Analysis of zz-www.sudokuoftheday.co.uk-20060511-absurd-base.sdk

Contents

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

level: medium

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

position: .56.....8..2......48....2.7......4..39...6.8...1..463.....7.1..6..2.3.5.1..549... initial

Autosolve

position: 756.....8912..7...483...2.7.6....4..394..6.8...1..463....6781..6..213.5.1..549... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # F4: 5 => CTR => F4: 1,2
* DIS # D1: 1,9 => CTR => D1: 3,4
* DIS # D4: 1,9 => CTR => D4: 3,7,8
* PRF # F4: 2 => SOL
* PRF # D1: 3,9 => SOL
* DIS # I2: 4,6 => CTR => I2: 3,5
* DIS # I2: 4,6 => CTR => I2: 3,5
* PRF # B9: 2,7 => SOL
* DIS # B9: 3 => CTR => B9: 2,7
* PRF # D4: 1,7 => SOL
* DIS # E4: 2,5 => CTR => E4: 3,8,9
* DIS # E6: 2,5 => CTR => E6: 8,9
* PRF # I5: 2,5 => SOL
* DIS # I5: 1 => CTR => I5: 2,5
* PRF # C8: 7,8 => SOL
* DIS # C8: 9 => CTR => C8: 7,8
* DIS # G9: 7,8 => CTR => G9: 3
* PRF # G9: 3 => SOL
* DIS # H7: 4,9 => CTR => H7: 2
* PRF # H7: 2 => SOL
* PRF # I7: 4,9 => SOL
* CNT  21 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 # F4: 5 => CTR => F4: 1,2
* DIS F4: 1,2 # D1: 1,9 => CTR => D1: 3,4
* DIS F4: 1,2 + D1: 3,4 # H3: 6 => CTR => H3: 1,9
* DIS F4: 1,2 + D1: 3,4 + H3: 1,9 # D4: 1,9 => CTR => D4: 3,7,8
* PRF F4: 1,2 + D1: 3,4 + H3: 1,9 + D4: 3,7,8 # I2: 3,5 => SOL
* STA F4: 1,2 + D1: 3,4 + H3: 1,9 + D4: 3,7,8 + I2: 3,5
* CNT   5 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

.56.....8..2......48....2.7......4..39...6.8...1..463.....7.1..6..2.3.5.1..549... initial
756.....8912..7...483...2.7.6....4..394..6.8...1..463....6781..6..213.5.1..549... autosolve
756321948912487563483965217865732491394156782271894635539678124647213859128549376 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
F1: 1,2
D3: 1,9
F3: 1,5
G1: 3,9
G2: 3,5
H2: 4,6
C4: 5,7
B6: 2,7
D5: 1,7
E5: 2,5
G5: 5,7
A7: 2,5
C7: 5,9
B8: 4,7
C9: 7,8
I8: 4,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H3: 1.. / H1 = 1  => 19 pairs (_) / H3 = 1  => 19 pairs (_)
I4,I5: 1.. / I4 = 1  =>  0 pairs (*) / I5 = 1  =>  0 pairs (X)
D5,I5: 1.. / D5 = 1  =>  0 pairs (*) / I5 = 1  =>  0 pairs (X)
E1,F1: 2.. / E1 = 2  =>  0 pairs (*) / F1 = 2  =>  0 pairs (X)
E5,I5: 2.. / E5 = 2  => 20 pairs (_) / I5 = 2  =>  0 pairs (*)
F1,F4: 2.. / F1 = 2  => 19 pairs (_) / F4 = 2  =>  0 pairs (*)
D4,E4: 3.. / D4 = 3  => 17 pairs (_) / E4 = 3  => 20 pairs (_)
B7,B9: 3.. / B7 = 3  =>  0 pairs (*) / B9 = 3  =>  0 pairs (X)
B7,I7: 3.. / B7 = 3  =>  0 pairs (*) / I7 = 3  =>  0 pairs (X)
D1,D2: 4.. / D1 = 4  => 18 pairs (_) / D2 = 4  => 23 pairs (_)
B7,B8: 4.. / B7 = 4  =>  0 pairs (X) / B8 = 4  =>  0 pairs (_)
D1,H1: 4.. / D1 = 4  => 18 pairs (_) / H1 = 4  => 23 pairs (_)
B8,I8: 4.. / B8 = 4  =>  0 pairs (*) / I8 = 4  =>  0 pairs (X)
E3,F3: 5.. / E3 = 5  =>  0 pairs (X) / F3 = 5  => 17 pairs (_)
G2,I2: 5.. / G2 = 5  =>  0 pairs (*) / I2 = 5  =>  0 pairs (X)
A7,C7: 5.. / A7 = 5  =>  0 pairs (*) / C7 = 5  =>  0 pairs (X)
C4,C7: 5.. / C4 = 5  =>  0 pairs (*) / C7 = 5  =>  0 pairs (X)
F3,F4: 5.. / F3 = 5  => 17 pairs (_) / F4 = 5  =>  0 pairs (X)
G2,G5: 5.. / G2 = 5  =>  0 pairs (*) / G5 = 5  =>  0 pairs (X)
E2,E3: 6.. / E2 = 6  => 23 pairs (_) / E3 = 6  => 18 pairs (_)
H9,I9: 6.. / H9 = 6  =>  0 pairs (X) / I9 = 6  => 17 pairs (_)
E3,H3: 6.. / E3 = 6  => 18 pairs (_) / H3 = 6  => 23 pairs (_)
I2,I9: 6.. / I2 = 6  =>  0 pairs (X) / I9 = 6  => 17 pairs (_)
C4,B6: 7.. / C4 = 7  =>  0 pairs (X) / B6 = 7  =>  0 pairs (_)
H4,G5: 7.. / H4 = 7  =>  0 pairs (X) / G5 = 7  =>  0 pairs (_)
D5,G5: 7.. / D5 = 7  =>  0 pairs (X) / G5 = 7  =>  0 pairs (_)
B6,D6: 7.. / B6 = 7  =>  0 pairs (*) / D6 = 7  =>  0 pairs (X)
H4,H9: 7.. / H4 = 7  =>  0 pairs (X) / H9 = 7  =>  0 pairs (_)
D2,E2: 8.. / D2 = 8  => 19 pairs (_) / E2 = 8  => 18 pairs (_)
A4,A6: 8.. / A4 = 8  => 18 pairs (_) / A6 = 8  => 22 pairs (_)
C8,C9: 8.. / C8 = 8  =>  0 pairs (X) / C9 = 8  => 28 pairs (_)
G8,G9: 8.. / G8 = 8  => 28 pairs (_) / G9 = 8  =>  0 pairs (X)
C8,G8: 8.. / C8 = 8  =>  0 pairs (X) / G8 = 8  => 28 pairs (_)
C9,G9: 8.. / C9 = 8  => 28 pairs (_) / G9 = 8  =>  0 pairs (X)
C7,C8: 9.. / C7 = 9  =>  0 pairs (*) / C8 = 9  =>  0 pairs (X)
G1,G8: 9.. / G1 = 9  => 27 pairs (_) / G8 = 9  =>  0 pairs (X)
* DURATION: 0:00:39.017984  START: 23:04:32.917117  END: 23:05:11.935101 2019-04-30
* CP COUNT: (36)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B6,B8,C4,C7,C9,D3,D5,E5,F1,F3,G1,G2,G5,H2,I8)
* 756.....8912..7...483...2.7.6....4..394..6.8...1..463....6781..6..213.5.1..549...
* PAIR F1: 1,2 COL F
F4: 1,2,5                                # reduction candidate for 1,2
F4: 5 => CTR
* 756..2918912..7.4.483951267867..54..394.267855217846392456781936.92138541.8549...
F4: 1,2                                  # 17 pairs
* PAIR D3: 1,9 BLK 2
D1: 1,9,3,4                              # reduction candidate for 1,9
D1: 1,9 => CTR
* 756.32948912487.6.48396521786.3.14..3947.6581.718.463....6781..64.213.591..549..6
D1: 3,4                                  # 17 pairs
* PAIR D3: 1,9 ROW 3
H3: 1,9,6                                # reduction candidate for 1,9
H3: 6                                    # 23 pairs
H3: 1,9                                  # 18 pairs
* PAIR D3: 1,9 COL D
D4: 1,9,3,7,8                            # reduction candidate for 1,9
D4: 1,9 => CTR
* 756.....8912.87...483.652.786..3.4..3947.6581.718546395.96781..64.213.5.1..549...
D4: 3,7,8                                # 16 pairs
* PAIR F3: 1,5 COL F
F4: 1,5,2                                # reduction candidate for 1,5
F4: 2 => SOLVED
* 756321948912487563483965217865732491394156782271894635539678124647213859128549376
F4: 1,5                                  # 19 pairs
* PAIR G1: 3,9 ROW 1
D1: 3,9,1,4                              # reduction candidate for 3,9
D1: 3,9 => SOLVED
* 756321948912487563483965217865732491394156782271894635539678124647213859128549376
D1: 1,4                                  # 17 pairs
E1: 3,9,2                                # reduction candidate for 3,9
E1: 3,9                                  # 19 pairs
* PAIR G2: 3,5 BLK 3
I2: 3,5,4,6                              # reduction candidate for 3,5
I2: 4,6 => CTR
* 756...3.8912..75.4483...2.7.6....4..3941.678...1..463....67814.6..213.5.1..549.76
I2: 3,5                                  # 27 pairs
* PAIR H2: 4,6 BLK 3
I2: 4,6,3,5                              # reduction candidate for 4,6
I2: 4,6 => CTR
* 756...3.8912..75.4483...2.7.6....4..3941.678...1..463....67814.6..213.5.1..549.76
I2: 3,5                                  # 27 pairs
* PAIR B6: 2,7 COL B
B9: 2,7,3                                # reduction candidate for 2,7
B9: 2,7 => SOLVED
* 756321948912487563483965217865732491394156782271894635539678124647213859128549376
B9: 3 => CTR
* 756...9.8912..73.5483...2.7.6....47.3947.6581.71..463..2.6781.36..213.5.13.549...
* PAIR D5: 1,7 BLK 5
D4: 1,7,3,8,9                            # reduction candidate for 1,7
D4: 1,7 => SOLVED
* 756321948912487563483965217865732491394156782271894635539678124647213859128549376
D4: 3,8,9                                # 16 pairs
* PAIR E5: 2,5 BLK 5
E4: 2,5,3,8,9                            # reduction candidate for 2,5
E4: 2,5 => CTR
* 756.....8912..75..483...2.786532147.394..6.8...1..46355.96781..6..213.5.1..549...
E4: 3,8,9                                # 16 pairs
F4: 2,5,1                                # reduction candidate for 2,5
F4: 2,5                                  # 22 pairs
E6: 2,5,8,9                              # reduction candidate for 2,5
E6: 2,5 => CTR
* 756..2..8912..7...483..52.7.6...14..3947.6581.71.5463....6781..64.213.591..549...
E6: 8,9                                  # 17 pairs
* PAIR E5: 2,5 ROW 5
I5: 2,5,1                                # reduction candidate for 2,5
I5: 2,5 => SOLVED
* 756321948912487563483965217865732491394156782271894635539678124647213859128549376
I5: 1 => CTR
* 756..2..8912..73.5483...2.7.6....47.394726581.71..463....6781..64.213.591..549..6
* PAIR A7: 2,5 COL A
A4: 2,5,8                                # reduction candidate for 2,5
A4: 2,5                                  # 22 pairs
A6: 2,5,8                                # reduction candidate for 2,5
A6: 2,5                                  # 18 pairs
* PAIR C9: 7,8 BLK 7
C8: 7,8,9                                # reduction candidate for 7,8
C8: 7,8 => SOLVED
* 756321948912487563483965217865732491394156782271894635539678124647213859128549376
C8: 9 => CTR
* 756...9.8912..7...483...2.7.67...4..394..678..217.463.2456781936.92138541.8549...
* PAIR C9: 7,8 ROW 9
G9: 7,8,3                                # reduction candidate for 7,8
G9: 7,8 => CTR
* 756.....8912..7...483...2.7.6....47.3947.6581.71..463....6781..64.213.591..549...
G9: 3 => SOLVED
* 756321948912487563483965217865732491394156782271894635539678124647213859128549376
* PAIR I8: 4,9 BLK 9
H7: 4,9,2                                # reduction candidate for 4,9
H7: 4,9 => CTR
* 756...9.8912..7...483...2.7.67...42.394.26785.217.46392456781936.92138541.8549..6
H7: 2 => SOLVED
* 756321948912487563483965217865732491394156782271894635539678124647213859128549376
I7: 4,9,2,3                              # reduction candidate for 4,9
I7: 4,9 => SOLVED
* 756321948912487563483965217865732491394156782271894635539678124647213859128549376
I7: 2,3                                  # 17 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060511-absurd-base-pr-000.dot
* REASONING
* DIS # F4: 5 => CTR => F4: 1,2
* DIS # D1: 1,9 => CTR => D1: 3,4
* DIS # D4: 1,9 => CTR => D4: 3,7,8
* PRF # F4: 2 => SOL
* PRF # D1: 3,9 => SOL
* DIS # I2: 4,6 => CTR => I2: 3,5
* DIS # I2: 4,6 => CTR => I2: 3,5
* PRF # B9: 2,7 => SOL
* DIS # B9: 3 => CTR => B9: 2,7
* PRF # D4: 1,7 => SOL
* DIS # E4: 2,5 => CTR => E4: 3,8,9
* DIS # E6: 2,5 => CTR => E6: 8,9
* PRF # I5: 2,5 => SOL
* DIS # I5: 1 => CTR => I5: 2,5
* PRF # C8: 7,8 => SOL
* DIS # C8: 9 => CTR => C8: 7,8
* DIS # G9: 7,8 => CTR => G9: 3
* PRF # G9: 3 => SOL
* DIS # H7: 4,9 => CTR => H7: 2
* PRF # H7: 2 => SOL
* PRF # I7: 4,9 => SOL
* CNT  21 HDP CHAINS /  38 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B6,B8,C4,C7,C9,D3,D5,E5,F1,F3,G1,G2,G5,H2,I8)
* 756.....8912..7...483...2.7.6....4..394..6.8...1..463....6781..6..213.5.1..549...
* PAIR F1: 1,2 COL F
F4: 1,2,5                                # reduction candidate for 1,2
F4: 5 => CTR
* 756..2918912..7.4.483951267867..54..394.267855217846392456781936.92138541.8549...
* PAIR RESTART
* PAIR D3: 1,9 BLK 2
D1: 1,9,3,4                              # reduction candidate for 1,9
D1: 1,9 => CTR
* 756.32948912487.6.48396521786.3.14..3947.6581.718.463....6781..64.213.591..549..6
* PAIR D3: 1,9 ROW 3
H3: 1,9,6                                # reduction candidate for 1,9
H3: 6 => CTR
* 756....18912..7...483195267.6...14..3947.6581.71..463....6781..64.213.591..549..6
* PAIR D3: 1,9 COL D
D4: 1,9,3,7,8                            # reduction candidate for 1,9
D4: 1,9 => CTR
* 756.....8912.87...483.652.786..3.4..3947.6581.718546395.96781..64.213.5.1..549...
* PAIR RESTART
* PAIR G2: 3,5 BLK 3
I2: 3,5,4,6                              # reduction candidate for 3,5
I2: 3,5 => SOLVED
* 756321948912487563483965217865732491394156782271894635539678124647213859128549376
* DURATION: 0:00:06.663989  START: 23:05:37.265448  END: 23:05:43.929437 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060511-absurd-base-pr-001.dot
* REASONING
* DIS # F4: 5 => CTR => F4: 1,2
* DIS F4: 1,2 # D1: 1,9 => CTR => D1: 3,4
* DIS F4: 1,2 + D1: 3,4 # H3: 6 => CTR => H3: 1,9
* DIS F4: 1,2 + D1: 3,4 + H3: 1,9 # D4: 1,9 => CTR => D4: 3,7,8
* PRF F4: 1,2 + D1: 3,4 + H3: 1,9 + D4: 3,7,8 # I2: 3,5 => SOL
* STA F4: 1,2 + D1: 3,4 + H3: 1,9 + D4: 3,7,8 + I2: 3,5
* CNT   5 HDP CHAINS /   7 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060511, absurd

Solution

position: 756321948912487563483965217865732491394156782271894635539678124647213859128549376 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 # F4: 1,2 => UNS
* DIS # F4: 5 => CTR => F4: 1,2
* DIS # D1: 1,9 => CTR => D1: 3,4
* INC # D1: 3,4 => UNS
* INC # H3: 1,9 => UNS
* INC # H3: 6 => UNS
* DIS # D4: 1,9 => CTR => D4: 3,7,8
* INC # D4: 3,7,8 => UNS
* INC # F4: 1,5 => UNS
* PRF # F4: 2 => SOL
* PRF # D1: 3,9 => SOL
* INC # D1: 1,4 => UNS
* INC # E1: 3,9 => UNS
* INC # I2: 3,5 => UNS
* DIS # I2: 4,6 => CTR => I2: 3,5
* DIS # I2: 4,6 => CTR => I2: 3,5
* INC # I2: 3,5 => UNS
* PRF # B9: 2,7 => SOL
* DIS # B9: 3 => CTR => B9: 2,7
* PRF # D4: 1,7 => SOL
* INC # D4: 3,8,9 => UNS
* DIS # E4: 2,5 => CTR => E4: 3,8,9
* INC # E4: 3,8,9 => UNS
* INC # F4: 2,5 => UNS
* DIS # E6: 2,5 => CTR => E6: 8,9
* INC # E6: 8,9 => UNS
* PRF # I5: 2,5 => SOL
* DIS # I5: 1 => CTR => I5: 2,5
* INC # A4: 2,5 => UNS
* INC # A6: 2,5 => UNS
* PRF # C8: 7,8 => SOL
* DIS # C8: 9 => CTR => C8: 7,8
* DIS # G9: 7,8 => CTR => G9: 3
* PRF # G9: 3 => SOL
* DIS # H7: 4,9 => CTR => H7: 2
* PRF # H7: 2 => SOL
* PRF # I7: 4,9 => SOL
* INC # I7: 2,3 => UNS
* CNT  38 HDP CHAINS /  38 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F4: 1,2 => UNS
* DIS # F4: 5 => CTR => F4: 1,2
* DIS F4: 1,2 # D1: 1,9 => CTR => D1: 3,4
* INC F4: 1,2 + D1: 3,4 # H3: 1,9 => UNS
* DIS F4: 1,2 + D1: 3,4 # H3: 6 => CTR => H3: 1,9
* DIS F4: 1,2 + D1: 3,4 + H3: 1,9 # D4: 1,9 => CTR => D4: 3,7,8
* PRF F4: 1,2 + D1: 3,4 + H3: 1,9 + D4: 3,7,8 # I2: 3,5 => SOL
* STA F4: 1,2 + D1: 3,4 + H3: 1,9 + D4: 3,7,8 + I2: 3,5
* CNT   7 HDP CHAINS /   7 HYP OPENED