Analysis of zz-www.sudokuoftheday.co.uk-20190409-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: .25.....1.1.94...28.....4.6.6..1...5...68.2....3......5......1..9...6....31....5. initial

Autosolve

position: 425.6...131694.5.2879521436.6..1...51..68.2....3...16.5.2.3.61.79.156.2.631....5. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # F7: 7,8 => CTR => F7: 4,9
* DIS # F9: 7,8 => CTR => F9: 2,4,9
* PRF # B6: 4,5 => SOL
* DIS # F5: 4,5 => CTR => F5: 3,7,9
* PRF # C4: 8 => SOL
* DIS # F6: 2,9 => CTR => F6: 4,5,7
* DIS # F6: 7,9 => CTR => F6: 2,4,5
* PRF # I6: 8 => SOL
* DIS # F7: 4,8 => CTR => F7: 7,9
* DIS # I7: 4,8 => CTR => I7: 7,9
* DIS # B6: 5 => CTR => B6: 4,8
* PRF # I8: 3 => SOL
* DIS # F9: 7,9 => CTR => F9: 2,4,8
* DIS # I9: 7,9 => CTR => I9: 4,8
* PRF # I8: 3,8 => SOL
* CNT  15 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 # F7: 7,8 => CTR => F7: 4,9
* DIS F7: 4,9 # F9: 7,8 => CTR => F9: 2,4,9
* DIS F7: 4,9 + F9: 2,4,9 # F1: 3 => CTR => F1: 7,8
* DIS F7: 4,9 + F9: 2,4,9 + F1: 7,8 # F4: 2,9 => CTR => F4: 3,4
* PRF F7: 4,9 + F9: 2,4,9 + F1: 7,8 + F4: 3,4 # B6: 4,5 => SOL
* STA F7: 4,9 + F9: 2,4,9 + F1: 7,8 + F4: 3,4 + B6: 4,5
* CNT   5 HDP CHAINS /  12 HYP OPENED

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

Details

Positions

.25.....1.1.94...28.....4.6.6..1...5...68.2....3......5......1..9...6....31....5. initial
425.6...131694.5.2879521436.6..1...51..68.2....3...16.5.2.3.61.79.156.2.631....5. autosolve
425368791316947582879521436968214375157683249243795168582439617794156823631872954 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
F2: 7,8
H2: 7,8
A4: 2,9
B5: 4,5
C5: 4,7
A6: 2,9
E6: 7,9
B7: 4,8
C8: 4,8
E9: 7,9
G8: 3,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A4,A6: 2.. / A4 = 2  =>  0 pairs (X) / A6 = 2  => 10 pairs (_)
D9,F9: 2.. / D9 = 2  => 12 pairs (_) / F9 = 2  => 11 pairs (_)
D1,F1: 3.. / D1 = 3  => 13 pairs (_) / F1 = 3  => 12 pairs (_)
G4,I5: 3.. / G4 = 3  =>  0 pairs (*) / I5 = 3  =>  0 pairs (X)
G8,I8: 3.. / G8 = 3  => 11 pairs (_) / I8 = 3  =>  0 pairs (*)
F5,I5: 3.. / F5 = 3  =>  0 pairs (*) / I5 = 3  =>  0 pairs (X)
D1,D4: 3.. / D1 = 3  => 13 pairs (_) / D4 = 3  => 12 pairs (_)
G4,G8: 3.. / G4 = 3  =>  0 pairs (*) / G8 = 3  =>  0 pairs (X)
I5,I8: 3.. / I5 = 3  => 11 pairs (_) / I8 = 3  =>  0 pairs (*)
H4,H5: 4.. / H4 = 4  => 14 pairs (_) / H5 = 4  => 13 pairs (_)
B7,C8: 4.. / B7 = 4  => 13 pairs (_) / C8 = 4  =>  0 pairs (*)
C8,I8: 4.. / C8 = 4  =>  0 pairs (*) / I8 = 4  =>  0 pairs (X)
B5,B6: 5.. / B5 = 5  => 11 pairs (_) / B6 = 5  =>  0 pairs (X)
F5,F6: 5.. / F5 = 5  =>  0 pairs (X) / F6 = 5  => 11 pairs (_)
B5,F5: 5.. / B5 = 5  => 11 pairs (_) / F5 = 5  =>  0 pairs (X)
B6,F6: 5.. / B6 = 5  =>  0 pairs (X) / F6 = 5  => 11 pairs (_)
C4,C5: 7.. / C4 = 7  => 12 pairs (_) / C5 = 7  => 13 pairs (_)
F2,H2: 7.. / F2 = 7  => 13 pairs (_) / H2 = 7  => 14 pairs (_)
E6,E9: 7.. / E6 = 7  =>  0 pairs (X) / E9 = 7  =>  0 pairs (_)
C4,B6: 8.. / C4 = 8  =>  0 pairs (*) / B6 = 8  =>  0 pairs (X)
B7,C8: 8.. / B7 = 8  =>  0 pairs (*) / C8 = 8  =>  0 pairs (X)
F2,H2: 8.. / F2 = 8  => 14 pairs (_) / H2 = 8  => 13 pairs (_)
B6,I6: 8.. / B6 = 8  => 13 pairs (_) / I6 = 8  =>  0 pairs (*)
B6,B7: 8.. / B6 = 8  => 13 pairs (_) / B7 = 8  =>  0 pairs (*)
C4,C8: 8.. / C4 = 8  =>  0 pairs (*) / C8 = 8  =>  0 pairs (X)
G1,H1: 9.. / G1 = 9  => 17 pairs (_) / H1 = 9  => 15 pairs (_)
A4,A6: 9.. / A4 = 9  => 10 pairs (_) / A6 = 9  =>  0 pairs (X)
F7,I7: 9.. / F7 = 9  =>  0 pairs (*) / I7 = 9  =>  0 pairs (X)
E6,E9: 9.. / E6 = 9  =>  0 pairs (*) / E9 = 9  =>  0 pairs (X)
* DURATION: 0:00:31.442921  START: 05:09:39.449318  END: 05:10:10.892239 2019-05-01
* CP COUNT: (29)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B5,B7,C5,C8,E6,E9,F2,G8,H2)
* 425.6...131694.5.2879521436.6..1...51..68.2....3...16.5.2.3.61.79.156.2.631....5.
* PAIR F2: 7,8 BLK 2
D1: 7,8,3                                # reduction candidate for 7,8
D1: 7,8                                  # 12 pairs
F1: 7,8,3                                # reduction candidate for 7,8
F1: 7,8                                  # 13 pairs
* PAIR F2: 7,8 COL F
F7: 7,8,4,9                              # reduction candidate for 7,8
F7: 7,8 => CTR
* 425.6...131694.5.2879521436.6..1...51..68.2....3.7.168582437619794156823631.9.754
F7: 4,9                                  # 12 pairs
F9: 7,8,2,4,9                            # reduction candidate for 7,8
F9: 7,8 => CTR
* 425863791316947582879521436.6831...51.768.2....3...168582.3.6177941568236312.8954
F9: 2,4,9                                # 11 pairs
* PAIR H2: 7,8 BLK 3
G1: 7,8,9                                # reduction candidate for 7,8
G1: 7,8                                  # 15 pairs
H1: 7,8,9                                # reduction candidate for 7,8
H1: 7,8                                  # 17 pairs
* PAIR H2: 7,8 COL H
H4: 7,8,4,9                              # reduction candidate for 7,8
H4: 7,8                                  # 15 pairs
H4: 4,9                                  # 13 pairs
* PAIR A4: 2,9 ROW 4
F4: 2,9,3,4,7                            # reduction candidate for 2,9
F4: 2,9                                  # 12 pairs
F4: 3,4,7                                # 11 pairs
* PAIR B5: 4,5 BLK 4
B6: 4,5,8                                # reduction candidate for 4,5
B6: 4,5 => SOLVED
* 425368791316947582879521436968214375157683249243795168582439617794156823631872954
B6: 8                                    # 13 pairs
* PAIR B5: 4,5 ROW 5
F5: 4,5,3,7,9                            # reduction candidate for 4,5
F5: 4,5 => CTR
* 425.6.9.131694.5.2879521436.6..1..451.768.293..3...16.5.2.3.61.794156328631...75.
F5: 3,7,9                                # 11 pairs
* PAIR C5: 4,7 BLK 4
C4: 4,7,8                                # reduction candidate for 4,7
C4: 8 => SOLVED
* 425368791316947582879521436968214375157683249243795168582439617794156823631872954
C4: 4,7                                  # 13 pairs
* PAIR C5: 4,7 ROW 5
F5: 4,7,3,5,9                            # reduction candidate for 4,7
F5: 4,7                                  # 18 pairs
H5: 4,7,9                                # reduction candidate for 4,7
H5: 4,7                                  # 14 pairs
* PAIR A6: 2,9 ROW 6
F6: 2,9,4,5,7                            # reduction candidate for 2,9
F6: 2,9 => CTR
* 425.6...131694.5.2879521436.6..1...51..6852.3.534..16858273.61.794156.2.631....5.
F6: 4,5,7                                # 11 pairs
* PAIR E6: 7,9 BLK 5
F4: 7,9,2,3,4                            # reduction candidate for 7,9
F4: 7,9                                  # 14 pairs
F5: 7,9,3,4,5                            # reduction candidate for 7,9
F5: 7,9                                  # 13 pairs
F6: 7,9,2,4,5                            # reduction candidate for 7,9
F6: 7,9 => CTR
* 425.6...131694.5.2879521436.6..1...51..6852.3.534..16858273.61.794156.2.631....5.
F6: 2,4,5                                # 11 pairs
* PAIR E6: 7,9 ROW 6
I6: 7,9,8                                # reduction candidate for 7,9
I6: 8 => SOLVED
* 425368791316947582879521436968214375157683249243795168582439617794156823631872954
I6: 7,9                                  # 13 pairs
* PAIR B7: 4,8 ROW 7
D7: 4,8,7                                # reduction candidate for 4,8
D7: 4,8                                  # 14 pairs
F7: 4,8,7,9                              # reduction candidate for 4,8
F7: 4,8 => CTR
* 425.6...131694.5.2879521436.6..1...51..68.2....3.7.168582734619794156823631.9.754
F7: 7,9                                  # 14 pairs
I7: 4,8,7,9                              # reduction candidate for 4,8
I7: 4,8 => CTR
* 425.6...131694.5.2879521436.6..1...51..68.2....3...16.5.2.3961.79.156.2.631.7..5.
I7: 7,9                                  # 12 pairs
* PAIR B7: 4,8 COL B
B6: 4,8,5                                # reduction candidate for 4,8
B6: 5 => CTR
* 425.6...131694.5.2879521436.68.1...51.768.2...53...168582.3.61.794156823631....5.
B6: 4,8                                  # 11 pairs
* PAIR C8: 4,8 ROW 8
I8: 4,8,3                                # reduction candidate for 4,8
I8: 3 => SOLVED
* 425368791316947582879521436968214375157683249243795168582439617794156823631872954
I8: 4,8                                  # 11 pairs
* PAIR C8: 4,8 COL C
C4: 4,8,7                                # reduction candidate for 4,8
C4: 4,8                                  # 13 pairs
C4: 7                                    # 12 pairs
* PAIR E9: 7,9 BLK 8
F7: 7,9,4,8                              # reduction candidate for 7,9
F7: 7,9                                  # 14 pairs
F9: 7,9,2,4,8                            # reduction candidate for 7,9
F9: 7,9 => CTR
* 425.6...131694.5.2879521436.6..1...51..68.2....3...16.5.2.3.61.794156.2.6312..854
F9: 2,4,8                                # 11 pairs
* PAIR E9: 7,9 ROW 9
G9: 7,9,8                                # reduction candidate for 7,9
G9: 7,9                                  # 14 pairs
I9: 7,9,4,8                              # reduction candidate for 7,9
I9: 7,9 => CTR
* 425.6...131694.5.2879521436.6..1...51..68.2.3..3...16858273961.79.15632.631...85.
I9: 4,8                                  # 14 pairs
* PAIR G8: 3,8 BLK 9
I8: 3,8,4                                # reduction candidate for 3,8
I8: 3,8 => SOLVED
* 425368791316947582879521436968214375157683249243795168582439617794156823631872954
I8: 4                                    # 13 pairs
* PAIR G8: 3,8 COL G
G4: 3,8,7,9                              # reduction candidate for 3,8
G4: 3,8                                  # 16 pairs
G4: 7,9                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190409-absurd-base-pr-000.dot
* REASONING
* DIS # F7: 7,8 => CTR => F7: 4,9
* DIS # F9: 7,8 => CTR => F9: 2,4,9
* PRF # B6: 4,5 => SOL
* DIS # F5: 4,5 => CTR => F5: 3,7,9
* PRF # C4: 8 => SOL
* DIS # F6: 2,9 => CTR => F6: 4,5,7
* DIS # F6: 7,9 => CTR => F6: 2,4,5
* PRF # I6: 8 => SOL
* DIS # F7: 4,8 => CTR => F7: 7,9
* DIS # I7: 4,8 => CTR => I7: 7,9
* DIS # B6: 5 => CTR => B6: 4,8
* PRF # I8: 3 => SOL
* DIS # F9: 7,9 => CTR => F9: 2,4,8
* DIS # I9: 7,9 => CTR => I9: 4,8
* PRF # I8: 3,8 => SOL
* CNT  15 HDP CHAINS /  49 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B5,B7,C5,C8,E6,E9,F2,G8,H2)
* 425.6...131694.5.2879521436.6..1...51..68.2....3...16.5.2.3.61.79.156.2.631....5.
* PAIR F2: 7,8 BLK 2
D1: 7,8,3                                # reduction candidate for 7,8
D1: 7,8                                  # 12 pairs
F1: 7,8,3                                # reduction candidate for 7,8
F1: 7,8                                  # 13 pairs
* PAIR F2: 7,8 COL F
F7: 7,8,4,9                              # reduction candidate for 7,8
F7: 7,8 => CTR
* 425.6...131694.5.2879521436.6..1...51..68.2....3.7.168582437619794156823631.9.754
F9: 7,8,2,4,9                            # reduction candidate for 7,8
F9: 7,8 => CTR
* 425863791316947582879521436.6831...51.768.2....3...168582.3.6177941568236312.8954
* RESTART
* PAIR RESTART
* PAIR F2: 7,8 BLK 2
F1: 7,8,3                                # reduction candidate for 7,8
F1: 3 => CTR
* 425763..1316948572879521436.6.31.7.51.768.2.3..3.9716858243961779415632.631.7..5.
* PAIR H2: 7,8 BLK 3
G1: 7,8,9                                # reduction candidate for 7,8
G1: 7,8                                  # 17 pairs
H1: 7,8,9                                # reduction candidate for 7,8
H1: 7,8                                  # 19 pairs
* PAIR H2: 7,8 COL H
H4: 7,8,4,9                              # reduction candidate for 7,8
H4: 7,8                                  # 17 pairs
H4: 4,9                                  # 15 pairs
* PAIR A4: 2,9 ROW 4
F4: 2,9,3,4                              # reduction candidate for 2,9
F4: 2,9 => CTR
* 42536...131694.5.2879521436.68.193.515768324994327516858273.61.79.1568236318.2.54
* PAIR RESTART
* PAIR B5: 4,5 BLK 4
B6: 4,5,8                                # reduction candidate for 4,5
B6: 4,5 => SOLVED
* 425368791316947582879521436968214375157683249243795168582439617794156823631872954
* DURATION: 0:00:09.415388  START: 05:10:41.104202  END: 05:10:50.519590 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190409-absurd-base-pr-001.dot
* REASONING
* DIS # F7: 7,8 => CTR => F7: 4,9
* DIS F7: 4,9 # F9: 7,8 => CTR => F9: 2,4,9
* DIS F7: 4,9 + F9: 2,4,9 # F1: 3 => CTR => F1: 7,8
* DIS F7: 4,9 + F9: 2,4,9 + F1: 7,8 # F4: 2,9 => CTR => F4: 3,4
* PRF F7: 4,9 + F9: 2,4,9 + F1: 7,8 + F4: 3,4 # B6: 4,5 => SOL
* STA F7: 4,9 + F9: 2,4,9 + F1: 7,8 + F4: 3,4 + B6: 4,5
* CNT   5 HDP CHAINS /  12 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190409, absurd

Solution

position: 425368791316947582879521436968214375157683249243795168582439617794156823631872954 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 # D1: 7,8 => UNS
* INC # F1: 7,8 => UNS
* DIS # F7: 7,8 => CTR => F7: 4,9
* INC # F7: 4,9 => UNS
* DIS # F9: 7,8 => CTR => F9: 2,4,9
* INC # F9: 2,4,9 => UNS
* INC # G1: 7,8 => UNS
* INC # H1: 7,8 => UNS
* INC # H4: 7,8 => UNS
* INC # H4: 4,9 => UNS
* INC # F4: 2,9 => UNS
* INC # F4: 3,4,7 => UNS
* PRF # B6: 4,5 => SOL
* INC # B6: 8 => UNS
* DIS # F5: 4,5 => CTR => F5: 3,7,9
* INC # F5: 3,7,9 => UNS
* INC # C4: 4,7 => UNS
* PRF # C4: 8 => SOL
* INC # F5: 4,7 => UNS
* INC # H5: 4,7 => UNS
* DIS # F6: 2,9 => CTR => F6: 4,5,7
* INC # F6: 4,5,7 => UNS
* INC # F4: 7,9 => UNS
* INC # F5: 7,9 => UNS
* DIS # F6: 7,9 => CTR => F6: 2,4,5
* INC # F6: 2,4,5 => UNS
* INC # I6: 7,9 => UNS
* PRF # I6: 8 => SOL
* INC # D7: 4,8 => UNS
* DIS # F7: 4,8 => CTR => F7: 7,9
* INC # F7: 7,9 => UNS
* DIS # I7: 4,8 => CTR => I7: 7,9
* INC # I7: 7,9 => UNS
* INC # B6: 4,8 => UNS
* DIS # B6: 5 => CTR => B6: 4,8
* INC # I8: 4,8 => UNS
* PRF # I8: 3 => SOL
* INC # C4: 4,8 => UNS
* INC # C4: 7 => UNS
* INC # F7: 7,9 => UNS
* DIS # F9: 7,9 => CTR => F9: 2,4,8
* INC # F9: 2,4,8 => UNS
* INC # G9: 7,9 => UNS
* DIS # I9: 7,9 => CTR => I9: 4,8
* INC # I9: 4,8 => UNS
* PRF # I8: 3,8 => SOL
* INC # I8: 4 => UNS
* INC # G4: 3,8 => UNS
* INC # G4: 7,9 => UNS
* CNT  49 HDP CHAINS /  49 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D1: 7,8 => UNS
* INC # F1: 7,8 => UNS
* DIS # F7: 7,8 => CTR => F7: 4,9
* DIS F7: 4,9 # F9: 7,8 => CTR => F9: 2,4,9
* INC F7: 4,9 + F9: 2,4,9 # F1: 7,8 => UNS
* DIS F7: 4,9 + F9: 2,4,9 # F1: 3 => CTR => F1: 7,8
* INC F7: 4,9 + F9: 2,4,9 + F1: 7,8 # G1: 7,8 => UNS
* INC F7: 4,9 + F9: 2,4,9 + F1: 7,8 # H1: 7,8 => UNS
* INC F7: 4,9 + F9: 2,4,9 + F1: 7,8 # H4: 7,8 => UNS
* INC F7: 4,9 + F9: 2,4,9 + F1: 7,8 # H4: 4,9 => UNS
* DIS F7: 4,9 + F9: 2,4,9 + F1: 7,8 # F4: 2,9 => CTR => F4: 3,4
* PRF F7: 4,9 + F9: 2,4,9 + F1: 7,8 + F4: 3,4 # B6: 4,5 => SOL
* STA F7: 4,9 + F9: 2,4,9 + F1: 7,8 + F4: 3,4 + B6: 4,5
* CNT  12 HDP CHAINS /  12 HYP OPENED