Analysis of zz-www.sudokuoftheday.co.uk-20060826-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: .5.2...7.....4.2..9..5...43.75......2.8......49..2......6.8..9..8..61..75...3...6 initial

Autosolve

position: .542.3.7.....4.2..9..57..43.75......2.8.5....49..2......6.8539.38..61..75...32..6 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B3: 6 => CTR => B3: 1,2
* PRF # G1: 1,9 => SOL
* DIS # F2: 6,8 => CTR => F2: 9
* DIS # G3: 1 => CTR => G3: 6,8
* PRF # F4: 6,8 => SOL
* DIS # F6: 6,8 => CTR => F6: 7
* DIS # B5: 3 => CTR => B5: 1,6
* DIS # D4: 1,6 => CTR => D4: 3,8
* DIS # H4: 1,6 => CTR => H4: 2,3,8
* PRF # A1: 1,6 => SOL
* DIS # A2: 1,6 => CTR => A2: 7,8
* PRF # B5: 6 => SOL
* DIS # C2: 1,3 => CTR => C2: 7
* PRF # C2: 7 => SOL
* DIS # I4: 1,9 => CTR => I4: 2,4,8
* PRF # I4: 4,9 => SOL
* DIS # G5: 4,9 => CTR => G5: 7
* DIS # F5: 7 => CTR => F5: 4,9
* PRF # A2: 6,8 => SOL
* PRF # B7: 1,4 => SOL
* DIS # B7: 2 => CTR => B7: 1,4
* DIS # G9: 4 => CTR => G9: 1,8
* DIS # H4: 1,8 => CTR => H4: 2,3,6
* CNT  23 HDP CHAINS /  53 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 # B3: 6 => CTR => B3: 1,2
* PRF B3: 1,2 # G1: 1,9 => SOL
* STA B3: 1,2 + G1: 1,9
* CNT   2 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

.5.2...7.....4.2..9..5...43.75......2.8......49..2......6.8..9..8..61..75...3...6 initial
.542.3.7.....4.2..9..57..43.75......2.8.5....49..2......6.8539.38..61..75...32..6 autosolve
654213978837649215921578643175396824268154739493827561716485392382961457549732186 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (17)
C3: 1,2
E1: 1,9
F3: 6,8
A4: 1,6
C6: 1,3
E4: 1,9
I5: 4,9
A7: 1,7
C8: 2,9
B9: 1,4
C9: 7,9
D7: 4,7
D8: 4,9
D9: 7,9
G8: 4,5
H8: 2,5
H9: 1,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E1,D2: 1.. / E1 = 1  => 19 pairs (_) / D2 = 1  =>  0 pairs (X)
E1,E4: 1.. / E1 = 1  => 19 pairs (_) / E4 = 1  =>  0 pairs (X)
B3,C3: 2.. / B3 = 2  =>  0 pairs (*) / C3 = 2  =>  0 pairs (X)
H4,I4: 2.. / H4 = 2  =>  0 pairs (*) / I4 = 2  =>  0 pairs (X)
B7,C8: 2.. / B7 = 2  =>  0 pairs (X) / C8 = 2  =>  0 pairs (_)
I7,H8: 2.. / I7 = 2  =>  0 pairs (*) / H8 = 2  =>  0 pairs (X)
B7,I7: 2.. / B7 = 2  =>  0 pairs (X) / I7 = 2  =>  0 pairs (_)
C8,H8: 2.. / C8 = 2  =>  0 pairs (*) / H8 = 2  =>  0 pairs (X)
B3,B7: 2.. / B3 = 2  =>  0 pairs (*) / B7 = 2  =>  0 pairs (X)
C3,C8: 2.. / C3 = 2  =>  0 pairs (X) / C8 = 2  =>  0 pairs (_)
H4,H8: 2.. / H4 = 2  =>  0 pairs (*) / H8 = 2  =>  0 pairs (X)
I4,I7: 2.. / I4 = 2  =>  0 pairs (X) / I7 = 2  =>  0 pairs (_)
B2,C2: 3.. / B2 = 3  => 20 pairs (_) / C2 = 3  =>  0 pairs (X)
B5,C6: 3.. / B5 = 3  =>  0 pairs (X) / C6 = 3  => 20 pairs (_)
D4,H4: 3.. / D4 = 3  => 18 pairs (_) / H4 = 3  =>  0 pairs (X)
B2,B5: 3.. / B2 = 3  => 20 pairs (_) / B5 = 3  =>  0 pairs (X)
C2,C6: 3.. / C2 = 3  =>  0 pairs (X) / C6 = 3  => 20 pairs (_)
F4,F5: 4.. / F4 = 4  => 18 pairs (_) / F5 = 4  =>  0 pairs (*)
B7,B9: 4.. / B7 = 4  =>  0 pairs (X) / B9 = 4  => 19 pairs (_)
D7,D8: 4.. / D7 = 4  =>  0 pairs (*) / D8 = 4  =>  0 pairs (X)
D8,G8: 4.. / D8 = 4  =>  0 pairs (X) / G8 = 4  =>  0 pairs (_)
B9,G9: 4.. / B9 = 4  => 19 pairs (_) / G9 = 4  =>  0 pairs (X)
H2,I2: 5.. / H2 = 5  =>  0 pairs (X) / I2 = 5  => 20 pairs (_)
G8,H8: 5.. / G8 = 5  =>  0 pairs (X) / H8 = 5  =>  0 pairs (_)
G6,G8: 5.. / G6 = 5  =>  0 pairs (*) / G8 = 5  =>  0 pairs (X)
I2,I6: 5.. / I2 = 5  => 20 pairs (_) / I6 = 5  =>  0 pairs (X)
A4,B5: 6.. / A4 = 6  => 21 pairs (_) / B5 = 6  =>  0 pairs (*)
A1,G1: 6.. / A1 = 6  =>  0 pairs (*) / G1 = 6  =>  0 pairs (X)
A2,C2: 7.. / A2 = 7  =>  0 pairs (X) / C2 = 7  =>  0 pairs (_)
F5,F6: 7.. / F5 = 7  =>  0 pairs (X) / F6 = 7  => 18 pairs (_)
G5,G6: 7.. / G5 = 7  => 18 pairs (_) / G6 = 7  =>  0 pairs (X)
A7,C9: 7.. / A7 = 7  =>  0 pairs (*) / C9 = 7  =>  0 pairs (X)
D7,D9: 7.. / D7 = 7  =>  0 pairs (X) / D9 = 7  =>  0 pairs (_)
F5,G5: 7.. / F5 = 7  =>  0 pairs (X) / G5 = 7  => 18 pairs (_)
F6,G6: 7.. / F6 = 7  => 18 pairs (_) / G6 = 7  =>  0 pairs (X)
A7,D7: 7.. / A7 = 7  =>  0 pairs (*) / D7 = 7  =>  0 pairs (X)
C9,D9: 7.. / C9 = 7  =>  0 pairs (X) / D9 = 7  =>  0 pairs (_)
A2,A7: 7.. / A2 = 7  =>  0 pairs (X) / A7 = 7  =>  0 pairs (_)
C2,C9: 7.. / C2 = 7  =>  0 pairs (*) / C9 = 7  =>  0 pairs (X)
A1,A2: 8.. / A1 = 8  => 21 pairs (_) / A2 = 8  =>  0 pairs (*)
G9,H9: 8.. / G9 = 8  => 25 pairs (_) / H9 = 8  => 17 pairs (_)
F3,G3: 8.. / F3 = 8  => 21 pairs (_) / G3 = 8  =>  0 pairs (X)
E1,F2: 9.. / E1 = 9  =>  0 pairs (X) / F2 = 9  => 19 pairs (_)
C8,C9: 9.. / C8 = 9  =>  0 pairs (X) / C9 = 9  =>  0 pairs (_)
D8,D9: 9.. / D8 = 9  =>  0 pairs (*) / D9 = 9  =>  0 pairs (X)
F2,I2: 9.. / F2 = 9  => 19 pairs (_) / I2 = 9  =>  0 pairs (X)
C8,D8: 9.. / C8 = 9  =>  0 pairs (X) / D8 = 9  =>  0 pairs (_)
C9,D9: 9.. / C9 = 9  =>  0 pairs (*) / D9 = 9  =>  0 pairs (X)
E1,E4: 9.. / E1 = 9  =>  0 pairs (X) / E4 = 9  => 19 pairs (_)
* DURATION: 0:01:00.480070  START: 02:05:21.313413  END: 02:06:21.793483 2019-05-01
* CP COUNT: (49)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,B9,C3,C6,C8,C9,D7,D8,D9,E1,E4,F3,G8,H8,H9,I5)
* .542.3.7.....4.2..9..57..43.75......2.8.5....49..2......6.8539.38..61..75...32..6
* PAIR C3: 1,2 BLK 1
B3: 1,2,6                                # reduction candidate for 1,2
B3: 6 => CTR
* 8542136797...4.2..962578143675.....22.8.5....49..2.7.1126785394389461527547932816
B3: 1,2                                  # 23 pairs
* PAIR E1: 1,9 ROW 1
G1: 1,9,6,8                              # reduction candidate for 1,9
G1: 1,9 => SOLVED
* 654213978837649215921578643175396824268154739493827561716485392382961457549732186
G1: 6,8                                  # 20 pairs
I1: 1,9,8                                # reduction candidate for 1,9
I1: 1,9                                  # 22 pairs
* PAIR F3: 6,8 BLK 2
D2: 6,8,1                                # reduction candidate for 6,8
D2: 6,8                                  # 19 pairs
F2: 6,8,9                                # reduction candidate for 6,8
F2: 6,8 => CTR
* .54293.7....14.2.99..57..43.75.1....2.8.5...449..2...5..6.8539.38..615275...32486
F2: 9                                    # 19 pairs
* PAIR F3: 6,8 ROW 3
G3: 6,8,1                                # reduction candidate for 6,8
G3: 1 => CTR
* 8542136797...4.2..962578143675.....22.8.5....49..2.7.1126785394389461527547932816
G3: 6,8                                  # 23 pairs
* PAIR F3: 6,8 COL F
F4: 6,8,4,9                              # reduction candidate for 6,8
F4: 6,8 => SOLVED
* 654213978837649215921578643175396824268154739493827561716485392382961457549732186
F4: 4,9                                  # 18 pairs
F6: 6,8,7                                # reduction candidate for 6,8
F6: 6,8 => CTR
* 854213.7.7...492..9.257..43.75.94..22.8.574.949..2.7..126785394389461527547932..6
F6: 7                                    # 18 pairs
* PAIR A4: 1,6 BLK 4
B5: 1,6,3                                # reduction candidate for 1,6
B5: 3 => CTR
* 8542.367.7.3.4.2..9.257..43675.....2238.5...9491.2....126785394389461527547932..6
B5: 1,6                                  # 20 pairs
* PAIR A4: 1,6 ROW 4
D4: 1,6,3,8                              # reduction candidate for 1,6
D4: 1,6 => CTR
* 8542.367.7...4.2..9.257..4367519..322.8.5.9..49..2....126785394389461527547932..6
D4: 3,8                                  # 18 pairs
G4: 1,6,4,8,9                            # reduction candidate for 1,6
G4: 1,6                                  # 22 pairs
H4: 1,6,2,3,8                            # reduction candidate for 1,6
H4: 1,6 => CTR
* 8542.367.7...4.2..9.257..436753...122.8.5...949..2....126785394389461527547932186
H4: 2,3,8                                # 17 pairs
* PAIR A4: 1,6 COL A
A1: 1,6,8                                # reduction candidate for 1,6
A1: 1,6 => SOLVED
* 654213978837649215921578643175396824268154739493827561716485392382961457549732186
A1: 8                                    # 21 pairs
A2: 1,6,7,8                              # reduction candidate for 1,6
A2: 1,6 => CTR
* 8542.367..37.4.2.59.157.843175.9....2.8.5....493.2....7.648539.38.961457549732..6
A2: 7,8                                  # 18 pairs
* PAIR C6: 1,3 BLK 4
B5: 1,3,6                                # reduction candidate for 1,3
B5: 6 => SOLVED
* 654213978837649215921578643175396824268154739493827561716485392382961457549732186
B5: 1,3                                  # 21 pairs
* PAIR C6: 1,3 ROW 6
D6: 1,3,6,8                              # reduction candidate for 1,3
D6: 1,3                                  # 19 pairs
H6: 1,3,5,6,8                            # reduction candidate for 1,3
H6: 1,3                                  # 20 pairs
* PAIR C6: 1,3 COL C
C2: 1,3,7                                # reduction candidate for 1,3
C2: 1,3 => CTR
* 8542.367.7...4.2..9.257..43675.....22.8.5...949..2....126785394389461527547932..6
C2: 7 => SOLVED
* 654213978837649215921578643175396824268154739493827561716485392382961457549732186
* PAIR E4: 1,9 ROW 4
G4: 1,9,4,6,8                            # reduction candidate for 1,9
G4: 1,9                                  # 24 pairs
I4: 1,9,2,4,8                            # reduction candidate for 1,9
I4: 1,9 => CTR
* .542.3.7...7.4.2.592157..43.753.482.2.8.5...4493.2.5.1716485392382961457549732186
I4: 2,4,8                                # 17 pairs
* PAIR I5: 4,9 BLK 6
G4: 4,9,1,6,8                            # reduction candidate for 4,9
G4: 4,9                                  # 19 pairs
I4: 4,9,1,2,8                            # reduction candidate for 4,9
I4: 4,9 => SOLVED
* 654213978837649215921578643175396824268154739493827561716485392382961457549732186
I4: 1,2,8                                # 17 pairs
G5: 4,9,7                                # reduction candidate for 4,9
G5: 4,9 => CTR
* 854213.7.7...492..9.257..43.75.94..22.8.574.949..2.7..126785394389461527547932..6
G5: 7                                    # 18 pairs
* PAIR I5: 4,9 ROW 5
F5: 4,9,7                                # reduction candidate for 4,9
F5: 7 => CTR
* 854213.7.7...492..9.257..43.75.94..22.8.574.949..2.7..126785394389461527547932..6
F5: 4,9                                  # 18 pairs
* PAIR A7: 1,7 COL A
A2: 1,7,6,8                              # reduction candidate for 1,7
A2: 6,8 => SOLVED
* 654213978837649215921578643175396824268154739493827561716485392382961457549732186
A2: 1,7                                  # 22 pairs
* PAIR B9: 1,4 BLK 7
B7: 1,4,2                                # reduction candidate for 1,4
B7: 1,4 => SOLVED
* 654213978837649215921578643175396824268154739493827561716485392382961457549732186
B7: 2 => CTR
* 8542.367.7...4.2..9.257..43675.....22.8.5...949..2....126785394389461527547932..6
* PAIR B9: 1,4 ROW 9
G9: 1,4,8                                # reduction candidate for 1,4
G9: 8                                    # 25 pairs
G9: 1,4                                  # 17 pairs
* PAIR H9: 1,8 BLK 9
G9: 1,8,4                                # reduction candidate for 1,8
G9: 4 => CTR
* .542.3.7.....4.2..9..57..43.75......2.8.5....49..2.....4678539.38..61..75...32486
G9: 1,8                                  # 19 pairs
* PAIR H9: 1,8 COL H
H2: 1,8,5,6                              # reduction candidate for 1,8
H2: 1,8                                  # 22 pairs
H4: 1,8,2,3,6                            # reduction candidate for 1,8
H4: 1,8 => CTR
* 8542.367.7...4.2..9.257..436753....22.8.5...949..2....126785394389461527547932..6
H4: 2,3,6                                # 17 pairs
H6: 1,8,3,5,6                            # reduction candidate for 1,8
H6: 1,8                                  # 20 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060826-absurd-base-pr-000.dot
* REASONING
* DIS # B3: 6 => CTR => B3: 1,2
* PRF # G1: 1,9 => SOL
* DIS # F2: 6,8 => CTR => F2: 9
* DIS # G3: 1 => CTR => G3: 6,8
* PRF # F4: 6,8 => SOL
* DIS # F6: 6,8 => CTR => F6: 7
* DIS # B5: 3 => CTR => B5: 1,6
* DIS # D4: 1,6 => CTR => D4: 3,8
* DIS # H4: 1,6 => CTR => H4: 2,3,8
* PRF # A1: 1,6 => SOL
* DIS # A2: 1,6 => CTR => A2: 7,8
* PRF # B5: 6 => SOL
* DIS # C2: 1,3 => CTR => C2: 7
* PRF # C2: 7 => SOL
* DIS # I4: 1,9 => CTR => I4: 2,4,8
* PRF # I4: 4,9 => SOL
* DIS # G5: 4,9 => CTR => G5: 7
* DIS # F5: 7 => CTR => F5: 4,9
* PRF # A2: 6,8 => SOL
* PRF # B7: 1,4 => SOL
* DIS # B7: 2 => CTR => B7: 1,4
* DIS # G9: 4 => CTR => G9: 1,8
* DIS # H4: 1,8 => CTR => H4: 2,3,6
* CNT  23 HDP CHAINS /  53 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,B9,C3,C6,C8,C9,D7,D8,D9,E1,E4,F3,G8,H8,H9,I5)
* .542.3.7.....4.2..9..57..43.75......2.8.5....49..2......6.8539.38..61..75...32..6
* PAIR C3: 1,2 BLK 1
B3: 1,2,6                                # reduction candidate for 1,2
B3: 6 => CTR
* 8542136797...4.2..962578143675.....22.8.5....49..2.7.1126785394389461527547932816
* PAIR E1: 1,9 ROW 1
G1: 1,9,6,8                              # reduction candidate for 1,9
G1: 1,9 => SOLVED
* 654213978837649215921578643175396824268154739493827561716485392382961457549732186
* DURATION: 0:00:03.077322  START: 02:06:57.205896  END: 02:07:00.283218 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060826-absurd-base-pr-001.dot
* REASONING
* DIS # B3: 6 => CTR => B3: 1,2
* PRF B3: 1,2 # G1: 1,9 => SOL
* STA B3: 1,2 + G1: 1,9
* CNT   2 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060826, absurd

Solution

position: 654213978837649215921578643175396824268154739493827561716485392382961457549732186 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 # B3: 1,2 => UNS
* DIS # B3: 6 => CTR => B3: 1,2
* PRF # G1: 1,9 => SOL
* INC # G1: 6,8 => UNS
* INC # I1: 1,9 => UNS
* INC # D2: 6,8 => UNS
* DIS # F2: 6,8 => CTR => F2: 9
* INC # F2: 9 => UNS
* INC # G3: 6,8 => UNS
* DIS # G3: 1 => CTR => G3: 6,8
* PRF # F4: 6,8 => SOL
* INC # F4: 4,9 => UNS
* DIS # F6: 6,8 => CTR => F6: 7
* INC # F6: 7 => UNS
* INC # B5: 1,6 => UNS
* DIS # B5: 3 => CTR => B5: 1,6
* DIS # D4: 1,6 => CTR => D4: 3,8
* INC # D4: 3,8 => UNS
* INC # G4: 1,6 => UNS
* DIS # H4: 1,6 => CTR => H4: 2,3,8
* INC # H4: 2,3,8 => UNS
* PRF # A1: 1,6 => SOL
* INC # A1: 8 => UNS
* DIS # A2: 1,6 => CTR => A2: 7,8
* INC # A2: 7,8 => UNS
* INC # B5: 1,3 => UNS
* PRF # B5: 6 => SOL
* INC # D6: 1,3 => UNS
* INC # H6: 1,3 => UNS
* DIS # C2: 1,3 => CTR => C2: 7
* PRF # C2: 7 => SOL
* INC # G4: 1,9 => UNS
* DIS # I4: 1,9 => CTR => I4: 2,4,8
* INC # I4: 2,4,8 => UNS
* INC # G4: 4,9 => UNS
* PRF # I4: 4,9 => SOL
* INC # I4: 1,2,8 => UNS
* DIS # G5: 4,9 => CTR => G5: 7
* INC # G5: 7 => UNS
* INC # F5: 4,9 => UNS
* DIS # F5: 7 => CTR => F5: 4,9
* INC # A2: 1,7 => UNS
* PRF # A2: 6,8 => SOL
* PRF # B7: 1,4 => SOL
* DIS # B7: 2 => CTR => B7: 1,4
* INC # G9: 1,4 => UNS
* INC # G9: 8 => UNS
* INC # G9: 1,8 => UNS
* DIS # G9: 4 => CTR => G9: 1,8
* INC # H2: 1,8 => UNS
* DIS # H4: 1,8 => CTR => H4: 2,3,6
* INC # H4: 2,3,6 => UNS
* INC # H6: 1,8 => UNS
* CNT  53 HDP CHAINS /  53 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B3: 1,2 => UNS
* DIS # B3: 6 => CTR => B3: 1,2
* PRF B3: 1,2 # G1: 1,9 => SOL
* STA B3: 1,2 + G1: 1,9
* CNT   3 HDP CHAINS /   3 HYP OPENED