Analysis of zz-www.sudokuoftheday.co.uk-20060323-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: .5......2.3.1.46..4...5...98.2.39....9..2..3....64.2..1....742..84.....19........ initial

Autosolve

position: .5.....4223.1.46..4...5...9842.39....9..2..34...64.29.16...742..84.6.9.192.41.... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C1: 6,7 => CTR => C1: 1,8,9
* DIS # G3: 1,7 => CTR => G3: 3,8
* DIS # C5: 1,7 => CTR => C5: 5,6
* PRF # D5: 8 => SOL
* DIS # C9: 3,5 => CTR => C9: 7
* DIS # D7: 3,5 => CTR => D7: 8,9
* DIS # D7: 3,5 => CTR => D7: 8,9
* DIS # H9: 5,7 => CTR => H9: 6,8
* CNT   8 HDP CHAINS /  38 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 # C1: 6,7 => CTR => C1: 1,8,9
* DIS C1: 1,8,9 # G3: 1,7 => CTR => G3: 3,8
* DIS C1: 1,8,9 + G3: 3,8 # C5: 1,7 => CTR => C5: 5,6
* DIS C1: 1,8,9 + G3: 3,8 + C5: 5,6 # D5: 5,7 => CTR => D5: 8
* PRF C1: 1,8,9 + G3: 3,8 + C5: 5,6 + D5: 8 => SOL
* STA C1: 1,8,9 + G3: 3,8 + C5: 5,6 + D5: 8
* CNT   5 HDP CHAINS /  21 HYP OPENED

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

Details

Positions

.5......2.3.1.46..4...5...98.2.39....9..2..3....64.2..1....742..84.....19........ initial
.5.....4223.1.46..4...5...9842.39....9..2..34...64.29.16...742..84.6.9.192.41.... autosolve
659378142238194657471256389842739516596821734713645298165987423384562971927413865 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
A1: 6,7
B3: 1,7
B6: 1,7
D4: 5,7
C7: 3,5
E7: 8,9
H8: 5,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F5,F6: 1.. / F5 = 1  =>  8 pairs (_) / F6 = 1  =>  0 pairs (X)
G4,H4: 1.. / G4 = 1  => 10 pairs (_) / H4 = 1  => 12 pairs (_)
C1,G1: 1.. / C1 = 1  => 10 pairs (_) / G1 = 1  => 11 pairs (_)
C5,F5: 1.. / C5 = 1  =>  0 pairs (X) / F5 = 1  =>  8 pairs (_)
B3,B6: 1.. / B3 = 1  => 13 pairs (_) / B6 = 1  => 11 pairs (_)
H3,H4: 1.. / H3 = 1  => 10 pairs (_) / H4 = 1  => 12 pairs (_)
D3,F3: 2.. / D3 = 2  =>  8 pairs (_) / F3 = 2  =>  0 pairs (X)
D8,F8: 2.. / D8 = 2  =>  0 pairs (X) / F8 = 2  =>  8 pairs (_)
D3,D8: 2.. / D3 = 2  =>  8 pairs (_) / D8 = 2  =>  0 pairs (X)
F3,F8: 2.. / F3 = 2  =>  0 pairs (X) / F8 = 2  =>  8 pairs (_)
G1,G3: 3.. / G1 = 3  =>  0 pairs (X) / G3 = 3  =>  8 pairs (_)
A6,C6: 3.. / A6 = 3  => 12 pairs (_) / C6 = 3  => 15 pairs (_)
I7,I9: 3.. / I7 = 3  => 10 pairs (_) / I9 = 3  => 13 pairs (_)
A6,A8: 3.. / A6 = 3  => 12 pairs (_) / A8 = 3  => 15 pairs (_)
H2,I2: 5.. / H2 = 5  => 13 pairs (_) / I2 = 5  => 11 pairs (_)
F1,F3: 6.. / F1 = 6  =>  0 pairs (X) / F3 = 6  =>  9 pairs (_)
A5,C5: 6.. / A5 = 6  =>  0 pairs (X) / C5 = 6  => 10 pairs (_)
H4,I4: 6.. / H4 = 6  => 15 pairs (_) / I4 = 6  =>  8 pairs (_)
H9,I9: 6.. / H9 = 6  =>  8 pairs (_) / I9 = 6  => 15 pairs (_)
C3,F3: 6.. / C3 = 6  =>  0 pairs (X) / F3 = 6  =>  9 pairs (_)
A1,A5: 6.. / A1 = 6  => 10 pairs (_) / A5 = 6  =>  0 pairs (X)
H4,H9: 6.. / H4 = 6  => 15 pairs (_) / H9 = 6  =>  8 pairs (_)
I4,I9: 6.. / I4 = 6  =>  8 pairs (_) / I9 = 6  => 15 pairs (_)
E1,E2: 7.. / E1 = 7  => 12 pairs (_) / E2 = 7  => 14 pairs (_)
D4,D5: 7.. / D4 = 7  => 11 pairs (_) / D5 = 7  => 18 pairs (_)
A8,C9: 7.. / A8 = 7  =>  0 pairs (X) / C9 = 7  => 11 pairs (_)
A8,H8: 7.. / A8 = 7  =>  0 pairs (X) / H8 = 7  => 11 pairs (_)
B3,B6: 7.. / B3 = 7  => 11 pairs (_) / B6 = 7  => 13 pairs (_)
G5,I6: 8.. / G5 = 8  => 18 pairs (_) / I6 = 8  => 14 pairs (_)
F6,I6: 8.. / F6 = 8  => 18 pairs (_) / I6 = 8  => 14 pairs (_)
C1,C2: 9.. / C1 = 9  => 16 pairs (_) / C2 = 9  =>  8 pairs (_)
D7,E7: 9.. / D7 = 9  => 11 pairs (_) / E7 = 9  => 10 pairs (_)
C2,E2: 9.. / C2 = 9  =>  8 pairs (_) / E2 = 9  => 16 pairs (_)
D1,D7: 9.. / D1 = 9  => 10 pairs (_) / D7 = 9  => 11 pairs (_)
* DURATION: 0:00:34.013249  START: 21:49:43.927813  END: 21:50:17.941062 2019-04-30
* CP COUNT: (34)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,B6,C7,D4,E7,H8)
* .5.....4223.1.46..4...5...9842.39....9..2..34...64.29.16...742..84.6.9.192.41....
* PAIR A1: 6,7 BLK 1
C1: 6,7,1,8,9                            # reduction candidate for 6,7
C1: 6,7 => CTR
* 657...142239174685418256379842.39.16596.21.3437164529816.5.742.784.6295192.41..67
C1: 1,8,9                                #  7 pairs
C3: 6,7,1,8                              # reduction candidate for 6,7
C3: 6,7                                  # 16 pairs
* PAIR A1: 6,7 COL A
A5: 6,7,5                                # reduction candidate for 6,7
A5: 5                                    # 14 pairs
A5: 6,7                                  # 13 pairs
* PAIR B3: 1,7 BLK 1
C1: 1,7,6,8,9                            # reduction candidate for 1,7
C1: 1,7                                  # 13 pairs
C3: 1,7,6,8                              # reduction candidate for 1,7
C3: 1,7                                  # 17 pairs
* PAIR B3: 1,7 ROW 3
G3: 1,7,3,8                              # reduction candidate for 1,7
G3: 1,7 => CTR
* .51...3422391.46..478.561.9842.39....9..2..34...64.29.16...742..84.6.9.192.41....
G3: 3,8                                  #  8 pairs
H3: 1,7,8                                # reduction candidate for 1,7
H3: 1,7                                  # 10 pairs
* PAIR B6: 1,7 BLK 4
C5: 1,7,5,6                              # reduction candidate for 1,7
C5: 1,7 => CTR
* 75.....4223.1746..41..5...9842.39.1669..2..34.7.64.29.16...742..84.6.97192741..6.
C5: 5,6                                  #  9 pairs
C6: 1,7,3,5                              # reduction candidate for 1,7
C6: 1,7                                  # 19 pairs
* PAIR D4: 5,7 BLK 5
D5: 5,7,8                                # reduction candidate for 5,7
D5: 8 => SOLVED
* 659378142238194657471256389842739516596821734713645298165987423384562971927413865
D5: 5,7                                  # 15 pairs
* PAIR D4: 5,7 ROW 4
G4: 5,7,1                                # reduction candidate for 5,7
G4: 5,7                                  # 12 pairs
H4: 5,7,1,6                              # reduction candidate for 5,7
H4: 5,7                                  # 14 pairs
I4: 5,7,6                                # reduction candidate for 5,7
I4: 5,7                                  # 15 pairs
* PAIR C7: 3,5 BLK 7
A8: 3,5,7                                # reduction candidate for 3,5
A8: 3,5                                  # 11 pairs
C9: 3,5,7                                # reduction candidate for 3,5
C9: 3,5 => CTR
* 65.....4223.1.46.54...56..9842.39...596.21.343..64529816.5.742.784.6.95192.41....
C9: 7                                    # 11 pairs
* PAIR C7: 3,5 ROW 7
D7: 3,5,8,9                              # reduction candidate for 3,5
D7: 3,5 => CTR
* .5.9...422391.46..4...5...9842.39....9..2..34...64.29.16..97428.84.6.9.192.418..3
D7: 8,9                                  # 10 pairs
I7: 3,5,8                                # reduction candidate for 3,5
I7: 3,5                                  # 10 pairs
* PAIR C7: 3,5 COL C
C6: 3,5,1,7                              # reduction candidate for 3,5
C6: 1,7                                  # 19 pairs
C6: 3,5                                  # 13 pairs
* PAIR E7: 8,9 BLK 8
D7: 8,9,3,5                              # reduction candidate for 8,9
D7: 3,5 => CTR
* .5.9...422391.46..4...5...9842.39....9..2..34...64.29.16..97428.84.6.9.192.418..3
D7: 8,9                                  # 10 pairs
* PAIR E7: 8,9 COL E
E1: 8,9,7                                # reduction candidate for 8,9
E1: 8,9                                  # 14 pairs
E2: 8,9,7                                # reduction candidate for 8,9
E2: 8,9                                  # 12 pairs
* PAIR H8: 5,7 BLK 9
G9: 5,7,8                                # reduction candidate for 5,7
G9: 5,7                                  # 10 pairs
H9: 5,7,6,8                              # reduction candidate for 5,7
H9: 5,7 => CTR
* .51....422391.4685478.56319842539167.9672..34.1.64.29.16...7423.84.6.9.192.41.8.6
H9: 6,8                                  #  8 pairs
I9: 5,7,3,6,8                            # reduction candidate for 5,7
I9: 5,7                                  # 17 pairs
* PAIR H8: 5,7 ROW 8
A8: 5,7,3                                # reduction candidate for 5,7
A8: 3                                    # 15 pairs
A8: 5,7                                  # 12 pairs
* PAIR H8: 5,7 COL H
H2: 5,7,8                                # reduction candidate for 5,7
H2: 5,7                                  # 11 pairs
H4: 5,7,1,6                              # reduction candidate for 5,7
H4: 5,7                                  # 14 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060323-absurd-base-pr-000.dot
* REASONING
* DIS # C1: 6,7 => CTR => C1: 1,8,9
* DIS # G3: 1,7 => CTR => G3: 3,8
* DIS # C5: 1,7 => CTR => C5: 5,6
* PRF # D5: 8 => SOL
* DIS # C9: 3,5 => CTR => C9: 7
* DIS # D7: 3,5 => CTR => D7: 8,9
* DIS # D7: 3,5 => CTR => D7: 8,9
* DIS # H9: 5,7 => CTR => H9: 6,8
* CNT   8 HDP CHAINS /  38 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B3,B6,C7,D4,E7,H8)
* .5.....4223.1.46..4...5...9842.39....9..2..34...64.29.16...742..84.6.9.192.41....
* PAIR A1: 6,7 BLK 1
C1: 6,7,1,8,9                            # reduction candidate for 6,7
C1: 6,7 => CTR
* 657...142239174685418256379842.39.16596.21.3437164529816.5.742.784.6295192.41..67
C3: 6,7,1,8                              # reduction candidate for 6,7
C3: 6,7                                  # 16 pairs
* RESTART
* PAIR A1: 6,7 BLK 1
C3: 6,7,1,8                              # reduction candidate for 6,7
C3: 6,7                                  # 16 pairs
C3: 1,8                                  # 11 pairs
* PAIR A1: 6,7 COL A
A5: 6,7,5                                # reduction candidate for 6,7
A5: 5                                    # 14 pairs
A5: 6,7                                  # 13 pairs
* PAIR B3: 1,7 BLK 1
C3: 1,7,6,8                              # reduction candidate for 1,7
C3: 1,7                                  # 17 pairs
C3: 6,8                                  #  8 pairs
* PAIR B3: 1,7 ROW 3
G3: 1,7,3,8                              # reduction candidate for 1,7
G3: 1,7 => CTR
* .51...3422391.46..478.561.9842.39....9..2..34...64.29.16...742..84.6.9.192.41....
H3: 1,7,8                                # reduction candidate for 1,7
H3: 1,7                                  # 10 pairs
* RESTART
* PAIR B3: 1,7 ROW 3
H3: 1,7,8                                # reduction candidate for 1,7
H3: 8                                    # 17 pairs
H3: 1,7                                  # 10 pairs
* PAIR RESTART
* PAIR B3: 1,7 BLK 1
C3: 1,7,6,8                              # reduction candidate for 1,7
C3: 1,7                                  # 17 pairs
C3: 6,8                                  # 10 pairs
* PAIR B3: 1,7 ROW 3
H3: 1,7,8                                # reduction candidate for 1,7
H3: 8                                    # 17 pairs
H3: 1,7                                  # 10 pairs
* PAIR B6: 1,7 BLK 4
C5: 1,7,5,6                              # reduction candidate for 1,7
C5: 1,7 => CTR
* 75...6.4223.1746..416.5..79842.39.1669..2..34.7.64.29.16...742..84.6.951927415863
C6: 1,7,3,5                              # reduction candidate for 1,7
C6: 1,7                                  # 20 pairs
* RESTART
* PAIR B6: 1,7 BLK 4
C6: 1,7,3,5                              # reduction candidate for 1,7
C6: 1,7                                  # 20 pairs
C6: 3,5                                  # 14 pairs
* PAIR D4: 5,7 BLK 5
D5: 5,7,8                                # reduction candidate for 5,7
D5: 5,7 => CTR
* 65..7314223.1.46.54..2563.9842.39516.96521834...64829.165..7423.843629519234157..
D5: 8 => SOLVED
* 659378142238194657471256389842739516596821734713645298165987423384562971927413865
* DURATION: 0:00:14.347973  START: 21:50:39.348164  END: 21:50:53.696137 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060323-absurd-base-pr-001.dot
* REASONING
* DIS # C1: 6,7 => CTR => C1: 1,8,9
* DIS C1: 1,8,9 # G3: 1,7 => CTR => G3: 3,8
* DIS C1: 1,8,9 + G3: 3,8 # C5: 1,7 => CTR => C5: 5,6
* DIS C1: 1,8,9 + G3: 3,8 + C5: 5,6 # D5: 5,7 => CTR => D5: 8
* PRF C1: 1,8,9 + G3: 3,8 + C5: 5,6 + D5: 8 => SOL
* STA C1: 1,8,9 + G3: 3,8 + C5: 5,6 + D5: 8
* CNT   5 HDP CHAINS /  21 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060323, absurd

Solution

position: 659378142238194657471256389842739516596821734713645298165987423384562971927413865 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 # C1: 6,7 => CTR => C1: 1,8,9
* INC # C1: 1,8,9 => UNS
* INC # C3: 6,7 => UNS
* INC # A5: 6,7 => UNS
* INC # A5: 5 => UNS
* INC # C1: 1,7 => UNS
* INC # C3: 1,7 => UNS
* DIS # G3: 1,7 => CTR => G3: 3,8
* INC # G3: 3,8 => UNS
* INC # H3: 1,7 => UNS
* DIS # C5: 1,7 => CTR => C5: 5,6
* INC # C5: 5,6 => UNS
* INC # C6: 1,7 => UNS
* INC # D5: 5,7 => UNS
* PRF # D5: 8 => SOL
* INC # G4: 5,7 => UNS
* INC # H4: 5,7 => UNS
* INC # I4: 5,7 => UNS
* INC # A8: 3,5 => UNS
* DIS # C9: 3,5 => CTR => C9: 7
* INC # C9: 7 => UNS
* DIS # D7: 3,5 => CTR => D7: 8,9
* INC # D7: 8,9 => UNS
* INC # I7: 3,5 => UNS
* INC # C6: 3,5 => UNS
* INC # C6: 1,7 => UNS
* INC # D7: 8,9 => UNS
* DIS # D7: 3,5 => CTR => D7: 8,9
* INC # E1: 8,9 => UNS
* INC # E2: 8,9 => UNS
* INC # G9: 5,7 => UNS
* DIS # H9: 5,7 => CTR => H9: 6,8
* INC # H9: 6,8 => UNS
* INC # I9: 5,7 => UNS
* INC # A8: 5,7 => UNS
* INC # A8: 3 => UNS
* INC # H2: 5,7 => UNS
* INC # H4: 5,7 => UNS
* CNT  38 HDP CHAINS /  38 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # C1: 6,7 => CTR => C1: 1,8,9
* INC C1: 1,8,9 # C3: 6,7 => UNS
* INC C1: 1,8,9 # C3: 6,7 => UNS
* INC C1: 1,8,9 # C3: 1,8 => UNS
* INC C1: 1,8,9 # A5: 6,7 => UNS
* INC C1: 1,8,9 # A5: 5 => UNS
* INC C1: 1,8,9 # C3: 1,7 => UNS
* INC C1: 1,8,9 # C3: 6,8 => UNS
* DIS C1: 1,8,9 # G3: 1,7 => CTR => G3: 3,8
* INC C1: 1,8,9 + G3: 3,8 # H3: 1,7 => UNS
* INC C1: 1,8,9 + G3: 3,8 # H3: 1,7 => UNS
* INC C1: 1,8,9 + G3: 3,8 # H3: 8 => UNS
* INC C1: 1,8,9 + G3: 3,8 # C3: 1,7 => UNS
* INC C1: 1,8,9 + G3: 3,8 # C3: 6,8 => UNS
* INC C1: 1,8,9 + G3: 3,8 # H3: 1,7 => UNS
* INC C1: 1,8,9 + G3: 3,8 # H3: 8 => UNS
* DIS C1: 1,8,9 + G3: 3,8 # C5: 1,7 => CTR => C5: 5,6
* INC C1: 1,8,9 + G3: 3,8 + C5: 5,6 # C6: 1,7 => UNS
* INC C1: 1,8,9 + G3: 3,8 + C5: 5,6 # C6: 1,7 => UNS
* INC C1: 1,8,9 + G3: 3,8 + C5: 5,6 # C6: 3,5 => UNS
* DIS C1: 1,8,9 + G3: 3,8 + C5: 5,6 # D5: 5,7 => CTR => D5: 8
* PRF C1: 1,8,9 + G3: 3,8 + C5: 5,6 + D5: 8 => SOL
* STA C1: 1,8,9 + G3: 3,8 + C5: 5,6 + D5: 8
* CNT  22 HDP CHAINS /  21 HYP OPENED