Analysis of zz-www.sudokuoftheday.co.uk-20060811-absurd-base.sdk

Contents

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

level: medium

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

position: 46.7....99.5..3............2....9..8.7.3..9..3...72.5.....1.4..8.4...5..6.3.24..1 initial

Autosolve

position: 46.7....99.5..3..7.3..9...52....9..8.7.3..9..3...72.5.....1.4.3814.375..6.3.24..1 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C3: 2,8 => CTR => C3: 1,7
* DIS # C3: 2,8 => CTR => C3: 1,7
* DIS # C6: 1,6 => CTR => C6: 8,9
* PRF # H5: 1,6 => SOL
* DIS # C6: 1,6 => CTR => C6: 8,9
* PRF # D6: 1,6 => SOL
* PRF # I5: 2 => SOL
* PRF # B7: 5,9 => SOL
* PRF # H8: 2 => SOL
* PRF # I5: 2,6 => SOL
* CNT  10 HDP CHAINS /  46 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 # C3: 2,8 => CTR => C3: 1,7
* DIS C3: 1,7 # D2: 2,8 => CTR => D2: 1,4,6
* PRF C3: 1,7 + D2: 1,4,6 # G2: 1,6 => SOL
* STA C3: 1,7 + D2: 1,4,6 + G2: 1,6
* CNT   3 HDP CHAINS /   6 HYP OPENED

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

Details

Positions

46.7....99.5..3............2....9..8.7.3..9..3...72.5.....1.4..8.4...5..6.3.24..1 initial
46.7....99.5..3..7.3..9...52....9..8.7.3..9..3...72.5.....1.4.3814.375..6.3.24..1 autosolve
468751239925483167137296845241569378576348912389172654792615483814937526653824791 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
B2: 2,8
A3: 1,7
E1: 5,8
B4: 4,5
C4: 1,6
A5: 1,5
G4: 3,7
H4: 3,7
G6: 1,6
I6: 4,6
A7: 5,7
B9: 5,9
D8: 6,9
I8: 2,6
G9: 7,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H5,G6: 1.. / H5 = 1  =>  0 pairs (*) / G6 = 1  =>  0 pairs (X)
C4,D4: 1.. / C4 = 1  => 24 pairs (_) / D4 = 1  => 18 pairs (_)
A3,A5: 1.. / A3 = 1  => 16 pairs (_) / A5 = 1  =>  0 pairs (X)
D2,D3: 2.. / D2 = 2  => 22 pairs (_) / D3 = 2  => 15 pairs (_)
H5,I5: 2.. / H5 = 2  => 15 pairs (_) / I5 = 2  =>  0 pairs (*)
B7,C7: 2.. / B7 = 2  => 18 pairs (_) / C7 = 2  =>  0 pairs (*)
H8,I8: 2.. / H8 = 2  =>  0 pairs (*) / I8 = 2  =>  0 pairs (X)
C1,G1: 2.. / C1 = 2  => 19 pairs (_) / G1 = 2  => 17 pairs (_)
B2,B7: 2.. / B2 = 2  =>  0 pairs (*) / B7 = 2  =>  0 pairs (X)
H5,H8: 2.. / H5 = 2  => 15 pairs (_) / H8 = 2  =>  0 pairs (*)
I5,I8: 2.. / I5 = 2  =>  0 pairs (*) / I8 = 2  =>  0 pairs (X)
G1,H1: 3.. / G1 = 3  => 20 pairs (_) / H1 = 3  => 13 pairs (_)
G4,H4: 3.. / G4 = 3  => 13 pairs (_) / H4 = 3  => 20 pairs (_)
G1,G4: 3.. / G1 = 3  => 20 pairs (_) / G4 = 3  => 13 pairs (_)
H1,H4: 3.. / H1 = 3  => 13 pairs (_) / H4 = 3  => 20 pairs (_)
H2,H3: 4.. / H2 = 4  =>  0 pairs (X) / H3 = 4  => 15 pairs (_)
B4,B6: 4.. / B4 = 4  => 16 pairs (_) / B6 = 4  =>  0 pairs (X)
I5,I6: 4.. / I5 = 4  => 15 pairs (_) / I6 = 4  =>  0 pairs (*)
D3,H3: 4.. / D3 = 4  =>  0 pairs (X) / H3 = 4  => 15 pairs (_)
E5,I5: 4.. / E5 = 4  =>  0 pairs (*) / I5 = 4  =>  0 pairs (X)
E1,F1: 5.. / E1 = 5  => 16 pairs (_) / F1 = 5  => 19 pairs (_)
B4,A5: 5.. / B4 = 5  =>  0 pairs (X) / A5 = 5  => 16 pairs (_)
B9,D9: 5.. / B9 = 5  => 18 pairs (_) / D9 = 5  => 20 pairs (_)
A5,A7: 5.. / A5 = 5  => 16 pairs (_) / A7 = 5  =>  0 pairs (X)
A3,C3: 7.. / A3 = 7  =>  0 pairs (X) / C3 = 7  => 16 pairs (_)
G4,H4: 7.. / G4 = 7  => 20 pairs (_) / H4 = 7  => 13 pairs (_)
A7,C7: 7.. / A7 = 7  => 16 pairs (_) / C7 = 7  =>  0 pairs (X)
G9,H9: 7.. / G9 = 7  => 13 pairs (_) / H9 = 7  => 20 pairs (_)
A3,A7: 7.. / A3 = 7  =>  0 pairs (X) / A7 = 7  => 16 pairs (_)
C3,C7: 7.. / C3 = 7  => 16 pairs (_) / C7 = 7  =>  0 pairs (X)
G4,G9: 7.. / G4 = 7  => 20 pairs (_) / G9 = 7  => 13 pairs (_)
H4,H9: 7.. / H4 = 7  => 13 pairs (_) / H9 = 7  => 20 pairs (_)
B2,B6: 8.. / B2 = 8  => 18 pairs (_) / B6 = 8  =>  0 pairs (*)
B6,C6: 9.. / B6 = 9  => 14 pairs (_) / C6 = 9  => 17 pairs (_)
D8,H8: 9.. / D8 = 9  => 17 pairs (_) / H8 = 9  => 17 pairs (_)
C6,C7: 9.. / C6 = 9  => 17 pairs (_) / C7 = 9  => 14 pairs (_)
* DURATION: 0:00:43.720613  START: 01:42:55.119686  END: 01:43:38.840299 2019-05-01
* CP COUNT: (36)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,A7,B2,B4,B9,C4,D8,E1,G4,G6,G9,H4,I6,I8)
* 46.7....99.5..3..7.3..9...52....9..8.7.3..9..3...72.5.....1.4.3814.375..6.3.24..1
* PAIR B2: 2,8 BLK 1
C1: 2,8,1                                # reduction candidate for 2,8
C1: 2,8                                  # 18 pairs
C3: 2,8,1,7                              # reduction candidate for 2,8
C3: 2,8 => CTR
* 461785239985263..7732.91..52561493781783..9.4349872156527.184.3814.375.2693524781
C3: 1,7                                  # 18 pairs
* PAIR B2: 2,8 ROW 2
D2: 2,8,1,4,6                            # reduction candidate for 2,8
D2: 2,8                                  # 21 pairs
G2: 2,8,1,6                              # reduction candidate for 2,8
G2: 2,8                                  # 18 pairs
* PAIR A3: 1,7 BLK 1
C3: 1,7,2,8                              # reduction candidate for 1,7
C3: 2,8 => CTR
* 461785239985263..7732.91..52561493781783..9.4349872156527.184.3814.375.2693524781
C3: 1,7                                  # 18 pairs
* PAIR E1: 5,8 BLK 2
F1: 5,8,1                                # reduction candidate for 5,8
F1: 5,8                                  # 20 pairs
F1: 1                                    # 19 pairs
* PAIR E1: 5,8 COL E
E5: 5,8,4,6                              # reduction candidate for 5,8
E5: 5,8                                  # 18 pairs
E5: 4,6                                  # 18 pairs
* PAIR B4: 4,5 ROW 4
D4: 4,5,1,6                              # reduction candidate for 4,5
D4: 4,5                                  # 27 pairs
E4: 4,5,6                                # reduction candidate for 4,5
E4: 4,5                                  # 18 pairs
* PAIR C4: 1,6 BLK 4
C5: 1,6,8                                # reduction candidate for 1,6
C5: 1,6                                  # 18 pairs
C6: 1,6,8,9                              # reduction candidate for 1,6
C6: 1,6 => CTR
* 46.7....9985..3..7.37.9...524...9..857834.926396872154729518463814637592653924..1
C6: 8,9                                  # 16 pairs
* PAIR C4: 1,6 ROW 4
D4: 1,6,4,5                              # reduction candidate for 1,6
D4: 4,5                                  # 27 pairs
D4: 1,6                                  # 18 pairs
* PAIR A5: 1,5 ROW 5
F5: 1,5,6,8                              # reduction candidate for 1,5
F5: 6,8                                  # 17 pairs
F5: 1,5                                  # 17 pairs
* PAIR G6: 1,6 BLK 6
H5: 1,6,2                                # reduction candidate for 1,6
H5: 1,6 => SOLVED
* 468751239925483167137296845241569378576348912389172654792615483814937526653824791
H5: 2                                    # 15 pairs
* PAIR G6: 1,6 ROW 6
C6: 1,6,8,9                              # reduction candidate for 1,6
C6: 1,6 => CTR
* 46.7....9985..3..7.37.9...524...9..857834.926396872154729518463814637592653924..1
C6: 8,9                                  # 16 pairs
D6: 1,6,4,8                              # reduction candidate for 1,6
D6: 1,6 => SOLVED
* 468751239925483167137296845241569378576348912389172654792615483814937526653824791
D6: 4,8                                  # 16 pairs
* PAIR G6: 1,6 COL G
G2: 1,6,2,8                              # reduction candidate for 1,6
G2: 1,6                                  # 17 pairs
G3: 1,6,2,8                              # reduction candidate for 1,6
G3: 1,6                                  # 20 pairs
* PAIR I6: 4,6 BLK 6
I5: 4,6,2                                # reduction candidate for 4,6
I5: 2 => SOLVED
* 468751239925483167137296845241569378576348912389172654792615483814937526653824791
I5: 4,6                                  # 15 pairs
* PAIR I6: 4,6 ROW 6
D6: 4,6,1,8                              # reduction candidate for 4,6
D6: 4,6                                  # 20 pairs
D6: 1,8                                  # 16 pairs
* PAIR B9: 5,9 BLK 7
B7: 5,9,2                                # reduction candidate for 5,9
B7: 5,9 => SOLVED
* 468751239925483167137296845241569378576348912389172654792615483814937526653824791
B7: 2                                    # 18 pairs
* PAIR B9: 5,9 ROW 9
D9: 5,9,8                                # reduction candidate for 5,9
D9: 8                                    # 18 pairs
D9: 5,9                                  # 18 pairs
* PAIR D8: 6,9 BLK 8
D7: 6,9,5,8                              # reduction candidate for 6,9
D7: 6,9                                  # 18 pairs
D7: 5,8                                  # 16 pairs
* PAIR D8: 6,9 ROW 8
H8: 6,9,2                                # reduction candidate for 6,9
H8: 2 => SOLVED
* 468751239925483167137296845241569378576348912389172654792615483814937526653824791
H8: 6,9                                  # 15 pairs
* PAIR I8: 2,6 BLK 9
H8: 2,6,9                                # reduction candidate for 2,6
H8: 9                                    # 17 pairs
H8: 2,6                                  # 17 pairs
* PAIR I8: 2,6 COL I
I5: 2,6,4                                # reduction candidate for 2,6
I5: 2,6 => SOLVED
* 468751239925483167137296845241569378576348912389172654792615483814937526653824791
I5: 4                                    # 15 pairs
* PAIR G9: 7,8 BLK 9
H9: 7,8,9                                # reduction candidate for 7,8
H9: 9                                    # 18 pairs
H9: 7,8                                  # 18 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060811-absurd-base-pr-000.dot
* REASONING
* DIS # C3: 2,8 => CTR => C3: 1,7
* DIS # C3: 2,8 => CTR => C3: 1,7
* DIS # C6: 1,6 => CTR => C6: 8,9
* PRF # H5: 1,6 => SOL
* DIS # C6: 1,6 => CTR => C6: 8,9
* PRF # D6: 1,6 => SOL
* PRF # I5: 2 => SOL
* PRF # B7: 5,9 => SOL
* PRF # H8: 2 => SOL
* PRF # I5: 2,6 => SOL
* CNT  10 HDP CHAINS /  46 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,A7,B2,B4,B9,C4,D8,E1,G4,G6,G9,H4,I6,I8)
* 46.7....99.5..3..7.3..9...52....9..8.7.3..9..3...72.5.....1.4.3814.375..6.3.24..1
* PAIR B2: 2,8 BLK 1
C1: 2,8,1                                # reduction candidate for 2,8
C1: 2,8                                  # 18 pairs
C3: 2,8,1,7                              # reduction candidate for 2,8
C3: 2,8 => CTR
* 461785239985263..7732.91..52561493781783..9.4349872156527.184.3814.375.2693524781
* RESTART
* PAIR B2: 2,8 ROW 2
D2: 2,8,1,4,6                            # reduction candidate for 2,8
D2: 2,8 => CTR
* 46.751..99.5..3617.3..9..452...69..8.763859243...721565.7.1.4.3814.375.2693524..1
G2: 2,8,1,6                              # reduction candidate for 2,8
G2: 2,8                                  # 22 pairs
* RESTART
* PAIR B2: 2,8 ROW 2
G2: 2,8,1,6                              # reduction candidate for 2,8
G2: 1,6 => SOLVED
* 468751239925483167137296845241569378576348912389172654792615483814937526653824791
* DURATION: 0:00:05.177607  START: 01:44:10.286785  END: 01:44:15.464392 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060811-absurd-base-pr-001.dot
* REASONING
* DIS # C3: 2,8 => CTR => C3: 1,7
* DIS C3: 1,7 # D2: 2,8 => CTR => D2: 1,4,6
* PRF C3: 1,7 + D2: 1,4,6 # G2: 1,6 => SOL
* STA C3: 1,7 + D2: 1,4,6 + G2: 1,6
* CNT   3 HDP CHAINS /   6 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060811, absurd

Solution

position: 468751239925483167137296845241569378576348912389172654792615483814937526653824791 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 # C1: 2,8 => UNS
* DIS # C3: 2,8 => CTR => C3: 1,7
* INC # C3: 1,7 => UNS
* INC # D2: 2,8 => UNS
* INC # G2: 2,8 => UNS
* INC # C3: 1,7 => UNS
* DIS # C3: 2,8 => CTR => C3: 1,7
* INC # F1: 5,8 => UNS
* INC # F1: 1 => UNS
* INC # E5: 5,8 => UNS
* INC # E5: 4,6 => UNS
* INC # D4: 4,5 => UNS
* INC # E4: 4,5 => UNS
* INC # C5: 1,6 => UNS
* DIS # C6: 1,6 => CTR => C6: 8,9
* INC # C6: 8,9 => UNS
* INC # D4: 1,6 => UNS
* INC # D4: 4,5 => UNS
* INC # F5: 1,5 => UNS
* INC # F5: 6,8 => UNS
* PRF # H5: 1,6 => SOL
* INC # H5: 2 => UNS
* DIS # C6: 1,6 => CTR => C6: 8,9
* INC # C6: 8,9 => UNS
* PRF # D6: 1,6 => SOL
* INC # D6: 4,8 => UNS
* INC # G2: 1,6 => UNS
* INC # G3: 1,6 => UNS
* INC # I5: 4,6 => UNS
* PRF # I5: 2 => SOL
* INC # D6: 4,6 => UNS
* INC # D6: 1,8 => UNS
* PRF # B7: 5,9 => SOL
* INC # B7: 2 => UNS
* INC # D9: 5,9 => UNS
* INC # D9: 8 => UNS
* INC # D7: 6,9 => UNS
* INC # D7: 5,8 => UNS
* INC # H8: 6,9 => UNS
* PRF # H8: 2 => SOL
* INC # H8: 2,6 => UNS
* INC # H8: 9 => UNS
* PRF # I5: 2,6 => SOL
* INC # I5: 4 => UNS
* INC # H9: 7,8 => UNS
* INC # H9: 9 => UNS
* CNT  46 HDP CHAINS /  46 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 2,8 => UNS
* DIS # C3: 2,8 => CTR => C3: 1,7
* DIS C3: 1,7 # D2: 2,8 => CTR => D2: 1,4,6
* INC C3: 1,7 + D2: 1,4,6 # G2: 2,8 => UNS
* INC C3: 1,7 + D2: 1,4,6 # G2: 2,8 => UNS
* PRF C3: 1,7 + D2: 1,4,6 # G2: 1,6 => SOL
* STA C3: 1,7 + D2: 1,4,6 + G2: 1,6
* CNT   6 HDP CHAINS /   6 HYP OPENED