Analysis of zz-www.sudokuoftheday.co.uk-20060626-absurd-base.sdk

Contents

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

level: medium

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

position: 4.327.6.......3....7.6...5........9.35....42.6..13...89...1.8.....7.6...1........ initial

Autosolve

position: 4.32756.......3....7.6.1.5.7......9.35...742.6..13.5789...1.8.....7.6...1........ autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # B2: 2,8 => SOL
* DIS # C2: 2,8 => CTR => C2: 1,5,6,9
* DIS # B1: 9 => CTR => B1: 1,8
* DIS # I2: 1,9 => CTR => I2: 2,4,7
* DIS # B1: 8 => CTR => B1: 1,9
* DIS # I8: 1,9 => CTR => I8: 2,4,5
* DIS # E5: 8,9 => CTR => E5: 6
* DIS # C5: 1 => CTR => C5: 8,9
* DIS # D9: 8,9 => CTR => D9: 3,4,5
* DIS # I4: 1,3 => CTR => I4: 6
* DIS # I4: 3 => CTR => I4: 1,6
* DIS # F9: 2,4 => CTR => F9: 8,9
* DIS # C7: 2,4 => CTR => C7: 5,6,7
* DIS # I7: 2,4 => CTR => I7: 5,7
* DIS # F4: 2,4 => CTR => F4: 8
* CNT  15 HDP CHAINS /  42 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 # B2: 2,8 => SOL
* STA B2: 2,8
* CNT   1 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

4.327.6.......3....7.6...5........9.35....42.6..13...89...1.8.....7.6...1........ initial
4.32756.......3....7.6.1.5.7......9.35...742.6..13.5789...1.8.....7.6...1........ autosolve
413275689526893147879641253741528396358967421692134578967412835235786914184359762 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
A3: 2,8
H1: 1,8
I1: 1,9
D5: 8,9
G4: 1,3
I5: 1,6
F7: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C5,I5: 1.. / C5 = 1  =>  0 pairs (X) / I5 = 1  => 12 pairs (_)
G3,I3: 3.. / G3 = 3  =>  0 pairs (X) / I3 = 3  => 12 pairs (_)
G4,I4: 3.. / G4 = 3  => 12 pairs (_) / I4 = 3  =>  0 pairs (X)
D7,D9: 3.. / D7 = 3  => 10 pairs (_) / D9 = 3  =>  9 pairs (_)
B8,H8: 3.. / B8 = 3  => 10 pairs (_) / H8 = 3  => 12 pairs (_)
G3,G4: 3.. / G3 = 3  =>  0 pairs (X) / G4 = 3  => 12 pairs (_)
I3,I4: 3.. / I3 = 3  => 12 pairs (_) / I4 = 3  =>  0 pairs (X)
E3,I3: 4.. / E3 = 4  => 12 pairs (_) / I3 = 4  =>  0 pairs (X)
A2,C2: 5.. / A2 = 5  =>  8 pairs (_) / C2 = 5  => 12 pairs (_)
D4,E4: 5.. / D4 = 5  => 10 pairs (_) / E4 = 5  =>  0 pairs (X)
A2,A8: 5.. / A2 = 5  =>  8 pairs (_) / A8 = 5  => 12 pairs (_)
B2,C2: 6.. / B2 = 6  =>  9 pairs (_) / C2 = 6  =>  8 pairs (_)
E4,E5: 6.. / E4 = 6  =>  0 pairs (X) / E5 = 6  => 12 pairs (_)
I4,I5: 6.. / I4 = 6  => 12 pairs (_) / I5 = 6  =>  0 pairs (X)
H7,H9: 6.. / H7 = 6  =>  8 pairs (_) / H9 = 6  =>  8 pairs (_)
E4,I4: 6.. / E4 = 6  =>  0 pairs (X) / I4 = 6  => 12 pairs (_)
E5,I5: 6.. / E5 = 6  => 12 pairs (_) / I5 = 6  =>  0 pairs (X)
G2,I2: 7.. / G2 = 7  =>  8 pairs (_) / I2 = 7  =>  7 pairs (_)
C7,C9: 7.. / C7 = 7  =>  7 pairs (_) / C9 = 7  =>  8 pairs (_)
C7,I7: 7.. / C7 = 7  =>  7 pairs (_) / I7 = 7  =>  8 pairs (_)
G2,G9: 7.. / G2 = 7  =>  8 pairs (_) / G9 = 7  =>  7 pairs (_)
H1,H2: 8.. / H1 = 8  =>  8 pairs (_) / H2 = 8  =>  0 pairs (X)
B1,H1: 8.. / B1 = 8  =>  0 pairs (X) / H1 = 8  =>  8 pairs (_)
F4,F9: 8.. / F4 = 8  => 12 pairs (_) / F9 = 8  =>  0 pairs (X)
B1,I1: 9.. / B1 = 9  =>  0 pairs (X) / I1 = 9  =>  8 pairs (_)
F6,F9: 9.. / F6 = 9  =>  0 pairs (X) / F9 = 9  => 12 pairs (_)
* DURATION: 0:00:25.825347  START: 00:06:59.246599  END: 00:07:25.071946 2019-05-01
* CP COUNT: (26)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,D5,F7,G4,H1,I1,I5)
* 4.32756.......3....7.6.1.5.7......9.35...742.6..13.5789...1.8.....7.6...1........
* PAIR A3: 2,8 BLK 1
A2: 2,8,5                                # reduction candidate for 2,8
A2: 2,8                                  # 12 pairs
B2: 2,8,1,6,9                            # reduction candidate for 2,8
B2: 2,8 => SOLVED
* 413275689526893147879641253741528396358967421692134578967412835235786914184359762
B2: 1,6,9                                #  7 pairs
C2: 2,8,1,5,6,9                          # reduction candidate for 2,8
C2: 2,8 => CTR
* 413275689562.93147879641.5.7214583963589674216941325789.7.1486223.7.691.1....9...
C2: 1,5,6,9                              #  7 pairs
C3: 2,8,9                                # reduction candidate for 2,8
C3: 2,8                                  # 14 pairs
* PAIR A3: 2,8 COL A
A8: 2,8,5                                # reduction candidate for 2,8
A8: 5                                    # 12 pairs
A8: 2,8                                  #  8 pairs
* PAIR H1: 1,8 BLK 3
H2: 1,8,4                                # reduction candidate for 1,8
H2: 4                                    # 14 pairs
H2: 1,8                                  # 11 pairs
* PAIR H1: 1,8 ROW 1
B1: 1,8,9                                # reduction candidate for 1,8
B1: 9 => CTR
* 493275681.16..3.4..7.6413597...681933519.74266.913.5789...1.8.....7.6.1.1....9...
B1: 1,8                                  #  8 pairs
* PAIR I1: 1,9 BLK 3
G2: 1,9,2,7                              # reduction candidate for 1,9
G2: 1,9                                  # 12 pairs
I2: 1,9,2,4,7                            # reduction candidate for 1,9
I2: 1,9 => CTR
* 413275689.....37418796413527....819335...742.69.13.5789...1.8.....7.6...1....92..
I2: 2,4,7                                #  7 pairs
* PAIR I1: 1,9 ROW 1
B1: 1,9,8                                # reduction candidate for 1,9
B1: 8 => CTR
* 483275619.....3.8.2796813547.....19335189742669.13.5789...1.8..8..7.69.11........
B1: 1,9                                  #  8 pairs
* PAIR I1: 1,9 COL I
I8: 1,9,2,4,5                            # reduction candidate for 1,9
I8: 1,9 => CTR
* 4.32756.......3....7.6.135.7..56.193351..74266..13.5789...1.8.....7.6...1........
I8: 2,4,5                                #  7 pairs
* PAIR D5: 8,9 BLK 5
E5: 8,9,6                                # reduction candidate for 8,9
E5: 8,9 => CTR
* 4.32756.......3....7.6.1.5.7..56..9.351..74266..13.5789...1.8.....7.6...1........
E5: 6                                    # 12 pairs
* PAIR D5: 8,9 ROW 5
C5: 8,9,1                                # reduction candidate for 8,9
C5: 1 => CTR
* 4.32756.......3....7.6.1.5.7..56..9.351..74266..13.5789...1.8.....7.6...1........
C5: 8,9                                  # 12 pairs
* PAIR D5: 8,9 COL D
D2: 8,9,4                                # reduction candidate for 8,9
D2: 8,9                                  #  9 pairs
D9: 8,9,3,4,5                            # reduction candidate for 8,9
D9: 8,9 => CTR
* 4.32756.....4.3....7.6.13547..56.193351..74266..13.5789..31.8.....7.6...1........
D9: 3,4,5                                #  7 pairs
* PAIR G4: 1,3 BLK 6
I4: 1,3,6                                # reduction candidate for 1,3
I4: 1,3 => CTR
* 4.32756.......3....7.6.1.5.7..56..9.351..74266..13.5789...1.8.....7.6...1........
I4: 6                                    # 12 pairs
* PAIR I5: 1,6 BLK 6
I4: 1,6,3                                # reduction candidate for 1,6
I4: 3 => CTR
* 4.32756.......3....7.6.135.7..56.193351..74266..13.5789...1.8.....7.6...1........
I4: 1,6                                  # 12 pairs
* PAIR F7: 2,4 BLK 8
E8: 2,4,5,8,9                            # reduction candidate for 2,4
E8: 2,4                                  # 11 pairs
E9: 2,4,5,8,9                            # reduction candidate for 2,4
E9: 2,4                                  # 10 pairs
F9: 2,4,8,9                              # reduction candidate for 2,4
F9: 2,4 => CTR
* 4.32756.......3....7.6.1.5.7....8.9.3589674216..13.5789...1.8.....7.6...1........
F9: 8,9                                  #  8 pairs
* PAIR F7: 2,4 ROW 7
B7: 2,4,3,6                              # reduction candidate for 2,4
B7: 2,4                                  # 11 pairs
C7: 2,4,5,6,7                            # reduction candidate for 2,4
C7: 2,4 => CTR
* 4.32756.95.69.37...796412537.1452396358.674216..13.5789..51.8.7..57961..1.73289.5
C7: 5,6,7                                #  7 pairs
I7: 2,4,5,7                              # reduction candidate for 2,4
I7: 2,4 => CTR
* 413275689.6.8931478796412537214583963589674216941325789375148.2...7.691.1..3.976.
I7: 5,7                                  #  8 pairs
* PAIR F7: 2,4 COL F
F4: 2,4,8                                # reduction candidate for 2,4
F4: 2,4 => CTR
* 4.32756.9.96483.1..7.691.547.1....9.3598674216..1395789...1.8.....7.6...1....8...
F4: 8                                    # 12 pairs
F6: 2,4,9                                # reduction candidate for 2,4
F6: 2,4                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060626-absurd-base-pr-000.dot
* REASONING
* PRF # B2: 2,8 => SOL
* DIS # C2: 2,8 => CTR => C2: 1,5,6,9
* DIS # B1: 9 => CTR => B1: 1,8
* DIS # I2: 1,9 => CTR => I2: 2,4,7
* DIS # B1: 8 => CTR => B1: 1,9
* DIS # I8: 1,9 => CTR => I8: 2,4,5
* DIS # E5: 8,9 => CTR => E5: 6
* DIS # C5: 1 => CTR => C5: 8,9
* DIS # D9: 8,9 => CTR => D9: 3,4,5
* DIS # I4: 1,3 => CTR => I4: 6
* DIS # I4: 3 => CTR => I4: 1,6
* DIS # F9: 2,4 => CTR => F9: 8,9
* DIS # C7: 2,4 => CTR => C7: 5,6,7
* DIS # I7: 2,4 => CTR => I7: 5,7
* DIS # F4: 2,4 => CTR => F4: 8
* CNT  15 HDP CHAINS /  42 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,D5,F7,G4,H1,I1,I5)
* 4.32756.......3....7.6.1.5.7......9.35...742.6..13.5789...1.8.....7.6...1........
* PAIR A3: 2,8 BLK 1
A2: 2,8,5                                # reduction candidate for 2,8
A2: 2,8                                  # 12 pairs
B2: 2,8,1,6,9                            # reduction candidate for 2,8
B2: 2,8 => SOLVED
* 413275689526893147879641253741528396358967421692134578967412835235786914184359762
* DURATION: 0:00:02.621260  START: 00:07:48.572530  END: 00:07:51.193790 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060626-absurd-base-pr-001.dot
* REASONING
* PRF # B2: 2,8 => SOL
* STA B2: 2,8
* CNT   1 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060626, absurd

Solution

position: 413275689526893147879641253741528396358967421692134578967412835235786914184359762 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 # A2: 2,8 => UNS
* PRF # B2: 2,8 => SOL
* INC # B2: 1,6,9 => UNS
* DIS # C2: 2,8 => CTR => C2: 1,5,6,9
* INC # C2: 1,5,6,9 => UNS
* INC # C3: 2,8 => UNS
* INC # A8: 2,8 => UNS
* INC # A8: 5 => UNS
* INC # H2: 1,8 => UNS
* INC # H2: 4 => UNS
* INC # B1: 1,8 => UNS
* DIS # B1: 9 => CTR => B1: 1,8
* INC # G2: 1,9 => UNS
* DIS # I2: 1,9 => CTR => I2: 2,4,7
* INC # I2: 2,4,7 => UNS
* INC # B1: 1,9 => UNS
* DIS # B1: 8 => CTR => B1: 1,9
* DIS # I8: 1,9 => CTR => I8: 2,4,5
* INC # I8: 2,4,5 => UNS
* DIS # E5: 8,9 => CTR => E5: 6
* INC # E5: 6 => UNS
* INC # C5: 8,9 => UNS
* DIS # C5: 1 => CTR => C5: 8,9
* INC # D2: 8,9 => UNS
* DIS # D9: 8,9 => CTR => D9: 3,4,5
* INC # D9: 3,4,5 => UNS
* DIS # I4: 1,3 => CTR => I4: 6
* INC # I4: 6 => UNS
* INC # I4: 1,6 => UNS
* DIS # I4: 3 => CTR => I4: 1,6
* INC # E8: 2,4 => UNS
* INC # E9: 2,4 => UNS
* DIS # F9: 2,4 => CTR => F9: 8,9
* INC # F9: 8,9 => UNS
* INC # B7: 2,4 => UNS
* DIS # C7: 2,4 => CTR => C7: 5,6,7
* INC # C7: 5,6,7 => UNS
* DIS # I7: 2,4 => CTR => I7: 5,7
* INC # I7: 5,7 => UNS
* DIS # F4: 2,4 => CTR => F4: 8
* INC # F4: 8 => UNS
* INC # F6: 2,4 => UNS
* CNT  42 HDP CHAINS /  42 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 2,8 => UNS
* PRF # B2: 2,8 => SOL
* STA B2: 2,8
* CNT   2 HDP CHAINS /   2 HYP OPENED