Analysis of zz-www.sudokuoftheday.co.uk-20060809-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: ..6...1..8.1..6..32...........35..9.6.5...42......4......4..53...9.678..4...1.97. initial

Autosolve

position: 5.6.3.1..8.1..62532.31.576...435.69.635...42.9..6.43.5...4..53.3.9.678..4...1397. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B1: 4,9 => CTR => B1: 7
* DIS # E3: 4,9 => CTR => E3: 8
* DIS # D1: 7,9 => CTR => D1: 2,8
* DIS # E2: 7,9 => CTR => E2: 4
* DIS # B2: 4 => CTR => B2: 7,9
* DIS # D5: 8 => CTR => D5: 7,9
* DIS # I4: 8 => CTR => I4: 1,7
* DIS # I4: 1,8 => CTR => I4: 7
* PRF # I4: 7 => SOL
* PRF # I5: 1,8 => SOL
* DIS # I5: 7 => CTR => I5: 1,8
* DIS # B6: 2 => CTR => B6: 1,8
* DIS # B7: 2,8 => CTR => B7: 1,6
* PRF # C7: 2,8 => SOL
* DIS # C7: 7 => CTR => C7: 2,8
* DIS # B9: 2,8 => CTR => B9: 5,6
* DIS # D9: 5 => CTR => D9: 2,8
* DIS # C6: 2,8 => CTR => C6: 7
* PRF # C6: 7 => SOL
* DIS # D9: 2,5 => CTR => D9: 8
* PRF # D9: 8 => SOL
* PRF # B8: 1 => SOL
* PRF # I8: 2 => SOL
* PRF # I7: 1 => SOL
* DIS # B9: 2,6 => CTR => B9: 5,8
* CNT  25 HDP CHAINS /  44 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 # B1: 4,9 => CTR => B1: 7
* DIS B1: 7 # E3: 4,9 => CTR => E3: 8
* DIS B1: 7 + E3: 8 # I4: 8 => CTR => I4: 1,7
* DIS B1: 7 + E3: 8 + I4: 1,7 # B6: 2 => CTR => B6: 1,8
* PRF B1: 7 + E3: 8 + I4: 1,7 + B6: 1,8 # C7: 2,8 => SOL
* STA B1: 7 + E3: 8 + I4: 1,7 + B6: 1,8 + C7: 2,8
* CNT   5 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

..6...1..8.1..6..32...........35..9.6.5...42......4......4..53...9.678..4...1.97. initial
5.6.3.1..8.1..62532.31.576...435.69.635...42.9..6.43.5...4..53.3.9.678..4...1397. autosolve
576239184891746253243185769124358697635971428987624315768492531319567842452813976 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
B3: 4,9
D2: 7,9
H1: 4,8
A4: 1,7
H6: 1,8
A7: 1,7
C9: 2,8
D8: 2,5
H8: 1,4
I9: 2,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F4,F5: 1.. / F4 = 1  =>  0 pairs (X) / F5 = 1  => 12 pairs (_)
F5,I5: 1.. / F5 = 1  => 12 pairs (_) / I5 = 1  =>  0 pairs (X)
B6,H6: 1.. / B6 = 1  =>  0 pairs (X) / H6 = 1  => 21 pairs (_)
A4,A7: 1.. / A4 = 1  =>  0 pairs (*) / A7 = 1  =>  0 pairs (X)
H6,H8: 1.. / H6 = 1  => 21 pairs (_) / H8 = 1  =>  0 pairs (X)
D1,F1: 2.. / D1 = 2  =>  0 pairs (*) / F1 = 2  =>  0 pairs (X)
F4,E6: 2.. / F4 = 2  =>  0 pairs (X) / E6 = 2  =>  0 pairs (_)
B4,F4: 2.. / B4 = 2  =>  0 pairs (*) / F4 = 2  =>  0 pairs (X)
E6,E7: 2.. / E6 = 2  =>  0 pairs (*) / E7 = 2  =>  0 pairs (X)
E2,E3: 4.. / E2 = 4  => 13 pairs (_) / E3 = 4  =>  0 pairs (X)
H8,I8: 4.. / H8 = 4  => 21 pairs (_) / I8 = 4  =>  0 pairs (X)
B2,E2: 4.. / B2 = 4  =>  0 pairs (X) / E2 = 4  => 13 pairs (_)
H1,H8: 4.. / H1 = 4  =>  0 pairs (X) / H8 = 4  => 21 pairs (_)
B8,B9: 5.. / B8 = 5  =>  0 pairs (X) / B9 = 5  => 12 pairs (_)
D8,D9: 5.. / D8 = 5  => 12 pairs (_) / D9 = 5  =>  0 pairs (X)
B8,D8: 5.. / B8 = 5  =>  0 pairs (X) / D8 = 5  => 12 pairs (_)
B9,D9: 5.. / B9 = 5  => 12 pairs (_) / D9 = 5  =>  0 pairs (X)
B7,B9: 6.. / B7 = 6  => 10 pairs (_) / B9 = 6  =>  0 pairs (X)
I7,I9: 6.. / I7 = 6  =>  0 pairs (X) / I9 = 6  => 10 pairs (_)
B7,I7: 6.. / B7 = 6  => 10 pairs (_) / I7 = 6  =>  0 pairs (X)
B9,I9: 6.. / B9 = 6  =>  0 pairs (X) / I9 = 6  => 10 pairs (_)
B1,B2: 7.. / B1 = 7  => 12 pairs (_) / B2 = 7  =>  0 pairs (X)
A4,C6: 7.. / A4 = 7  =>  0 pairs (X) / C6 = 7  =>  0 pairs (_)
I4,I5: 7.. / I4 = 7  =>  0 pairs (*) / I5 = 7  =>  0 pairs (X)
A7,C7: 7.. / A7 = 7  =>  0 pairs (*) / C7 = 7  =>  0 pairs (X)
B1,D1: 7.. / B1 = 7  => 12 pairs (_) / D1 = 7  =>  0 pairs (X)
A4,I4: 7.. / A4 = 7  =>  0 pairs (X) / I4 = 7  =>  0 pairs (_)
C6,E6: 7.. / C6 = 7  =>  0 pairs (*) / E6 = 7  =>  0 pairs (X)
A4,A7: 7.. / A4 = 7  =>  0 pairs (X) / A7 = 7  =>  0 pairs (_)
C6,C7: 7.. / C6 = 7  =>  0 pairs (*) / C7 = 7  =>  0 pairs (X)
E3,I3: 8.. / E3 = 8  => 17 pairs (_) / I3 = 8  =>  0 pairs (X)
H1,H6: 8.. / H1 = 8  => 21 pairs (_) / H6 = 8  =>  0 pairs (X)
I1,I3: 9.. / I1 = 9  => 13 pairs (_) / I3 = 9  => 17 pairs (_)
E7,F7: 9.. / E7 = 9  =>  0 pairs (*) / F7 = 9  =>  0 pairs (X)
* DURATION: 0:00:38.492148  START: 01:40:05.241576  END: 01:40:43.733724 2019-05-01
* CP COUNT: (34)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,B3,C9,D2,D8,H1,H6,H8,I9)
* 5.6.3.1..8.1..62532.31.576...435.69.635...42.9..6.43.5...4..53.3.9.678..4...1397.
* PAIR B3: 4,9 BLK 1
B1: 4,9,7                                # reduction candidate for 4,9
B1: 4,9 => CTR
* 5.67321..8719462532.318576..2435169863587.42.9..6243.5...49853.3.9.678..4...1397.
B1: 7                                    # 12 pairs
B2: 4,9,7                                # reduction candidate for 4,9
B2: 4,9                                  # 12 pairs
* PAIR B3: 4,9 ROW 3
E3: 4,9,8                                # reduction candidate for 4,9
E3: 4,9 => CTR
* 5.6.3.1498.1..62532.31.5768.8435269.635..14279126743851.742.53.3.9.678144...1397.
E3: 8                                    # 17 pairs
I3: 4,9,8                                # reduction candidate for 4,9
I3: 4,9                                  # 17 pairs
* PAIR D2: 7,9 BLK 2
D1: 7,9,2,8                              # reduction candidate for 7,9
D1: 7,9 => CTR
* 5.6.321..8.1.462532.318576..243516986358..42.9..6243.5...49853.3.9.678..4...1397.
D1: 2,8                                  # 14 pairs
E2: 7,9,4                                # reduction candidate for 7,9
E2: 7,9 => CTR
* 576.3.149841..6253293145768.8435269.635..14279126743851.742.53.3.9.678144...1397.
E2: 4                                    # 13 pairs
* PAIR D2: 7,9 ROW 2
B2: 7,9,4                                # reduction candidate for 7,9
B2: 4 => CTR
* 576.3.149841..6253293145768.8435269.635..14279126743851.742.53.3.9.678144...1397.
B2: 7,9                                  # 13 pairs
* PAIR D2: 7,9 COL D
D5: 7,9,8                                # reduction candidate for 7,9
D5: 8 => CTR
* 5.6.321..8.1.462532.318576..243516986358.942.9..6.43.5...4.853.3.9.678..4...1397.
D5: 7,9                                  # 14 pairs
* PAIR H1: 4,8 BLK 3
I1: 4,8,9                                # reduction candidate for 4,8
I1: 4,8                                  # 17 pairs
I3: 4,8,9                                # reduction candidate for 4,8
I3: 4,8                                  # 13 pairs
* PAIR A4: 1,7 ROW 4
I4: 1,7,8                                # reduction candidate for 1,7
I4: 8 => CTR
* 5.6.3.1..8.1..62532.31.576.7.435.698635...4279..6743151.74295363.95678414...1397.
I4: 1,7                                  # 14 pairs
* PAIR H6: 1,8 BLK 6
I4: 1,8,7                                # reduction candidate for 1,8
I4: 1,8 => CTR
* 5.6.3.1..8.1..62532.31.576.7.435.69.635...4279..6743.51.74295363.95678..4...1397.
I4: 7 => SOLVED
* 576239184891746253243185769124358697635971428987624315768492531319567842452813976
I5: 1,8,7                                # reduction candidate for 1,8
I5: 1,8 => SOLVED
* 576239184891746253243185769124358697635971428987624315768492531319567842452813976
I5: 7 => CTR
* 5.6.3.1..8.1..62532.31.576...435.69.635..14279..6743.5..742953.3.95678..45.813976
* PAIR H6: 1,8 ROW 6
B6: 1,8,2                                # reduction candidate for 1,8
B6: 2 => CTR
* 5.62381..8.1..62532.31.576...435.69.635...42.92.6.4315...42953.3.9567842452813976
B6: 1,8                                  # 13 pairs
* PAIR C9: 2,8 BLK 7
B7: 2,8,1,6                              # reduction candidate for 2,8
B7: 2,8 => CTR
* 5.6.3.1..8.1..62532.31.576...435.69.635...42.9..6.43.51.74..5363592678..468513972
B7: 1,6                                  # 11 pairs
C7: 2,8,7                                # reduction candidate for 2,8
C7: 2,8 => SOLVED
* 576239184891746253243185769124358697635971428987624315768492531319567842452813976
C7: 7 => CTR
* 5.6.3.1..8.1..62532.31.576.7.435.69.635...4279..6743.51.74295363.95678..4...1397.
B9: 2,8,5,6                              # reduction candidate for 2,8
B9: 2,8 => CTR
* 5.6.321..8.1..62532.31.576..2435.69.635...42.9186.43.5.6.4..53.3592678..4..513976
B9: 5,6                                  # 11 pairs
* PAIR C9: 2,8 ROW 9
D9: 2,8,5                                # reduction candidate for 2,8
D9: 5 => CTR
* 5.6.321..8.1..62532.31.576.124358697635..1428987624315712489536359267841468513972
D9: 2,8                                  # 12 pairs
* PAIR C9: 2,8 COL C
C6: 2,8,7                                # reduction candidate for 2,8
C6: 2,8 => CTR
* 5.6.3.1..8.1..62532.31.576.7.435.69.635...4279..6743.51.74295363.95678..4...1397.
C6: 7 => SOLVED
* 576239184891746253243185769124358697635971428987624315768492531319567842452813976
* PAIR D8: 2,5 BLK 8
D9: 2,5,8                                # reduction candidate for 2,5
D9: 2,5 => CTR
* 5.6.321..8.1..62532.31.576.124358697635..14289876243157.248953.3.9.6784.4.8.1397.
D9: 8 => SOLVED
* 576239184891746253243185769124358697635971428987624315768492531319567842452813976
* PAIR D8: 2,5 ROW 8
B8: 2,5,1                                # reduction candidate for 2,5
B8: 1 => SOLVED
* 576239184891746253243185769124358697635971428987624315768492531319567842452813976
B8: 2,5                                  # 13 pairs
* PAIR H8: 1,4 BLK 9
I8: 1,4,2                                # reduction candidate for 1,4
I8: 2 => SOLVED
* 576239184891746253243185769124358697635971428987624315768492531319567842452813976
I8: 1,4                                  # 13 pairs
* PAIR I9: 2,6 BLK 9
I7: 2,6,1                                # reduction candidate for 2,6
I7: 1 => SOLVED
* 576239184891746253243185769124358697635971428987624315768492531319567842452813976
I7: 2,6                                  # 13 pairs
* PAIR I9: 2,6 ROW 9
B9: 2,6,5,8                              # reduction candidate for 2,6
B9: 2,6 => CTR
* 5.6.3218.8.1..62532.318576.124358697635..142898762431571249.536359267841468513972
B9: 5,8                                  # 11 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060809-absurd-base-pr-000.dot
* REASONING
* DIS # B1: 4,9 => CTR => B1: 7
* DIS # E3: 4,9 => CTR => E3: 8
* DIS # D1: 7,9 => CTR => D1: 2,8
* DIS # E2: 7,9 => CTR => E2: 4
* DIS # B2: 4 => CTR => B2: 7,9
* DIS # D5: 8 => CTR => D5: 7,9
* DIS # I4: 8 => CTR => I4: 1,7
* DIS # I4: 1,8 => CTR => I4: 7
* PRF # I4: 7 => SOL
* PRF # I5: 1,8 => SOL
* DIS # I5: 7 => CTR => I5: 1,8
* DIS # B6: 2 => CTR => B6: 1,8
* DIS # B7: 2,8 => CTR => B7: 1,6
* PRF # C7: 2,8 => SOL
* DIS # C7: 7 => CTR => C7: 2,8
* DIS # B9: 2,8 => CTR => B9: 5,6
* DIS # D9: 5 => CTR => D9: 2,8
* DIS # C6: 2,8 => CTR => C6: 7
* PRF # C6: 7 => SOL
* DIS # D9: 2,5 => CTR => D9: 8
* PRF # D9: 8 => SOL
* PRF # B8: 1 => SOL
* PRF # I8: 2 => SOL
* PRF # I7: 1 => SOL
* DIS # B9: 2,6 => CTR => B9: 5,8
* CNT  25 HDP CHAINS /  44 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,B3,C9,D2,D8,H1,H6,H8,I9)
* 5.6.3.1..8.1..62532.31.576...435.69.635...42.9..6.43.5...4..53.3.9.678..4...1397.
* PAIR B3: 4,9 BLK 1
B1: 4,9,7                                # reduction candidate for 4,9
B1: 4,9 => CTR
* 5.67321..8719462532.318576..2435169863587.42.9..6243.5...49853.3.9.678..4...1397.
* RESTART
* PAIR B3: 4,9 ROW 3
E3: 4,9,8                                # reduction candidate for 4,9
E3: 4,9 => CTR
* 576.3.1498.1..62532.31.5768.8435269.635..14279126743851.742.53.3.9.678144...1397.
* PAIR RESTART
* PAIR A4: 1,7 ROW 4
I4: 1,7,8                                # reduction candidate for 1,7
I4: 8 => CTR
* 576.3.1..8917462532431857697.435.698635...4279..6743151.74295363.95678..4...1397.
* PAIR RESTART
* PAIR H6: 1,8 ROW 6
B6: 1,8,2                                # reduction candidate for 1,8
B6: 2 => CTR
* 576.3.1..8917462532431857691.435.697635.7142892.6.43.5...4..53.3.9.678..4...1397.
* PAIR RESTART
* PAIR C9: 2,8 BLK 7
C7: 2,8,7                                # reduction candidate for 2,8
C7: 2,8 => SOLVED
* 576239184891746253243185769124358697635971428987624315768492531319567842452813976
* DURATION: 0:00:06.754159  START: 01:41:12.756020  END: 01:41:19.510179 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060809-absurd-base-pr-001.dot
* REASONING
* DIS # B1: 4,9 => CTR => B1: 7
* DIS B1: 7 # E3: 4,9 => CTR => E3: 8
* DIS B1: 7 + E3: 8 # I4: 8 => CTR => I4: 1,7
* DIS B1: 7 + E3: 8 + I4: 1,7 # B6: 2 => CTR => B6: 1,8
* PRF B1: 7 + E3: 8 + I4: 1,7 + B6: 1,8 # C7: 2,8 => SOL
* STA B1: 7 + E3: 8 + I4: 1,7 + B6: 1,8 + C7: 2,8
* CNT   5 HDP CHAINS /   7 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060809, absurd

Solution

position: 576239184891746253243185769124358697635971428987624315768492531319567842452813976 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 # B1: 4,9 => CTR => B1: 7
* INC # B1: 7 => UNS
* INC # B2: 4,9 => UNS
* DIS # E3: 4,9 => CTR => E3: 8
* INC # E3: 8 => UNS
* INC # I3: 4,9 => UNS
* DIS # D1: 7,9 => CTR => D1: 2,8
* INC # D1: 2,8 => UNS
* DIS # E2: 7,9 => CTR => E2: 4
* INC # E2: 4 => UNS
* INC # B2: 7,9 => UNS
* DIS # B2: 4 => CTR => B2: 7,9
* INC # D5: 7,9 => UNS
* DIS # D5: 8 => CTR => D5: 7,9
* INC # I1: 4,8 => UNS
* INC # I3: 4,8 => UNS
* INC # I4: 1,7 => UNS
* DIS # I4: 8 => CTR => I4: 1,7
* DIS # I4: 1,8 => CTR => I4: 7
* PRF # I4: 7 => SOL
* PRF # I5: 1,8 => SOL
* DIS # I5: 7 => CTR => I5: 1,8
* INC # B6: 1,8 => UNS
* DIS # B6: 2 => CTR => B6: 1,8
* DIS # B7: 2,8 => CTR => B7: 1,6
* INC # B7: 1,6 => UNS
* PRF # C7: 2,8 => SOL
* DIS # C7: 7 => CTR => C7: 2,8
* DIS # B9: 2,8 => CTR => B9: 5,6
* INC # B9: 5,6 => UNS
* INC # D9: 2,8 => UNS
* DIS # D9: 5 => CTR => D9: 2,8
* DIS # C6: 2,8 => CTR => C6: 7
* PRF # C6: 7 => SOL
* DIS # D9: 2,5 => CTR => D9: 8
* PRF # D9: 8 => SOL
* INC # B8: 2,5 => UNS
* PRF # B8: 1 => SOL
* INC # I8: 1,4 => UNS
* PRF # I8: 2 => SOL
* INC # I7: 2,6 => UNS
* PRF # I7: 1 => SOL
* DIS # B9: 2,6 => CTR => B9: 5,8
* INC # B9: 5,8 => UNS
* CNT  44 HDP CHAINS /  44 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B1: 4,9 => CTR => B1: 7
* DIS B1: 7 # E3: 4,9 => CTR => E3: 8
* INC B1: 7 + E3: 8 # I4: 1,7 => UNS
* DIS B1: 7 + E3: 8 # I4: 8 => CTR => I4: 1,7
* INC B1: 7 + E3: 8 + I4: 1,7 # B6: 1,8 => UNS
* DIS B1: 7 + E3: 8 + I4: 1,7 # B6: 2 => CTR => B6: 1,8
* PRF B1: 7 + E3: 8 + I4: 1,7 + B6: 1,8 # C7: 2,8 => SOL
* STA B1: 7 + E3: 8 + I4: 1,7 + B6: 1,8 + C7: 2,8
* CNT   7 HDP CHAINS /   7 HYP OPENED