Analysis of zz-www.sudokuoftheday.co.uk-20190218-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019

position: .975..1.......9..8.85.........73....628.....1..4.2.....6..45.2...23....7......46. initial

Autosolve

position: .9758.1.6.36..9..8.85.........73....628954..1374.21...76..45.2..423...17......46. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A3: 2,4 => CTR => A3: 1
* DIS # F3: 7 => CTR => F3: 2,3
* PRF # E3: 1,7 => SOL
* DIS # E3: 6 => CTR => E3: 1,7
* DIS # E9: 1,7 => CTR => E9: 9
* PRF # E9: 9 => SOL
* PRF # H3: 3,4 => SOL
* DIS # A3: 2,4 => CTR => A3: 1
* DIS # D3: 2,4 => CTR => D3: 1,6
* DIS # A9: 5,9 => CTR => A9: 8
* DIS # H3: 3,7 => CTR => H3: 4,9
* DIS # G6: 5,9 => CTR => G6: 6
* PRF # G6: 6 => SOL
* PRF # H6: 5,9 => SOL
* DIS # H6: 8 => CTR => H6: 5,9
* DIS # D9: 1,8 => CTR => D9: 2
* DIS # F3: 2,7 => CTR => F3: 3
* DIS # G8: 8,9 => CTR => G8: 5
* DIS # I9: 5 => CTR => I9: 3,9
* DIS # C7: 1 => CTR => C7: 3,9
* CNT  20 HDP CHAINS /  40 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 # A3: 2,4 => CTR => A3: 1
* DIS A3: 1 # F3: 7 => CTR => F3: 2,3
* PRF A3: 1 + F3: 2,3 # H3: 3,4 => SOL
* STA A3: 1 + F3: 2,3 + H3: 3,4
* CNT   3 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

.975..1.......9..8.85.........73....628.....1..4.2.....6..45.2...23....7......46. initial
.9758.1.6.36..9..8.85.........73....628954..1374.21...76..45.2..423...17......46. autosolve
497582136236419758185673942519736284628954371374821695763145829942368517851297463 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (23)
A1: 2,4
F1: 2,3
E2: 1,7
H1: 3,4
I3: 2,4
A4: 5,9
B4: 1,5
C4: 1,9
F4: 6,8
D6: 6,8
G4: 2,6
H4: 4,8
I4: 2,4
G5: 3,7
H5: 3,7
I6: 5,9
B9: 1,5
D7: 1,8
E8: 6,9
F8: 6,8
F9: 2,7
G7: 8,9
I7: 3,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A2,A3: 1.. / A2 = 1  =>  0 pairs (X) / A3 = 1  => 25 pairs (_)
B4,C4: 1.. / B4 = 1  => 23 pairs (_) / C4 = 1  => 25 pairs (_)
C7,D7: 1.. / C7 = 1  =>  0 pairs (X) / D7 = 1  => 26 pairs (_)
B4,B9: 1.. / B4 = 1  => 23 pairs (_) / B9 = 1  => 25 pairs (_)
G4,I4: 2.. / G4 = 2  =>  0 pairs (*) / I4 = 2  =>  0 pairs (X)
D9,F9: 2.. / D9 = 2  => 26 pairs (_) / F9 = 2  =>  0 pairs (X)
A1,F1: 2.. / A1 = 2  =>  0 pairs (X) / F1 = 2  => 24 pairs (_)
I3,I4: 2.. / I3 = 2  =>  0 pairs (*) / I4 = 2  =>  0 pairs (X)
F1,F3: 3.. / F1 = 3  =>  0 pairs (X) / F3 = 3  => 24 pairs (_)
G5,H5: 3.. / G5 = 3  => 22 pairs (_) / H5 = 3  =>  0 pairs (X)
C7,C9: 3.. / C7 = 3  => 27 pairs (_) / C9 = 3  => 24 pairs (_)
I7,I9: 3.. / I7 = 3  => 24 pairs (_) / I9 = 3  => 27 pairs (_)
F1,H1: 3.. / F1 = 3  =>  0 pairs (X) / H1 = 3  => 24 pairs (_)
C7,I7: 3.. / C7 = 3  => 27 pairs (_) / I7 = 3  => 24 pairs (_)
C9,I9: 3.. / C9 = 3  => 24 pairs (_) / I9 = 3  => 27 pairs (_)
G3,G5: 3.. / G3 = 3  =>  0 pairs (X) / G5 = 3  => 22 pairs (_)
D2,D3: 4.. / D2 = 4  => 25 pairs (_) / D3 = 4  =>  0 pairs (X)
H4,I4: 4.. / H4 = 4  =>  0 pairs (X) / I4 = 4  =>  0 pairs (_)
A1,H1: 4.. / A1 = 4  => 24 pairs (_) / H1 = 4  =>  0 pairs (X)
I3,I4: 4.. / I3 = 4  =>  0 pairs (X) / I4 = 4  =>  0 pairs (_)
G2,H2: 5.. / G2 = 5  =>  0 pairs (X) / H2 = 5  => 25 pairs (_)
A4,B4: 5.. / A4 = 5  => 23 pairs (_) / B4 = 5  => 25 pairs (_)
G8,I9: 5.. / G8 = 5  => 29 pairs (_) / I9 = 5  =>  0 pairs (X)
A8,G8: 5.. / A8 = 5  =>  0 pairs (X) / G8 = 5  => 29 pairs (_)
B4,B9: 5.. / B4 = 5  => 25 pairs (_) / B9 = 5  => 23 pairs (_)
H2,H6: 5.. / H2 = 5  => 25 pairs (_) / H6 = 5  =>  0 pairs (X)
I6,I9: 5.. / I6 = 5  => 29 pairs (_) / I9 = 5  =>  0 pairs (X)
D3,E3: 6.. / D3 = 6  =>  0 pairs (*) / E3 = 6  =>  0 pairs (X)
F4,D6: 6.. / F4 = 6  =>  0 pairs (*) / D6 = 6  =>  0 pairs (X)
G4,G6: 6.. / G4 = 6  =>  0 pairs (X) / G6 = 6  =>  0 pairs (_)
E8,F8: 6.. / E8 = 6  =>  0 pairs (*) / F8 = 6  =>  0 pairs (X)
F4,G4: 6.. / F4 = 6  =>  0 pairs (*) / G4 = 6  =>  0 pairs (X)
D6,G6: 6.. / D6 = 6  =>  0 pairs (X) / G6 = 6  =>  0 pairs (_)
D3,D6: 6.. / D3 = 6  =>  0 pairs (*) / D6 = 6  =>  0 pairs (X)
E3,E8: 6.. / E3 = 6  =>  0 pairs (X) / E8 = 6  =>  0 pairs (_)
F4,F8: 6.. / F4 = 6  =>  0 pairs (*) / F8 = 6  =>  0 pairs (X)
G5,H5: 7.. / G5 = 7  =>  0 pairs (X) / H5 = 7  => 22 pairs (_)
E9,F9: 7.. / E9 = 7  =>  0 pairs (X) / F9 = 7  => 26 pairs (_)
F3,F9: 7.. / F3 = 7  =>  0 pairs (X) / F9 = 7  => 26 pairs (_)
F4,D6: 8.. / F4 = 8  =>  0 pairs (X) / D6 = 8  =>  0 pairs (_)
H4,H6: 8.. / H4 = 8  =>  0 pairs (*) / H6 = 8  =>  0 pairs (X)
A8,A9: 8.. / A8 = 8  =>  0 pairs (X) / A9 = 8  => 25 pairs (_)
G7,G8: 8.. / G7 = 8  => 26 pairs (_) / G8 = 8  =>  0 pairs (X)
F4,H4: 8.. / F4 = 8  =>  0 pairs (X) / H4 = 8  =>  0 pairs (_)
D6,H6: 8.. / D6 = 8  =>  0 pairs (*) / H6 = 8  =>  0 pairs (X)
D7,G7: 8.. / D7 = 8  =>  0 pairs (X) / G7 = 8  => 26 pairs (_)
A9,D9: 8.. / A9 = 8  => 25 pairs (_) / D9 = 8  =>  0 pairs (X)
F4,F8: 8.. / F4 = 8  =>  0 pairs (X) / F8 = 8  =>  0 pairs (_)
G3,H3: 9.. / G3 = 9  =>  0 pairs (*) / H3 = 9  =>  0 pairs (X)
A4,C4: 9.. / A4 = 9  => 25 pairs (_) / C4 = 9  => 23 pairs (_)
E8,E9: 9.. / E8 = 9  =>  0 pairs (X) / E9 = 9  =>  0 pairs (_)
H3,H6: 9.. / H3 = 9  => 24 pairs (_) / H6 = 9  =>  0 pairs (*)
* DURATION: 0:01:09.046121  START: 03:49:23.724585  END: 03:50:32.770706 2019-05-01
* CP COUNT: (52)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B4,B9,C4,D6,D7,E2,E8,F1,F4,F8,F9,G4,G5,G7,H1,H4,H5,I3,I4,I6,I7)
* .9758.1.6.36..9..8.85.........73....628954..1374.21...76..45.2..423...17......46.
* PAIR A1: 2,4 BLK 1
A2: 2,4,1                                # reduction candidate for 2,4
A2: 2,4                                  # 25 pairs
A3: 2,4,1                                # reduction candidate for 2,4
A3: 2,4 => CTR
* .9758.1.6136479258.85.....4...73.642628954..1374621.8.76.845923.423.68178.32.746.
A3: 1                                    # 25 pairs
* PAIR F1: 2,3 BLK 2
F3: 2,3,7                                # reduction candidate for 2,3
F3: 7 => CTR
* .97583146.36..9..8.85..7..2...73.284628954..13748216..76.14582..423.8.178..2..46.
F3: 2,3                                  # 26 pairs
* PAIR E2: 1,7 BLK 2
E3: 1,7,6                                # reduction candidate for 1,7
E3: 1,7 => SOLVED
* 497582136236419758185673942519736284628954371374821695763145829942368517851297463
E3: 6 => CTR
* 497582136.364.9.58.85163794...738642628954371374621.8.761845923.4239681785....46.
* PAIR E2: 1,7 COL E
E9: 1,7,9                                # reduction candidate for 1,7
E9: 1,7 => CTR
* 497582136.364.9.58.85163.94...738642628954371374621.8.761845923.4239681785....46.
E9: 9 => SOLVED
* 497582136236419758185673942519736284628954371374821695763145829942368517851297463
* PAIR H1: 3,4 BLK 3
H3: 3,4,7,9                              # reduction candidate for 3,4
H3: 3,4 => SOLVED
* 497582136236419758185673942519736284628954371374821695763145829942368517851297463
H3: 7,9                                  # 24 pairs
* PAIR I3: 2,4 ROW 3
A3: 2,4,1                                # reduction candidate for 2,4
A3: 2,4 => CTR
* .9758.1.6136479258.85.....4...73.642628954..1374621.8.76.845923.423.68178.32.746.
A3: 1                                    # 25 pairs
D3: 2,4,1,6                              # reduction candidate for 2,4
D3: 2,4 => CTR
* 4975821362364.9.58185.6..9....738642628954.71374621.8.76..45.2..42396.17......46.
D3: 1,6                                  # 28 pairs
* PAIR A4: 5,9 COL A
A8: 5,9,8                                # reduction candidate for 5,9
A8: 5,9                                  # 25 pairs
A9: 5,9,8                                # reduction candidate for 5,9
A9: 5,9 => CTR
* 297583146.36..9.58.85.67..2...738...628954..1374.21...76..45.2.8423.6517...8.246.
A9: 8                                    # 25 pairs
* PAIR C4: 1,9 COL C
C7: 1,9,3                                # reduction candidate for 1,9
C7: 1,9                                  # 24 pairs
C9: 1,9,3                                # reduction candidate for 1,9
C9: 1,9                                  # 27 pairs
* PAIR G5: 3,7 COL G
G3: 3,7,2,9                              # reduction candidate for 3,7
G3: 2,9                                  # 28 pairs
G3: 3,7                                  # 26 pairs
* PAIR H5: 3,7 COL H
H3: 3,7,4,9                              # reduction candidate for 3,7
H3: 3,7 => CTR
* .9758.1.6.36..9758.85...932...73.28462895437137482169576.14582..423.85178512.746.
H3: 4,9                                  # 24 pairs
* PAIR I6: 5,9 BLK 6
G6: 5,9,6                                # reduction candidate for 5,9
G6: 5,9 => CTR
* 497582136.364.9.58.85163794...738642628954371374621.8.761845923.4239681785....46.
G6: 6 => SOLVED
* 497582136236419758185673942519736284628954371374821695763145829942368517851297463
H6: 5,9,8                                # reduction candidate for 5,9
H6: 5,9 => SOLVED
* 497582136236419758185673942519736284628954371374821695763145829942368517851297463
H6: 8 => CTR
* 497582136.364.9.58.85163794...738642628954371374621.8.761845923.4239681785...746.
* PAIR I6: 5,9 COL I
I9: 5,9,3                                # reduction candidate for 5,9
I9: 3                                    # 27 pairs
I9: 5,9                                  # 24 pairs
* PAIR D7: 1,8 BLK 8
D9: 1,8,2                                # reduction candidate for 1,8
D9: 1,8 => CTR
* 297583146.36..9..8.85..7..2...73.284628954..13748216..76.145.2..423...17.....246.
D9: 2                                    # 26 pairs
* PAIR F9: 2,7 COL F
F3: 2,7,3                                # reduction candidate for 2,7
F3: 2,7 => CTR
* .97583146.36..9..8.85.....2...73.284628954..13748216..76.14582..423.8.178..2.746.
F3: 3                                    # 24 pairs
* PAIR G7: 8,9 BLK 9
G8: 8,9,5                                # reduction candidate for 8,9
G8: 8,9 => CTR
* .9758.1462364.9..8.856...9.951736284628954..1374821659769145823542368917813297465
G8: 5                                    # 29 pairs
* PAIR I7: 3,9 BLK 9
I9: 3,9,5                                # reduction candidate for 3,9
I9: 5 => CTR
* .9758.1462364.9..8.856...9.951736284628954..1374821659769145823542368917813297465
I9: 3,9                                  # 29 pairs
* PAIR I7: 3,9 ROW 7
C7: 3,9,1                                # reduction candidate for 3,9
C7: 1 => CTR
* .9758.1.6.36..9..8.85.........73....628954..1374.21...761845923.423.681785....46.
C7: 3,9                                  # 26 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190218-absurd-base-pr-000.dot
* REASONING
* DIS # A3: 2,4 => CTR => A3: 1
* DIS # F3: 7 => CTR => F3: 2,3
* PRF # E3: 1,7 => SOL
* DIS # E3: 6 => CTR => E3: 1,7
* DIS # E9: 1,7 => CTR => E9: 9
* PRF # E9: 9 => SOL
* PRF # H3: 3,4 => SOL
* DIS # A3: 2,4 => CTR => A3: 1
* DIS # D3: 2,4 => CTR => D3: 1,6
* DIS # A9: 5,9 => CTR => A9: 8
* DIS # H3: 3,7 => CTR => H3: 4,9
* DIS # G6: 5,9 => CTR => G6: 6
* PRF # G6: 6 => SOL
* PRF # H6: 5,9 => SOL
* DIS # H6: 8 => CTR => H6: 5,9
* DIS # D9: 1,8 => CTR => D9: 2
* DIS # F3: 2,7 => CTR => F3: 3
* DIS # G8: 8,9 => CTR => G8: 5
* DIS # I9: 5 => CTR => I9: 3,9
* DIS # C7: 1 => CTR => C7: 3,9
* CNT  20 HDP CHAINS /  40 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B4,B9,C4,D6,D7,E2,E8,F1,F4,F8,F9,G4,G5,G7,H1,H4,H5,I3,I4,I6,I7)
* .9758.1.6.36..9..8.85.........73....628954..1374.21...76..45.2..423...17......46.
* PAIR A1: 2,4 BLK 1
A2: 2,4,1                                # reduction candidate for 2,4
A2: 2,4                                  # 25 pairs
A3: 2,4,1                                # reduction candidate for 2,4
A3: 2,4 => CTR
* .9758.1.6136479258.85.....4...73.642628954..1374621.8.76.845923.423.68178.32.746.
* RESTART
* PAIR F1: 2,3 BLK 2
F3: 2,3,7                                # reduction candidate for 2,3
F3: 7 => CTR
* .97583146436..9..8185467..2...73.284628954..1374.21...76..45.2..423...17......46.
* PAIR H1: 3,4 BLK 3
H3: 3,4,7,9                              # reduction candidate for 3,4
H3: 3,4 => SOLVED
* 497582136236419758185673942519736284628954371374821695763145829942368517851297463
* DURATION: 0:00:04.626925  START: 03:51:02.931633  END: 03:51:07.558558 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190218-absurd-base-pr-001.dot
* REASONING
* DIS # A3: 2,4 => CTR => A3: 1
* DIS A3: 1 # F3: 7 => CTR => F3: 2,3
* PRF A3: 1 + F3: 2,3 # H3: 3,4 => SOL
* STA A3: 1 + F3: 2,3 + H3: 3,4
* CNT   3 HDP CHAINS /   5 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190218, absurd

Solution

position: 497582136236419758185673942519736284628954371374821695763145829942368517851297463 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: 2,4 => UNS
* DIS # A3: 2,4 => CTR => A3: 1
* INC # A3: 1 => UNS
* INC # F3: 2,3 => UNS
* DIS # F3: 7 => CTR => F3: 2,3
* PRF # E3: 1,7 => SOL
* DIS # E3: 6 => CTR => E3: 1,7
* DIS # E9: 1,7 => CTR => E9: 9
* PRF # E9: 9 => SOL
* PRF # H3: 3,4 => SOL
* INC # H3: 7,9 => UNS
* DIS # A3: 2,4 => CTR => A3: 1
* INC # A3: 1 => UNS
* DIS # D3: 2,4 => CTR => D3: 1,6
* INC # D3: 1,6 => UNS
* INC # A8: 5,9 => UNS
* DIS # A9: 5,9 => CTR => A9: 8
* INC # A9: 8 => UNS
* INC # C7: 1,9 => UNS
* INC # C9: 1,9 => UNS
* INC # G3: 3,7 => UNS
* INC # G3: 2,9 => UNS
* DIS # H3: 3,7 => CTR => H3: 4,9
* INC # H3: 4,9 => UNS
* DIS # G6: 5,9 => CTR => G6: 6
* PRF # G6: 6 => SOL
* PRF # H6: 5,9 => SOL
* DIS # H6: 8 => CTR => H6: 5,9
* INC # I9: 5,9 => UNS
* INC # I9: 3 => UNS
* DIS # D9: 1,8 => CTR => D9: 2
* INC # D9: 2 => UNS
* DIS # F3: 2,7 => CTR => F3: 3
* INC # F3: 3 => UNS
* DIS # G8: 8,9 => CTR => G8: 5
* INC # G8: 5 => UNS
* INC # I9: 3,9 => UNS
* DIS # I9: 5 => CTR => I9: 3,9
* INC # C7: 3,9 => UNS
* DIS # C7: 1 => CTR => C7: 3,9
* CNT  40 HDP CHAINS /  40 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 2,4 => UNS
* DIS # A3: 2,4 => CTR => A3: 1
* INC A3: 1 # F3: 2,3 => UNS
* DIS A3: 1 # F3: 7 => CTR => F3: 2,3
* PRF A3: 1 + F3: 2,3 # H3: 3,4 => SOL
* STA A3: 1 + F3: 2,3 + H3: 3,4
* CNT   5 HDP CHAINS /   5 HYP OPENED