Analysis of zz-www.sudokuoftheday.co.uk-20060704-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: ....7...62.5.6...1.6.52.8...3.85..4...2....78..6..7..5.8.........3......5213..... initial

Autosolve

position: ..8.7...62.5.68.31.6.52.89..3.85..4..52....788.6..7..5.8......3..3......5213..... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 1,3 => CTR => A1: 4,9
* DIS # B2: 9 => CTR => B2: 4,7
* DIS # C7: 4,7 => CTR => C7: 9
* DIS # F1: 4,9 => CTR => F1: 1,3
* DIS # B2: 4,9 => CTR => B2: 7
* DIS # D5: 4,9 => CTR => D5: 1,6
* DIS # D6: 4,9 => CTR => D6: 1,2
* DIS # D7: 4,9 => CTR => D7: 1,2,6,7
* DIS # D8: 4,9 => CTR => D8: 1,2,6,7
* DIS # F1: 4,9 => CTR => F1: 1,3
* DIS # H7: 2,5 => CTR => H7: 1,6
* DIS # H8: 2,5 => CTR => H8: 1,6,8
* DIS # B2: 9 => CTR => B2: 4,7
* DIS # G9: 9 => CTR => G9: 4,7
* DIS # I9: 9 => CTR => I9: 4,7
* DIS # A4: 7,9 => CTR => A4: 1
* PRF # A4: 1 => SOL
* DIS # C7: 4 => CTR => C7: 7,9
* DIS # G4: 2,9 => CTR => G4: 1,6
* DIS # G6: 2,9 => CTR => G6: 1,3
* PRF # F4: 2,9 => SOL
* DIS # F4: 1,6 => CTR => F4: 2,9
* DIS # I8: 4 => CTR => I8: 2,9
* DIS # G4: 1,2 => CTR => G4: 6,9
* DIS # G6: 1,2 => CTR => G6: 3,9
* DIS # D6: 4,9 => CTR => D6: 1,2
* CNT  26 HDP CHAINS /  55 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: 1,3 => CTR => A1: 4,9
* DIS A1: 4,9 # B2: 9 => CTR => B2: 4,7
* DIS A1: 4,9 + B2: 4,7 # C7: 4,7 => CTR => C7: 9
* PRF A1: 4,9 + B2: 4,7 + C7: 9 => SOL
* STA A1: 4,9 + B2: 4,7 + C7: 9
* CNT   4 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

....7...62.5.6...1.6.52.8...3.85..4...2....78..6..7..5.8.........3......5213..... initial
..8.7...62.5.68.31.6.52.89..3.85..4..52....788.6..7..5.8......3..3......5213..... autosolve
918473256275968431364521897137852649452639178896147325789214563643785912521396784 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (12)
A3: 1,3
C3: 4,7
D2: 4,9
F3: 1,3
G1: 2,5
H1: 2,5
G2: 4,7
I3: 4,7
C4: 7,9
I4: 2,9
H6: 1,2
H9: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A3,F3: 1.. / A3 = 1  =>  0 pairs (X) / F3 = 1  => 16 pairs (_)
B1,B6: 1.. / B1 = 1  => 16 pairs (_) / B6 = 1  =>  0 pairs (X)
G1,H1: 2.. / G1 = 2  => 10 pairs (_) / H1 = 2  =>  0 pairs (X)
F4,D6: 2.. / F4 = 2  =>  0 pairs (*) / D6 = 2  =>  0 pairs (X)
I4,I8: 2.. / I4 = 2  =>  0 pairs (X) / I8 = 2  =>  0 pairs (_)
A1,A3: 3.. / A1 = 3  =>  0 pairs (X) / A3 = 3  => 16 pairs (_)
F1,F3: 3.. / F1 = 3  => 16 pairs (_) / F3 = 3  =>  0 pairs (X)
E5,E6: 3.. / E5 = 3  => 12 pairs (_) / E6 = 3  =>  0 pairs (X)
G5,G6: 3.. / G5 = 3  =>  0 pairs (X) / G6 = 3  => 12 pairs (_)
A1,F1: 3.. / A1 = 3  =>  0 pairs (X) / F1 = 3  => 16 pairs (_)
A3,F3: 3.. / A3 = 3  => 16 pairs (_) / F3 = 3  =>  0 pairs (X)
E5,G5: 3.. / E5 = 3  => 12 pairs (_) / G5 = 3  =>  0 pairs (X)
E6,G6: 3.. / E6 = 3  =>  0 pairs (X) / G6 = 3  => 12 pairs (_)
G2,I3: 4.. / G2 = 4  => 13 pairs (_) / I3 = 4  =>  0 pairs (X)
A5,B6: 4.. / A5 = 4  => 13 pairs (_) / B6 = 4  => 19 pairs (_)
C3,I3: 4.. / C3 = 4  => 13 pairs (_) / I3 = 4  =>  0 pairs (X)
C3,C7: 4.. / C3 = 4  => 13 pairs (_) / C7 = 4  =>  0 pairs (X)
G1,H1: 5.. / G1 = 5  =>  0 pairs (X) / H1 = 5  => 10 pairs (_)
F7,F8: 5.. / F7 = 5  => 12 pairs (_) / F8 = 5  => 12 pairs (_)
G4,G5: 6.. / G4 = 6  => 12 pairs (_) / G5 = 6  =>  0 pairs (X)
A7,A8: 6.. / A7 = 6  => 13 pairs (_) / A8 = 6  => 12 pairs (_)
F4,G4: 6.. / F4 = 6  =>  0 pairs (X) / G4 = 6  => 12 pairs (_)
F9,H9: 6.. / F9 = 6  => 12 pairs (_) / H9 = 6  => 12 pairs (_)
B2,C3: 7.. / B2 = 7  => 13 pairs (_) / C3 = 7  =>  0 pairs (X)
G2,I3: 7.. / G2 = 7  =>  0 pairs (X) / I3 = 7  => 13 pairs (_)
A4,C4: 7.. / A4 = 7  =>  0 pairs (X) / C4 = 7  => 19 pairs (_)
D7,D8: 7.. / D7 = 7  => 13 pairs (_) / D8 = 7  => 13 pairs (_)
G9,I9: 7.. / G9 = 7  => 13 pairs (_) / I9 = 7  =>  0 pairs (X)
B2,G2: 7.. / B2 = 7  => 13 pairs (_) / G2 = 7  =>  0 pairs (X)
C3,I3: 7.. / C3 = 7  =>  0 pairs (X) / I3 = 7  => 13 pairs (_)
B2,B8: 7.. / B2 = 7  => 13 pairs (_) / B8 = 7  =>  0 pairs (X)
G2,G9: 7.. / G2 = 7  =>  0 pairs (X) / G9 = 7  => 13 pairs (_)
I3,I9: 7.. / I3 = 7  => 13 pairs (_) / I9 = 7  =>  0 pairs (X)
E8,E9: 8.. / E8 = 8  => 12 pairs (_) / E9 = 8  => 12 pairs (_)
H8,H9: 8.. / H8 = 8  => 12 pairs (_) / H9 = 8  => 12 pairs (_)
E8,H8: 8.. / E8 = 8  => 12 pairs (_) / H8 = 8  => 12 pairs (_)
E9,H9: 8.. / E9 = 8  => 12 pairs (_) / H9 = 8  => 12 pairs (_)
B2,D2: 9.. / B2 = 9  =>  0 pairs (X) / D2 = 9  => 14 pairs (_)
C4,C7: 9.. / C4 = 9  =>  0 pairs (X) / C7 = 9  => 19 pairs (_)
* DURATION: 0:00:45.528638  START: 00:19:11.306153  END: 00:19:56.834791 2019-05-01
* CP COUNT: (39)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C3,C4,D2,F3,G1,G2,H1,H6,H9,I3,I4)
* ..8.7...62.5.68.31.6.52.89..3.85..4..52....788.6..7..5.8......3..3......5213.....
* PAIR A3: 1,3 BLK 1
A1: 1,3,4,9                              # reduction candidate for 1,3
A1: 1,3 => CTR
* ..8.7.2562.5.68.31.6.52.89..3.852.4..52....78816..7.25.8......3..3.....25213.....
A1: 4,9                                  # 16 pairs
* PAIR C3: 4,7 BLK 1
B2: 4,7,9                                # reduction candidate for 4,7
B2: 9 => CTR
* .18973..6295468731367521894739856.42.52....788.62.7.15.847....3.73.....95213..4.7
B2: 4,7                                  # 14 pairs
* PAIR C3: 4,7 COL C
C7: 4,7,9                                # reduction candidate for 4,7
C7: 4,7 => CTR
* .18.7...62.5.68.3136.52189..3985..42.52....788.62.7.15.8......3..3......5213.....
C7: 9                                    # 19 pairs
* PAIR D2: 4,9 BLK 2
D1: 4,9,1                                # reduction candidate for 4,9
D1: 4,9                                  # 16 pairs
F1: 4,9,1,3                              # reduction candidate for 4,9
F1: 4,9 => CTR
* 3.817.2562.5.68.3116.52389..3.852.4..52....78816..7.25.8......3..3.....25213.....
F1: 1,3                                  # 16 pairs
* PAIR D2: 4,9 ROW 2
B2: 4,9,7                                # reduction candidate for 4,9
B2: 4,9 => CTR
* .18.7...6295468731367521894739856.42.52....788.62.7.15.847....3.73.....95213..4.7
B2: 7                                    # 13 pairs
* PAIR D2: 4,9 COL D
D5: 4,9,1,6                              # reduction candidate for 4,9
D5: 4,9 => CTR
* ..817...62.5.68.3116.52389..3.85..4..52....788162.7..5.8......3..3....8.52138..6.
D5: 1,6                                  # 13 pairs
D6: 4,9,1,2                              # reduction candidate for 4,9
D6: 4,9 => CTR
* .18.7...6275968.31.6452.897137852649.52....788.6..7..5.892....3..37....25213..7.4
D6: 1,2                                  # 16 pairs
D7: 4,9,1,2,6,7                          # reduction candidate for 4,9
D7: 4,9 => CTR
* .18.7...6275968431.6452.897.3.85..4..526...788.62.7.15.8.4....3..37.....5213..7.4
D7: 1,2,6,7                              # 12 pairs
D8: 4,9,1,2,6,7                          # reduction candidate for 4,9
D8: 4,9 => CTR
* .18.7...62.5.68.3136.52189.137859642.52614378846237915.8974.1.3..3......5213.....
D8: 1,2,6,7                              # 12 pairs
* PAIR F3: 1,3 BLK 2
F1: 1,3,4,9                              # reduction candidate for 1,3
F1: 4,9 => CTR
* 3.817.2562.5.68.3116.52389..3.852.4..52....78816..7.25.8......3..3.....25213.....
F1: 1,3                                  # 16 pairs
* PAIR G1: 2,5 COL G
G7: 2,5,1,4,9                            # reduction candidate for 2,5
G7: 2,5                                  # 13 pairs
G8: 2,5,1,4,9                            # reduction candidate for 2,5
G8: 2,5                                  # 13 pairs
* PAIR H1: 2,5 COL H
H7: 2,5,1,6                              # reduction candidate for 2,5
H7: 2,5 => CTR
* 918473..627596843136452189713785..4.452....78896247315.89.14..3.43......5213..7.4
H7: 1,6                                  # 13 pairs
H8: 2,5,1,6,8                            # reduction candidate for 2,5
H8: 2,5 => CTR
* .18.73..627596843136452189713785.64.452619378896437.15789.4..6364378.1..521396.8.
H8: 1,6,8                                # 12 pairs
* PAIR G2: 4,7 ROW 2
B2: 4,7,9                                # reduction candidate for 4,7
B2: 9 => CTR
* .18973..6295468731367521894739856.42.52....788.62.7.15.847....3.73.....95213..4.7
B2: 4,7                                  # 14 pairs
* PAIR G2: 4,7 COL G
G9: 4,7,9                                # reduction candidate for 4,7
G9: 9 => CTR
* ..8.7...62.5.68731.6752.89473985..42.52....788.62.7.15.847....3.73...4.95213.....
G9: 4,7                                  # 13 pairs
* PAIR I3: 4,7 COL I
I9: 4,7,9                                # reduction candidate for 4,7
I9: 9 => CTR
* 918473..6275968431364521897.3.85..42.52....788462.7.1548......36937....45213..7.9
I9: 4,7                                  # 14 pairs
* PAIR C4: 7,9 BLK 4
A4: 7,9,1                                # reduction candidate for 7,9
A4: 7,9 => CTR
* .18.7...62.5.68.3136.52189..3.856.42.52....788.62.7.15.8......3..3......5213.....
A4: 1 => SOLVED
* 918473256275968431364521897137852649452639178896147325789214563643785912521396784
* PAIR C4: 7,9 COL C
C7: 7,9,4                                # reduction candidate for 7,9
C7: 4 => CTR
* .18.7...62.5.68.31367521894.3985..42.52....788.62.7.15.84.....3..3......5213.....
C7: 7,9                                  # 13 pairs
* PAIR I4: 2,9 BLK 6
G4: 2,9,1,6                              # reduction candidate for 2,9
G4: 2,9 => CTR
* .18.73..6275968431364521897137856.4..5213.678896247315.89.1...3.43.9.182521384769
G4: 1,6                                  # 13 pairs
G6: 2,9,1,3                              # reduction candidate for 2,9
G6: 2,9 => CTR
* .18.73..627596843136452189713785.64..52...378896437.15.89.....3..3......5213.....
G6: 1,3                                  # 13 pairs
* PAIR I4: 2,9 ROW 4
F4: 2,9,1,6                              # reduction candidate for 2,9
F4: 2,9 => SOLVED
* 918473256275968431364521897137852649452639178896147325789214563643785912521396784
F4: 1,6 => CTR
* .18.73..6275968431364521897137856.4..52.3.678896247315.89.1...3.43...18.52138.764
* PAIR I4: 2,9 COL I
I8: 2,9,4                                # reduction candidate for 2,9
I8: 4 => CTR
* .18.7...62.5.6843136452189713785..42.52....788462.7.15489.....3..3.....45213....9
I8: 2,9                                  # 14 pairs
* PAIR H6: 1,2 BLK 6
G4: 1,2,6,9                              # reduction candidate for 1,2
G4: 1,2 => CTR
* .18.73526275968431364521897137856249.5213.678896247315.89.1...3..3....8252138..6.
G4: 6,9                                  # 13 pairs
G6: 1,2,3,9                              # reduction candidate for 1,2
G6: 1,2 => CTR
* ..8.7...6275968431.6452.897137852649.526..378896437..57892....36437..9.25213..7.4
G6: 3,9                                  # 13 pairs
* PAIR H6: 1,2 ROW 6
D6: 1,2,4,9                              # reduction candidate for 1,2
D6: 4,9 => CTR
* .18.7...6275968.31.6452.897137852649.52....788.6..7..5.892....3..37....25213..7.4
D6: 1,2                                  # 16 pairs
* PAIR H6: 1,2 COL H
H7: 1,2,5,6                              # reduction candidate for 1,2
H7: 1,2                                  # 12 pairs
H8: 1,2,5,6,8                            # reduction candidate for 1,2
H8: 1,2                                  # 11 pairs
* PAIR H9: 6,8 BLK 9
H8: 6,8,1,2,5                            # reduction candidate for 6,8
H8: 6,8                                  # 13 pairs
H8: 1,2,5                                # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060704-absurd-base-pr-000.dot
* REASONING
* DIS # A1: 1,3 => CTR => A1: 4,9
* DIS # B2: 9 => CTR => B2: 4,7
* DIS # C7: 4,7 => CTR => C7: 9
* DIS # F1: 4,9 => CTR => F1: 1,3
* DIS # B2: 4,9 => CTR => B2: 7
* DIS # D5: 4,9 => CTR => D5: 1,6
* DIS # D6: 4,9 => CTR => D6: 1,2
* DIS # D7: 4,9 => CTR => D7: 1,2,6,7
* DIS # D8: 4,9 => CTR => D8: 1,2,6,7
* DIS # F1: 4,9 => CTR => F1: 1,3
* DIS # H7: 2,5 => CTR => H7: 1,6
* DIS # H8: 2,5 => CTR => H8: 1,6,8
* DIS # B2: 9 => CTR => B2: 4,7
* DIS # G9: 9 => CTR => G9: 4,7
* DIS # I9: 9 => CTR => I9: 4,7
* DIS # A4: 7,9 => CTR => A4: 1
* PRF # A4: 1 => SOL
* DIS # C7: 4 => CTR => C7: 7,9
* DIS # G4: 2,9 => CTR => G4: 1,6
* DIS # G6: 2,9 => CTR => G6: 1,3
* PRF # F4: 2,9 => SOL
* DIS # F4: 1,6 => CTR => F4: 2,9
* DIS # I8: 4 => CTR => I8: 2,9
* DIS # G4: 1,2 => CTR => G4: 6,9
* DIS # G6: 1,2 => CTR => G6: 3,9
* DIS # D6: 4,9 => CTR => D6: 1,2
* CNT  26 HDP CHAINS /  55 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C3,C4,D2,F3,G1,G2,H1,H6,H9,I3,I4)
* ..8.7...62.5.68.31.6.52.89..3.85..4..52....788.6..7..5.8......3..3......5213.....
* PAIR A3: 1,3 BLK 1
A1: 1,3,4,9                              # reduction candidate for 1,3
A1: 1,3 => CTR
* ..8.7.2562.5.68.31.6.52.89..3.852.4..52....78816..7.25.8......3..3.....25213.....
* PAIR C3: 4,7 BLK 1
B2: 4,7,9                                # reduction candidate for 4,7
B2: 9 => CTR
* .18.73..629546873136752189473985.142.52....788.6..7..5.8......3..3......5213.....
* PAIR C3: 4,7 COL C
C7: 4,7,9                                # reduction candidate for 4,7
C7: 4,7 => CTR
* 918473..62.5968.3136.52189..3985..42.52....788462.7.15.8......3.93.....45213....9
C7: 9 => SOLVED
* 918473256275968431364521897137852649452639178896147325789214563643785912521396784
* DURATION: 0:00:05.541284  START: 00:20:31.818431  END: 00:20:37.359715 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060704-absurd-base-pr-001.dot
* REASONING
* DIS # A1: 1,3 => CTR => A1: 4,9
* DIS A1: 4,9 # B2: 9 => CTR => B2: 4,7
* DIS A1: 4,9 + B2: 4,7 # C7: 4,7 => CTR => C7: 9
* PRF A1: 4,9 + B2: 4,7 + C7: 9 => SOL
* STA A1: 4,9 + B2: 4,7 + C7: 9
* CNT   4 HDP CHAINS /   4 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060704, absurd

Solution

position: 918473256275968431364521897137852649452639178896147325789214563643785912521396784 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: 1,3 => CTR => A1: 4,9
* INC # A1: 4,9 => UNS
* INC # B2: 4,7 => UNS
* DIS # B2: 9 => CTR => B2: 4,7
* DIS # C7: 4,7 => CTR => C7: 9
* INC # C7: 9 => UNS
* INC # D1: 4,9 => UNS
* DIS # F1: 4,9 => CTR => F1: 1,3
* INC # F1: 1,3 => UNS
* DIS # B2: 4,9 => CTR => B2: 7
* INC # B2: 7 => UNS
* DIS # D5: 4,9 => CTR => D5: 1,6
* INC # D5: 1,6 => UNS
* DIS # D6: 4,9 => CTR => D6: 1,2
* INC # D6: 1,2 => UNS
* DIS # D7: 4,9 => CTR => D7: 1,2,6,7
* INC # D7: 1,2,6,7 => UNS
* DIS # D8: 4,9 => CTR => D8: 1,2,6,7
* INC # D8: 1,2,6,7 => UNS
* INC # F1: 1,3 => UNS
* DIS # F1: 4,9 => CTR => F1: 1,3
* INC # G7: 2,5 => UNS
* INC # G8: 2,5 => UNS
* DIS # H7: 2,5 => CTR => H7: 1,6
* INC # H7: 1,6 => UNS
* DIS # H8: 2,5 => CTR => H8: 1,6,8
* INC # H8: 1,6,8 => UNS
* INC # B2: 4,7 => UNS
* DIS # B2: 9 => CTR => B2: 4,7
* INC # G9: 4,7 => UNS
* DIS # G9: 9 => CTR => G9: 4,7
* INC # I9: 4,7 => UNS
* DIS # I9: 9 => CTR => I9: 4,7
* DIS # A4: 7,9 => CTR => A4: 1
* PRF # A4: 1 => SOL
* INC # C7: 7,9 => UNS
* DIS # C7: 4 => CTR => C7: 7,9
* DIS # G4: 2,9 => CTR => G4: 1,6
* INC # G4: 1,6 => UNS
* DIS # G6: 2,9 => CTR => G6: 1,3
* INC # G6: 1,3 => UNS
* PRF # F4: 2,9 => SOL
* DIS # F4: 1,6 => CTR => F4: 2,9
* INC # I8: 2,9 => UNS
* DIS # I8: 4 => CTR => I8: 2,9
* DIS # G4: 1,2 => CTR => G4: 6,9
* INC # G4: 6,9 => UNS
* DIS # G6: 1,2 => CTR => G6: 3,9
* INC # G6: 3,9 => UNS
* INC # D6: 1,2 => UNS
* DIS # D6: 4,9 => CTR => D6: 1,2
* INC # H7: 1,2 => UNS
* INC # H8: 1,2 => UNS
* INC # H8: 6,8 => UNS
* INC # H8: 1,2,5 => UNS
* CNT  55 HDP CHAINS /  55 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 1,3 => CTR => A1: 4,9
* INC A1: 4,9 # B2: 4,7 => UNS
* DIS A1: 4,9 # B2: 9 => CTR => B2: 4,7
* DIS A1: 4,9 + B2: 4,7 # C7: 4,7 => CTR => C7: 9
* PRF A1: 4,9 + B2: 4,7 + C7: 9 => SOL
* STA A1: 4,9 + B2: 4,7 + C7: 9
* CNT   5 HDP CHAINS /   4 HYP OPENED