Analysis of zz-www.sudokuoftheday.co.uk-20190325-absurd-base.sdk

Contents

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

level: medium

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

position: 43.7....5......8..8.9....3..2.......6.4.....118...674..6.5.9........3..8.926..... initial

Autosolve

position: 4367....52.....8..8.9....3.92.......6.4.....118...674..685.9...541273..8.926..... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B2: 5,7 => CTR => B2: 1
* PRF # C4: 3 => SOL
* DIS # D2: 1,4 => CTR => D2: 3,9
* DIS # E2: 1,4 => CTR => E2: 3,5,6,9
* DIS # E3: 1,4 => CTR => E3: 2,5,6
* DIS # F3: 1,4 => CTR => F3: 2,5
* DIS # D4: 3,8 => CTR => D4: 1,4
* PRF # C4: 3 => SOL
* DIS # F5: 2 => CTR => F5: 5,7
* DIS # B2: 5,7 => CTR => B2: 1
* DIS # C4: 7 => CTR => C4: 3,5
* PRF # E6: 2,9 => SOL
* DIS # D5: 3,9 => CTR => D5: 8
* DIS # E6: 3,9 => CTR => E6: 2,5
* PRF # I6: 3,9 => SOL
* DIS # D2: 1,4 => CTR => D2: 3,9
* DIS # E9: 1,4 => CTR => E9: 8
* DIS # E2: 1,4 => CTR => E2: 3,5,6,9
* DIS # E3: 1,4 => CTR => E3: 2,5,6
* DIS # H2: 1,7 => CTR => H2: 6,9
* CNT  20 HDP CHAINS /  56 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: 5,7 => CTR => B2: 1
* PRF B2: 1 # C4: 3 => SOL
* STA B2: 1 + C4: 3
* CNT   2 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

43.7....5......8..8.9....3..2.......6.4.....118...674..6.5.9........3..8.926..... initial
4367....52.....8..8.9....3.92.......6.4.....118...674..685.9...541273..8.926..... autosolve
436798215217354869859162437923417586674835921185926743368549172541273698792681354 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
C2: 5,7
D3: 1,4
B5: 5,7
C6: 3,5
D6: 3,9
I4: 3,6
A7: 3,7
A9: 3,7
E7: 1,4
G8: 6,9
H8: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B2,B3: 1.. / B2 = 1  => 13 pairs (_) / B3 = 1  =>  0 pairs (X)
E6,I6: 2.. / E6 = 2  =>  0 pairs (*) / I6 = 2  =>  0 pairs (X)
D2,E2: 3.. / D2 = 3  => 18 pairs (_) / E2 = 3  => 12 pairs (_)
C4,C6: 3.. / C4 = 3  =>  0 pairs (*) / C6 = 3  =>  0 pairs (X)
A7,A9: 3.. / A7 = 3  => 11 pairs (_) / A9 = 3  => 11 pairs (_)
G9,H9: 5.. / G9 = 5  =>  0 pairs (X) / H9 = 5  => 12 pairs (_)
C6,E6: 5.. / C6 = 5  =>  0 pairs (*) / E6 = 5  =>  0 pairs (X)
E2,E3: 6.. / E2 = 6  =>  0 pairs (X) / E3 = 6  => 11 pairs (_)
G8,H8: 6.. / G8 = 6  => 11 pairs (_) / H8 = 6  => 11 pairs (_)
C4,B5: 7.. / C4 = 7  =>  0 pairs (X) / B5 = 7  => 25 pairs (_)
F4,F5: 7.. / F4 = 7  => 25 pairs (_) / F5 = 7  =>  0 pairs (X)
A7,A9: 7.. / A7 = 7  => 11 pairs (_) / A9 = 7  => 11 pairs (_)
B3,I3: 7.. / B3 = 7  =>  0 pairs (X) / I3 = 7  => 13 pairs (_)
C4,F4: 7.. / C4 = 7  =>  0 pairs (X) / F4 = 7  => 25 pairs (_)
B5,F5: 7.. / B5 = 7  => 25 pairs (_) / F5 = 7  =>  0 pairs (X)
C2,C4: 7.. / C2 = 7  => 25 pairs (_) / C4 = 7  =>  0 pairs (X)
E1,F1: 8.. / E1 = 8  =>  0 pairs (X) / F1 = 8  => 12 pairs (_)
D4,D5: 8.. / D4 = 8  =>  0 pairs (X) / D5 = 8  => 11 pairs (_)
H4,H5: 8.. / H4 = 8  => 11 pairs (_) / H5 = 8  =>  0 pairs (X)
E9,F9: 8.. / E9 = 8  => 12 pairs (_) / F9 = 8  =>  0 pairs (X)
D4,H4: 8.. / D4 = 8  =>  0 pairs (X) / H4 = 8  => 11 pairs (_)
D5,H5: 8.. / D5 = 8  => 11 pairs (_) / H5 = 8  =>  0 pairs (X)
E1,E9: 8.. / E1 = 8  =>  0 pairs (X) / E9 = 8  => 12 pairs (_)
F1,F9: 8.. / F1 = 8  => 12 pairs (_) / F9 = 8  =>  0 pairs (X)
G8,H8: 9.. / G8 = 9  => 11 pairs (_) / H8 = 9  => 11 pairs (_)
I2,I6: 9.. / I2 = 9  => 20 pairs (_) / I6 = 9  =>  0 pairs (X)
* DURATION: 0:00:24.748918  START: 04:47:43.216969  END: 04:48:07.965887 2019-05-01
* CP COUNT: (26)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,B5,C2,C6,D3,D6,E7,G8,H8,I4)
* 4367....52.....8..8.9....3.92.......6.4.....118...674..685.9...541273..8.926.....
* PAIR C2: 5,7 BLK 1
B2: 5,7,1                                # reduction candidate for 5,7
B2: 5,7 => CTR
* 4367....52...3.864819465237923..7..66.4.....118.3267493685.9.72541273..87926....3
B2: 1                                    # 13 pairs
B3: 5,7,1                                # reduction candidate for 5,7
B3: 5,7                                  # 13 pairs
* PAIR C2: 5,7 COL C
C4: 5,7,3                                # reduction candidate for 5,7
C4: 3 => SOLVED
* 436798215217354869859162437923417586674835921185926743368549172541273698792681354
C4: 5,7                                  # 22 pairs
* PAIR D3: 1,4 BLK 2
D2: 1,4,3,9                              # reduction candidate for 1,4
D2: 1,4 => CTR
* 436798..52...358..859.62.3792.......674.....118...674..685.9...541273..8.9268....
D2: 3,9                                  # 13 pairs
E2: 1,4,3,5,6,9                          # reduction candidate for 1,4
E2: 1,4 => CTR
* 436798..52..3.5869859.62.3792.....866748....118.9.674..685.9...541273698.9268....
E2: 3,5,6,9                              # 11 pairs
F2: 1,4,5                                # reduction candidate for 1,4
F2: 1,4                                  # 16 pairs
E3: 1,4,2,5,6                            # reduction candidate for 1,4
E3: 1,4 => CTR
* 436798..52..36.8.98.9..2.3.92.......6.48....118.9.674..685.9...541273..8.9268....
E3: 2,5,6                                # 11 pairs
F3: 1,4,2,5                              # reduction candidate for 1,4
F3: 1,4 => CTR
* 4367....521...58.4859....3792.....866748.2..118...674..685.9...541273..8.926.....
F3: 2,5                                  # 12 pairs
* PAIR D3: 1,4 ROW 3
G3: 1,4,2,6                              # reduction candidate for 1,4
G3: 1,4                                  # 15 pairs
G3: 2,6                                  # 14 pairs
* PAIR D3: 1,4 COL D
D4: 1,4,3,8                              # reduction candidate for 1,4
D4: 3,8 => CTR
* 4367....52....58..859..2.3792.......674.....118...674..685.9...541273..8.926.....
D4: 1,4                                  # 13 pairs
* PAIR B5: 5,7 BLK 4
C4: 5,7,3                                # reduction candidate for 5,7
C4: 3 => SOLVED
* 436798215217354869859162437923417586674835921185926743368549172541273698792681354
C4: 5,7                                  # 22 pairs
* PAIR B5: 5,7 ROW 5
F5: 5,7,2                                # reduction candidate for 5,7
F5: 2 => CTR
* 436798..52.7...8.98.9.2..3792...7..6674..2..118...6742.685.9...541273..8.926.....
F5: 5,7                                  # 13 pairs
* PAIR B5: 5,7 COL B
B2: 5,7,1                                # reduction candidate for 5,7
B2: 5,7 => CTR
* 4367....52...3.864819465237923..7..66.4.....118.3267493685.9.72541273..87926....3
B2: 1                                    # 13 pairs
B3: 5,7,1                                # reduction candidate for 5,7
B3: 5,7                                  # 13 pairs
* PAIR C6: 3,5 BLK 4
C4: 3,5,7                                # reduction candidate for 3,5
C4: 7 => CTR
* 43679...52.5...8.98.9..5.3.927......654.27..1183956742.685.9...541273..8.926.....
C4: 3,5                                  # 25 pairs
* PAIR C6: 3,5 ROW 6
E6: 3,5,2,9                              # reduction candidate for 3,5
E6: 2,9 => SOLVED
* 436798215217354869859162437923417586674835921185926743368549172541273698792681354
E6: 3,5                                  # 20 pairs
* PAIR D6: 3,9 BLK 5
D5: 3,9,8                                # reduction candidate for 3,9
D5: 3,9 => CTR
* 4367....52....58..859..2.3792.8.....674....8118...674..685.9...541273..8.926.....
D5: 8                                    # 11 pairs
E5: 3,9,2,5                              # reduction candidate for 3,9
E5: 3,9                                  # 15 pairs
E6: 3,9,2,5                              # reduction candidate for 3,9
E6: 3,9 => CTR
* 4367....52.7...8.98.9....37923..7..6674...391185936742.685.9...541273968.926.....
E6: 2,5                                  # 12 pairs
* PAIR D6: 3,9 ROW 6
I6: 3,9,2                                # reduction candidate for 3,9
I6: 3,9 => SOLVED
* 436798215217354869859162437923417586674835921185926743368549172541273698792681354
I6: 2                                    # 20 pairs
* PAIR D6: 3,9 COL D
D2: 3,9,1,4                              # reduction candidate for 3,9
D2: 1,4 => CTR
* 436798..52...358..859.62.3792.......674.....118...674..685.9...541273..8.9268....
D2: 3,9                                  # 13 pairs
* PAIR I4: 3,6 BLK 6
G4: 3,6,5                                # reduction candidate for 3,6
G4: 3,6                                  # 28 pairs
G4: 5                                    # 13 pairs
* PAIR A7: 3,7 ROW 7
I7: 3,7,2,4                              # reduction candidate for 3,7
I7: 3,7                                  # 13 pairs
I7: 2,4                                  # 12 pairs
* PAIR A9: 3,7 ROW 9
I9: 3,7,4                                # reduction candidate for 3,7
I9: 4                                    # 17 pairs
I9: 3,7                                  # 13 pairs
* PAIR E7: 1,4 BLK 8
E9: 1,4,8                                # reduction candidate for 1,4
E9: 1,4 => CTR
* 43678...52...3.8..8.9.6..3.923.57...6.4.....118.326749.685.9...541273..8.926.8...
E9: 8                                    # 12 pairs
F9: 1,4,8                                # reduction candidate for 1,4
F9: 1,4                                  # 12 pairs
* PAIR E7: 1,4 ROW 7
G7: 1,4,2,3                              # reduction candidate for 1,4
G7: 1,4                                  # 13 pairs
G7: 2,3                                  # 12 pairs
* PAIR E7: 1,4 COL E
E2: 1,4,3,5,6,9                          # reduction candidate for 1,4
E2: 1,4 => CTR
* 436798..52..3.5869859.62.3792.....866748....118.9.674..685.9...541273698.9268....
E2: 3,5,6,9                              # 11 pairs
E3: 1,4,2,5,6                            # reduction candidate for 1,4
E3: 1,4 => CTR
* 436798..52..36.8.98.9..2.3.92.......6.48....118.9.674..685.9...541273..8.9268....
E3: 2,5,6                                # 11 pairs
E4: 1,4,3,5                              # reduction candidate for 1,4
E4: 1,4                                  # 14 pairs
* PAIR H8: 6,9 COL H
H2: 6,9,1,7                              # reduction candidate for 6,9
H2: 1,7 => CTR
* 4367....52153.48798791.5.3.9274.15866548273.1183956742.685.9...541273968.926...5.
H2: 6,9                                  # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190325-absurd-base-pr-000.dot
* REASONING
* DIS # B2: 5,7 => CTR => B2: 1
* PRF # C4: 3 => SOL
* DIS # D2: 1,4 => CTR => D2: 3,9
* DIS # E2: 1,4 => CTR => E2: 3,5,6,9
* DIS # E3: 1,4 => CTR => E3: 2,5,6
* DIS # F3: 1,4 => CTR => F3: 2,5
* DIS # D4: 3,8 => CTR => D4: 1,4
* PRF # C4: 3 => SOL
* DIS # F5: 2 => CTR => F5: 5,7
* DIS # B2: 5,7 => CTR => B2: 1
* DIS # C4: 7 => CTR => C4: 3,5
* PRF # E6: 2,9 => SOL
* DIS # D5: 3,9 => CTR => D5: 8
* DIS # E6: 3,9 => CTR => E6: 2,5
* PRF # I6: 3,9 => SOL
* DIS # D2: 1,4 => CTR => D2: 3,9
* DIS # E9: 1,4 => CTR => E9: 8
* DIS # E2: 1,4 => CTR => E2: 3,5,6,9
* DIS # E3: 1,4 => CTR => E3: 2,5,6
* DIS # H2: 1,7 => CTR => H2: 6,9
* CNT  20 HDP CHAINS /  56 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,B5,C2,C6,D3,D6,E7,G8,H8,I4)
* 4367....52.....8..8.9....3.92.......6.4.....118...674..685.9...541273..8.926.....
* PAIR C2: 5,7 BLK 1
B2: 5,7,1                                # reduction candidate for 5,7
B2: 5,7 => CTR
* 4367....52...3.864819465237923..7..66.4.....118.3267493685.9.72541273..87926....3
* RESTART
* PAIR C2: 5,7 COL C
C4: 5,7,3                                # reduction candidate for 5,7
C4: 3 => SOLVED
* 436798215217354869859162437923417586674835921185926743368549172541273698792681354
* DURATION: 0:00:03.063116  START: 04:48:37.782229  END: 04:48:40.845345 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190325-absurd-base-pr-001.dot
* REASONING
* DIS # B2: 5,7 => CTR => B2: 1
* PRF B2: 1 # C4: 3 => SOL
* STA B2: 1 + C4: 3
* CNT   2 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190325, absurd

Solution

position: 436798215217354869859162437923417586674835921185926743368549172541273698792681354 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: 5,7 => CTR => B2: 1
* INC # B2: 1 => UNS
* INC # B3: 5,7 => UNS
* INC # C4: 5,7 => UNS
* PRF # C4: 3 => SOL
* DIS # D2: 1,4 => CTR => D2: 3,9
* INC # D2: 3,9 => UNS
* DIS # E2: 1,4 => CTR => E2: 3,5,6,9
* INC # E2: 3,5,6,9 => UNS
* INC # F2: 1,4 => UNS
* DIS # E3: 1,4 => CTR => E3: 2,5,6
* INC # E3: 2,5,6 => UNS
* DIS # F3: 1,4 => CTR => F3: 2,5
* INC # F3: 2,5 => UNS
* INC # G3: 1,4 => UNS
* INC # G3: 2,6 => UNS
* INC # D4: 1,4 => UNS
* DIS # D4: 3,8 => CTR => D4: 1,4
* INC # C4: 5,7 => UNS
* PRF # C4: 3 => SOL
* INC # F5: 5,7 => UNS
* DIS # F5: 2 => CTR => F5: 5,7
* DIS # B2: 5,7 => CTR => B2: 1
* INC # B2: 1 => UNS
* INC # B3: 5,7 => UNS
* INC # C4: 3,5 => UNS
* DIS # C4: 7 => CTR => C4: 3,5
* INC # E6: 3,5 => UNS
* PRF # E6: 2,9 => SOL
* DIS # D5: 3,9 => CTR => D5: 8
* INC # D5: 8 => UNS
* INC # E5: 3,9 => UNS
* DIS # E6: 3,9 => CTR => E6: 2,5
* INC # E6: 2,5 => UNS
* PRF # I6: 3,9 => SOL
* INC # I6: 2 => UNS
* INC # D2: 3,9 => UNS
* DIS # D2: 1,4 => CTR => D2: 3,9
* INC # G4: 3,6 => UNS
* INC # G4: 5 => UNS
* INC # I7: 3,7 => UNS
* INC # I7: 2,4 => UNS
* INC # I9: 3,7 => UNS
* INC # I9: 4 => UNS
* DIS # E9: 1,4 => CTR => E9: 8
* INC # E9: 8 => UNS
* INC # F9: 1,4 => UNS
* INC # G7: 1,4 => UNS
* INC # G7: 2,3 => UNS
* DIS # E2: 1,4 => CTR => E2: 3,5,6,9
* INC # E2: 3,5,6,9 => UNS
* DIS # E3: 1,4 => CTR => E3: 2,5,6
* INC # E3: 2,5,6 => UNS
* INC # E4: 1,4 => UNS
* INC # H2: 6,9 => UNS
* DIS # H2: 1,7 => CTR => H2: 6,9
* CNT  56 HDP CHAINS /  56 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B2: 5,7 => CTR => B2: 1
* INC B2: 1 # C4: 5,7 => UNS
* PRF B2: 1 # C4: 3 => SOL
* STA B2: 1 + C4: 3
* CNT   3 HDP CHAINS /   3 HYP OPENED