Analysis of zz-www.sudokuoftheday.co.uk-20060627-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: .....4.2......96181...6...37...4...1....7.86..869...4.5.1.....6..2....39.....71.. initial

Autosolve

position: .....492.2....96181...6.4.3725.4.391.1..7.86.3869...4.5.1...2.6..2....39.....71.4 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A9: 6,8 => CTR => A9: 9
* DIS # D1: 3,5 => CTR => D1: 1,7,8
* DIS # D2: 3,5 => CTR => D2: 7
* DIS # B2: 4 => CTR => B2: 3,5
* DIS # I6: 2 => CTR => I6: 5,7
* DIS # D9: 6,8 => CTR => D9: 2,3,5
* DIS # I6: 2,5 => CTR => I6: 7
* DIS # D5: 2,5 => CTR => D5: 3
* DIS # I6: 2 => CTR => I6: 5,7
* DIS # D7: 3,8 => CTR => D7: 4
* DIS # E7: 3,8 => CTR => E7: 9
* DIS # D9: 3,8 => CTR => D9: 2,5,6
* PRF # E9: 3,8 => SOL
* DIS # D9: 5,8 => CTR => D9: 2,3,6
* CNT  14 HDP CHAINS /  41 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 # A9: 6,8 => CTR => A9: 9
* DIS A9: 9 # E1: 3,5 => CTR => E1: 1,8
* DIS A9: 9 + E1: 1,8 # I6: 2 => CTR => I6: 5,7
* DIS A9: 9 + E1: 1,8 + I6: 5,7 # D8: 6,8 => CTR => D8: 1,4
* DIS A9: 9 + E1: 1,8 + I6: 5,7 + D8: 1,4 # D9: 6,8 => CTR => D9: 2
* PRF A9: 9 + E1: 1,8 + I6: 5,7 + D8: 1,4 + D9: 2 # D1: 1,8 => SOL
* STA A9: 9 + E1: 1,8 + I6: 5,7 + D8: 1,4 + D9: 2 + D1: 1,8
* CNT   6 HDP CHAINS /   8 HYP OPENED

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

Details

Positions

.....4.2......96181...6...37...4...1....7.86..869...4.5.1.....6..2....39.....71.. initial
.....492.2....96181...6.4.3725.4.391.1..7.86.3869...4.5.1...2.6..2....39.....71.4 autosolve
637814925254739618198562473725648391419375862386921547571493286842156739963287154 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
A1: 6,8
B3: 5,9
E2: 3,5
I1: 5,7
H3: 5,7
A5: 4,9
C5: 4,9
D4: 6,8
F4: 6,8
I5: 2,5
G6: 5,7
F7: 3,8
H7: 7,8
G8: 5,7
H9: 5,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D1,E1: 1.. / D1 = 1  => 15 pairs (_) / E1 = 1  => 22 pairs (_)
E6,F6: 1.. / E6 = 1  => 17 pairs (_) / F6 = 1  => 16 pairs (_)
D1,D8: 1.. / D1 = 1  => 15 pairs (_) / D8 = 1  => 22 pairs (_)
F6,F8: 1.. / F6 = 1  => 16 pairs (_) / F8 = 1  => 17 pairs (_)
D3,F3: 2.. / D3 = 2  => 19 pairs (_) / F3 = 2  => 17 pairs (_)
I5,I6: 2.. / I5 = 2  => 19 pairs (_) / I6 = 2  =>  0 pairs (X)
D9,E9: 2.. / D9 = 2  => 19 pairs (_) / E9 = 2  => 17 pairs (_)
E6,E9: 2.. / E6 = 2  => 19 pairs (_) / E9 = 2  => 17 pairs (_)
D5,F5: 3.. / D5 = 3  => 18 pairs (_) / F5 = 3  =>  0 pairs (X)
F5,F7: 3.. / F5 = 3  =>  0 pairs (X) / F7 = 3  => 18 pairs (_)
B2,C2: 4.. / B2 = 4  =>  0 pairs (X) / C2 = 4  => 19 pairs (_)
A5,C5: 4.. / A5 = 4  => 19 pairs (_) / C5 = 4  =>  0 pairs (X)
D7,D8: 4.. / D7 = 4  => 15 pairs (_) / D8 = 4  =>  0 pairs (X)
B7,D7: 4.. / B7 = 4  =>  0 pairs (X) / D7 = 4  => 15 pairs (_)
A5,A8: 4.. / A5 = 4  => 19 pairs (_) / A8 = 4  =>  0 pairs (X)
C2,C5: 4.. / C2 = 4  => 19 pairs (_) / C5 = 4  =>  0 pairs (X)
I1,H3: 5.. / I1 = 5  => 15 pairs (_) / H3 = 5  =>  0 pairs (X)
G8,H9: 5.. / G8 = 5  =>  0 pairs (X) / H9 = 5  => 15 pairs (_)
G6,G8: 5.. / G6 = 5  => 15 pairs (_) / G8 = 5  =>  0 pairs (X)
H3,H9: 5.. / H3 = 5  =>  0 pairs (X) / H9 = 5  => 15 pairs (_)
A1,B1: 6.. / A1 = 6  => 18 pairs (_) / B1 = 6  =>  0 pairs (X)
D4,F4: 6.. / D4 = 6  => 20 pairs (_) / F4 = 6  => 14 pairs (_)
F4,F8: 6.. / F4 = 6  => 14 pairs (_) / F8 = 6  => 20 pairs (_)
I1,H3: 7.. / I1 = 7  =>  0 pairs (X) / H3 = 7  => 15 pairs (_)
G6,I6: 7.. / G6 = 7  =>  0 pairs (X) / I6 = 7  => 15 pairs (_)
B7,B8: 7.. / B7 = 7  => 15 pairs (_) / B8 = 7  =>  0 pairs (X)
H7,G8: 7.. / H7 = 7  =>  0 pairs (X) / G8 = 7  => 15 pairs (_)
C2,D2: 7.. / C2 = 7  =>  0 pairs (X) / D2 = 7  => 16 pairs (_)
B7,H7: 7.. / B7 = 7  => 15 pairs (_) / H7 = 7  =>  0 pairs (X)
B8,G8: 7.. / B8 = 7  =>  0 pairs (X) / G8 = 7  => 15 pairs (_)
G6,G8: 7.. / G6 = 7  =>  0 pairs (X) / G8 = 7  => 15 pairs (_)
H3,H7: 7.. / H3 = 7  => 15 pairs (_) / H7 = 7  =>  0 pairs (X)
I1,I6: 7.. / I1 = 7  =>  0 pairs (X) / I6 = 7  => 15 pairs (_)
D4,F4: 8.. / D4 = 8  => 14 pairs (_) / F4 = 8  => 20 pairs (_)
H7,H9: 8.. / H7 = 8  => 15 pairs (_) / H9 = 8  =>  0 pairs (X)
B3,C3: 9.. / B3 = 9  => 16 pairs (_) / C3 = 9  =>  0 pairs (X)
A5,C5: 9.. / A5 = 9  =>  0 pairs (X) / C5 = 9  => 19 pairs (_)
E7,E9: 9.. / E7 = 9  => 15 pairs (_) / E9 = 9  =>  0 pairs (X)
B7,E7: 9.. / B7 = 9  =>  0 pairs (X) / E7 = 9  => 15 pairs (_)
A5,A9: 9.. / A5 = 9  =>  0 pairs (X) / A9 = 9  => 19 pairs (_)
* DURATION: 0:00:51.195460  START: 00:08:00.114906  END: 00:08:51.310366 2019-05-01
* CP COUNT: (40)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,B3,C5,D4,E2,F4,F7,G6,G8,H3,H7,H9,I1,I5)
* .....492.2....96181...6.4.3725.4.391.1..7.86.3869...4.5.1...2.6..2....39.....71.4
* PAIR A1: 6,8 COL A
A8: 6,8,4                                # reduction candidate for 6,8
A8: 6,8                                  # 19 pairs
A9: 6,8,9                                # reduction candidate for 6,8
A9: 6,8 => CTR
* 63871492524...9618159.6.473725.4.391914.7.8623869..547571493286462...739893627154
A9: 9                                    # 19 pairs
* PAIR E2: 3,5 BLK 2
D1: 3,5,1,7,8                            # reduction candidate for 3,5
D1: 3,5 => CTR
* ...514927254739618197.6.453725.4.39141937.86.3869.174.5714.32.6..21...39.....71.4
D1: 1,7,8                                # 15 pairs
E1: 3,5,1,8                              # reduction candidate for 3,5
E1: 3,5                                  # 26 pairs
D2: 3,5,7                                # reduction candidate for 3,5
D2: 3,5 => CTR
* 638714925247..9618159.6.473725.4.391914.7.8623869..547571493286462...739893627154
D2: 7                                    # 16 pairs
* PAIR E2: 3,5 ROW 2
B2: 3,5,4                                # reduction candidate for 3,5
B2: 4 => CTR
* 63871492524...9618159.6.473725.4.391914.7.8623869..547571493286462...739893627154
B2: 3,5                                  # 19 pairs
* PAIR E2: 3,5 COL E
E9: 3,5,2,8,9                            # reduction candidate for 3,5
E9: 3,5                                  # 22 pairs
E9: 2,8,9                                # 15 pairs
* PAIR I1: 5,7 ROW 1
D1: 5,7,1,3,8                            # reduction candidate for 5,7
D1: 5,7                                  # 30 pairs
D1: 1,3,8                                # 15 pairs
* PAIR I1: 5,7 COL I
I6: 5,7,2                                # reduction candidate for 5,7
I6: 2 => CTR
* .....49272....961819..6.453725.4.391.1..7.8653869.57425.1.9.27687241.539....27184
I6: 5,7                                  # 19 pairs
* PAIR H3: 5,7 ROW 3
D3: 5,7,2,8                              # reduction candidate for 5,7
D3: 5,7                                  # 26 pairs
D3: 2,8                                  # 16 pairs
* PAIR D4: 6,8 COL D
D8: 6,8,1,4,5                            # reduction candidate for 6,8
D8: 6,8                                  # 18 pairs
D9: 6,8,2,3,5                            # reduction candidate for 6,8
D9: 6,8 => CTR
* ..71349252..759618159268473725846391914375862386912547571493286462581739...627154
D9: 2,3,5                                # 17 pairs
* PAIR F4: 6,8 COL F
F8: 6,8,1,5                              # reduction candidate for 6,8
F8: 6,8                                  # 21 pairs
F8: 1,5                                  # 15 pairs
* PAIR I5: 2,5 BLK 6
I6: 2,5,7                                # reduction candidate for 2,5
I6: 2,5 => CTR
* 6..1849272....9618198762453725648391419.7.86.3869..74.5.1.9.276872416539.....7184
I6: 7                                    # 15 pairs
* PAIR I5: 2,5 ROW 5
D5: 2,5,3                                # reduction candidate for 2,5
D5: 2,5 => CTR
* .....492.2....96181...6.4.3725.4.391.1..7386.3869...4.5.1..82768724.6.39.....71.4
D5: 3                                    # 18 pairs
F5: 2,5,3                                # reduction candidate for 2,5
F5: 2,5                                  # 18 pairs
* PAIR G6: 5,7 BLK 6
I6: 5,7,2                                # reduction candidate for 5,7
I6: 2 => CTR
* .....49272....961819..6.453725.4.391.1..7.8653869.57425.1.9.27687241.539....27184
I6: 5,7                                  # 19 pairs
* PAIR F7: 3,8 BLK 8
D7: 3,8,4                                # reduction candidate for 3,8
D7: 3,8 => CTR
* 6.81.49272.47.9618197.6.453725648391419.7.86.3869.174.541893276872416539963..7184
D7: 4                                    # 15 pairs
E7: 3,8,9                                # reduction candidate for 3,8
E7: 3,8 => CTR
* .....492.2....96181...6.4.3725.4.391.1..7.86.3869...4.5914..276.72...539....97184
E7: 9                                    # 15 pairs
D9: 3,8,2,5,6                            # reduction candidate for 3,8
D9: 3,8 => CTR
* .....49252....96181...6.473725.4.391.1..7.8623869.2547571493286..2..1739...827154
D9: 2,5,6                                # 15 pairs
E9: 3,8,2,5,9                            # reduction candidate for 3,8
E9: 3,8 => SOLVED
* 637814925254739618198562473725648391419375862386921547571493286842156739963287154
E9: 2,5,9                                # 15 pairs
* PAIR H9: 5,8 ROW 9
D9: 5,8,2,3,6                            # reduction candidate for 5,8
D9: 5,8 => CTR
* 637184925254739618198.6.473725648391419375862386912.47571493286842...739963827154
D9: 2,3,6                                # 15 pairs
E9: 5,8,2,3,9                            # reduction candidate for 5,8
E9: 5,8                                  # 23 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060627-absurd-base-pr-000.dot
* REASONING
* DIS # A9: 6,8 => CTR => A9: 9
* DIS # D1: 3,5 => CTR => D1: 1,7,8
* DIS # D2: 3,5 => CTR => D2: 7
* DIS # B2: 4 => CTR => B2: 3,5
* DIS # I6: 2 => CTR => I6: 5,7
* DIS # D9: 6,8 => CTR => D9: 2,3,5
* DIS # I6: 2,5 => CTR => I6: 7
* DIS # D5: 2,5 => CTR => D5: 3
* DIS # I6: 2 => CTR => I6: 5,7
* DIS # D7: 3,8 => CTR => D7: 4
* DIS # E7: 3,8 => CTR => E7: 9
* DIS # D9: 3,8 => CTR => D9: 2,5,6
* PRF # E9: 3,8 => SOL
* DIS # D9: 5,8 => CTR => D9: 2,3,6
* CNT  14 HDP CHAINS /  41 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,B3,C5,D4,E2,F4,F7,G6,G8,H3,H7,H9,I1,I5)
* .....492.2....96181...6.4.3725.4.391.1..7.86.3869...4.5.1...2.6..2....39.....71.4
* PAIR A1: 6,8 COL A
A8: 6,8,4                                # reduction candidate for 6,8
A8: 6,8                                  # 19 pairs
A9: 6,8,9                                # reduction candidate for 6,8
A9: 6,8 => CTR
* 63871492524...9618159.6.473725.4.391914.7.8623869..547571493286462...739893627154
* RESTART
* PAIR RESTART
* PAIR E2: 3,5 BLK 2
E1: 3,5,1,8                              # reduction candidate for 3,5
E1: 3,5 => CTR
* ...1.492.2.47.9618197.6.453725.4.391419.7.86.3869...4.5.1.9.2.6..2....399....71.4
* PAIR I1: 5,7 COL I
I6: 5,7,2                                # reduction candidate for 5,7
I6: 2 => CTR
* .....4927254739618197.6.453725.4.391419.7.8653869..7425.1.9.276.724..5399...27184
* PAIR RESTART
* PAIR D4: 6,8 COL D
D8: 6,8,1,4                              # reduction candidate for 6,8
D8: 6,8 => CTR
* ...184925254739618198.6.473725.4.391419.7.8623869..547571493286842651.399....71.4
D9: 6,8,2                                # reduction candidate for 6,8
D9: 6,8 => CTR
* .631.492.25473961819.26.4.3725.4.391419.7.8623869.2.4.5.1.9.2.6..2..1.399..627154
* PAIR RESTART

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (B7,B8,C1,C3,D3,D7,D8,E1,E8,E9,G6,G8,H3,H7,H9,I1,I6)
* 63...492.25473961819..624.3725648391419375862386921.4.5.1.932.68.2..6.399632.71.4
* PAIR E1: 1,8 BLK 2
D1: 1,8,5                                # reduction candidate for 1,8
D1: 1,8 => SOLVED
* 637814925254739618198562473725648391419375862386921547571493286842156739963287154
* DURATION: 0:00:08.965392  START: 00:09:18.845945  END: 00:09:27.811337 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060627-absurd-base-pr-001.dot
* REASONING
* DIS # A9: 6,8 => CTR => A9: 9
* DIS A9: 9 # E1: 3,5 => CTR => E1: 1,8
* DIS A9: 9 + E1: 1,8 # I6: 2 => CTR => I6: 5,7
* DIS A9: 9 + E1: 1,8 + I6: 5,7 # D8: 6,8 => CTR => D8: 1,4
* DIS A9: 9 + E1: 1,8 + I6: 5,7 + D8: 1,4 # D9: 6,8 => CTR => D9: 2
* PRF A9: 9 + E1: 1,8 + I6: 5,7 + D8: 1,4 + D9: 2 # D1: 1,8 => SOL
* STA A9: 9 + E1: 1,8 + I6: 5,7 + D8: 1,4 + D9: 2 + D1: 1,8
* CNT   6 HDP CHAINS /   8 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060627, absurd

Solution

position: 637814925254739618198562473725648391419375862386921547571493286842156739963287154 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 # A8: 6,8 => UNS
* DIS # A9: 6,8 => CTR => A9: 9
* INC # A9: 9 => UNS
* DIS # D1: 3,5 => CTR => D1: 1,7,8
* INC # D1: 1,7,8 => UNS
* INC # E1: 3,5 => UNS
* DIS # D2: 3,5 => CTR => D2: 7
* INC # D2: 7 => UNS
* INC # B2: 3,5 => UNS
* DIS # B2: 4 => CTR => B2: 3,5
* INC # E9: 3,5 => UNS
* INC # E9: 2,8,9 => UNS
* INC # D1: 5,7 => UNS
* INC # D1: 1,3,8 => UNS
* INC # I6: 5,7 => UNS
* DIS # I6: 2 => CTR => I6: 5,7
* INC # D3: 5,7 => UNS
* INC # D3: 2,8 => UNS
* INC # D8: 6,8 => UNS
* DIS # D9: 6,8 => CTR => D9: 2,3,5
* INC # D9: 2,3,5 => UNS
* INC # F8: 6,8 => UNS
* INC # F8: 1,5 => UNS
* DIS # I6: 2,5 => CTR => I6: 7
* INC # I6: 7 => UNS
* DIS # D5: 2,5 => CTR => D5: 3
* INC # D5: 3 => UNS
* INC # F5: 2,5 => UNS
* INC # I6: 5,7 => UNS
* DIS # I6: 2 => CTR => I6: 5,7
* DIS # D7: 3,8 => CTR => D7: 4
* INC # D7: 4 => UNS
* DIS # E7: 3,8 => CTR => E7: 9
* INC # E7: 9 => UNS
* DIS # D9: 3,8 => CTR => D9: 2,5,6
* INC # D9: 2,5,6 => UNS
* PRF # E9: 3,8 => SOL
* INC # E9: 2,5,9 => UNS
* DIS # D9: 5,8 => CTR => D9: 2,3,6
* INC # D9: 2,3,6 => UNS
* INC # E9: 5,8 => UNS
* CNT  41 HDP CHAINS /  41 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A8: 6,8 => UNS
* DIS # A9: 6,8 => CTR => A9: 9
* DIS A9: 9 # E1: 3,5 => CTR => E1: 1,8
* INC A9: 9 + E1: 1,8 # I6: 5,7 => UNS
* DIS A9: 9 + E1: 1,8 # I6: 2 => CTR => I6: 5,7
* DIS A9: 9 + E1: 1,8 + I6: 5,7 # D8: 6,8 => CTR => D8: 1,4
* DIS A9: 9 + E1: 1,8 + I6: 5,7 + D8: 1,4 # D9: 6,8 => CTR => D9: 2
* PRF A9: 9 + E1: 1,8 + I6: 5,7 + D8: 1,4 + D9: 2 # D1: 1,8 => SOL
* STA A9: 9 + E1: 1,8 + I6: 5,7 + D8: 1,4 + D9: 2 + D1: 1,8
* CNT   8 HDP CHAINS /   8 HYP OPENED