Analysis of zz-www.sudokuoftheday.co.uk-20060723-absurd-base.sdk

Contents

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

level: medium

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

position: 5.87........5.........1.56...9...4.3....7..2931.4.....7....8..4.34..7.1...5..12.. initial

Autosolve

position: 5.87....11..5.........1.56...91..4.3..6.7.12931.4.....7.1..8..4.34..7.1...5.412.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # G2: 3,9 => CTR => G2: 7,8
* DIS # G7: 6 => CTR => G7: 3,9
* DIS # B4: 2,8 => CTR => B4: 5,7
* PRF # B5: 4,8 => SOL
* DIS # B5: 5 => CTR => B5: 4,8
* DIS # B4: 2,7 => CTR => B4: 5,8
* DIS # C3: 2,7 => CTR => C3: 3
* DIS # D3: 2,9 => CTR => D3: 3,8
* DIS # D7: 2,9 => CTR => D7: 3,6
* DIS # E7: 2,9 => CTR => E7: 3,5
* DIS # B3: 2,9 => CTR => B3: 4,7
* DIS # H9: 8,9 => CTR => H9: 3,7
* CNT  12 HDP CHAINS /  37 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 # G2: 3,9 => CTR => G2: 7,8
* DIS G2: 7,8 # G7: 6 => CTR => G7: 3,9
* DIS G2: 7,8 + G7: 3,9 # B4: 2,8 => CTR => B4: 5,7
* DIS G2: 7,8 + G7: 3,9 + B4: 5,7 # A8: 2,8 => CTR => A8: 6,9
* PRF G2: 7,8 + G7: 3,9 + B4: 5,7 + A8: 6,9 # B5: 4,8 => SOL
* STA G2: 7,8 + G7: 3,9 + B4: 5,7 + A8: 6,9 + B5: 4,8
* CNT   5 HDP CHAINS /  18 HYP OPENED

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

Details

Positions

5.87........5.........1.56...9...4.3....7..2931.4.....7....8..4.34..7.1...5..12.. initial
5.87....11..5.........1.56...91..4.3..6.7.12931.4.....7.1..8..4.34..7.1...5.412.. autosolve
568724391192563748473819562259186473846375129317492685721638954934257816685941237 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
G1: 3,9
A4: 2,8
A5: 4,8
C6: 2,7
D5: 3,8
F5: 3,5
B7: 2,9
B9: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I2,I3: 2.. / I2 = 2  => 10 pairs (_) / I3 = 2  =>  0 pairs (*)
B7,A8: 2.. / B7 = 2  =>  8 pairs (_) / A8 = 2  =>  0 pairs (X)
C2,C3: 3.. / C2 = 3  =>  0 pairs (X) / C3 = 3  =>  9 pairs (_)
D5,F5: 3.. / D5 = 3  =>  0 pairs (*) / F5 = 3  =>  0 pairs (X)
D9,H9: 3.. / D9 = 3  =>  0 pairs (X) / H9 = 3  => 21 pairs (_)
H1,H2: 4.. / H1 = 4  =>  8 pairs (_) / H2 = 4  => 11 pairs (_)
A5,B5: 4.. / A5 = 4  =>  9 pairs (_) / B5 = 4  =>  0 pairs (*)
A3,A5: 4.. / A3 = 4  =>  0 pairs (*) / A5 = 4  =>  0 pairs (X)
B4,B5: 5.. / B4 = 5  =>  0 pairs (*) / B5 = 5  =>  0 pairs (X)
E7,E8: 5.. / E7 = 5  =>  0 pairs (X) / E8 = 5  => 19 pairs (_)
H7,I8: 5.. / H7 = 5  => 19 pairs (_) / I8 = 5  =>  0 pairs (X)
B5,F5: 5.. / B5 = 5  =>  0 pairs (X) / F5 = 5  =>  0 pairs (_)
E7,H7: 5.. / E7 = 5  =>  0 pairs (X) / H7 = 5  => 19 pairs (_)
E8,I8: 5.. / E8 = 5  => 19 pairs (_) / I8 = 5  =>  0 pairs (X)
I6,I8: 5.. / I6 = 5  => 19 pairs (_) / I8 = 5  =>  0 pairs (X)
B1,B2: 6.. / B1 = 6  =>  9 pairs (_) / B2 = 6  =>  8 pairs (_)
E4,F4: 6.. / E4 = 6  =>  9 pairs (_) / F4 = 6  => 12 pairs (_)
G6,I6: 6.. / G6 = 6  => 17 pairs (_) / I6 = 6  =>  0 pairs (X)
A8,A9: 6.. / A8 = 6  => 14 pairs (_) / A9 = 6  => 12 pairs (_)
D7,G7: 6.. / D7 = 6  => 13 pairs (_) / G7 = 6  =>  0 pairs (X)
B4,C6: 7.. / B4 = 7  =>  0 pairs (X) / C6 = 7  => 21 pairs (_)
H9,I9: 7.. / H9 = 7  =>  0 pairs (X) / I9 = 7  => 13 pairs (_)
B4,H4: 7.. / B4 = 7  =>  0 pairs (X) / H4 = 7  => 21 pairs (_)
G2,G6: 7.. / G2 = 7  => 14 pairs (_) / G6 = 7  =>  0 pairs (X)
E2,D3: 8.. / E2 = 8  =>  0 pairs (X) / D3 = 8  =>  0 pairs (_)
D3,I3: 8.. / D3 = 8  =>  0 pairs (*) / I3 = 8  =>  0 pairs (X)
D3,D5: 8.. / D3 = 8  =>  0 pairs (*) / D5 = 8  =>  0 pairs (X)
E6,F6: 9.. / E6 = 9  => 11 pairs (_) / F6 = 9  => 10 pairs (_)
* DURATION: 0:00:30.572054  START: 00:55:09.192649  END: 00:55:39.764703 2019-05-01
* CP COUNT: (28)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,B7,B9,C6,D5,F5,G1)
* 5.87....11..5.........1.56...91..4.3..6.7.12931.4.....7.1..8..4.34..7.1...5.412..
* PAIR G1: 3,9 BLK 3
H1: 3,9,4                                # reduction candidate for 3,9
H1: 3,9                                  # 11 pairs
G2: 3,9,7,8                              # reduction candidate for 3,9
G2: 3,9 => CTR
* 5.87...411.35..97...731.5688791..4534568731293124957867.1.58634.34.27815.85.41297
G2: 7,8                                  #  9 pairs
H2: 3,9,4,7,8                            # reduction candidate for 3,9
H2: 3,9                                  # 10 pairs
* PAIR G1: 3,9 ROW 1
E1: 3,9,2,6                              # reduction candidate for 3,9
E1: 3,9                                  # 11 pairs
F1: 3,9,2,4,6                            # reduction candidate for 3,9
F1: 3,9                                  # 11 pairs
* PAIR G1: 3,9 COL G
G7: 3,9,6                                # reduction candidate for 3,9
G7: 6 => CTR
* 5.873.9411..58.372..3.1.568..91..4.345687312931.4....67.1.586.4.34..7.15..5.412.7
G7: 3,9                                  # 13 pairs
* PAIR A4: 2,8 BLK 4
B4: 2,8,5,7                              # reduction candidate for 2,8
B4: 2,8 => CTR
* 5.87..3.11.358.7.2972314568..91654734568731293174..6..7.1.38.54.34.57.166.5941237
B4: 5,7                                  #  9 pairs
* PAIR A4: 2,8 ROW 4
E4: 2,8,6                                # reduction candidate for 2,8
E4: 2,8                                  # 12 pairs
E4: 6                                    #  9 pairs
* PAIR A4: 2,8 COL A
A8: 2,8,6,9                              # reduction candidate for 2,8
A8: 2,8                                  # 14 pairs
A8: 6,9                                  # 10 pairs
* PAIR A5: 4,8 BLK 4
B5: 4,8,5                                # reduction candidate for 4,8
B5: 4,8 => SOLVED
* 568724391192563748473819562259186473846375129317492685721638954934257816685941237
B5: 5 => CTR
* 5.87..3.11.358...2...31.568..91.54734568731293174..6857.1638954934257816685941237
* PAIR C6: 2,7 BLK 4
B4: 2,7,5,8                              # reduction candidate for 2,7
B4: 2,7 => CTR
* 5.87..3.11.358...2...31.5688.91.54734568731293174..6857.1638954934257816685941237
B4: 5,8                                  # 20 pairs
* PAIR C6: 2,7 COL C
C2: 2,7,3                                # reduction candidate for 2,7
C2: 2,7                                  #  9 pairs
C3: 2,7,3                                # reduction candidate for 2,7
C3: 2,7 => CTR
* 5.87..3.11.358.7.2...31.5688.91.5473..687312931.4..685721638954934257816685941237
C3: 3                                    #  9 pairs
* PAIR D5: 3,8 COL D
D3: 3,8,2,9                              # reduction candidate for 3,8
D3: 2,9 => CTR
* 5.873.9411.758.3.2..3.1.568..916.4.3456873129312495...7.1..8..4.34..7.15..5.412..
D3: 3,8                                  # 17 pairs
* PAIR B7: 2,9 BLK 7
A8: 2,9,6,8                              # reduction candidate for 2,9
A8: 2,9                                  # 17 pairs
A8: 6,8                                  # 10 pairs
* PAIR B7: 2,9 ROW 7
D7: 2,9,3,6                              # reduction candidate for 2,9
D7: 2,9 => CTR
* 5.873.9411..58.372..3.1.568..91..4.345687312931.4....67.1.58634.346.7.156.53412.7
D7: 3,6                                  #  9 pairs
E7: 2,9,3,5                              # reduction candidate for 2,9
E7: 2,9 => CTR
* 5.87..9.11..58.7.2..3.1.56...91..4.3..687312931.4..6857.16.8354.34.57816685341297
E7: 3,5                                  #  9 pairs
* PAIR B7: 2,9 COL B
B1: 2,9,4,6                              # reduction candidate for 2,9
B1: 2,9                                  # 13 pairs
B2: 2,9,4,6,7                            # reduction candidate for 2,9
B2: 2,9                                  # 15 pairs
B3: 2,9,4,7                              # reduction candidate for 2,9
B3: 2,9 => CTR
* 5.87....11..5.......7.1.56..791.54838.6.7.12931.4....57.1.38.54.34.57.1..85.41237
B3: 4,7                                  #  9 pairs
* PAIR B9: 8,9 BLK 7
A8: 8,9,2,6                              # reduction candidate for 8,9
A8: 8,9                                  # 16 pairs
A9: 8,9,6                                # reduction candidate for 8,9
A9: 8,9                                  # 14 pairs
* PAIR B9: 8,9 ROW 9
H9: 8,9,3,7                              # reduction candidate for 8,9
H9: 8,9 => CTR
* 5.873.9411.758.3.2..3.1.568..91..4.3456873129312495..67.1..8..4.34..7.156.53412.7
H9: 3,7                                  #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060723-absurd-base-pr-000.dot
* REASONING
* DIS # G2: 3,9 => CTR => G2: 7,8
* DIS # G7: 6 => CTR => G7: 3,9
* DIS # B4: 2,8 => CTR => B4: 5,7
* PRF # B5: 4,8 => SOL
* DIS # B5: 5 => CTR => B5: 4,8
* DIS # B4: 2,7 => CTR => B4: 5,8
* DIS # C3: 2,7 => CTR => C3: 3
* DIS # D3: 2,9 => CTR => D3: 3,8
* DIS # D7: 2,9 => CTR => D7: 3,6
* DIS # E7: 2,9 => CTR => E7: 3,5
* DIS # B3: 2,9 => CTR => B3: 4,7
* DIS # H9: 8,9 => CTR => H9: 3,7
* CNT  12 HDP CHAINS /  37 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,B7,B9,C6,D5,F5,G1)
* 5.87....11..5.........1.56...91..4.3..6.7.12931.4.....7.1..8..4.34..7.1...5.412..
* PAIR G1: 3,9 BLK 3
H1: 3,9,4                                # reduction candidate for 3,9
H1: 3,9                                  # 11 pairs
G2: 3,9,7,8                              # reduction candidate for 3,9
G2: 3,9 => CTR
* 5.87...411.35..97...731.5688791..4534568731293124957867.1.58634.34.27815.85.41297
H2: 3,9,4                                # reduction candidate for 3,9
H2: 3,9                                  # 10 pairs
* PAIR G1: 3,9 ROW 1
E1: 3,9,2,6                              # reduction candidate for 3,9
E1: 3,9                                  # 13 pairs
F1: 3,9,2,4,6                            # reduction candidate for 3,9
F1: 3,9                                  # 13 pairs
* PAIR G1: 3,9 COL G
G7: 3,9,6                                # reduction candidate for 3,9
G7: 6 => CTR
* 5.87..3.11..53....9...1.56...91..4.3..6.7.12931.4....67.1.586348346279156953412..
* PAIR RESTART
* PAIR G1: 3,9 BLK 3
H1: 3,9,4                                # reduction candidate for 3,9
H1: 3,9                                  # 15 pairs
H2: 3,9,4                                # reduction candidate for 3,9
H2: 3,9                                  # 14 pairs
* PAIR G1: 3,9 ROW 1
E1: 3,9,2,6                              # reduction candidate for 3,9
E1: 3,9                                  # 17 pairs
F1: 3,9,2,4,6                            # reduction candidate for 3,9
F1: 3,9                                  # 17 pairs
* PAIR A4: 2,8 BLK 4
B4: 2,8,5,7                              # reduction candidate for 2,8
B4: 2,8 => CTR
* 5.87..3.11.358.7.29723145682891654734568731293174.....7.1638954.34257.166.5941237
* PAIR A4: 2,8 ROW 4
E4: 2,8,6                                # reduction candidate for 2,8
E4: 2,8                                  # 17 pairs
E4: 6                                    # 15 pairs
* PAIR A4: 2,8 COL A
A8: 2,8,6,9                              # reduction candidate for 2,8
A8: 2,8 => CTR
* 5287..9.116.58974294.21.568..91..4.34.687312931.4.....7.16.8..4.349.7.1.685341297
* PAIR RESTART
* PAIR A4: 2,8 ROW 4
E4: 2,8,6                                # reduction candidate for 2,8
E4: 2,8                                  # 19 pairs
E4: 6                                    # 17 pairs
* PAIR A5: 4,8 BLK 4
B5: 4,8,5                                # reduction candidate for 4,8
B5: 4,8 => SOLVED
* 568724391192563748473819562259186473846375129317492685721638954934257816685941237
* DURATION: 0:00:13.155721  START: 00:56:01.984637  END: 00:56:15.140358 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060723-absurd-base-pr-001.dot
* REASONING
* DIS # G2: 3,9 => CTR => G2: 7,8
* DIS G2: 7,8 # G7: 6 => CTR => G7: 3,9
* DIS G2: 7,8 + G7: 3,9 # B4: 2,8 => CTR => B4: 5,7
* DIS G2: 7,8 + G7: 3,9 + B4: 5,7 # A8: 2,8 => CTR => A8: 6,9
* PRF G2: 7,8 + G7: 3,9 + B4: 5,7 + A8: 6,9 # B5: 4,8 => SOL
* STA G2: 7,8 + G7: 3,9 + B4: 5,7 + A8: 6,9 + B5: 4,8
* CNT   5 HDP CHAINS /  18 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060723, absurd

Solution

position: 568724391192563748473819562259186473846375129317492685721638954934257816685941237 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 # H1: 3,9 => UNS
* DIS # G2: 3,9 => CTR => G2: 7,8
* INC # G2: 7,8 => UNS
* INC # H2: 3,9 => UNS
* INC # E1: 3,9 => UNS
* INC # F1: 3,9 => UNS
* INC # G7: 3,9 => UNS
* DIS # G7: 6 => CTR => G7: 3,9
* DIS # B4: 2,8 => CTR => B4: 5,7
* INC # B4: 5,7 => UNS
* INC # E4: 2,8 => UNS
* INC # E4: 6 => UNS
* INC # A8: 2,8 => UNS
* INC # A8: 6,9 => UNS
* PRF # B5: 4,8 => SOL
* DIS # B5: 5 => CTR => B5: 4,8
* DIS # B4: 2,7 => CTR => B4: 5,8
* INC # B4: 5,8 => UNS
* INC # C2: 2,7 => UNS
* DIS # C3: 2,7 => CTR => C3: 3
* INC # C3: 3 => UNS
* INC # D3: 3,8 => UNS
* DIS # D3: 2,9 => CTR => D3: 3,8
* INC # A8: 2,9 => UNS
* INC # A8: 6,8 => UNS
* DIS # D7: 2,9 => CTR => D7: 3,6
* INC # D7: 3,6 => UNS
* DIS # E7: 2,9 => CTR => E7: 3,5
* INC # E7: 3,5 => UNS
* INC # B1: 2,9 => UNS
* INC # B2: 2,9 => UNS
* DIS # B3: 2,9 => CTR => B3: 4,7
* INC # B3: 4,7 => UNS
* INC # A8: 8,9 => UNS
* INC # A9: 8,9 => UNS
* DIS # H9: 8,9 => CTR => H9: 3,7
* INC # H9: 3,7 => UNS
* CNT  37 HDP CHAINS /  37 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # H1: 3,9 => UNS
* DIS # G2: 3,9 => CTR => G2: 7,8
* INC G2: 7,8 # H2: 3,9 => UNS
* INC G2: 7,8 # E1: 3,9 => UNS
* INC G2: 7,8 # F1: 3,9 => UNS
* INC G2: 7,8 # G7: 3,9 => UNS
* DIS G2: 7,8 # G7: 6 => CTR => G7: 3,9
* INC G2: 7,8 + G7: 3,9 # H1: 3,9 => UNS
* INC G2: 7,8 + G7: 3,9 # H2: 3,9 => UNS
* INC G2: 7,8 + G7: 3,9 # E1: 3,9 => UNS
* INC G2: 7,8 + G7: 3,9 # F1: 3,9 => UNS
* DIS G2: 7,8 + G7: 3,9 # B4: 2,8 => CTR => B4: 5,7
* INC G2: 7,8 + G7: 3,9 + B4: 5,7 # E4: 2,8 => UNS
* INC G2: 7,8 + G7: 3,9 + B4: 5,7 # E4: 6 => UNS
* DIS G2: 7,8 + G7: 3,9 + B4: 5,7 # A8: 2,8 => CTR => A8: 6,9
* INC G2: 7,8 + G7: 3,9 + B4: 5,7 + A8: 6,9 # E4: 2,8 => UNS
* INC G2: 7,8 + G7: 3,9 + B4: 5,7 + A8: 6,9 # E4: 6 => UNS
* PRF G2: 7,8 + G7: 3,9 + B4: 5,7 + A8: 6,9 # B5: 4,8 => SOL
* STA G2: 7,8 + G7: 3,9 + B4: 5,7 + A8: 6,9 + B5: 4,8
* CNT  18 HDP CHAINS /  18 HYP OPENED