Analysis of zz-www.sudokuoftheday.co.uk-20060316-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: .6.....4..47......95..1.6.3.7...3.8.5......9489....7.1..98.61.......1.6..1.37.... initial

Autosolve

position: .6.....4..47....1.95..1.6.3.7...3.865......9489....7.1..98.61...8...1.6.61.37.... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A7: 2,3 => SOL
* DIS # A8: 2,3 => CTR => A8: 4,7
* DIS # H7: 2,7 => CTR => H7: 3,5
* DIS # C6: 4,6 => CTR => C6: 2,3
* DIS # D5: 7 => CTR => D5: 1,6
* DIS # H6: 2,5 => CTR => H6: 3
* PRF # H6: 3 => SOL
* DIS # G1: 2,5 => CTR => G1: 8,9
* DIS # G2: 2,5 => CTR => G2: 8,9
* DIS # G8: 2,5 => CTR => G8: 3,4,9
* DIS # G9: 2,5 => CTR => G9: 4,8,9
* DIS # H6: 5 => CTR => H6: 2,3
* DIS # G8: 4,5,9 => CTR => G8: 2,3
* PRF # A7: 2,3 => SOL
* DIS # A8: 2,3 => CTR => A8: 4,7
* PRF # H7: 5,7 => SOL
* PRF # H7: 2,5 => SOL
* DIS # G8: 2,5 => CTR => G8: 3,4,9
* DIS # I8: 2,5 => CTR => I8: 7,9
* DIS # G9: 2,5 => CTR => G9: 4,8,9
* DIS # I9: 2,5 => CTR => I9: 8,9
* DIS # F9: 2,5 => CTR => F9: 4,9
* DIS # H6: 2,5 => CTR => H6: 3
* PRF # H6: 3 => SOL
* CNT  24 HDP CHAINS /  65 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # A7: 2,3 => SOL
* STA A7: 2,3
* CNT   1 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

.6.....4..47......95..1.6.3.7...3.8.5......9489....7.1..98.61.......1.6..1.37.... initial
.6.....4..47....1.95..1.6.3.7...3.865......9489....7.1..98.61...8...1.6.61.37.... autosolve
163795842247638915958412673471923586536187294892564731329846157784251369615379428 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
A2: 2,3
C3: 2,8
H3: 2,7
B5: 2,3
C5: 1,6
E5: 6,8
F5: 7,8
G4: 2,5
G5: 2,3
B7: 2,3
H9: 2,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,C1: 1.. / A1 = 1  => 12 pairs (_) / C1 = 1  => 15 pairs (_)
D4,D5: 1.. / D4 = 1  =>  0 pairs (X) / D5 = 1  =>  8 pairs (_)
C5,D5: 1.. / C5 = 1  =>  0 pairs (X) / D5 = 1  =>  8 pairs (_)
A1,A4: 1.. / A1 = 1  => 12 pairs (_) / A4 = 1  => 15 pairs (_)
B5,G5: 2.. / B5 = 2  =>  0 pairs (X) / G5 = 2  =>  0 pairs (_)
B5,B7: 2.. / B5 = 2  =>  0 pairs (X) / B7 = 2  =>  0 pairs (_)
E1,E2: 3.. / E1 = 3  => 11 pairs (_) / E2 = 3  => 13 pairs (_)
B5,C6: 3.. / B5 = 3  =>  0 pairs (*) / C6 = 3  =>  0 pairs (X)
G5,H6: 3.. / G5 = 3  =>  0 pairs (X) / H6 = 3  =>  0 pairs (_)
H7,G8: 3.. / H7 = 3  =>  0 pairs (X) / G8 = 3  =>  0 pairs (_)
A2,E2: 3.. / A2 = 3  => 11 pairs (_) / E2 = 3  => 13 pairs (_)
B5,G5: 3.. / B5 = 3  =>  0 pairs (*) / G5 = 3  =>  0 pairs (X)
C6,H6: 3.. / C6 = 3  =>  0 pairs (X) / H6 = 3  =>  0 pairs (_)
B5,B7: 3.. / B5 = 3  =>  0 pairs (*) / B7 = 3  =>  0 pairs (X)
G5,G8: 3.. / G5 = 3  =>  0 pairs (X) / G8 = 3  =>  0 pairs (_)
H6,H7: 3.. / H6 = 3  =>  0 pairs (*) / H7 = 3  =>  0 pairs (X)
D3,F3: 4.. / D3 = 4  => 11 pairs (_) / F3 = 4  => 12 pairs (_)
G8,G9: 4.. / G8 = 4  =>  0 pairs (X) / G9 = 4  => 12 pairs (_)
A7,E7: 4.. / A7 = 4  => 16 pairs (_) / E7 = 4  => 17 pairs (_)
G4,H6: 5.. / G4 = 5  => 12 pairs (_) / H6 = 5  =>  0 pairs (X)
C8,C9: 5.. / C8 = 5  => 12 pairs (_) / C9 = 5  => 15 pairs (_)
D2,E2: 6.. / D2 = 6  => 12 pairs (_) / E2 = 6  => 10 pairs (_)
C5,C6: 6.. / C5 = 6  =>  8 pairs (_) / C6 = 6  =>  0 pairs (X)
I1,H3: 7.. / I1 = 7  =>  0 pairs (X) / H3 = 7  => 11 pairs (_)
D5,F5: 7.. / D5 = 7  =>  0 pairs (X) / F5 = 7  => 10 pairs (_)
A7,A8: 7.. / A7 = 7  =>  0 pairs (X) / A8 = 7  => 11 pairs (_)
A8,I8: 7.. / A8 = 7  => 11 pairs (_) / I8 = 7  =>  0 pairs (X)
H3,H7: 7.. / H3 = 7  => 11 pairs (_) / H7 = 7  =>  0 pairs (X)
C1,C3: 8.. / C1 = 8  => 10 pairs (_) / C3 = 8  => 10 pairs (_)
E5,F5: 8.. / E5 = 8  => 10 pairs (_) / F5 = 8  =>  0 pairs (X)
G9,I9: 8.. / G9 = 8  =>  0 pairs (X) / I9 = 8  => 11 pairs (_)
C3,F3: 8.. / C3 = 8  => 10 pairs (_) / F3 = 8  => 10 pairs (_)
D4,E4: 9.. / D4 = 9  =>  8 pairs (_) / E4 = 9  => 11 pairs (_)
* DURATION: 0:00:31.678973  START: 19:50:25.020085  END: 19:50:56.699058 2019-04-30
* CP COUNT: (33)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B5,B7,C3,C5,E5,F5,G4,G5,H3,H9)
* .6.....4..47....1.95..1.6.3.7...3.865......9489....7.1..98.61...8...1.6.61.37....
* PAIR A2: 2,3 BLK 1
A1: 2,3,1                                # reduction candidate for 2,3
A1: 2,3                                  # 15 pairs
C1: 2,3,1,8                              # reduction candidate for 2,3
C1: 2,3                                  # 12 pairs
* PAIR A2: 2,3 ROW 2
E2: 2,3,5,6,8,9                          # reduction candidate for 2,3
E2: 2,3                                  # 13 pairs
E2: 5,6,8,9                              # 11 pairs
* PAIR A2: 2,3 COL A
A7: 2,3,4,7                              # reduction candidate for 2,3
A7: 2,3 => SOLVED
* 163795842247638915958412673471923586536187294892564731329846157784251369615379428
A7: 4,7                                  # 12 pairs
A8: 2,3,4,7                              # reduction candidate for 2,3
A8: 2,3 => CTR
* 16.....4..47....1.95..1.67347...3.865......9489....7.172984613538...1.6761.37..2.
A8: 4,7                                  # 12 pairs
* PAIR C3: 2,8 BLK 1
C1: 2,8,1,3                              # reduction candidate for 2,8
C1: 2,8                                  # 14 pairs
C1: 1,3                                  # 12 pairs
* PAIR C3: 2,8 ROW 3
F3: 2,8,4,7                              # reduction candidate for 2,8
F3: 4,7                                  # 11 pairs
F3: 2,8                                  # 11 pairs
* PAIR H3: 2,7 BLK 3
I1: 2,7,5,8,9                            # reduction candidate for 2,7
I1: 2,7                                  # 12 pairs
I1: 5,8,9                                # 11 pairs
* PAIR H3: 2,7 ROW 3
D3: 2,7,4                                # reduction candidate for 2,7
D3: 2,7                                  # 12 pairs
F3: 2,7,4,8                              # reduction candidate for 2,7
F3: 2,7                                  # 11 pairs
* PAIR H3: 2,7 COL H
H7: 2,7,3,5                              # reduction candidate for 2,7
H7: 2,7 => CTR
* .63....4.247.3..1.958.1.6.3.7...358653....29489....7313298.61...8...136.61.37.458
H7: 3,5                                  # 12 pairs
* PAIR B5: 2,3 BLK 4
C6: 2,3,4,6                              # reduction candidate for 2,3
C6: 4,6 => CTR
* 163....4224763.915958.1.673472193586531768294896...7313298461..784..1369615379428
C6: 2,3                                  # 11 pairs
* PAIR C5: 1,6 ROW 5
D5: 1,6,7                                # reduction candidate for 1,6
D5: 7 => CTR
* 163....4.24763.81.958.1.6.3472193586531768294896...7313298461..784..1369615379428
D5: 1,6                                  # 10 pairs
* PAIR E5: 6,8 COL E
E2: 6,8,2,3,5,9                          # reduction candidate for 6,8
E2: 6,8                                  # 12 pairs
E2: 2,3,5,9                              # 12 pairs
* PAIR F5: 7,8 COL F
F1: 7,8,2,5,9                            # reduction candidate for 7,8
F1: 7,8                                  # 12 pairs
F3: 7,8,2,4                              # reduction candidate for 7,8
F3: 7,8                                  # 12 pairs
* PAIR G4: 2,5 BLK 6
H6: 2,5,3                                # reduction candidate for 2,5
H6: 2,5 => CTR
* .6.....4..47....1.95..1.6.3.7...3.865.....394893...7.1.398.61...8...1.6.61.37....
H6: 3 => SOLVED
* 163795842247638915958412673471923586536187294892564731329846157784251369615379428
* PAIR G4: 2,5 ROW 4
D4: 2,5,1,4,9                            # reduction candidate for 2,5
D4: 2,5                                  # 12 pairs
E4: 2,5,4,9                              # reduction candidate for 2,5
E4: 2,5                                  # 12 pairs
* PAIR G4: 2,5 COL G
G1: 2,5,8,9                              # reduction candidate for 2,5
G1: 2,5 => CTR
* .6.....4..47....1.95..1.6.3.7...3.8652....394893...7.1.398.61...8...1.6.61.37....
G1: 8,9                                  # 12 pairs
G2: 2,5,8,9                              # reduction candidate for 2,5
G2: 2,5 => CTR
* .6.....4..47....1.95..1.6.3.7...3.8652....394893...7.1.398.61...8...1.6.61.37....
G2: 8,9                                  # 12 pairs
G8: 2,5,3,4,9                            # reduction candidate for 2,5
G8: 2,5 => CTR
* .6.....4..47....1.95..1.6.3.7...3.865.....394893...7.1.398.61...8...1.6.61.37.4.8
G8: 3,4,9                                # 11 pairs
G9: 2,5,4,8,9                            # reduction candidate for 2,5
G9: 2,5 => CTR
* .6.....4..47....1.95..1.6.3.7...3.865.....394893...7.1.398.61...8...146961.379..8
G9: 4,8,9                                # 11 pairs
* PAIR G5: 2,3 BLK 6
H6: 2,3,5                                # reduction candidate for 2,3
H6: 5 => CTR
* .6.....4..47....1.95..1.6.3.7...3.865.....394893...751.398.61...8...1.6.61.37..2.
H6: 2,3                                  # 12 pairs
* PAIR G5: 2,3 COL G
G8: 2,3,4,5,9                            # reduction candidate for 2,3
G8: 4,5,9 => CTR
* .6.....4..47....1.95..1.6.3.7...3.865.....394893...7.1.398.61...8...1.6.61.37....
G8: 2,3                                  # 17 pairs
* PAIR B7: 2,3 BLK 7
A7: 2,3,4,7                              # reduction candidate for 2,3
A7: 2,3 => SOLVED
* 163795842247638915958412673471923586536187294892564731329846157784251369615379428
A7: 4,7                                  # 12 pairs
A8: 2,3,4,7                              # reduction candidate for 2,3
A8: 2,3 => CTR
* 16.....4..47....1.95..1.67347...3.865......9489....7.172984613538...1.6761.37..2.
A8: 4,7                                  # 12 pairs
C8: 2,3,4,5                              # reduction candidate for 2,3
C8: 2,3                                  # 19 pairs
* PAIR B7: 2,3 ROW 7
H7: 2,3,5,7                              # reduction candidate for 2,3
H7: 5,7 => SOLVED
* 163795842247638915958412673471923586536187294892564731329846157784251369615379428
H7: 2,3                                  # 15 pairs
* PAIR H9: 2,5 BLK 9
H7: 2,5,3,7                              # reduction candidate for 2,5
H7: 2,5 => SOLVED
* 163795842247638915958412673471923586536187294892564731329846157784251369615379428
H7: 3,7                                  # 12 pairs
I7: 2,5,7                                # reduction candidate for 2,5
I7: 2,5                                  # 15 pairs
G8: 2,5,3,4,9                            # reduction candidate for 2,5
G8: 2,5 => CTR
* .6.....4..47....1.95..1.6.3.7...3.865.....394893...7.1.398.61...8...1.6.61.37.4.8
G8: 3,4,9                                # 11 pairs
I8: 2,5,7,9                              # reduction candidate for 2,5
I8: 2,5 => CTR
* .6.....4..47....1.95..1.673.7...3.865.....394893...7.1.398.61..78...1.6.61.37....
I8: 7,9                                  # 12 pairs
G9: 2,5,4,8,9                            # reduction candidate for 2,5
G9: 2,5 => CTR
* .6.....4..47....1.95..1.6.3.7...3.865.....394893...7.1.398.61...8...146961.379..8
G9: 4,8,9                                # 11 pairs
I9: 2,5,8,9                              # reduction candidate for 2,5
I9: 2,5 => CTR
* .6.....4..47....1.95..1.6.3.7...3.865.....394893...7.1.398.61...8...146961.3798..
I9: 8,9                                  # 12 pairs
* PAIR H9: 2,5 ROW 9
C9: 2,5,4                                # reduction candidate for 2,5
C9: 2,5                                  # 14 pairs
F9: 2,5,4,9                              # reduction candidate for 2,5
F9: 2,5 => CTR
* .6.....4..47....1.95..1.673.7...3.865.....394893...7.1..98.61...8...1.6.61.37....
F9: 4,9                                  # 12 pairs
* PAIR H9: 2,5 COL H
H6: 2,5,3                                # reduction candidate for 2,5
H6: 2,5 => CTR
* .6.....4..47....1.95..1.6.3.7...3.865.....394893...7.1.398.61...8...1.6.61.37....
H6: 3 => SOLVED
* 163795842247638915958412673471923586536187294892564731329846157784251369615379428
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060316-absurd-base-pr-000.dot
* REASONING
* PRF # A7: 2,3 => SOL
* DIS # A8: 2,3 => CTR => A8: 4,7
* DIS # H7: 2,7 => CTR => H7: 3,5
* DIS # C6: 4,6 => CTR => C6: 2,3
* DIS # D5: 7 => CTR => D5: 1,6
* DIS # H6: 2,5 => CTR => H6: 3
* PRF # H6: 3 => SOL
* DIS # G1: 2,5 => CTR => G1: 8,9
* DIS # G2: 2,5 => CTR => G2: 8,9
* DIS # G8: 2,5 => CTR => G8: 3,4,9
* DIS # G9: 2,5 => CTR => G9: 4,8,9
* DIS # H6: 5 => CTR => H6: 2,3
* DIS # G8: 4,5,9 => CTR => G8: 2,3
* PRF # A7: 2,3 => SOL
* DIS # A8: 2,3 => CTR => A8: 4,7
* PRF # H7: 5,7 => SOL
* PRF # H7: 2,5 => SOL
* DIS # G8: 2,5 => CTR => G8: 3,4,9
* DIS # I8: 2,5 => CTR => I8: 7,9
* DIS # G9: 2,5 => CTR => G9: 4,8,9
* DIS # I9: 2,5 => CTR => I9: 8,9
* DIS # F9: 2,5 => CTR => F9: 4,9
* DIS # H6: 2,5 => CTR => H6: 3
* PRF # H6: 3 => SOL
* CNT  24 HDP CHAINS /  65 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B5,B7,C3,C5,E5,F5,G4,G5,H3,H9)
* .6.....4..47....1.95..1.6.3.7...3.865......9489....7.1..98.61...8...1.6.61.37....
* PAIR A2: 2,3 BLK 1
A1: 2,3,1                                # reduction candidate for 2,3
A1: 2,3                                  # 15 pairs
C1: 2,3,1,8                              # reduction candidate for 2,3
C1: 2,3                                  # 12 pairs
* PAIR A2: 2,3 ROW 2
E2: 2,3,5,6,8,9                          # reduction candidate for 2,3
E2: 2,3                                  # 13 pairs
E2: 5,6,8,9                              # 11 pairs
* PAIR A2: 2,3 COL A
A7: 2,3,4,7                              # reduction candidate for 2,3
A7: 2,3 => SOLVED
* 163795842247638915958412673471923586536187294892564731329846157784251369615379428
* DURATION: 0:00:03.646258  START: 19:51:29.486223  END: 19:51:33.132481 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060316-absurd-base-pr-001.dot
* REASONING
* PRF # A7: 2,3 => SOL
* STA A7: 2,3
* CNT   1 HDP CHAINS /   5 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060316, absurd

Solution

position: 163795842247638915958412673471923586536187294892564731329846157784251369615379428 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 # A1: 2,3 => UNS
* INC # C1: 2,3 => UNS
* INC # E2: 2,3 => UNS
* INC # E2: 5,6,8,9 => UNS
* PRF # A7: 2,3 => SOL
* INC # A7: 4,7 => UNS
* DIS # A8: 2,3 => CTR => A8: 4,7
* INC # A8: 4,7 => UNS
* INC # C1: 2,8 => UNS
* INC # C1: 1,3 => UNS
* INC # F3: 2,8 => UNS
* INC # F3: 4,7 => UNS
* INC # I1: 2,7 => UNS
* INC # I1: 5,8,9 => UNS
* INC # D3: 2,7 => UNS
* INC # F3: 2,7 => UNS
* DIS # H7: 2,7 => CTR => H7: 3,5
* INC # H7: 3,5 => UNS
* INC # C6: 2,3 => UNS
* DIS # C6: 4,6 => CTR => C6: 2,3
* INC # D5: 1,6 => UNS
* DIS # D5: 7 => CTR => D5: 1,6
* INC # E2: 6,8 => UNS
* INC # E2: 2,3,5,9 => UNS
* INC # F1: 7,8 => UNS
* INC # F3: 7,8 => UNS
* DIS # H6: 2,5 => CTR => H6: 3
* PRF # H6: 3 => SOL
* INC # D4: 2,5 => UNS
* INC # E4: 2,5 => UNS
* DIS # G1: 2,5 => CTR => G1: 8,9
* INC # G1: 8,9 => UNS
* DIS # G2: 2,5 => CTR => G2: 8,9
* INC # G2: 8,9 => UNS
* DIS # G8: 2,5 => CTR => G8: 3,4,9
* INC # G8: 3,4,9 => UNS
* DIS # G9: 2,5 => CTR => G9: 4,8,9
* INC # G9: 4,8,9 => UNS
* INC # H6: 2,3 => UNS
* DIS # H6: 5 => CTR => H6: 2,3
* INC # G8: 2,3 => UNS
* DIS # G8: 4,5,9 => CTR => G8: 2,3
* PRF # A7: 2,3 => SOL
* INC # A7: 4,7 => UNS
* DIS # A8: 2,3 => CTR => A8: 4,7
* INC # A8: 4,7 => UNS
* INC # C8: 2,3 => UNS
* INC # H7: 2,3 => UNS
* PRF # H7: 5,7 => SOL
* PRF # H7: 2,5 => SOL
* INC # H7: 3,7 => UNS
* INC # I7: 2,5 => UNS
* DIS # G8: 2,5 => CTR => G8: 3,4,9
* INC # G8: 3,4,9 => UNS
* DIS # I8: 2,5 => CTR => I8: 7,9
* INC # I8: 7,9 => UNS
* DIS # G9: 2,5 => CTR => G9: 4,8,9
* INC # G9: 4,8,9 => UNS
* DIS # I9: 2,5 => CTR => I9: 8,9
* INC # I9: 8,9 => UNS
* INC # C9: 2,5 => UNS
* DIS # F9: 2,5 => CTR => F9: 4,9
* INC # F9: 4,9 => UNS
* DIS # H6: 2,5 => CTR => H6: 3
* PRF # H6: 3 => SOL
* CNT  65 HDP CHAINS /  65 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 2,3 => UNS
* INC # C1: 2,3 => UNS
* INC # E2: 2,3 => UNS
* INC # E2: 5,6,8,9 => UNS
* PRF # A7: 2,3 => SOL
* STA A7: 2,3
* CNT   5 HDP CHAINS /   5 HYP OPENED