2: 5,6 => CTR => B2: 1,3,8
* INC # B2: 1,3,8 => UNS
* INC # C2: 5,6 => UNS
* DIS # C5: 5,6 => CTR => C5: 3,9
* INC # C5: 3,9 => UNS
* PRF # D2: 6,8 => SOL
* DIS # D2: 3 => CTR => D2: 6,8
* DIS # D7: 6,8 => CTR => D7: 1,3
* INC # D7: 1,3 => UNS
* DIS # B1: 2,8 => CTR => B1: 3,5
* PRF # B1: 3,5 => SOL
* PRF # I3: 5,8 => SOL
* DIS # I3: 4 => CTR => I3: 5,8
* DIS # B1: 5,8 => CTR => B1: 2,3
* INC # B1: 2,3 => UNS
* PRF # F1: 5,8 => SOL
* DIS # F1: 3 => CTR => F1: 5,8
* INC # B5: 4,8 => UNS
* DIS # B5: 3,5,6,9 => CTR => B5: 4,8
* INC # G5: 4,8 => UNS
* INC # H5: 4,8 => UNS
* DIS # I3: 4,8 => CTR => I3: 5
* PRF # I3: 5 => SOL
* INC # G5: 3,6 => UNS
* INC # G6: 3,6 => UNS
* INC # A5: 3,6 => UNS
* DIS # B5: 3,6 => CTR => B5: 4,5,8,9
* INC # B5: 4,5,8,9 => UNS
* DIS # C5: 3,6 => CTR => C5: 5,9
* INC # C5: 5,9 => UNS
* PRF # D7: 3,8 => SOL
* INC # D7: 1,6 => UNS
* DIS # F7: 3,8 => CTR => F7: 4
* PRF # F7: 4 => SOL
* INC # G9: 3,8 => UNS
* INC # G9: 6 => UNS
* DIS # F1: 3,8 => CTR => F1: 5
* PRF # F1: 5 => SOL
* PRF # F2: 3,8 => SOL
* INC # F2: 4,5 => UNS
* DIS # G8: 3,6 => CTR => G8: 4,5
* INC # G8: 4,5 => UNS
* INC # G9: 3,6 => UNS
* INC # A8: 3,6 => UNS
* INC # D8: 3,6 => UNS
* INC # H7: 1,8 => UNS
* DIS # H7: 5 => CTR => H7: 1,8
* CNT  49 HDP CHAINS /  49 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A2: 5,6 => CTR => A2: 1,3,8
* DIS A2: 1,3,8 # B2: 5,6 => CTR => B2: 1,3,8
* INC A2: 1,3,8 + B2: 1,3,8 # C2: 5,6 => UNS
* INC A2: 1,3,8 + B2: 1,3,8 # C2: 5,6 => UNS
* DIS A2: 1,3,8 + B2: 1,3,8 # C2: 3 => CTR => C2: 5,6
* PRF A2: 1,3,8 + B2: 1,3,8 + C2: 5,6 # D2: 6,8 => SOL
* STA A2: 1,3,8 + B2: 1,3,8 + C2: 5,6 + D2: 6,8
* CNT   6 HDP CHAINS /   6 HYP OPENED