Analysis of zz-www.sudokuoftheday.co.uk-20060630-absurd-base.sdk

Contents

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

level: medium

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

position: .....247...5.....22.6.4.........91...623.8...87....3..6..........8.64..7..7.8.5.. initial

Autosolve

position: 18.6.24757458.16.22.6.4......4..91..9623187548714563296......4...8.64..74.7.835.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # H3: 3,9 => CTR => H3: 1,8
* PRF # B7: 3,9 => SOL
* DIS # H3: 3,9 => CTR => H3: 1,8
* DIS # H8: 1 => CTR => H8: 3,9
* DIS # H3: 8,9 => CTR => H3: 1,3
* PRF # G7: 2 => SOL
* PRF # B7: 3,5 => SOL
* DIS # B8: 3,5 => CTR => B8: 1,2,9
* PRF # B7: 3,9 => SOL
* PRF # B7: 3,5 => SOL
* DIS # B8: 3,5 => CTR => B8: 1,2,9
* PRF # G7: 2,9 => SOL
* DIS # G7: 8 => CTR => G7: 2,9
* DIS # H9: 9 => CTR => H9: 1,6
* CNT  14 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 # H3: 3,9 => CTR => H3: 1,8
* PRF H3: 1,8 # B7: 3,9 => SOL
* STA H3: 1,8 + B7: 3,9
* CNT   2 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

.....247...5.....22.6.4.........91...623.8...87....3..6..........8.64..7..7.8.5.. initial
18.6.24757458.16.22.6.4......4..91..9623187548714563296......4...8.64..74.7.835.. autosolve
183692475745831692296547813354729186962318754871456329639175248518264937427983561 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (20)
C1: 3,9
B3: 3,9
E1: 3,9
E2: 3,9
D3: 5,7
F3: 5,7
H2: 3,9
G3: 8,9
A4: 3,5
B4: 3,5
D4: 2,7
E4: 2,7
H4: 6,8
I4: 6,8
C7: 3,9
A8: 3,5
E7: 2,7
F7: 5,7
G8: 2,9
I9: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H3,I3: 1.. / H3 = 1  => 22 pairs (_) / I3 = 1  =>  0 pairs (X)
D4,E4: 2.. / D4 = 2  => 18 pairs (_) / E4 = 2  => 14 pairs (_)
G7,G8: 2.. / G7 = 2  =>  0 pairs (*) / G8 = 2  =>  0 pairs (X)
B9,D9: 2.. / B9 = 2  => 21 pairs (_) / D9 = 2  => 17 pairs (_)
E4,E7: 2.. / E4 = 2  => 14 pairs (_) / E7 = 2  => 18 pairs (_)
C1,B3: 3.. / C1 = 3  =>  0 pairs (*) / B3 = 3  =>  0 pairs (X)
E1,E2: 3.. / E1 = 3  =>  0 pairs (X) / E2 = 3  =>  0 pairs (_)
A4,B4: 3.. / A4 = 3  => 17 pairs (_) / B4 = 3  =>  0 pairs (X)
I7,H8: 3.. / I7 = 3  =>  0 pairs (X) / H8 = 3  =>  0 pairs (_)
C1,E1: 3.. / C1 = 3  =>  0 pairs (*) / E1 = 3  =>  0 pairs (X)
E2,H2: 3.. / E2 = 3  =>  0 pairs (*) / H2 = 3  =>  0 pairs (X)
A4,A8: 3.. / A4 = 3  => 17 pairs (_) / A8 = 3  =>  0 pairs (X)
C1,C7: 3.. / C1 = 3  =>  0 pairs (*) / C7 = 3  =>  0 pairs (X)
I3,I7: 3.. / I3 = 3  =>  0 pairs (*) / I7 = 3  =>  0 pairs (X)
D3,F3: 5.. / D3 = 5  => 17 pairs (_) / F3 = 5  => 15 pairs (_)
A4,B4: 5.. / A4 = 5  =>  0 pairs (X) / B4 = 5  => 17 pairs (_)
A4,A8: 5.. / A4 = 5  =>  0 pairs (X) / A8 = 5  => 17 pairs (_)
F3,F7: 5.. / F3 = 5  => 15 pairs (_) / F7 = 5  => 17 pairs (_)
H4,I4: 6.. / H4 = 6  =>  0 pairs (X) / I4 = 6  => 22 pairs (_)
H9,I9: 6.. / H9 = 6  => 22 pairs (_) / I9 = 6  =>  0 pairs (X)
H4,H9: 6.. / H4 = 6  =>  0 pairs (X) / H9 = 6  => 22 pairs (_)
I4,I9: 6.. / I4 = 6  => 22 pairs (_) / I9 = 6  =>  0 pairs (X)
D3,F3: 7.. / D3 = 7  => 15 pairs (_) / F3 = 7  => 17 pairs (_)
D4,E4: 7.. / D4 = 7  => 14 pairs (_) / E4 = 7  => 18 pairs (_)
E4,E7: 7.. / E4 = 7  => 18 pairs (_) / E7 = 7  => 14 pairs (_)
F3,F7: 7.. / F3 = 7  => 17 pairs (_) / F7 = 7  => 15 pairs (_)
H4,I4: 8.. / H4 = 8  => 22 pairs (_) / I4 = 8  =>  0 pairs (X)
G7,I7: 8.. / G7 = 8  =>  0 pairs (X) / I7 = 8  =>  0 pairs (_)
G3,G7: 8.. / G3 = 8  =>  0 pairs (*) / G7 = 8  =>  0 pairs (X)
H3,H4: 8.. / H3 = 8  =>  0 pairs (X) / H4 = 8  => 22 pairs (_)
C1,B3: 9.. / C1 = 9  =>  0 pairs (X) / B3 = 9  =>  0 pairs (_)
E1,E2: 9.. / E1 = 9  =>  0 pairs (*) / E2 = 9  =>  0 pairs (X)
C1,E1: 9.. / C1 = 9  =>  0 pairs (X) / E1 = 9  =>  0 pairs (_)
E2,H2: 9.. / E2 = 9  =>  0 pairs (X) / H2 = 9  =>  0 pairs (_)
C1,C7: 9.. / C1 = 9  =>  0 pairs (X) / C7 = 9  =>  0 pairs (_)
* DURATION: 0:00:56.733108  START: 00:12:40.902002  END: 00:13:37.635110 2019-05-01
* CP COUNT: (35)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B3,B4,C1,C7,D3,D4,E1,E2,E4,E7,F3,F7,G3,G8,H2,H4,I4,I9)
* 18.6.24757458.16.22.6.4......4..91..9623187548714563296......4...8.64..74.7.835..
* PAIR B3: 3,9 ROW 3
H3: 3,9,1,8                              # reduction candidate for 3,9
H3: 3,9 => CTR
* 18.6.24757458.16.22.6.4...1..4..91869623187548714563296......4...8.64..74.7.835..
H3: 1,8                                  # 21 pairs
* PAIR B3: 3,9 COL B
B7: 3,9,1,2,5                            # reduction candidate for 3,9
B7: 3,9 => SOLVED
* 183692475745831692296547813354729186962318754871456329639175248518264937427983561
B7: 1,2,5                                # 20 pairs
B8: 3,9,1,2,5                            # reduction candidate for 3,9
B8: 3,9                                  # 20 pairs
* PAIR D3: 5,7 COL D
D7: 5,7,1,2,9                            # reduction candidate for 5,7
D7: 5,7                                  # 20 pairs
D7: 1,2,9                                # 20 pairs
* PAIR H2: 3,9 BLK 3
H3: 3,9,1,8                              # reduction candidate for 3,9
H3: 3,9 => CTR
* 18.6.24757458.16.22.6.4...1..4..91869623187548714563296......4...8.64..74.7.835..
H3: 1,8                                  # 21 pairs
* PAIR H2: 3,9 COL H
H8: 3,9,1                                # reduction candidate for 3,9
H8: 1 => CTR
* 1836924757458316922.6.4......4..91..9623187548714563296......43..8.64.174.7.835.6
H8: 3,9                                  # 26 pairs
* PAIR G3: 8,9 BLK 3
H3: 8,9,1,3                              # reduction candidate for 8,9
H3: 8,9 => CTR
* 1836924757458316.22.6.4...1..4..91..9623187548714563296......43..8.64..74.7.835.6
H3: 1,3                                  # 22 pairs
* PAIR G3: 8,9 COL G
G7: 8,9,2                                # reduction candidate for 8,9
G7: 2 => SOLVED
* 183692475745831692296547813354729186962318754871456329639175248518264937427983561
G7: 8,9                                  # 20 pairs
* PAIR B4: 3,5 COL B
B7: 3,5,1,2,9                            # reduction candidate for 3,5
B7: 3,5 => SOLVED
* 183692475745831692296547813354729186962318754871456329639175248518264937427983561
B7: 1,2,9                                # 20 pairs
B8: 3,5,1,2,9                            # reduction candidate for 3,5
B8: 3,5 => CTR
* 183692475745831692296.4.831..4..91..9623187548714563296......4...8.64..74.7.835..
B8: 1,2,9                                # 20 pairs
* PAIR D4: 2,7 COL D
D7: 2,7,1,5,9                            # reduction candidate for 2,7
D7: 2,7                                  # 20 pairs
D7: 1,5,9                                # 20 pairs
* PAIR C7: 3,9 BLK 7
B7: 3,9,1,2,5                            # reduction candidate for 3,9
B7: 3,9 => SOLVED
* 183692475745831692296547813354729186962318754871456329639175248518264937427983561
B7: 1,2,5                                # 20 pairs
B8: 3,9,1,2,5                            # reduction candidate for 3,9
B8: 3,9                                  # 20 pairs
* PAIR A8: 3,5 BLK 7
B7: 3,5,1,2,9                            # reduction candidate for 3,5
B7: 3,5 => SOLVED
* 183692475745831692296547813354729186962318754871456329639175248518264937427983561
B7: 1,2,9                                # 20 pairs
B8: 3,5,1,2,9                            # reduction candidate for 3,5
B8: 3,5 => CTR
* 183692475745831692296.4.831..4..91..9623187548714563296......4...8.64..74.7.835..
B8: 1,2,9                                # 20 pairs
* PAIR E7: 2,7 BLK 8
D7: 2,7,1,5,9                            # reduction candidate for 2,7
D7: 2,7                                  # 20 pairs
D7: 1,5,9                                # 20 pairs
* PAIR F7: 5,7 BLK 8
D7: 5,7,1,2,9                            # reduction candidate for 5,7
D7: 5,7                                  # 20 pairs
D7: 1,2,9                                # 20 pairs
* PAIR G8: 2,9 BLK 9
G7: 2,9,8                                # reduction candidate for 2,9
G7: 2,9 => SOLVED
* 183692475745831692296547813354729186962318754871456329639175248518264937427983561
G7: 8 => CTR
* 189632475745891632236.4.9..354..91..9623187548714563296.3...8415.8.642974.7.8356.
* PAIR G8: 2,9 ROW 8
B8: 2,9,1,3,5                            # reduction candidate for 2,9
B8: 2,9                                  # 23 pairs
D8: 2,9,1,5                              # reduction candidate for 2,9
D8: 2,9                                  # 22 pairs
* PAIR I9: 1,6 BLK 9
H9: 1,6,9                                # reduction candidate for 1,6
H9: 9 => CTR
* 18.6.2475745891632236.4.981354..91689623187548714563296.3...84...8.642.74.7.83596
H9: 1,6                                  # 26 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060630-absurd-base-pr-000.dot
* REASONING
* DIS # H3: 3,9 => CTR => H3: 1,8
* PRF # B7: 3,9 => SOL
* DIS # H3: 3,9 => CTR => H3: 1,8
* DIS # H8: 1 => CTR => H8: 3,9
* DIS # H3: 8,9 => CTR => H3: 1,3
* PRF # G7: 2 => SOL
* PRF # B7: 3,5 => SOL
* DIS # B8: 3,5 => CTR => B8: 1,2,9
* PRF # B7: 3,9 => SOL
* PRF # B7: 3,5 => SOL
* DIS # B8: 3,5 => CTR => B8: 1,2,9
* PRF # G7: 2,9 => SOL
* DIS # G7: 8 => CTR => G7: 2,9
* DIS # H9: 9 => CTR => H9: 1,6
* CNT  14 HDP CHAINS /  38 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B3,B4,C1,C7,D3,D4,E1,E2,E4,E7,F3,F7,G3,G8,H2,H4,I4,I9)
* 18.6.24757458.16.22.6.4......4..91..9623187548714563296......4...8.64..74.7.835..
* PAIR B3: 3,9 ROW 3
H3: 3,9,1,8                              # reduction candidate for 3,9
H3: 3,9 => CTR
* 18.6.24757458.16.22.6.4...1..4..91869623187548714563296......4...8.64..74.7.835..
* PAIR B3: 3,9 COL B
B7: 3,9,1,2,5                            # reduction candidate for 3,9
B7: 3,9 => SOLVED
* 183692475745831692296547813354729186962318754871456329639175248518264937427983561
* DURATION: 0:00:03.640084  START: 00:14:13.207657  END: 00:14:16.847741 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060630-absurd-base-pr-001.dot
* REASONING
* DIS # H3: 3,9 => CTR => H3: 1,8
* PRF H3: 1,8 # B7: 3,9 => SOL
* STA H3: 1,8 + B7: 3,9
* CNT   2 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060630, absurd

Solution

position: 183692475745831692296547813354729186962318754871456329639175248518264937427983561 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 # H3: 3,9 => CTR => H3: 1,8
* INC # H3: 1,8 => UNS
* PRF # B7: 3,9 => SOL
* INC # B7: 1,2,5 => UNS
* INC # B8: 3,9 => UNS
* INC # D7: 5,7 => UNS
* INC # D7: 1,2,9 => UNS
* DIS # H3: 3,9 => CTR => H3: 1,8
* INC # H3: 1,8 => UNS
* INC # H8: 3,9 => UNS
* DIS # H8: 1 => CTR => H8: 3,9
* DIS # H3: 8,9 => CTR => H3: 1,3
* INC # H3: 1,3 => UNS
* INC # G7: 8,9 => UNS
* PRF # G7: 2 => SOL
* PRF # B7: 3,5 => SOL
* INC # B7: 1,2,9 => UNS
* DIS # B8: 3,5 => CTR => B8: 1,2,9
* INC # B8: 1,2,9 => UNS
* INC # D7: 2,7 => UNS
* INC # D7: 1,5,9 => UNS
* PRF # B7: 3,9 => SOL
* INC # B7: 1,2,5 => UNS
* INC # B8: 3,9 => UNS
* PRF # B7: 3,5 => SOL
* INC # B7: 1,2,9 => UNS
* DIS # B8: 3,5 => CTR => B8: 1,2,9
* INC # B8: 1,2,9 => UNS
* INC # D7: 2,7 => UNS
* INC # D7: 1,5,9 => UNS
* INC # D7: 5,7 => UNS
* INC # D7: 1,2,9 => UNS
* PRF # G7: 2,9 => SOL
* DIS # G7: 8 => CTR => G7: 2,9
* INC # B8: 2,9 => UNS
* INC # D8: 2,9 => UNS
* INC # H9: 1,6 => UNS
* DIS # H9: 9 => CTR => H9: 1,6
* CNT  38 HDP CHAINS /  38 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # H3: 3,9 => CTR => H3: 1,8
* PRF H3: 1,8 # B7: 3,9 => SOL
* STA H3: 1,8 + B7: 3,9
* CNT   2 HDP CHAINS /   2 HYP OPENED