Analysis of zz-www.sudokuoftheday.co.uk-20060816-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: ....4...1.1....63.7.2.......572...83.8179...4..........7..861...43.7...........9. initial

Autosolve

position: ....4..71.1...763.7.2...45..572..983.8179...4......71..7.38614..43.7..........397 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # E9: 1 => SOL
* DIS # G8: 5 => CTR => G8: 2,8
* DIS # I2: 2 => CTR => I2: 8,9
* DIS # A6: 4,6 => CTR => A6: 2,3,9
* DIS # C6: 4,6 => CTR => C6: 9
* PRF # C6: 9 => SOL
* DIS # E3: 1,6 => CTR => E3: 3
* DIS # F6: 3,5 => CTR => F6: 4,8
* DIS # I6: 2,5 => CTR => I6: 6
* PRF # I6: 6 => SOL
* DIS # G8: 2,5 => CTR => G8: 8
* DIS # I6: 5 => CTR => I6: 2,6
* DIS # A5: 3 => CTR => A5: 2,6
* PRF # A7: 5,9 => SOL
* DIS # A7: 2 => CTR => A7: 5,9
* DIS # C1: 5,9 => CTR => C1: 6,8
* DIS # C2: 5,9 => CTR => C2: 4,8
* DIS # A9: 2,6 => CTR => A9: 1,5,8
* PRF # B6: 3,9 => SOL
* DIS # G8: 2,5 => CTR => G8: 8
* PRF # I8: 2,5 => SOL
* DIS # A7: 2,5 => CTR => A7: 9
* PRF # A7: 9 => SOL
* DIS # I6: 2,5 => CTR => I6: 6
* PRF # I6: 6 => SOL
* DIS # I8: 2,6 => CTR => I8: 5,8
* PRF # I8: 5,8 => SOL
* CNT  27 HDP CHAINS /  55 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 # E9: 1 => SOL
* STA E9: 1
* CNT   1 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

....4...1.1....63.7.2.......572...83.8179...4..........7..861...43.7...........9. initial
....4..71.1...763.7.2...45..572..983.8179...4......71..7.38614..43.7..........397 autosolve
398645271514827639762139458457261983681793524239458716975386142143972865826514397 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
E2: 2,5
G1: 2,8
I3: 8,9
A4: 4,6
E4: 1,6
F4: 1,4
F5: 3,5
G5: 2,5
H5: 2,6
C7: 5,9
B9: 2,6
I7: 2,5
H8: 2,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E4,F4: 1.. / E4 = 1  =>  0 pairs (X) / F4 = 1  => 15 pairs (_)
A8,A9: 1.. / A8 = 1  => 14 pairs (_) / A9 = 1  => 24 pairs (_)
F1,E2: 2.. / F1 = 2  =>  0 pairs (X) / E2 = 2  => 15 pairs (_)
G1,I2: 2.. / G1 = 2  => 15 pairs (_) / I2 = 2  =>  0 pairs (X)
F1,G1: 2.. / F1 = 2  =>  0 pairs (X) / G1 = 2  => 15 pairs (_)
E2,I2: 2.. / E2 = 2  => 15 pairs (_) / I2 = 2  =>  0 pairs (X)
A7,I7: 2.. / A7 = 2  =>  0 pairs (X) / I7 = 2  =>  0 pairs (_)
B6,B9: 2.. / B6 = 2  => 17 pairs (_) / B9 = 2  =>  0 pairs (*)
E2,E9: 2.. / E2 = 2  => 15 pairs (_) / E9 = 2  =>  0 pairs (X)
H5,H8: 2.. / H5 = 2  =>  0 pairs (*) / H8 = 2  =>  0 pairs (X)
A5,F5: 3.. / A5 = 3  =>  0 pairs (X) / F5 = 3  => 16 pairs (_)
E3,E6: 3.. / E3 = 3  => 15 pairs (_) / E6 = 3  =>  0 pairs (X)
A2,C2: 4.. / A2 = 4  =>  0 pairs (X) / C2 = 4  => 14 pairs (_)
D9,F9: 4.. / D9 = 4  => 13 pairs (_) / F9 = 4  => 15 pairs (_)
A4,F4: 4.. / A4 = 4  => 15 pairs (_) / F4 = 4  =>  0 pairs (X)
C2,C6: 4.. / C2 = 4  => 14 pairs (_) / C6 = 4  =>  0 pairs (X)
D6,D9: 4.. / D6 = 4  => 15 pairs (_) / D9 = 4  => 13 pairs (_)
G5,I6: 5.. / G5 = 5  => 16 pairs (_) / I6 = 5  =>  0 pairs (X)
F5,G5: 5.. / F5 = 5  =>  0 pairs (X) / G5 = 5  => 16 pairs (_)
G5,G8: 5.. / G5 = 5  => 16 pairs (_) / G8 = 5  =>  0 pairs (X)
H5,I6: 6.. / H5 = 6  =>  0 pairs (X) / I6 = 6  =>  0 pairs (_)
H8,I8: 6.. / H8 = 6  =>  0 pairs (*) / I8 = 6  =>  0 pairs (X)
A4,E4: 6.. / A4 = 6  =>  0 pairs (X) / E4 = 6  => 15 pairs (_)
A5,H5: 6.. / A5 = 6  =>  0 pairs (*) / H5 = 6  =>  0 pairs (X)
H5,H8: 6.. / H5 = 6  =>  0 pairs (X) / H8 = 6  =>  0 pairs (_)
I6,I8: 6.. / I6 = 6  =>  0 pairs (*) / I8 = 6  =>  0 pairs (X)
D6,F6: 8.. / D6 = 8  => 15 pairs (_) / F6 = 8  => 13 pairs (_)
A9,C9: 8.. / A9 = 8  => 15 pairs (_) / C9 = 8  => 13 pairs (_)
G8,I8: 8.. / G8 = 8  => 15 pairs (_) / I8 = 8  =>  0 pairs (X)
G1,G8: 8.. / G1 = 8  =>  0 pairs (X) / G8 = 8  => 15 pairs (_)
I2,I3: 9.. / I2 = 9  => 15 pairs (_) / I3 = 9  => 15 pairs (_)
A7,C7: 9.. / A7 = 9  =>  0 pairs (*) / C7 = 9  =>  0 pairs (X)
D8,F8: 9.. / D8 = 9  => 14 pairs (_) / F8 = 9  => 18 pairs (_)
* DURATION: 0:00:33.751323  START: 01:49:43.935072  END: 01:50:17.686395 2019-05-01
* CP COUNT: (33)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B9,C7,E2,E4,F4,F5,G1,G5,H5,H8,I3,I7)
* ....4..71.1...763.7.2...45..572..983.8179...4......71..7.38614..43.7..........397
* PAIR E2: 2,5 BLK 2
F1: 2,5,3,8,9                            # reduction candidate for 2,5
F1: 3,8,9                                # 19 pairs
F1: 2,5                                  # 16 pairs
* PAIR E2: 2,5 COL E
E9: 2,5,1                                # reduction candidate for 2,5
E9: 1 => SOLVED
* 398645271514827639762139458457261983681793524239458716975386142143972865826514397
E9: 2,5                                  # 15 pairs
* PAIR G1: 2,8 BLK 3
I2: 2,8,9                                # reduction candidate for 2,8
I2: 9                                    # 15 pairs
I2: 2,8                                  # 15 pairs
* PAIR G1: 2,8 ROW 1
F1: 2,8,3,5,9                            # reduction candidate for 2,8
F1: 2,8                                  # 20 pairs
F1: 3,5,9                                # 16 pairs
* PAIR G1: 2,8 COL G
G8: 2,8,5                                # reduction candidate for 2,8
G8: 5 => CTR
* ....4.871.1...76327.2...459.572..983.8179.264......715.7.38614..43.7..........397
G8: 2,8                                  # 16 pairs
* PAIR I3: 8,9 BLK 3
I2: 8,9,2                                # reduction candidate for 8,9
I2: 2 => CTR
* ....42871.1..57632732...459.572..983.8179.524.2..3.71.279386145.43.7...8.6..2.397
I2: 8,9                                  # 15 pairs
* PAIR I3: 8,9 ROW 3
D3: 8,9,1,6                              # reduction candidate for 8,9
D3: 8,9                                  # 18 pairs
F3: 8,9,1,3                              # reduction candidate for 8,9
F3: 8,9                                  # 16 pairs
* PAIR A4: 4,6 BLK 4
A6: 4,6,2,3,9                            # reduction candidate for 4,6
A6: 4,6 => CTR
* ....4..71.14..763.7.2...45..572..983.8179..64..9...71.975386142.43.7..........397
A6: 2,3,9                                # 13 pairs
C6: 4,6,9                                # reduction candidate for 4,6
C6: 4,6 => CTR
* ....4..71.1...763.7.2...45..572..983.8179..64......71.279386145.43.7.826......397
C6: 9 => SOLVED
* 398645271514827639762139458457261983681793524239458716975386142143972865826514397
* PAIR E4: 1,6 COL E
E3: 1,6,3                                # reduction candidate for 1,6
E3: 1,6 => CTR
* ....4..71.1...763.7.2...45..572..983381795264....3.715.7.386142.43.7..........397
E3: 3                                    # 15 pairs
* PAIR F4: 1,4 COL F
F9: 1,4,2,5                              # reduction candidate for 1,4
F9: 2,5                                  # 14 pairs
F9: 1,4                                  # 14 pairs
* PAIR F5: 3,5 BLK 5
E6: 3,5,6                                # reduction candidate for 3,5
E6: 3,5                                  # 15 pairs
F6: 3,5,4,8                              # reduction candidate for 3,5
F6: 3,5 => CTR
* ....4..71.1...763.7.2.3.45.657214983.8179..64...86.71.279386145.43.7.826...4..397
F6: 4,8                                  # 14 pairs
* PAIR F5: 3,5 COL F
F1: 3,5,2,8,9                            # reduction candidate for 3,5
F1: 3,5                                  # 20 pairs
F1: 2,8,9                                # 14 pairs
* PAIR G5: 2,5 BLK 6
I6: 2,5,6                                # reduction candidate for 2,5
I6: 2,5 => CTR
* ....4..71.1...763.7.2...45..572..983.8179..64......71.279386145.43.7.826......397
I6: 6 => SOLVED
* 398645271514827639762139458457261983681793524239458716975386142143972865826514397
* PAIR G5: 2,5 COL G
G8: 2,5,8                                # reduction candidate for 2,5
G8: 2,5 => CTR
* ....42871.1..57632732...459.572..9836817935243.....71.279386145.43.7.268.6..2.397
G8: 8                                    # 15 pairs
* PAIR H5: 2,6 BLK 6
I6: 2,6,5                                # reduction candidate for 2,6
I6: 5 => CTR
* ....4..71.1...763.7.2...45..572..983.8179..64......715.7.386142.43.7..........397
I6: 2,6                                  # 16 pairs
* PAIR H5: 2,6 ROW 5
A5: 2,6,3                                # reduction candidate for 2,6
A5: 3 => CTR
* ....4..71.1...763.7.2...45..572..983381795264......715.7.386142.43.7..........397
A5: 2,6                                  # 16 pairs
* PAIR C7: 5,9 BLK 7
A7: 5,9,2                                # reduction candidate for 5,9
A7: 5,9 => SOLVED
* 398645271514827639762139458457261983681793524239458716975386142143972865826514397
A7: 2 => CTR
* ..6.4..71.1...763.7.26..45..57261983681793524.2....716279386145.43.7..6..6....397
* PAIR C7: 5,9 COL C
C1: 5,9,6,8                              # reduction candidate for 5,9
C1: 5,9 => CTR
* ....4..71.1...763.7.2...45..572..983.8179..64......71.279386145.43.7.826......397
C1: 6,8                                  # 14 pairs
C2: 5,9,4,8                              # reduction candidate for 5,9
C2: 5,9 => CTR
* ....4..7141...763.7.2...45.657214983.8179..64..4...71.279386145.43.7.826...4..397
C2: 4,8                                  # 14 pairs
* PAIR B9: 2,6 BLK 7
A9: 2,6,1,5,8                            # reduction candidate for 2,6
A9: 2,6 => CTR
* ..6.4.271.1..2763.7.26314584572..983681793524......716.7.386142143972865268...397
A9: 1,5,8                                # 13 pairs
* PAIR B9: 2,6 COL B
B6: 2,6,3,9                              # reduction candidate for 2,6
B6: 3,9 => SOLVED
* 398645271514827639762139458457261983681793524239458716975386142143972865826514397
B6: 2,6                                  # 16 pairs
* PAIR I7: 2,5 BLK 9
G8: 2,5,8                                # reduction candidate for 2,5
G8: 2,5 => CTR
* ....42871.1..57632732...459.572..9836817935243.....71.279386145.43.7.268.6..2.397
G8: 8                                    # 15 pairs
I8: 2,5,6,8                              # reduction candidate for 2,5
I8: 2,5 => SOLVED
* 398645271514827639762139458457261983681793524239458716975386142143972865826514397
I8: 6,8                                  # 14 pairs
* PAIR I7: 2,5 ROW 7
A7: 2,5,9                                # reduction candidate for 2,5
A7: 2,5 => CTR
* ....4..71.1...763.7.2...45..572..983.8179..64......71.279386145.43.7.826......397
A7: 9 => SOLVED
* 398645271514827639762139458457261983681793524239458716975386142143972865826514397
* PAIR I7: 2,5 COL I
I6: 2,5,6                                # reduction candidate for 2,5
I6: 2,5 => CTR
* ....4..71.1...763.7.2...45..572..983.8179..64......71.279386145.43.7.826......397
I6: 6 => SOLVED
* 398645271514827639762139458457261983681793524239458716975386142143972865826514397
* PAIR H8: 2,6 BLK 9
I8: 2,6,5,8                              # reduction candidate for 2,6
I8: 2,6 => CTR
* ....4.271.1..2763.7.2.3.45..572..983681793524.24...71.279386145.43.7.8...6...2397
I8: 5,8 => SOLVED
* 398645271514827639762139458457261983681793524239458716975386142143972865826514397
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060816-absurd-base-pr-000.dot
* REASONING
* PRF # E9: 1 => SOL
* DIS # G8: 5 => CTR => G8: 2,8
* DIS # I2: 2 => CTR => I2: 8,9
* DIS # A6: 4,6 => CTR => A6: 2,3,9
* DIS # C6: 4,6 => CTR => C6: 9
* PRF # C6: 9 => SOL
* DIS # E3: 1,6 => CTR => E3: 3
* DIS # F6: 3,5 => CTR => F6: 4,8
* DIS # I6: 2,5 => CTR => I6: 6
* PRF # I6: 6 => SOL
* DIS # G8: 2,5 => CTR => G8: 8
* DIS # I6: 5 => CTR => I6: 2,6
* DIS # A5: 3 => CTR => A5: 2,6
* PRF # A7: 5,9 => SOL
* DIS # A7: 2 => CTR => A7: 5,9
* DIS # C1: 5,9 => CTR => C1: 6,8
* DIS # C2: 5,9 => CTR => C2: 4,8
* DIS # A9: 2,6 => CTR => A9: 1,5,8
* PRF # B6: 3,9 => SOL
* DIS # G8: 2,5 => CTR => G8: 8
* PRF # I8: 2,5 => SOL
* DIS # A7: 2,5 => CTR => A7: 9
* PRF # A7: 9 => SOL
* DIS # I6: 2,5 => CTR => I6: 6
* PRF # I6: 6 => SOL
* DIS # I8: 2,6 => CTR => I8: 5,8
* PRF # I8: 5,8 => SOL
* CNT  27 HDP CHAINS /  55 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B9,C7,E2,E4,F4,F5,G1,G5,H5,H8,I3,I7)
* ....4..71.1...763.7.2...45..572..983.8179...4......71..7.38614..43.7..........397
* PAIR E2: 2,5 BLK 2
F1: 2,5,3,8,9                            # reduction candidate for 2,5
F1: 3,8,9                                # 19 pairs
F1: 2,5                                  # 16 pairs
* PAIR E2: 2,5 COL E
E9: 2,5,1                                # reduction candidate for 2,5
E9: 1 => SOLVED
* 398645271514827639762139458457261983681793524239458716975386142143972865826514397
* DURATION: 0:00:03.332469  START: 01:50:51.817052  END: 01:50:55.149521 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060816-absurd-base-pr-001.dot
* REASONING
* PRF # E9: 1 => SOL
* STA E9: 1
* CNT   1 HDP CHAINS /   4 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060816, absurd

Solution

position: 398645271514827639762139458457261983681793524239458716975386142143972865826514397 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 # F1: 2,5 => UNS
* INC # F1: 3,8,9 => UNS
* INC # E9: 2,5 => UNS
* PRF # E9: 1 => SOL
* INC # I2: 2,8 => UNS
* INC # I2: 9 => UNS
* INC # F1: 2,8 => UNS
* INC # F1: 3,5,9 => UNS
* INC # G8: 2,8 => UNS
* DIS # G8: 5 => CTR => G8: 2,8
* INC # I2: 8,9 => UNS
* DIS # I2: 2 => CTR => I2: 8,9
* INC # D3: 8,9 => UNS
* INC # F3: 8,9 => UNS
* DIS # A6: 4,6 => CTR => A6: 2,3,9
* INC # A6: 2,3,9 => UNS
* DIS # C6: 4,6 => CTR => C6: 9
* PRF # C6: 9 => SOL
* DIS # E3: 1,6 => CTR => E3: 3
* INC # E3: 3 => UNS
* INC # F9: 1,4 => UNS
* INC # F9: 2,5 => UNS
* INC # E6: 3,5 => UNS
* DIS # F6: 3,5 => CTR => F6: 4,8
* INC # F6: 4,8 => UNS
* INC # F1: 3,5 => UNS
* INC # F1: 2,8,9 => UNS
* DIS # I6: 2,5 => CTR => I6: 6
* PRF # I6: 6 => SOL
* DIS # G8: 2,5 => CTR => G8: 8
* INC # G8: 8 => UNS
* INC # I6: 2,6 => UNS
* DIS # I6: 5 => CTR => I6: 2,6
* INC # A5: 2,6 => UNS
* DIS # A5: 3 => CTR => A5: 2,6
* PRF # A7: 5,9 => SOL
* DIS # A7: 2 => CTR => A7: 5,9
* DIS # C1: 5,9 => CTR => C1: 6,8
* INC # C1: 6,8 => UNS
* DIS # C2: 5,9 => CTR => C2: 4,8
* INC # C2: 4,8 => UNS
* DIS # A9: 2,6 => CTR => A9: 1,5,8
* INC # A9: 1,5,8 => UNS
* INC # B6: 2,6 => UNS
* PRF # B6: 3,9 => SOL
* DIS # G8: 2,5 => CTR => G8: 8
* INC # G8: 8 => UNS
* PRF # I8: 2,5 => SOL
* INC # I8: 6,8 => UNS
* DIS # A7: 2,5 => CTR => A7: 9
* PRF # A7: 9 => SOL
* DIS # I6: 2,5 => CTR => I6: 6
* PRF # I6: 6 => SOL
* DIS # I8: 2,6 => CTR => I8: 5,8
* PRF # I8: 5,8 => SOL
* CNT  55 HDP CHAINS /  55 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F1: 2,5 => UNS
* INC # F1: 3,8,9 => UNS
* INC # E9: 2,5 => UNS
* PRF # E9: 1 => SOL
* STA E9: 1
* CNT   4 HDP CHAINS /   4 HYP OPENED