Analysis of zz-www.sudokuoftheday.co.uk-20060331-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006

position: 9..4......17.8..........45..2.......689..7......91..8.5.3...2.9....3...6....92..4 initial

Autosolve

position: 9..4.....417.8...3.....945..2.......689..7.4....91..825.3...2.9.9..3...6....92.34 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B1: 3,6 => CTR => B1: 5
* DIS # D2: 2 => CTR => D2: 5,6
* DIS # H2: 9 => CTR => H2: 2,6
* DIS # H2: 6,9 => CTR => H2: 2
* PRF # C8: 1,4 => SOL
* DIS # C8: 2,8 => CTR => C8: 1,4
* DIS # B6: 3,7 => CTR => B6: 4,5
* DIS # B6: 3,7 => CTR => B6: 4,5
* DIS # H2: 6,9 => CTR => H2: 2
* PRF # B7: 6,7 => SOL
* DIS # B7: 4 => CTR => B7: 6,7
* DIS # D9: 1,5 => CTR => D9: 6,7
* PRF # F7: 4,6 => SOL
* PRF # B7: 7 => SOL
* DIS # E4: 5 => CTR => E4: 4,6
* DIS # A8: 1,7 => CTR => A8: 2,8
* CNT  16 HDP CHAINS /  42 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 # B1: 3,6 => CTR => B1: 5
* DIS B1: 5 # D2: 2 => CTR => D2: 5,6
* DIS B1: 5 + D2: 5,6 # B6: 3,7 => CTR => B6: 4
* PRF B1: 5 + D2: 5,6 + B6: 4 => SOL
* STA B1: 5 + D2: 5,6 + B6: 4
* CNT   4 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

9..4......17.8..........45..2.......689..7......91..8.5.3...2.9....3...6....92..4 initial
9..4.....417.8...3.....945..2.......689..7.4....91..825.3...2.9.9..3...6....92.34 autosolve
952473168417685923836129457721348695689257341345916782573864219294531876168792534 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (22)
B3: 3,6
F1: 1,3
F2: 5,6
D3: 1,3
G1: 1,7
H1: 2,6
G2: 6,9
C4: 1,4
A6: 3,7
C6: 4,5
D5: 2,3
E5: 2,5
H4: 6,9
I4: 5,7
G5: 1,3
I5: 1,5
B9: 6,7
E7: 4,6
H7: 1,7
G8: 5,8
H8: 1,7
G9: 5,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F1,D3: 1.. / F1 = 1  =>  0 pairs (X) / D3 = 1  => 24 pairs (_)
A4,C4: 1.. / A4 = 1  =>  0 pairs (X) / C4 = 1  => 27 pairs (_)
G5,I5: 1.. / G5 = 1  =>  0 pairs (X) / I5 = 1  => 22 pairs (_)
H7,H8: 1.. / H7 = 1  => 21 pairs (_) / H8 = 1  => 25 pairs (_)
D3,I3: 1.. / D3 = 1  => 24 pairs (_) / I3 = 1  =>  0 pairs (X)
G1,G5: 1.. / G1 = 1  => 22 pairs (_) / G5 = 1  =>  0 pairs (X)
H1,H2: 2.. / H1 = 2  =>  0 pairs (X) / H2 = 2  => 22 pairs (_)
D5,E5: 2.. / D5 = 2  => 22 pairs (_) / E5 = 2  =>  0 pairs (X)
A8,C8: 2.. / A8 = 2  => 23 pairs (_) / C8 = 2  =>  0 pairs (X)
D2,H2: 2.. / D2 = 2  =>  0 pairs (X) / H2 = 2  => 22 pairs (_)
A3,A8: 2.. / A3 = 2  =>  0 pairs (X) / A8 = 2  => 23 pairs (_)
D2,D5: 2.. / D2 = 2  =>  0 pairs (X) / D5 = 2  => 22 pairs (_)
F1,D3: 3.. / F1 = 3  => 24 pairs (_) / D3 = 3  =>  0 pairs (X)
B1,F1: 3.. / B1 = 3  =>  0 pairs (X) / F1 = 3  => 24 pairs (_)
D5,G5: 3.. / D5 = 3  =>  0 pairs (X) / G5 = 3  => 22 pairs (_)
B7,C8: 4.. / B7 = 4  =>  0 pairs (X) / C8 = 4  =>  0 pairs (_)
C8,F8: 4.. / C8 = 4  =>  0 pairs (*) / F8 = 4  =>  0 pairs (X)
B6,B7: 4.. / B6 = 4  =>  0 pairs (*) / B7 = 4  =>  0 pairs (X)
E4,E7: 4.. / E4 = 4  =>  0 pairs (*) / E7 = 4  =>  0 pairs (X)
B1,C1: 5.. / B1 = 5  => 22 pairs (_) / C1 = 5  =>  0 pairs (X)
D2,F2: 5.. / D2 = 5  =>  0 pairs (X) / F2 = 5  => 23 pairs (_)
B6,C6: 5.. / B6 = 5  =>  0 pairs (X) / C6 = 5  => 22 pairs (_)
E4,E5: 5.. / E4 = 5  =>  0 pairs (X) / E5 = 5  => 22 pairs (_)
I4,I5: 5.. / I4 = 5  => 22 pairs (_) / I5 = 5  =>  0 pairs (X)
G8,G9: 5.. / G8 = 5  =>  0 pairs (X) / G9 = 5  => 20 pairs (_)
E4,I4: 5.. / E4 = 5  =>  0 pairs (X) / I4 = 5  => 22 pairs (_)
E5,I5: 5.. / E5 = 5  => 22 pairs (_) / I5 = 5  =>  0 pairs (X)
D9,G9: 5.. / D9 = 5  =>  0 pairs (X) / G9 = 5  => 20 pairs (_)
B1,B6: 5.. / B1 = 5  => 22 pairs (_) / B6 = 5  =>  0 pairs (X)
C1,C6: 5.. / C1 = 5  =>  0 pairs (X) / C6 = 5  => 22 pairs (_)
F2,F8: 5.. / F2 = 5  => 23 pairs (_) / F8 = 5  =>  0 pairs (X)
F6,G6: 6.. / F6 = 6  => 31 pairs (_) / G6 = 6  => 24 pairs (_)
E1,E3: 7.. / E1 = 7  => 20 pairs (_) / E3 = 7  => 26 pairs (_)
H7,H8: 7.. / H7 = 7  => 25 pairs (_) / H8 = 7  => 21 pairs (_)
E3,I3: 7.. / E3 = 7  => 26 pairs (_) / I3 = 7  => 20 pairs (_)
I1,I3: 8.. / I1 = 8  => 23 pairs (_) / I3 = 8  => 27 pairs (_)
D4,F4: 8.. / D4 = 8  => 22 pairs (_) / F4 = 8  => 23 pairs (_)
D7,F7: 8.. / D7 = 8  => 23 pairs (_) / F7 = 8  => 22 pairs (_)
G8,G9: 8.. / G8 = 8  => 20 pairs (_) / G9 = 8  =>  0 pairs (X)
C1,I1: 8.. / C1 = 8  => 27 pairs (_) / I1 = 8  => 23 pairs (_)
D4,D7: 8.. / D4 = 8  => 22 pairs (_) / D7 = 8  => 23 pairs (_)
F4,F7: 8.. / F4 = 8  => 23 pairs (_) / F7 = 8  => 22 pairs (_)
G2,H2: 9.. / G2 = 9  => 21 pairs (_) / H2 = 9  =>  0 pairs (X)
G4,H4: 9.. / G4 = 9  =>  0 pairs (X) / H4 = 9  => 21 pairs (_)
G2,G4: 9.. / G2 = 9  => 21 pairs (_) / G4 = 9  =>  0 pairs (X)
H2,H4: 9.. / H2 = 9  =>  0 pairs (X) / H4 = 9  => 21 pairs (_)
* DURATION: 0:01:02.844572  START: 22:02:20.133605  END: 22:03:22.978177 2019-04-30
* CP COUNT: (46)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B3,B9,C4,C6,D3,D5,E5,E7,F1,F2,G1,G2,G5,G8,G9,H1,H4,H7,H8,I4,I5)
* 9..4.....417.8...3.....945..2.......689..7.4....91..825.3...2.9.9..3...6....92.34
* PAIR B3: 3,6 BLK 1
B1: 3,6,5                                # reduction candidate for 3,6
B1: 3,6 => CTR
* 9354.1..8417.85..3.6...945..21.4...5689.57.41.5491..82543.6.2.9.9..34..6.76.92.34
B1: 5                                    # 22 pairs
* PAIR F2: 5,6 BLK 2
D2: 5,6,2                                # reduction candidate for 5,6
D2: 2 => CTR
* 9.8463721417285..3..2179458.21.54..7689327145.459163825.3.48219294531876....92.34
D2: 5,6                                  # 22 pairs
* PAIR G1: 1,7 BLK 3
I1: 1,7,8                                # reduction candidate for 1,7
I1: 1,7                                  # 27 pairs
I3: 1,7,8                                # reduction candidate for 1,7
I3: 1,7                                  # 23 pairs
* PAIR H1: 2,6 BLK 3
H2: 2,6,9                                # reduction candidate for 2,6
H2: 9 => CTR
* 9..4.3721417285693.3.1794583218549676893271457..9163825.3.48219.94.31.761...92.34
H2: 2,6                                  # 21 pairs
* PAIR H1: 2,6 ROW 1
C1: 2,6,5,8                              # reduction candidate for 2,6
C1: 2,6                                  # 20 pairs
E1: 2,6,7                                # reduction candidate for 2,6
E1: 2,6                                  # 26 pairs
* PAIR G2: 6,9 BLK 3
H2: 6,9,2                                # reduction candidate for 6,9
H2: 6,9 => CTR
* 9.8463721417285..3..2179458.21.54..7689327145.459163825.3.48219294531876....92.34
H2: 2                                    # 22 pairs
* PAIR G2: 6,9 COL G
G4: 6,9,3,7                              # reduction candidate for 6,9
G4: 6,9                                  # 31 pairs
G4: 3,7                                  # 24 pairs
* PAIR C4: 1,4 COL C
C8: 1,4,2,8                              # reduction candidate for 1,4
C8: 1,4 => SOLVED
* 952473168417685923836129457721348695689257341345916782573864219294531876168792534
C8: 2,8 => CTR
* 9.54..1.8417685923...1.945..2..4...5689.57.41..491..82543.6.2.9.9..34..6....92.34
* PAIR A6: 3,7 BLK 4
A4: 3,7,1                                # reduction candidate for 3,7
A4: 3,7                                  # 27 pairs
B6: 3,7,4,5                              # reduction candidate for 3,7
B6: 3,7 => CTR
* 95.4.3...417.8...3...1.945..2.......689..7.4...5914682543.6.2.9.9..3...6....92.34
B6: 4,5                                  # 27 pairs
* PAIR A6: 3,7 ROW 6
G6: 3,7,6                                # reduction candidate for 3,7
G6: 3,7                                  # 31 pairs
G6: 6                                    # 24 pairs
* PAIR C6: 4,5 BLK 4
B6: 4,5,3,7                              # reduction candidate for 4,5
B6: 3,7 => CTR
* 95.4.3...417.8...3...1.945..2.......689..7.4...5914682543.6.2.9.9..3...6....92.34
B6: 4,5                                  # 27 pairs
* PAIR H4: 6,9 BLK 6
G4: 6,9,3,7                              # reduction candidate for 6,9
G4: 6,9                                  # 31 pairs
G4: 3,7                                  # 24 pairs
* PAIR H4: 6,9 COL H
H2: 6,9,2                                # reduction candidate for 6,9
H2: 6,9 => CTR
* 9.8463721417285..3..2179458.21.54..7689327145.459163825.3.48219294531876....92.34
H2: 2                                    # 22 pairs
* PAIR B9: 6,7 BLK 7
B7: 6,7,4                                # reduction candidate for 6,7
B7: 6,7 => SOLVED
* 952473168417685923836129457721348695689257341345916782573864219294531876168792534
B7: 4 => CTR
* 9.54..1.8417685923...1.945..2..4...5689.57.41..491..82543.6.2.9.9..34..6....92.34
* PAIR B9: 6,7 ROW 9
D9: 6,7,1,5                              # reduction candidate for 6,7
D9: 1,5 => CTR
* 9.54..1.8417685923...1.945..2..4...5689.57.41..491..82543.6.2.9.9..34..6....92.34
D9: 6,7                                  # 26 pairs
* PAIR E7: 4,6 BLK 8
F7: 4,6,1,8                              # reduction candidate for 4,6
F7: 4,6 => SOLVED
* 952473168417685923836129457721348695689257341345916782573864219294531876168792534
F7: 1,8                                  # 23 pairs
* PAIR E7: 4,6 ROW 7
B7: 4,6,7                                # reduction candidate for 4,6
B7: 7 => SOLVED
* 952473168417685923836129457721348695689257341345916782573864219294531876168792534
B7: 4,6                                  # 24 pairs
* PAIR E7: 4,6 COL E
E4: 4,6,5                                # reduction candidate for 4,6
E4: 5 => CTR
* 9..4..7..417285..3....7945..21.54..7689327145.459163825.3.482.9294.318761.8.92534
E4: 4,6                                  # 22 pairs
* PAIR H7: 1,7 ROW 7
D7: 1,7,6,8                              # reduction candidate for 1,7
D7: 1,7                                  # 24 pairs
D7: 6,8                                  # 23 pairs
* PAIR H8: 1,7 ROW 8
A8: 1,7,2,8                              # reduction candidate for 1,7
A8: 1,7 => CTR
* 9.542.16.417.85..32....945..2..4...5689.57.41..491..82543.6.2.9.925348.68...92534
A8: 2,8                                  # 23 pairs
D8: 1,7,5                                # reduction candidate for 1,7
D8: 1,7                                  # 25 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060331-absurd-base-pr-000.dot
* REASONING
* DIS # B1: 3,6 => CTR => B1: 5
* DIS # D2: 2 => CTR => D2: 5,6
* DIS # H2: 9 => CTR => H2: 2,6
* DIS # H2: 6,9 => CTR => H2: 2
* PRF # C8: 1,4 => SOL
* DIS # C8: 2,8 => CTR => C8: 1,4
* DIS # B6: 3,7 => CTR => B6: 4,5
* DIS # B6: 3,7 => CTR => B6: 4,5
* DIS # H2: 6,9 => CTR => H2: 2
* PRF # B7: 6,7 => SOL
* DIS # B7: 4 => CTR => B7: 6,7
* DIS # D9: 1,5 => CTR => D9: 6,7
* PRF # F7: 4,6 => SOL
* PRF # B7: 7 => SOL
* DIS # E4: 5 => CTR => E4: 4,6
* DIS # A8: 1,7 => CTR => A8: 2,8
* CNT  16 HDP CHAINS /  42 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B3,B9,C4,C6,D3,D5,E5,E7,F1,F2,G1,G2,G5,G8,G9,H1,H4,H7,H8,I4,I5)
* 9..4.....417.8...3.....945..2.......689..7.4....91..825.3...2.9.9..3...6....92.34
* PAIR B3: 3,6 BLK 1
B1: 3,6,5                                # reduction candidate for 3,6
B1: 3,6 => CTR
* 9354.1..8417.85..3.6...945..21.4...5689.57.41.5491..82543.6.2.9.9..34..6.76.92.34
* PAIR F2: 5,6 BLK 2
D2: 5,6,2                                # reduction candidate for 5,6
D2: 2 => CTR
* 958463721417285..3..2179458.21.54..7689327145.459163825.3.48219294531876....92.34
* PAIR A6: 3,7 BLK 4
B6: 3,7,4                                # reduction candidate for 3,7
B6: 3,7 => CTR
* 95.4.316.417.8.923...1.945..24368795689257341..59146825438..2.9.9..3...6....92.34
B6: 4 => SOLVED
* 952473168417685923836129457721348695689257341345916782573864219294531876168792534
* DURATION: 0:00:06.277176  START: 22:03:55.725003  END: 22:04:02.002179 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060331-absurd-base-pr-001.dot
* REASONING
* DIS # B1: 3,6 => CTR => B1: 5
* DIS B1: 5 # D2: 2 => CTR => D2: 5,6
* DIS B1: 5 + D2: 5,6 # B6: 3,7 => CTR => B6: 4
* PRF B1: 5 + D2: 5,6 + B6: 4 => SOL
* STA B1: 5 + D2: 5,6 + B6: 4
* CNT   4 HDP CHAINS /   4 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060331, absurd

Solution

position: 952473168417685923836129457721348695689257341345916782573864219294531876168792534 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 # B1: 3,6 => CTR => B1: 5
* INC # B1: 5 => UNS
* INC # D2: 5,6 => UNS
* DIS # D2: 2 => CTR => D2: 5,6
* INC # I1: 1,7 => UNS
* INC # I3: 1,7 => UNS
* INC # H2: 2,6 => UNS
* DIS # H2: 9 => CTR => H2: 2,6
* INC # C1: 2,6 => UNS
* INC # E1: 2,6 => UNS
* DIS # H2: 6,9 => CTR => H2: 2
* INC # H2: 2 => UNS
* INC # G4: 6,9 => UNS
* INC # G4: 3,7 => UNS
* PRF # C8: 1,4 => SOL
* DIS # C8: 2,8 => CTR => C8: 1,4
* INC # A4: 3,7 => UNS
* DIS # B6: 3,7 => CTR => B6: 4,5
* INC # B6: 4,5 => UNS
* INC # G6: 3,7 => UNS
* INC # G6: 6 => UNS
* INC # B6: 4,5 => UNS
* DIS # B6: 3,7 => CTR => B6: 4,5
* INC # G4: 6,9 => UNS
* INC # G4: 3,7 => UNS
* DIS # H2: 6,9 => CTR => H2: 2
* INC # H2: 2 => UNS
* PRF # B7: 6,7 => SOL
* DIS # B7: 4 => CTR => B7: 6,7
* INC # D9: 6,7 => UNS
* DIS # D9: 1,5 => CTR => D9: 6,7
* PRF # F7: 4,6 => SOL
* INC # F7: 1,8 => UNS
* INC # B7: 4,6 => UNS
* PRF # B7: 7 => SOL
* INC # E4: 4,6 => UNS
* DIS # E4: 5 => CTR => E4: 4,6
* INC # D7: 1,7 => UNS
* INC # D7: 6,8 => UNS
* DIS # A8: 1,7 => CTR => A8: 2,8
* INC # A8: 2,8 => UNS
* INC # D8: 1,7 => UNS
* CNT  42 HDP CHAINS /  42 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B1: 3,6 => CTR => B1: 5
* INC B1: 5 # D2: 5,6 => UNS
* DIS B1: 5 # D2: 2 => CTR => D2: 5,6
* DIS B1: 5 + D2: 5,6 # B6: 3,7 => CTR => B6: 4
* PRF B1: 5 + D2: 5,6 + B6: 4 => SOL
* STA B1: 5 + D2: 5,6 + B6: 4
* CNT   5 HDP CHAINS /   4 HYP OPENED