Analysis of zz-www.sudokuoftheday.co.uk-20060717-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: .372.....86.........2..39.....71...5....2......19.4.....8..7.2..2.6.945.41..3.8.. initial

Autosolve

position: .372.....86.4......428.39.....71...5...32......19.4.....8147.2.72368945141.5328.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 5,9 => CTR => A1: 1
* PRF # A1: 1 => SOL
* DIS # E2: 5,9 => CTR => E2: 7
* PRF # E2: 7 => SOL
* DIS # C5: 4,6 => CTR => C5: 5,9
* PRF # A1: 1,5 => SOL
* DIS # A1: 9 => CTR => A1: 1,5
* PRF # F1: 1,5 => SOL
* DIS # F1: 6 => CTR => F1: 1,5
* PRF # G2: 1,5 => SOL
* DIS # H3: 6,7 => CTR => H3: 1
* PRF # H3: 1 => SOL
* PRF # E3: 6,7 => SOL
* DIS # E3: 5 => CTR => E3: 6,7
* DIS # I5: 6,7 => CTR => I5: 4,8,9
* DIS # G4: 6 => CTR => G4: 2,3
* DIS # B5: 8,9 => CTR => B5: 5,7
* PRF # H4: 8,9 => SOL
* PRF # F5: 6,8 => SOL
* DIS # F5: 5 => CTR => F5: 6,8
* PRF # H4: 6,8 => SOL
* DIS # F5: 5,6 => CTR => F5: 8
* PRF # F5: 8 => SOL
* DIS # E1: 5,6 => CTR => E1: 9
* PRF # E1: 9 => SOL
* PRF # E3: 5,6 => SOL
* DIS # E3: 7 => CTR => E3: 5,6
* DIS # A7: 6 => CTR => A7: 5,9
* DIS # B5: 5,9 => CTR => B5: 7,8
* PRF # A7: 6,9 => SOL
* DIS # A7: 5 => CTR => A7: 6,9
* DIS # C4: 6,9 => CTR => C4: 4
* DIS # C5: 6,9 => CTR => C5: 4,5
* DIS # I7: 9 => CTR => I7: 3,6
* CNT  34 HDP CHAINS /  58 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 # A1: 5,9 => CTR => A1: 1
* PRF A1: 1 => SOL
* STA A1: 1
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

.372.....86.........2..39.....71...5....2......19.4.....8..7.2..2.6.945.41..3.8.. initial
.372.....86.4......428.39.....71...5...32......19.4.....8147.2.72368945141.5328.. autosolve
137295648869471532542863917394716285675328194281954763958147326723689451416532879 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
C2: 5,9
A3: 1,5
F2: 1,5
H1: 4,8
I1: 4,8
I3: 6,7
A4: 2,3
B4: 8,9
A6: 2,3
F4: 6,8
E6: 5,6
B7: 5,9
C9: 6,9
G7: 3,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,A3: 1.. / A1 = 1  =>  0 pairs (*) / A3 = 1  =>  0 pairs (X)
F1,F2: 1.. / F1 = 1  =>  0 pairs (X) / F2 = 1  => 15 pairs (_)
G5,H5: 1.. / G5 = 1  => 15 pairs (_) / H5 = 1  =>  0 pairs (X)
A3,H3: 1.. / A3 = 1  =>  0 pairs (X) / H3 = 1  =>  0 pairs (_)
G2,I2: 2.. / G2 = 2  => 22 pairs (_) / I2 = 2  => 14 pairs (_)
A4,A6: 2.. / A4 = 2  => 17 pairs (_) / A6 = 2  => 12 pairs (_)
A4,G4: 2.. / A4 = 2  => 17 pairs (_) / G4 = 2  => 12 pairs (_)
I2,I6: 2.. / I2 = 2  => 14 pairs (_) / I6 = 2  => 22 pairs (_)
A4,A6: 3.. / A4 = 3  => 12 pairs (_) / A6 = 3  => 17 pairs (_)
G7,I7: 3.. / G7 = 3  => 20 pairs (_) / I7 = 3  => 22 pairs (_)
H1,I1: 4.. / H1 = 4  => 15 pairs (_) / I1 = 4  => 12 pairs (_)
C4,C5: 4.. / C4 = 4  => 16 pairs (_) / C5 = 4  =>  0 pairs (X)
C4,H4: 4.. / C4 = 4  => 16 pairs (_) / H4 = 4  =>  0 pairs (X)
I1,I5: 4.. / I1 = 4  => 12 pairs (_) / I5 = 4  => 15 pairs (_)
G1,G2: 5.. / G1 = 5  => 18 pairs (_) / G2 = 5  =>  0 pairs (*)
F5,E6: 5.. / F5 = 5  =>  0 pairs (X) / E6 = 5  =>  0 pairs (_)
A7,B7: 5.. / A7 = 5  =>  0 pairs (X) / B7 = 5  =>  0 pairs (_)
A3,E3: 5.. / A3 = 5  =>  0 pairs (*) / E3 = 5  =>  0 pairs (X)
B6,E6: 5.. / B6 = 5  =>  0 pairs (X) / E6 = 5  =>  0 pairs (_)
C2,C5: 5.. / C2 = 5  =>  0 pairs (X) / C5 = 5  =>  0 pairs (_)
A7,C9: 6.. / A7 = 6  =>  0 pairs (X) / C9 = 6  => 20 pairs (_)
A5,A7: 6.. / A5 = 6  => 20 pairs (_) / A7 = 6  =>  0 pairs (X)
E2,E3: 7.. / E2 = 7  =>  0 pairs (*) / E3 = 7  =>  0 pairs (X)
B5,B6: 7.. / B5 = 7  => 16 pairs (_) / B6 = 7  =>  0 pairs (X)
H9,I9: 7.. / H9 = 7  => 17 pairs (_) / I9 = 7  => 19 pairs (_)
H1,I1: 8.. / H1 = 8  => 12 pairs (_) / I1 = 8  => 15 pairs (_)
F4,F5: 8.. / F4 = 8  =>  0 pairs (X) / F5 = 8  =>  0 pairs (_)
A1,C2: 9.. / A1 = 9  =>  0 pairs (X) / C2 = 9  =>  0 pairs (_)
E1,E2: 9.. / E1 = 9  =>  0 pairs (*) / E2 = 9  =>  0 pairs (X)
A1,E1: 9.. / A1 = 9  =>  0 pairs (X) / E1 = 9  =>  0 pairs (_)
C2,E2: 9.. / C2 = 9  =>  0 pairs (*) / E2 = 9  =>  0 pairs (X)
* DURATION: 0:00:35.571432  START: 00:45:07.332055  END: 00:45:42.903487 2019-05-01
* CP COUNT: (31)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A6,B4,B7,C2,C9,E6,F2,F4,G7,H1,I1,I3)
* .372.....86.4......428.39.....71...5...32......19.4.....8147.2.72368945141.5328..
* PAIR C2: 5,9 BLK 1
A1: 5,9,1                                # reduction candidate for 5,9
A1: 5,9 => CTR
* .372.....86.4.....1428539.....71...5...325....51964...598147.2.7236894514165328..
A1: 1 => SOLVED
* 137295648869471532542863917394716285675328194281954763958147326723689451416532879
* PAIR C2: 5,9 ROW 2
E2: 5,9,7                                # reduction candidate for 5,9
E2: 5,9 => CTR
* .372.....86.4.....542873916...71...5..532.1....1954....58147.2.72368945141.5328..
E2: 7 => SOLVED
* 137295648869471532542863917394716285675328194281954763958147326723689451416532879
* PAIR C2: 5,9 COL C
C5: 5,9,4,6                              # reduction candidate for 5,9
C5: 4,6 => CTR
* .372.....865491....428.39.....71...5...32......19.4.....8147.2.72368945141.5328..
C5: 5,9                                  # 20 pairs
* PAIR A3: 1,5 BLK 1
A1: 1,5,9                                # reduction candidate for 1,5
A1: 1,5 => SOLVED
* 137295648869471532542863917394716285675328194281954763958147326723689451416532879
A1: 9 => CTR
* 9372.....865491....428.39.....71...5...32......19.4.....8147.2.72368945141.5328..
* PAIR F2: 1,5 BLK 2
F1: 1,5,6                                # reduction candidate for 1,5
F1: 1,5 => SOLVED
* 137295648869471532542863917394716285675328194281954763958147326723689451416532879
F1: 6 => CTR
* .372.6...86.4.1....428.39.....718..5...325....51964...598147.2.72368945141.5328..
* PAIR F2: 1,5 ROW 2
G2: 1,5,2,3,7                            # reduction candidate for 1,5
G2: 1,5 => SOLVED
* 137295648869471532542863917394716285675328194281954763958147326723689451416532879
G2: 2,3,7                                # 18 pairs
* PAIR H1: 4,8 COL H
H4: 4,8,3,6,9                            # reduction candidate for 4,8
H4: 4,8                                  # 17 pairs
H5: 4,8,1,6,7,9                          # reduction candidate for 4,8
H5: 4,8                                  # 17 pairs
* PAIR I1: 4,8 COL I
I5: 4,8,6,7,9                            # reduction candidate for 4,8
I5: 6,7,9                                # 21 pairs
I5: 4,8                                  # 16 pairs
* PAIR I3: 6,7 BLK 3
H3: 6,7,1                                # reduction candidate for 6,7
H3: 6,7 => CTR
* .372.....86.4.....1428539.....71...5...325....51964...598147.2.7236894514165328..
H3: 1 => SOLVED
* 137295648869471532542863917394716285675328194281954763958147326723689451416532879
* PAIR I3: 6,7 ROW 3
E3: 6,7,5                                # reduction candidate for 6,7
E3: 6,7 => SOLVED
* 137295648869471532542863917394716285675328194281954763958147326723689451416532879
E3: 5 => CTR
* .372.....86.47.....428539.....71...5...325....51964...598147.2.7236894514165328..
* PAIR I3: 6,7 COL I
I5: 6,7,4,8,9                            # reduction candidate for 6,7
I5: 6,7 => CTR
* .372...8486.4..7325428739.....71...56..32...7.71954.68..8147623723689451416532879
I5: 4,8,9                                # 14 pairs
I6: 6,7,2,3,8                            # reduction candidate for 6,7
I6: 6,7                                  # 23 pairs
I9: 6,7,9                                # reduction candidate for 6,7
I9: 6,7                                  # 17 pairs
* PAIR A4: 2,3 ROW 4
G4: 2,3,6                                # reduction candidate for 2,3
G4: 6 => CTR
* .372.6...86.4.1.73.428739.62.4718635...325...351964.82..814732.72368945141.5328..
G4: 2,3                                  # 15 pairs
* PAIR B4: 8,9 BLK 4
B5: 8,9,5,7                              # reduction candidate for 8,9
B5: 8,9 => CTR
* 13729....869471532542863917..471...56.5328174.71954...958147.2.72368945141653289.
B5: 5,7                                  # 15 pairs
* PAIR B4: 8,9 ROW 4
H4: 8,9,3,4,6                            # reduction candidate for 8,9
H4: 8,9 => SOLVED
* 137295648869471532542863917394716285675328194281954763958147326723689451416532879
H4: 3,4,6                                # 15 pairs
* PAIR A6: 2,3 ROW 6
G6: 2,3,6,7                              # reduction candidate for 2,3
G6: 2,3                                  # 22 pairs
I6: 2,3,6,7,8                            # reduction candidate for 2,3
I6: 2,3                                  # 18 pairs
* PAIR F4: 6,8 BLK 5
F5: 6,8,5                                # reduction candidate for 6,8
F5: 6,8 => SOLVED
* 137295648869471532542863917394716285675328194281954763958147326723689451416532879
F5: 5 => CTR
* .372.....86.4......428.39.....718..5...325....51964...598147.2.72368945141.5328..
* PAIR F4: 6,8 ROW 4
H4: 6,8,3,4,9                            # reduction candidate for 6,8
H4: 6,8 => SOLVED
* 137295648869471532542863917394716285675328194281954763958147326723689451416532879
H4: 3,4,9                                # 14 pairs
* PAIR E6: 5,6 BLK 5
F5: 5,6,8                                # reduction candidate for 5,6
F5: 5,6 => CTR
* .372.....86.4.....5428.391..9.718..56..32......1954....58147.2.72368945141.5328..
F5: 8 => SOLVED
* 137295648869471532542863917394716285675328194281954763958147326723689451416532879
* PAIR E6: 5,6 COL E
E1: 5,6,9                                # reduction candidate for 5,6
E1: 5,6 => CTR
* 9372.....865491....428.39.....71...5...32......19.4.....8147.2.72368945141.5328..
E1: 9 => SOLVED
* 137295648869471532542863917394716285675328194281954763958147326723689451416532879
E3: 5,6,7                                # reduction candidate for 5,6
E3: 5,6 => SOLVED
* 137295648869471532542863917394716285675328194281954763958147326723689451416532879
E3: 7 => CTR
* .372.....86.4.....542873916...71...5..532.1....1954....58147.2.72368945141.5328..
* PAIR B7: 5,9 BLK 7
A7: 5,9,6                                # reduction candidate for 5,9
A7: 6 => CTR
* 9372.....865491....428.39.....71...5...32......19.4...6581473297236894514195328..
A7: 5,9                                  # 20 pairs
* PAIR B7: 5,9 COL B
B5: 5,9,7,8                              # reduction candidate for 5,9
B5: 5,9 => CTR
* 1372956..86.4.....5428.391..8.716..5..53281...71954....58147.2.7236894514165328..
B5: 7,8                                  # 15 pairs
* PAIR C9: 6,9 BLK 7
A7: 6,9,5                                # reduction candidate for 6,9
A7: 6,9 => SOLVED
* 137295648869471532542863917394716285675328194281954763958147326723689451416532879
A7: 5 => CTR
* 9372.....865491....428.39.....71...56..32......19.4...598147.2.7236894514165328..
* PAIR C9: 6,9 ROW 9
H9: 6,9,7                                # reduction candidate for 6,9
H9: 6,9                                  # 19 pairs
I9: 6,9,7                                # reduction candidate for 6,9
I9: 6,9                                  # 17 pairs
* PAIR C9: 6,9 COL C
C4: 6,9,4                                # reduction candidate for 6,9
C4: 6,9 => CTR
* .372...84865491....428.39.....71..45..432......19.4.....8147.2.72368945141.5328..
C4: 4                                    # 16 pairs
C5: 6,9,4,5                              # reduction candidate for 6,9
C5: 6,9 => CTR
* .372.....865491....428.39.....71...5...32......19.4.....8147.2.72368945141.5328..
C5: 4,5                                  # 15 pairs
* PAIR G7: 3,6 BLK 9
I7: 3,6,9                                # reduction candidate for 3,6
I7: 9 => CTR
* 9372.....865491....428.39.....71...5...32......19.4.....81473297236894514195328..
I7: 3,6                                  # 20 pairs
* PAIR G7: 3,6 COL G
G4: 3,6,2                                # reduction candidate for 3,6
G4: 3,6                                  # 17 pairs
G6: 3,6,2,7                              # reduction candidate for 3,6
G6: 3,6                                  # 16 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060717-absurd-base-pr-000.dot
* REASONING
* DIS # A1: 5,9 => CTR => A1: 1
* PRF # A1: 1 => SOL
* DIS # E2: 5,9 => CTR => E2: 7
* PRF # E2: 7 => SOL
* DIS # C5: 4,6 => CTR => C5: 5,9
* PRF # A1: 1,5 => SOL
* DIS # A1: 9 => CTR => A1: 1,5
* PRF # F1: 1,5 => SOL
* DIS # F1: 6 => CTR => F1: 1,5
* PRF # G2: 1,5 => SOL
* DIS # H3: 6,7 => CTR => H3: 1
* PRF # H3: 1 => SOL
* PRF # E3: 6,7 => SOL
* DIS # E3: 5 => CTR => E3: 6,7
* DIS # I5: 6,7 => CTR => I5: 4,8,9
* DIS # G4: 6 => CTR => G4: 2,3
* DIS # B5: 8,9 => CTR => B5: 5,7
* PRF # H4: 8,9 => SOL
* PRF # F5: 6,8 => SOL
* DIS # F5: 5 => CTR => F5: 6,8
* PRF # H4: 6,8 => SOL
* DIS # F5: 5,6 => CTR => F5: 8
* PRF # F5: 8 => SOL
* DIS # E1: 5,6 => CTR => E1: 9
* PRF # E1: 9 => SOL
* PRF # E3: 5,6 => SOL
* DIS # E3: 7 => CTR => E3: 5,6
* DIS # A7: 6 => CTR => A7: 5,9
* DIS # B5: 5,9 => CTR => B5: 7,8
* PRF # A7: 6,9 => SOL
* DIS # A7: 5 => CTR => A7: 6,9
* DIS # C4: 6,9 => CTR => C4: 4
* DIS # C5: 6,9 => CTR => C5: 4,5
* DIS # I7: 9 => CTR => I7: 3,6
* CNT  34 HDP CHAINS /  58 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A6,B4,B7,C2,C9,E6,F2,F4,G7,H1,I1,I3)
* .372.....86.4......428.39.....71...5...32......19.4.....8147.2.72368945141.5328..
* PAIR C2: 5,9 BLK 1
A1: 5,9,1                                # reduction candidate for 5,9
A1: 5,9 => CTR
* .372.....86.4.....1428539.....71...5...325....51964...598147.2.7236894514165328..
A1: 1 => SOLVED
* 137295648869471532542863917394716285675328194281954763958147326723689451416532879
* DURATION: 0:00:02.154174  START: 00:46:21.674714  END: 00:46:23.828888 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060717-absurd-base-pr-001.dot
* REASONING
* DIS # A1: 5,9 => CTR => A1: 1
* PRF A1: 1 => SOL
* STA A1: 1
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060717, absurd

Solution

position: 137295648869471532542863917394716285675328194281954763958147326723689451416532879 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 # A1: 5,9 => CTR => A1: 1
* PRF # A1: 1 => SOL
* DIS # E2: 5,9 => CTR => E2: 7
* PRF # E2: 7 => SOL
* INC # C5: 5,9 => UNS
* DIS # C5: 4,6 => CTR => C5: 5,9
* PRF # A1: 1,5 => SOL
* DIS # A1: 9 => CTR => A1: 1,5
* PRF # F1: 1,5 => SOL
* DIS # F1: 6 => CTR => F1: 1,5
* PRF # G2: 1,5 => SOL
* INC # G2: 2,3,7 => UNS
* INC # H4: 4,8 => UNS
* INC # H5: 4,8 => UNS
* INC # I5: 4,8 => UNS
* INC # I5: 6,7,9 => UNS
* DIS # H3: 6,7 => CTR => H3: 1
* PRF # H3: 1 => SOL
* PRF # E3: 6,7 => SOL
* DIS # E3: 5 => CTR => E3: 6,7
* DIS # I5: 6,7 => CTR => I5: 4,8,9
* INC # I5: 4,8,9 => UNS
* INC # I6: 6,7 => UNS
* INC # I9: 6,7 => UNS
* INC # G4: 2,3 => UNS
* DIS # G4: 6 => CTR => G4: 2,3
* DIS # B5: 8,9 => CTR => B5: 5,7
* INC # B5: 5,7 => UNS
* PRF # H4: 8,9 => SOL
* INC # H4: 3,4,6 => UNS
* INC # G6: 2,3 => UNS
* INC # I6: 2,3 => UNS
* PRF # F5: 6,8 => SOL
* DIS # F5: 5 => CTR => F5: 6,8
* PRF # H4: 6,8 => SOL
* INC # H4: 3,4,9 => UNS
* DIS # F5: 5,6 => CTR => F5: 8
* PRF # F5: 8 => SOL
* DIS # E1: 5,6 => CTR => E1: 9
* PRF # E1: 9 => SOL
* PRF # E3: 5,6 => SOL
* DIS # E3: 7 => CTR => E3: 5,6
* INC # A7: 5,9 => UNS
* DIS # A7: 6 => CTR => A7: 5,9
* DIS # B5: 5,9 => CTR => B5: 7,8
* INC # B5: 7,8 => UNS
* PRF # A7: 6,9 => SOL
* DIS # A7: 5 => CTR => A7: 6,9
* INC # H9: 6,9 => UNS
* INC # I9: 6,9 => UNS
* DIS # C4: 6,9 => CTR => C4: 4
* INC # C4: 4 => UNS
* DIS # C5: 6,9 => CTR => C5: 4,5
* INC # C5: 4,5 => UNS
* INC # I7: 3,6 => UNS
* DIS # I7: 9 => CTR => I7: 3,6
* INC # G4: 3,6 => UNS
* INC # G6: 3,6 => UNS
* CNT  58 HDP CHAINS /  58 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 5,9 => CTR => A1: 1
* PRF A1: 1 => SOL
* STA A1: 1
* CNT   2 HDP CHAINS /   1 HYP OPENED