Analysis of zz-www.sudokuoftheday.co.uk-20060823-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: ..8.42...5.....41...35...8......9.6..6....74...2...3.9...4...7......1.....435.69. initial

Autosolve

position: ..8.4293552...341...35..28......9.6..6...574...2..4359...42..73.....1.242.435.69. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A1: 1,7 => SOL
* PRF # D1: 6 => SOL
* DIS # B6: 1,7 => CTR => B6: 8
* DIS # A3: 1 => CTR => A3: 4,9
* DIS # D2: 6,7 => CTR => D2: 8,9
* DIS # E2: 6,7 => CTR => E2: 8,9
* DIS # D2: 6,7 => CTR => D2: 8,9
* DIS # E2: 6,7 => CTR => E2: 8,9
* DIS # A4: 1,8 => CTR => A4: 3,4,7
* DIS # E4: 1,8 => CTR => E4: 3,7
* DIS # B9: 1 => CTR => B9: 7,8
* DIS # G7: 1 => CTR => G7: 5,8
* PRF # B9: 7 => SOL
* CNT  13 HDP CHAINS /  50 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # A1: 1,7 => SOL
* STA A1: 1,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

..8.42...5.....41...35...8......9.6..6....74...2...3.9...4...7......1.....435.69. initial
..8.4293552...341...35..28......9.6..6...574...2..4359...42..73.....1.242.435.69. autosolve
718642935526893417943517286457239168369185742182764359891426573635971824274358691 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
B1: 1,7
B3: 4,9
E3: 1,9
F3: 6,7
I2: 6,7
I3: 6,7
C5: 1,9
G4: 1,8
B7: 5,9
B8: 3,5
F7: 6,8
F9: 7,8
G8: 5,8
I9: 1,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D1,E3: 1.. / D1 = 1  =>  0 pairs (X) / E3 = 1  => 19 pairs (_)
G7,I9: 1.. / G7 = 1  =>  0 pairs (X) / I9 = 1  => 17 pairs (_)
A3,E3: 1.. / A3 = 1  =>  0 pairs (X) / E3 = 1  => 19 pairs (_)
B9,I9: 1.. / B9 = 1  =>  0 pairs (X) / I9 = 1  => 17 pairs (_)
G4,G7: 1.. / G4 = 1  => 17 pairs (_) / G7 = 1  =>  0 pairs (X)
D4,D5: 2.. / D4 = 2  => 18 pairs (_) / D5 = 2  => 15 pairs (_)
I4,I5: 2.. / I4 = 2  => 15 pairs (_) / I5 = 2  => 18 pairs (_)
D4,I4: 2.. / D4 = 2  => 18 pairs (_) / I4 = 2  => 15 pairs (_)
D5,I5: 2.. / D5 = 2  => 15 pairs (_) / I5 = 2  => 18 pairs (_)
E4,E5: 3.. / E4 = 3  => 19 pairs (_) / E5 = 3  => 18 pairs (_)
A8,B8: 3.. / A8 = 3  => 15 pairs (_) / B8 = 3  => 14 pairs (_)
A5,E5: 3.. / A5 = 3  => 19 pairs (_) / E5 = 3  => 18 pairs (_)
B4,B8: 3.. / B4 = 3  => 15 pairs (_) / B8 = 3  => 14 pairs (_)
A3,B3: 4.. / A3 = 4  => 21 pairs (_) / B3 = 4  => 14 pairs (_)
A4,B4: 4.. / A4 = 4  => 14 pairs (_) / B4 = 4  => 21 pairs (_)
A3,A4: 4.. / A3 = 4  => 21 pairs (_) / A4 = 4  => 14 pairs (_)
B3,B4: 4.. / B3 = 4  => 14 pairs (_) / B4 = 4  => 21 pairs (_)
B4,C4: 5.. / B4 = 5  => 16 pairs (_) / C4 = 5  => 17 pairs (_)
G7,G8: 5.. / G7 = 5  => 16 pairs (_) / G8 = 5  => 17 pairs (_)
A1,C2: 6.. / A1 = 6  => 16 pairs (_) / C2 = 6  =>  0 pairs (*)
I2,I3: 6.. / I2 = 6  => 27 pairs (_) / I3 = 6  =>  0 pairs (*)
D6,E6: 6.. / D6 = 6  => 17 pairs (_) / E6 = 6  => 15 pairs (_)
A1,D1: 6.. / A1 = 6  => 16 pairs (_) / D1 = 6  =>  0 pairs (*)
F3,I3: 6.. / F3 = 6  => 27 pairs (_) / I3 = 6  =>  0 pairs (*)
F3,F7: 6.. / F3 = 6  => 27 pairs (_) / F7 = 6  =>  0 pairs (*)
I2,I3: 7.. / I2 = 7  =>  0 pairs (*) / I3 = 7  =>  0 pairs (X)
F3,I3: 7.. / F3 = 7  =>  0 pairs (*) / I3 = 7  =>  0 pairs (X)
B9,F9: 7.. / B9 = 7  =>  0 pairs (*) / F9 = 7  =>  0 pairs (X)
F3,F9: 7.. / F3 = 7  =>  0 pairs (*) / F9 = 7  =>  0 pairs (X)
D2,E2: 8.. / D2 = 8  => 16 pairs (_) / E2 = 8  => 15 pairs (_)
F7,F9: 8.. / F7 = 8  => 27 pairs (_) / F9 = 8  =>  0 pairs (*)
A8,G8: 8.. / A8 = 8  => 17 pairs (_) / G8 = 8  => 16 pairs (_)
B6,B9: 8.. / B6 = 8  => 16 pairs (_) / B9 = 8  =>  0 pairs (X)
A5,C5: 9.. / A5 = 9  => 26 pairs (_) / C5 = 9  => 18 pairs (_)
D8,E8: 9.. / D8 = 9  => 15 pairs (_) / E8 = 9  => 23 pairs (_)
B3,B7: 9.. / B3 = 9  => 21 pairs (_) / B7 = 9  => 14 pairs (_)
D2,D8: 9.. / D2 = 9  => 23 pairs (_) / D8 = 9  => 15 pairs (_)
* DURATION: 0:00:47.010227  START: 02:00:39.902807  END: 02:01:26.913034 2019-05-01
* CP COUNT: (37)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B3,B7,B8,C5,E3,F3,F7,F9,G4,G8,I2,I3,I9)
* ..8.4293552...341...35..28......9.6..6...574...2..4359...42..73.....1.242.435.69.
* PAIR B1: 1,7 BLK 1
A1: 1,7,6                                # reduction candidate for 1,7
A1: 1,7 => SOLVED
* 718642935526893417943517286457239168369185742182764359891426573635971824274358691
A1: 6                                    # 16 pairs
* PAIR B1: 1,7 ROW 1
D1: 1,7,6                                # reduction candidate for 1,7
D1: 6 => SOLVED
* 718642935526893417943517286457239168369185742182764359891426573635971824274358691
D1: 1,7                                  # 16 pairs
* PAIR B1: 1,7 COL B
B6: 1,7,8                                # reduction candidate for 1,7
B6: 1,7 => CTR
* 6.8.4293552...3416.435.62874....916..61..574..72..4359196428573735..1824284357691
B6: 8                                    # 16 pairs
B9: 1,7,8                                # reduction candidate for 1,7
B9: 1,7                                  # 16 pairs
* PAIR B3: 4,9 BLK 1
A3: 4,9,1                                # reduction candidate for 4,9
A3: 1 => CTR
* .78142935529..341.14359.28.4....9.6.961.3574..82.14359.9.42.17335.9.1.242.435.69.
A3: 4,9                                  # 19 pairs
* PAIR E3: 1,9 ROW 3
A3: 1,9,4                                # reduction candidate for 1,9
A3: 4                                    # 21 pairs
A3: 1,9                                  # 14 pairs
* PAIR F3: 6,7 BLK 2
D1: 6,7,1                                # reduction candidate for 6,7
D1: 6,7                                  # 19 pairs
D2: 6,7,8,9                              # reduction candidate for 6,7
D2: 6,7 => CTR
* ..8142935529.8341.14359.28.4....9.6.961.3574...2.14359.9.42.17335.9.1.242.435.69.
D2: 8,9                                  # 15 pairs
E2: 6,7,8,9                              # reduction candidate for 6,7
E2: 6,7 => CTR
* ..81429355298.341.14359.28.4....9.6.961235748..2614359.9.42.173...9.1.242.435.69.
E2: 8,9                                  # 15 pairs
* PAIR I2: 6,7 ROW 2
C2: 6,7,9                                # reduction candidate for 6,7
C2: 6,7                                  # 19 pairs
D2: 6,7,8,9                              # reduction candidate for 6,7
D2: 6,7 => CTR
* ..8142935529.8341.14359.28.4....9.6.961.3574...2.14359.9.42.17335.9.1.242.435.69.
D2: 8,9                                  # 15 pairs
E2: 6,7,8,9                              # reduction candidate for 6,7
E2: 6,7 => CTR
* ..81429355298.341.14359.28.4....9.6.961235748..2614359.9.42.173...9.1.242.435.69.
E2: 8,9                                  # 15 pairs
* PAIR C5: 1,9 BLK 4
A5: 1,9,3,8                              # reduction candidate for 1,9
A5: 1,9                                  # 26 pairs
A5: 3,8                                  # 22 pairs
* PAIR C5: 1,9 COL C
C7: 1,9,5,6                              # reduction candidate for 1,9
C7: 5,6                                  # 24 pairs
C7: 1,9                                  # 21 pairs
* PAIR G4: 1,8 BLK 6
I4: 1,8,2                                # reduction candidate for 1,8
I4: 1,8                                  # 18 pairs
I5: 1,8,2                                # reduction candidate for 1,8
I5: 1,8                                  # 15 pairs
* PAIR G4: 1,8 ROW 4
A4: 1,8,3,4,7                            # reduction candidate for 1,8
A4: 1,8 => CTR
* ..8.4293552...341.49351.28..45.39.6.369.8574...2..4359951426873836..1524274358691
A4: 3,4,7                                # 14 pairs
D4: 1,8,2,7                              # reduction candidate for 1,8
D4: 1,8                                  # 18 pairs
E4: 1,8,3,7                              # reduction candidate for 1,8
E4: 1,8 => CTR
* 6781429355298734161435962874357.9.6296.23574...2..4359..6428.73..7..1.242.435769.
E4: 3,7                                  # 15 pairs
* PAIR G4: 1,8 COL G
G7: 1,8,5                                # reduction candidate for 1,8
G7: 1,8                                  # 17 pairs
G7: 5                                    # 16 pairs
* PAIR B7: 5,9 BLK 7
C7: 5,9,1,6                              # reduction candidate for 5,9
C7: 5,9                                  # 29 pairs
C7: 1,6                                  # 15 pairs
* PAIR B8: 3,5 COL B
B4: 3,5,4                                # reduction candidate for 3,5
B4: 4                                    # 21 pairs
B4: 3,5                                  # 14 pairs
* PAIR F7: 6,8 ROW 7
A7: 6,8,1,9                              # reduction candidate for 6,8
A7: 6,8                                  # 16 pairs
A7: 1,9                                  # 15 pairs
* PAIR F9: 7,8 ROW 9
B9: 7,8,1                                # reduction candidate for 7,8
B9: 1 => CTR
* 678142935529..341614359628745...986..6...574..82..4359...428173837..1524214357698
B9: 7,8                                  # 17 pairs
* PAIR G8: 5,8 BLK 9
G7: 5,8,1                                # reduction candidate for 5,8
G7: 1 => CTR
* 678142935529..341614359628745...986..6...574..82..4359...428173837..1524214357698
G7: 5,8                                  # 17 pairs
* PAIR I9: 1,8 BLK 9
G7: 1,8,5                                # reduction candidate for 1,8
G7: 1,8                                  # 17 pairs
G7: 5                                    # 16 pairs
* PAIR I9: 1,8 ROW 9
B9: 1,8,7                                # reduction candidate for 1,8
B9: 7 => SOLVED
* 718642935526893417943517286457239168369185742182764359891426573635971824274358691
B9: 1,8                                  # 27 pairs
* PAIR I9: 1,8 COL I
I4: 1,8,2                                # reduction candidate for 1,8
I4: 1,8                                  # 18 pairs
I5: 1,8,2                                # reduction candidate for 1,8
I5: 1,8                                  # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060823-absurd-base-pr-000.dot
* REASONING
* PRF # A1: 1,7 => SOL
* PRF # D1: 6 => SOL
* DIS # B6: 1,7 => CTR => B6: 8
* DIS # A3: 1 => CTR => A3: 4,9
* DIS # D2: 6,7 => CTR => D2: 8,9
* DIS # E2: 6,7 => CTR => E2: 8,9
* DIS # D2: 6,7 => CTR => D2: 8,9
* DIS # E2: 6,7 => CTR => E2: 8,9
* DIS # A4: 1,8 => CTR => A4: 3,4,7
* DIS # E4: 1,8 => CTR => E4: 3,7
* DIS # B9: 1 => CTR => B9: 7,8
* DIS # G7: 1 => CTR => G7: 5,8
* PRF # B9: 7 => SOL
* CNT  13 HDP CHAINS /  50 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B3,B7,B8,C5,E3,F3,F7,F9,G4,G8,I2,I3,I9)
* ..8.4293552...341...35..28......9.6..6...574...2..4359...42..73.....1.242.435.69.
* PAIR B1: 1,7 BLK 1
A1: 1,7,6                                # reduction candidate for 1,7
A1: 1,7 => SOLVED
* 718642935526893417943517286457239168369185742182764359891426573635971824274358691
* DURATION: 0:00:01.705468  START: 02:02:00.863084  END: 02:02:02.568552 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060823-absurd-base-pr-001.dot
* REASONING
* PRF # A1: 1,7 => SOL
* STA A1: 1,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060823, absurd

Solution

position: 718642935526893417943517286457239168369185742182764359891426573635971824274358691 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:

* PRF # A1: 1,7 => SOL
* INC # A1: 6 => UNS
* INC # D1: 1,7 => UNS
* PRF # D1: 6 => SOL
* DIS # B6: 1,7 => CTR => B6: 8
* INC # B6: 8 => UNS
* INC # B9: 1,7 => UNS
* INC # A3: 4,9 => UNS
* DIS # A3: 1 => CTR => A3: 4,9
* INC # A3: 1,9 => UNS
* INC # A3: 4 => UNS
* INC # D1: 6,7 => UNS
* DIS # D2: 6,7 => CTR => D2: 8,9
* INC # D2: 8,9 => UNS
* DIS # E2: 6,7 => CTR => E2: 8,9
* INC # E2: 8,9 => UNS
* INC # C2: 6,7 => UNS
* DIS # D2: 6,7 => CTR => D2: 8,9
* INC # D2: 8,9 => UNS
* DIS # E2: 6,7 => CTR => E2: 8,9
* INC # E2: 8,9 => UNS
* INC # A5: 1,9 => UNS
* INC # A5: 3,8 => UNS
* INC # C7: 1,9 => UNS
* INC # C7: 5,6 => UNS
* INC # I4: 1,8 => UNS
* INC # I5: 1,8 => UNS
* DIS # A4: 1,8 => CTR => A4: 3,4,7
* INC # A4: 3,4,7 => UNS
* INC # D4: 1,8 => UNS
* DIS # E4: 1,8 => CTR => E4: 3,7
* INC # E4: 3,7 => UNS
* INC # G7: 1,8 => UNS
* INC # G7: 5 => UNS
* INC # C7: 5,9 => UNS
* INC # C7: 1,6 => UNS
* INC # B4: 3,5 => UNS
* INC # B4: 4 => UNS
* INC # A7: 6,8 => UNS
* INC # A7: 1,9 => UNS
* INC # B9: 7,8 => UNS
* DIS # B9: 1 => CTR => B9: 7,8
* INC # G7: 5,8 => UNS
* DIS # G7: 1 => CTR => G7: 5,8
* INC # G7: 1,8 => UNS
* INC # G7: 5 => UNS
* INC # B9: 1,8 => UNS
* PRF # B9: 7 => SOL
* INC # I4: 1,8 => UNS
* INC # I5: 1,8 => UNS
* CNT  50 HDP CHAINS /  50 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # A1: 1,7 => SOL
* STA A1: 1,7
* CNT   1 HDP CHAINS /   1 HYP OPENED