Analysis of zz-www.sudokuoftheday.co.uk-20060522-absurd-base.sdk

Contents

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

level: medium

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

position: .......7..97.18......7.54.9.516.....7..1.....2...89...3..9....6..2.....7..6.379.4 initial

Autosolve

position: ....9..7..97.18......7.54.9.5167..9.7.91.....2...897..37.9....69.2.....7..6.379.4 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C1: 3,8 => CTR => C1: 4,5
* DIS # F1: 3,4 => CTR => F1: 2,6
* DIS # D6: 3,4 => CTR => D6: 5
* PRF # B8: 1,8 => SOL
* DIS # B1: 1,8 => CTR => B1: 2,3,4
* CNT   5 HDP CHAINS /  29 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 # C1: 3,8 => CTR => C1: 4,5
* DIS C1: 4,5 # F1: 3,4 => CTR => F1: 2,6
* PRF C1: 4,5 + F1: 2,6 # B5: 3,4 => SOL
* STA C1: 4,5 + F1: 2,6 + B5: 3,4
* CNT   3 HDP CHAINS /  16 HYP OPENED

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

Details

Positions

.......7..97.18......7.54.9.516.....7..1.....2...89...3..9....6..2.....7..6.379.4 initial
....9..7..97.18......7.54.9.5167..9.7.91.....2...897..37.9....69.2.....7..6.379.4 autosolve
635492178497318562128765439851674293749123685263589741374951826912846357586237914 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
C3: 3,8
E3: 2,6
A4: 4,8
C6: 3,4
B9: 1,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H6,I6: 1.. / H6 = 1  => 15 pairs (_) / I6 = 1  =>  5 pairs (_)
F7,F8: 1.. / F7 = 1  =>  6 pairs (_) / F8 = 1  =>  0 pairs (X)
I1,I6: 1.. / I1 = 1  => 15 pairs (_) / I6 = 1  =>  5 pairs (_)
B1,B3: 2.. / B1 = 2  =>  6 pairs (_) / B3 = 2  =>  6 pairs (_)
D9,H9: 2.. / D9 = 2  => 13 pairs (_) / H9 = 2  =>  0 pairs (X)
G8,H8: 3.. / G8 = 3  =>  6 pairs (_) / H8 = 3  =>  5 pairs (_)
H5,H6: 4.. / H5 = 4  => 10 pairs (_) / H6 = 4  => 13 pairs (_)
C7,B8: 4.. / C7 = 4  =>  0 pairs (*) / B8 = 4  =>  0 pairs (X)
A2,D2: 4.. / A2 = 4  => 17 pairs (_) / D2 = 4  =>  9 pairs (_)
A4,F4: 4.. / A4 = 4  =>  0 pairs (X) / F4 = 4  => 16 pairs (_)
E5,D6: 5.. / E5 = 5  =>  0 pairs (X) / D6 = 5  =>  9 pairs (_)
C7,A9: 5.. / C7 = 5  => 13 pairs (_) / A9 = 5  =>  8 pairs (_)
C1,C7: 5.. / C1 = 5  =>  8 pairs (_) / C7 = 5  => 13 pairs (_)
F1,E3: 6.. / F1 = 6  =>  0 pairs (X) / E3 = 6  =>  6 pairs (_)
B5,B6: 6.. / B5 = 6  => 19 pairs (_) / B6 = 6  =>  5 pairs (_)
E8,F8: 6.. / E8 = 6  =>  0 pairs (X) / F8 = 6  =>  6 pairs (_)
B6,H6: 6.. / B6 = 6  =>  5 pairs (_) / H6 = 6  => 19 pairs (_)
E3,E8: 6.. / E3 = 6  =>  6 pairs (_) / E8 = 6  =>  0 pairs (X)
F1,F8: 6.. / F1 = 6  =>  0 pairs (X) / F8 = 6  =>  6 pairs (_)
A4,B5: 8.. / A4 = 8  => 16 pairs (_) / B5 = 8  =>  0 pairs (X)
D8,D9: 8.. / D8 = 8  =>  7 pairs (_) / D9 = 8  =>  0 pairs (X)
* DURATION: 0:00:19.695618  START: 23:19:54.067328  END: 23:20:13.762946 2019-04-30
* CP COUNT: (21)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B9,C3,C6,E3)
* ....9..7..97.18......7.54.9.5167..9.7.91.....2...897..37.9....69.2.....7..6.379.4
* PAIR C3: 3,8 BLK 1
B1: 3,8,1,2,4                            # reduction candidate for 3,8
B1: 3,8                                  #  9 pairs
C1: 3,8,4,5                              # reduction candidate for 3,8
C1: 3,8 => CTR
* ....9..7..97.18...6..7254.9851674.9.7.9152.4.2.43897..375941..6942.....7186.379.4
C1: 4,5                                  #  6 pairs
B3: 3,8,1,2                              # reduction candidate for 3,8
B3: 3,8                                  # 10 pairs
* PAIR C3: 3,8 ROW 3
H3: 3,8,1,2,6                            # reduction candidate for 3,8
H3: 3,8                                  #  8 pairs
H3: 1,2,6                                #  6 pairs
* PAIR E3: 2,6 BLK 2
F1: 2,6,3,4                              # reduction candidate for 2,6
F1: 3,4 => CTR
* ..5.9..7..97.18....28765439851674.9.7.9152...2.3.897..374921..69.2..6..7516837924
F1: 2,6                                  # 13 pairs
* PAIR E3: 2,6 ROW 3
H3: 2,6,1,3,8                            # reduction candidate for 2,6
H3: 2,6                                  # 13 pairs
H3: 1,3,8                                #  5 pairs
* PAIR A4: 4,8 BLK 4
B5: 4,8,3,6                              # reduction candidate for 4,8
B5: 3,6                                  # 17 pairs
B5: 4,8                                  # 12 pairs
* PAIR A4: 4,8 COL A
A1: 4,8,1,5,6                            # reduction candidate for 4,8
A1: 4,8                                  # 12 pairs
A1: 1,5,6                                #  5 pairs
* PAIR C6: 3,4 BLK 4
B5: 3,4,6,8                              # reduction candidate for 3,4
B5: 3,4                                  # 17 pairs
B6: 3,4,6                                # reduction candidate for 3,4
B6: 3,4                                  # 19 pairs
* PAIR C6: 3,4 ROW 6
D6: 3,4,5                                # reduction candidate for 3,4
D6: 3,4 => CTR
* ..5.9..7..97.18....28765439851674.9.7.9152...2.3.897..374921..69.2.46..7516837924
D6: 5                                    #  9 pairs
H6: 3,4,1,5,6                            # reduction candidate for 3,4
H6: 3,4                                  #  9 pairs
* PAIR C6: 3,4 COL C
C1: 3,4,5,8                              # reduction candidate for 3,4
C1: 3,4                                  # 13 pairs
C1: 5,8                                  #  6 pairs
* PAIR B9: 1,8 BLK 7
B8: 1,8,4                                # reduction candidate for 1,8
B8: 1,8 => SOLVED
* 635492178497318562128765439851674293749123685263589741374951826912846357586237914
B8: 4                                    # 10 pairs
A9: 1,8,5                                # reduction candidate for 1,8
A9: 1,8                                  # 13 pairs
* PAIR B9: 1,8 ROW 9
H9: 1,8,2,5                              # reduction candidate for 1,8
H9: 1,8                                  # 16 pairs
H9: 2,5                                  #  7 pairs
* PAIR B9: 1,8 COL B
B1: 1,8,2,3,4                            # reduction candidate for 1,8
B1: 1,8 => CTR
* .85.92173.97.18...12.7654.9851674.9.769123.4.23458976137.941..6942856..7516237984
B1: 2,3,4                                #  5 pairs
B3: 1,8,2,3                              # reduction candidate for 1,8
B3: 1,8                                  # 22 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060522-absurd-base-pr-000.dot
* REASONING
* DIS # C1: 3,8 => CTR => C1: 4,5
* DIS # F1: 3,4 => CTR => F1: 2,6
* DIS # D6: 3,4 => CTR => D6: 5
* PRF # B8: 1,8 => SOL
* DIS # B1: 1,8 => CTR => B1: 2,3,4
* CNT   5 HDP CHAINS /  29 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B9,C3,C6,E3)
* ....9..7..97.18......7.54.9.5167..9.7.91.....2...897..37.9....69.2.....7..6.379.4
* PAIR C3: 3,8 BLK 1
B1: 3,8,1,2,4                            # reduction candidate for 3,8
B1: 3,8                                  #  9 pairs
C1: 3,8,4,5                              # reduction candidate for 3,8
C1: 3,8 => CTR
* ....9..7..97.18...6..7254.9851674.9.7.9152.4.2.43897..375941..6942.....7186.379.4
B3: 3,8,1,2                              # reduction candidate for 3,8
B3: 3,8                                  # 10 pairs
* PAIR C3: 3,8 ROW 3
H3: 3,8,1,2,6                            # reduction candidate for 3,8
H3: 3,8                                  #  9 pairs
H3: 1,2,6                                #  6 pairs
* PAIR RESTART
* PAIR C3: 3,8 BLK 1
B1: 3,8,1,2,4                            # reduction candidate for 3,8
B1: 3,8                                  #  9 pairs
B3: 3,8,1,2                              # reduction candidate for 3,8
B3: 3,8                                  # 10 pairs
* PAIR C3: 3,8 ROW 3
H3: 3,8,1,2,6                            # reduction candidate for 3,8
H3: 3,8                                  #  9 pairs
H3: 1,2,6                                #  6 pairs
* PAIR E3: 2,6 BLK 2
F1: 2,6,3,4                              # reduction candidate for 2,6
F1: 3,4 => CTR
* ..5.9..7..97.18....28765439851674.9.7.9152...2.3.897..374921..69.2..6..7516837924
* PAIR A4: 4,8 BLK 4
B5: 4,8,3,6                              # reduction candidate for 4,8
B5: 4,8                                  # 20 pairs
B5: 3,6                                  # 19 pairs
* PAIR A4: 4,8 COL A
A1: 4,8,1,5,6                            # reduction candidate for 4,8
A1: 4,8                                  # 16 pairs
A1: 1,5,6                                # 14 pairs
* PAIR C6: 3,4 BLK 4
B5: 3,4,6,8                              # reduction candidate for 3,4
B5: 3,4 => SOLVED
* 635492178497318562128765439851674293749123685263589741374951826912846357586237914
* DURATION: 0:00:09.910080  START: 23:20:29.006059  END: 23:20:38.916139 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060522-absurd-base-pr-001.dot
* REASONING
* DIS # C1: 3,8 => CTR => C1: 4,5
* DIS C1: 4,5 # F1: 3,4 => CTR => F1: 2,6
* PRF C1: 4,5 + F1: 2,6 # B5: 3,4 => SOL
* STA C1: 4,5 + F1: 2,6 + B5: 3,4
* CNT   3 HDP CHAINS /  16 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060522, absurd

Solution

position: 635492178497318562128765439851674293749123685263589741374951826912846357586237914 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 # B1: 3,8 => UNS
* DIS # C1: 3,8 => CTR => C1: 4,5
* INC # C1: 4,5 => UNS
* INC # B3: 3,8 => UNS
* INC # H3: 3,8 => UNS
* INC # H3: 1,2,6 => UNS
* INC # F1: 2,6 => UNS
* DIS # F1: 3,4 => CTR => F1: 2,6
* INC # H3: 2,6 => UNS
* INC # H3: 1,3,8 => UNS
* INC # B5: 4,8 => UNS
* INC # B5: 3,6 => UNS
* INC # A1: 4,8 => UNS
* INC # A1: 1,5,6 => UNS
* INC # B5: 3,4 => UNS
* INC # B6: 3,4 => UNS
* DIS # D6: 3,4 => CTR => D6: 5
* INC # D6: 5 => UNS
* INC # H6: 3,4 => UNS
* INC # C1: 3,4 => UNS
* INC # C1: 5,8 => UNS
* PRF # B8: 1,8 => SOL
* INC # B8: 4 => UNS
* INC # A9: 1,8 => UNS
* INC # H9: 1,8 => UNS
* INC # H9: 2,5 => UNS
* DIS # B1: 1,8 => CTR => B1: 2,3,4
* INC # B1: 2,3,4 => UNS
* INC # B3: 1,8 => UNS
* CNT  29 HDP CHAINS /  29 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 3,8 => UNS
* DIS # C1: 3,8 => CTR => C1: 4,5
* INC C1: 4,5 # B3: 3,8 => UNS
* INC C1: 4,5 # H3: 3,8 => UNS
* INC C1: 4,5 # H3: 1,2,6 => UNS
* INC C1: 4,5 # B1: 3,8 => UNS
* INC C1: 4,5 # B3: 3,8 => UNS
* INC C1: 4,5 # H3: 3,8 => UNS
* INC C1: 4,5 # H3: 1,2,6 => UNS
* INC C1: 4,5 # F1: 2,6 => UNS
* DIS C1: 4,5 # F1: 3,4 => CTR => F1: 2,6
* INC C1: 4,5 + F1: 2,6 # B5: 4,8 => UNS
* INC C1: 4,5 + F1: 2,6 # B5: 3,6 => UNS
* INC C1: 4,5 + F1: 2,6 # A1: 4,8 => UNS
* INC C1: 4,5 + F1: 2,6 # A1: 1,5,6 => UNS
* PRF C1: 4,5 + F1: 2,6 # B5: 3,4 => SOL
* STA C1: 4,5 + F1: 2,6 + B5: 3,4
* CNT  16 HDP CHAINS /  16 HYP OPENED