Analysis of zz-www.sudokuoftheday.co.uk-20190303-absurd-base.sdk

Contents

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

level: medium

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

position: ...67.......2.5..16.....8.23.....52......3..7...94..3...6....749.7.1.3...1....... initial

Autosolve

position: 1..67.9.3...2.576167....8.23.....529.....34177..94.638..6...1749.7.1.38..1....29. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B2: 4,8 => CTR => B2: 3,9
* DIS # C2: 4,8 => CTR => C2: 3,9
* DIS # A9: 4,8 => CTR => A9: 5
* PRF # A9: 5 => SOL
* PRF # F9: 4,8 => SOL
* DIS # E2: 3,9 => CTR => E2: 8
* PRF # E2: 8 => SOL
* DIS # C3: 3,9 => CTR => C3: 5
* PRF # C3: 5 => SOL
* DIS # E7: 3,9 => CTR => E7: 2,5,8
* DIS # B5: 2,8 => CTR => B5: 6,9
* DIS # C5: 2,8 => CTR => C5: 9
* PRF # C5: 9 => SOL
* DIS # E5: 2,8 => CTR => E5: 5,6
* PRF # E5: 5,6 => SOL
* PRF # A7: 2,8 => SOL
* DIS # A7: 5 => CTR => A7: 2,8
* DIS # C6: 2,5 => CTR => C6: 1
* PRF # C6: 1 => SOL
* DIS # B1: 2,5 => CTR => B1: 8
* PRF # B1: 8 => SOL
* DIS # F4: 6,8 => CTR => F4: 1,7
* DIS # E5: 6,8 => CTR => E5: 2,5
* PRF # E5: 2,5 => SOL
* DIS # B4: 6,8 => CTR => B4: 4
* PRF # B4: 4 => SOL
* DIS # E9: 6,8 => CTR => E9: 3,5
* PRF # E5: 5,8 => SOL
* DIS # E5: 2,6 => CTR => E5: 5,8
* PRF # D7: 5,8 => SOL
* DIS # D7: 3 => CTR => D7: 5,8
* DIS # D9: 5,8 => CTR => D9: 3,4,7
* DIS # C6: 5 => CTR => C6: 1,2
* DIS # F8: 2,4 => CTR => F8: 6
* PRF # F8: 6 => SOL
* DIS # D9: 4,5 => CTR => D9: 3,7,8
* DIS # E9: 5,6 => CTR => E9: 3,8
* PRF # E9: 3,8 => SOL
* CNT  38 HDP CHAINS /  48 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 # B2: 4,8 => CTR => B2: 3,9
* DIS B2: 3,9 # C2: 4,8 => CTR => C2: 3,9
* PRF B2: 3,9 + C2: 3,9 => SOL
* STA B2: 3,9 + C2: 3,9
* CNT   3 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

...67.......2.5..16.....8.23.....52......3..7...94..3...6....749.7.1.3...1....... initial
1..67.9.3...2.576167....8.23.....529.....34177..94.638..6...1749.7.1.38..1....29. autosolve
182674953493285761675391842348167529269853417751942638836529174927416385514738296 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
A2: 4,8
F1: 4,8
E3: 3,9
H1: 4,5
H3: 4,5
A5: 2,8
B6: 2,5
E4: 6,8
D5: 5,8
F6: 1,2
B8: 2,4
D8: 4,5
I8: 5,6
I9: 5,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D3,F3: 1.. / D3 = 1  => 17 pairs (_) / F3 = 1  =>  0 pairs (*)
C4,C6: 1.. / C4 = 1  =>  0 pairs (X) / C6 = 1  =>  0 pairs (_)
C6,F6: 1.. / C6 = 1  =>  0 pairs (*) / F6 = 1  =>  0 pairs (X)
D3,D4: 1.. / D3 = 1  => 17 pairs (_) / D4 = 1  =>  0 pairs (*)
B1,C1: 2.. / B1 = 2  =>  0 pairs (X) / C1 = 2  => 17 pairs (_)
E5,F6: 2.. / E5 = 2  =>  0 pairs (X) / F6 = 2  =>  0 pairs (_)
B8,F8: 2.. / B8 = 2  =>  0 pairs (*) / F8 = 2  =>  0 pairs (X)
A5,A7: 2.. / A5 = 2  =>  0 pairs (*) / A7 = 2  =>  0 pairs (X)
E5,E7: 2.. / E5 = 2  =>  0 pairs (X) / E7 = 2  =>  0 pairs (_)
B7,C9: 3.. / B7 = 3  =>  0 pairs (*) / C9 = 3  =>  0 pairs (X)
B2,B7: 3.. / B2 = 3  =>  0 pairs (X) / B7 = 3  =>  0 pairs (_)
H1,H3: 4.. / H1 = 4  =>  0 pairs (X) / H3 = 4  =>  0 pairs (_)
B4,C4: 4.. / B4 = 4  =>  0 pairs (*) / C4 = 4  =>  0 pairs (X)
F1,H1: 4.. / F1 = 4  =>  0 pairs (*) / H1 = 4  =>  0 pairs (X)
A2,A9: 4.. / A2 = 4  => 14 pairs (_) / A9 = 4  =>  0 pairs (X)
H1,H3: 5.. / H1 = 5  =>  0 pairs (*) / H3 = 5  =>  0 pairs (X)
B6,C6: 5.. / B6 = 5  => 15 pairs (_) / C6 = 5  =>  0 pairs (X)
D5,E5: 5.. / D5 = 5  =>  0 pairs (X) / E5 = 5  =>  0 pairs (_)
A7,A9: 5.. / A7 = 5  =>  0 pairs (X) / A9 = 5  =>  0 pairs (_)
I8,I9: 5.. / I8 = 5  =>  0 pairs (*) / I9 = 5  =>  0 pairs (X)
C3,H3: 5.. / C3 = 5  =>  0 pairs (*) / H3 = 5  =>  0 pairs (X)
D8,I8: 5.. / D8 = 5  =>  0 pairs (X) / I8 = 5  =>  0 pairs (_)
B1,B6: 5.. / B1 = 5  =>  0 pairs (X) / B6 = 5  => 15 pairs (_)
B4,B5: 6.. / B4 = 6  =>  0 pairs (X) / B5 = 6  =>  0 pairs (_)
I8,I9: 6.. / I8 = 6  =>  0 pairs (X) / I9 = 6  =>  0 pairs (_)
B5,E5: 6.. / B5 = 6  =>  0 pairs (*) / E5 = 6  =>  0 pairs (X)
F8,I8: 6.. / F8 = 6  =>  0 pairs (*) / I8 = 6  =>  0 pairs (X)
D4,F4: 7.. / D4 = 7  => 16 pairs (_) / F4 = 7  => 15 pairs (_)
D9,F9: 7.. / D9 = 7  => 15 pairs (_) / F9 = 7  => 16 pairs (_)
D4,D9: 7.. / D4 = 7  => 16 pairs (_) / D9 = 7  => 15 pairs (_)
F4,F9: 7.. / F4 = 7  => 15 pairs (_) / F9 = 7  => 16 pairs (_)
F1,E2: 8.. / F1 = 8  =>  0 pairs (X) / E2 = 8  =>  0 pairs (_)
B5,C5: 9.. / B5 = 9  =>  0 pairs (X) / C5 = 9  =>  0 pairs (_)
E7,F7: 9.. / E7 = 9  =>  0 pairs (X) / F7 = 9  => 15 pairs (_)
B2,B5: 9.. / B2 = 9  =>  0 pairs (*) / B5 = 9  =>  0 pairs (X)
F3,F7: 9.. / F3 = 9  =>  0 pairs (X) / F7 = 9  => 15 pairs (_)
* DURATION: 0:00:55.206457  START: 04:11:08.336592  END: 04:12:03.543049 2019-05-01
* CP COUNT: (36)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B6,B8,D5,D8,E3,E4,F1,F6,H1,H3,I8,I9)
* 1..67.9.3...2.576167....8.23.....529.....34177..94.638..6...1749.7.1.38..1....29.
* PAIR A2: 4,8 BLK 1
B2: 4,8,3,9                              # reduction candidate for 4,8
B2: 4,8 => CTR
* 1.267.9.3...2.576167....8.2364.8.529298.634177..942638.36.29174927.1.38..1..5.296
B2: 3,9                                  # 15 pairs
C2: 4,8,3,9                              # reduction candidate for 4,8
C2: 4,8 => CTR
* 1..678943...2.576167....8523.4...529.....34177.19426382.6..917494751638..1....29.
C2: 3,9                                  # 15 pairs
* PAIR A2: 4,8 COL A
A9: 4,8,5                                # reduction candidate for 4,8
A9: 4,8 => CTR
* 1826749534..285761675.91842348167529269853417751942638536.29174927.1.38..1....29.
A9: 5 => SOLVED
* 182674953493285761675391842348167529269853417751942638836529174927416385514738296
* PAIR F1: 4,8 COL F
F9: 4,8,6,7                              # reduction candidate for 4,8
F9: 4,8 => SOLVED
* 182674953493285761675391842348167529269853417751942638836529174927416385514738296
F9: 6,7                                  # 15 pairs
* PAIR E3: 3,9 BLK 2
E2: 3,9,8                                # reduction candidate for 3,9
E2: 3,9 => CTR
* 1..678943...2.576167....8523.4...529.....34177.19426382.6..917494751638..1....29.
E2: 8 => SOLVED
* 182674953493285761675391842348167529269853417751942638836529174927416385514738296
* PAIR E3: 3,9 ROW 3
C3: 3,9,5                                # reduction candidate for 3,9
C3: 3,9 => CTR
* 1..678943...2.576167....8523.4...529.....34177.19426382.6..917494751638..1....29.
C3: 5 => SOLVED
* 182674953493285761675391842348167529269853417751942638836529174927416385514738296
* PAIR E3: 3,9 COL E
E7: 3,9,2,5,8                            # reduction candidate for 3,9
E7: 3,9 => CTR
* 1..67.9.3...2.576167....8.23.....529....234177..9416382.65..174947.1.38..1....29.
E7: 2,5,8                                # 15 pairs
* PAIR A5: 2,8 BLK 4
B5: 2,8,6,9                              # reduction candidate for 2,8
B5: 2,8 => CTR
* 1..67.9.3.9.2.576167....8.2364.8.529..95634177.1942638.36...1749.7.1.38..1....29.
B5: 6,9                                  # 15 pairs
C5: 2,8,9                                # reduction candidate for 2,8
C5: 2,8 => CTR
* 1.267.9.3...2.576167....8.2364.8.5292985634177519426385.6.29174927416385413.5.296
C5: 9 => SOLVED
* 182674953493285761675391842348167529269853417751942638836529174927416385514738296
* PAIR A5: 2,8 ROW 5
E5: 2,8,5,6                              # reduction candidate for 2,8
E5: 2,8 => CTR
* 182674953493285761675...84234.768529.695.34177..94.638.368..174927416385.1...7296
E5: 5,6 => SOLVED
* 182674953493285761675391842348167529269853417751942638836529174927416385514738296
* PAIR A5: 2,8 COL A
A7: 2,8,5                                # reduction candidate for 2,8
A7: 2,8 => SOLVED
* 182674953493285761675391842348167529269853417751942638836529174927416385514738296
A7: 5 => CTR
* 1826749534..285761675.91842348167529269853417751942638536.29174927.1.38..1....29.
* PAIR B6: 2,5 BLK 4
C6: 2,5,1                                # reduction candidate for 2,5
C6: 2,5 => CTR
* 1..67.9.3...2.576167.1..8.2341...529.69.234177..9416382.6...1749.7.1.38..1....29.
C6: 1 => SOLVED
* 182674953493285761675391842348167529269853417751942638836529174927416385514738296
* PAIR B6: 2,5 COL B
B1: 2,5,8                                # reduction candidate for 2,5
B1: 2,5 => CTR
* 1..67.9.3...2.576167....8.23.4...529.....34177.19426382.6...17494751638..1....29.
B1: 8 => SOLVED
* 182674953493285761675391842348167529269853417751942638836529174927416385514738296
* PAIR E4: 6,8 BLK 5
F4: 6,8,1,7                              # reduction candidate for 6,8
F4: 6,8 => CTR
* 1..67.9.3...2.576167.1..8.23.17..529....234177..9416382.6...17494751238651...729.
F4: 1,7                                  # 15 pairs
E5: 6,8,2,5                              # reduction candidate for 6,8
E5: 6,8 => CTR
* 1826749534..285761675...8.23.....5292..5.34177519426385.6.29174927416385.1..5.296
E5: 2,5 => SOLVED
* 182674953493285761675391842348167529269853417751942638836529174927416385514738296
* PAIR E4: 6,8 ROW 4
B4: 6,8,4                                # reduction candidate for 6,8
B4: 6,8 => CTR
* 1.267.9.384.2.5761675...8.23.4...529.....34177.1942638..6.29174927.1.38.41....29.
B4: 4 => SOLVED
* 182674953493285761675391842348167529269853417751942638836529174927416385514738296
* PAIR E4: 6,8 COL E
E9: 6,8,3,5                              # reduction candidate for 6,8
E9: 6,8 => CTR
* 1..678943.9.235761673.9.85238476152926985341775.94.638.36..91749.7.1.38..1.3.729.
E9: 3,5                                  # 15 pairs
* PAIR D5: 5,8 BLK 5
E5: 5,8,2,6                              # reduction candidate for 5,8
E5: 5,8 => SOLVED
* 182674953493285761675391842348167529269853417751942638836529174927416385514738296
E5: 2,6 => CTR
* 1826749534..28576167....8.23.....5292..563417751942638..6.29174927416385.1..5.296
* PAIR D5: 5,8 COL D
D7: 5,8,3                                # reduction candidate for 5,8
D7: 5,8 => SOLVED
* 182674953493285761675391842348167529269853417751942638836529174927416385514738296
D7: 3 => CTR
* 1..67.9.3.3.2.576167..3.8.23.....529.9..634177..942638..6329174927.1.38.413.5.296
D9: 5,8,3,4,7                            # reduction candidate for 5,8
D9: 5,8 => CTR
* 1..67.9.3.3.2.576167.13.8.234.7..529.....34177..94.638..63..1749.741.385.13..7296
D9: 3,4,7                                # 14 pairs
* PAIR F6: 1,2 ROW 6
C6: 1,2,5                                # reduction candidate for 1,2
C6: 5 => CTR
* 152678943...2.576167.1.4852341...529.69.23417725941638..6...1749.7.1.38..1....29.
C6: 1,2                                  # 15 pairs
* PAIR B8: 2,4 ROW 8
F8: 2,4,6                                # reduction candidate for 2,4
F8: 2,4 => CTR
* 1..67.9.3...2.576167....8.23.....5292..8534177519426385.6329174927514386.137..295
F8: 6 => SOLVED
* 182674953493285761675391842348167529269853417751942638836529174927416385514738296
* PAIR D8: 4,5 BLK 8
D9: 4,5,3,7,8                            # reduction candidate for 4,5
D9: 4,5 => CTR
* 1..67.9.3.3.2.576167.13.8.23..7..529.9.8.34177..94.638..63..1749.7.1.38..13..729.
D9: 3,7,8                                # 14 pairs
* PAIR I9: 5,6 ROW 9
E9: 5,6,3,8                              # reduction candidate for 5,6
E9: 5,6 => CTR
* 1826749534..285761675...8.23.....5292....34177519426385.6.29174927.1.38..1....29.
E9: 3,8 => SOLVED
* 182674953493285761675391842348167529269853417751942638836529174927416385514738296
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190303-absurd-base-pr-000.dot
* REASONING
* DIS # B2: 4,8 => CTR => B2: 3,9
* DIS # C2: 4,8 => CTR => C2: 3,9
* DIS # A9: 4,8 => CTR => A9: 5
* PRF # A9: 5 => SOL
* PRF # F9: 4,8 => SOL
* DIS # E2: 3,9 => CTR => E2: 8
* PRF # E2: 8 => SOL
* DIS # C3: 3,9 => CTR => C3: 5
* PRF # C3: 5 => SOL
* DIS # E7: 3,9 => CTR => E7: 2,5,8
* DIS # B5: 2,8 => CTR => B5: 6,9
* DIS # C5: 2,8 => CTR => C5: 9
* PRF # C5: 9 => SOL
* DIS # E5: 2,8 => CTR => E5: 5,6
* PRF # E5: 5,6 => SOL
* PRF # A7: 2,8 => SOL
* DIS # A7: 5 => CTR => A7: 2,8
* DIS # C6: 2,5 => CTR => C6: 1
* PRF # C6: 1 => SOL
* DIS # B1: 2,5 => CTR => B1: 8
* PRF # B1: 8 => SOL
* DIS # F4: 6,8 => CTR => F4: 1,7
* DIS # E5: 6,8 => CTR => E5: 2,5
* PRF # E5: 2,5 => SOL
* DIS # B4: 6,8 => CTR => B4: 4
* PRF # B4: 4 => SOL
* DIS # E9: 6,8 => CTR => E9: 3,5
* PRF # E5: 5,8 => SOL
* DIS # E5: 2,6 => CTR => E5: 5,8
* PRF # D7: 5,8 => SOL
* DIS # D7: 3 => CTR => D7: 5,8
* DIS # D9: 5,8 => CTR => D9: 3,4,7
* DIS # C6: 5 => CTR => C6: 1,2
* DIS # F8: 2,4 => CTR => F8: 6
* PRF # F8: 6 => SOL
* DIS # D9: 4,5 => CTR => D9: 3,7,8
* DIS # E9: 5,6 => CTR => E9: 3,8
* PRF # E9: 3,8 => SOL
* CNT  38 HDP CHAINS /  48 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B6,B8,D5,D8,E3,E4,F1,F6,H1,H3,I8,I9)
* 1..67.9.3...2.576167....8.23.....529.....34177..94.638..6...1749.7.1.38..1....29.
* PAIR A2: 4,8 BLK 1
B2: 4,8,3,9                              # reduction candidate for 4,8
B2: 4,8 => CTR
* 1.267.9.3...2.576167....8.2364.8.529298.634177..942638.36.29174927.1.38..1..5.296
C2: 4,8,3,9                              # reduction candidate for 4,8
C2: 4,8 => CTR
* 1..678943...2.576167....8523.4...529.....34177.19426382.6..917494751638..1....29.
C2: 3,9 => SOLVED
* 182674953493285761675391842348167529269853417751942638836529174927416385514738296
* DURATION: 0:00:02.568158  START: 04:12:49.913782  END: 04:12:52.481940 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190303-absurd-base-pr-001.dot
* REASONING
* DIS # B2: 4,8 => CTR => B2: 3,9
* DIS B2: 3,9 # C2: 4,8 => CTR => C2: 3,9
* PRF B2: 3,9 + C2: 3,9 => SOL
* STA B2: 3,9 + C2: 3,9
* CNT   3 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190303, absurd

Solution

position: 182674953493285761675391842348167529269853417751942638836529174927416385514738296 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:

* DIS # B2: 4,8 => CTR => B2: 3,9
* INC # B2: 3,9 => UNS
* DIS # C2: 4,8 => CTR => C2: 3,9
* INC # C2: 3,9 => UNS
* DIS # A9: 4,8 => CTR => A9: 5
* PRF # A9: 5 => SOL
* PRF # F9: 4,8 => SOL
* INC # F9: 6,7 => UNS
* DIS # E2: 3,9 => CTR => E2: 8
* PRF # E2: 8 => SOL
* DIS # C3: 3,9 => CTR => C3: 5
* PRF # C3: 5 => SOL
* DIS # E7: 3,9 => CTR => E7: 2,5,8
* INC # E7: 2,5,8 => UNS
* DIS # B5: 2,8 => CTR => B5: 6,9
* INC # B5: 6,9 => UNS
* DIS # C5: 2,8 => CTR => C5: 9
* PRF # C5: 9 => SOL
* DIS # E5: 2,8 => CTR => E5: 5,6
* PRF # E5: 5,6 => SOL
* PRF # A7: 2,8 => SOL
* DIS # A7: 5 => CTR => A7: 2,8
* DIS # C6: 2,5 => CTR => C6: 1
* PRF # C6: 1 => SOL
* DIS # B1: 2,5 => CTR => B1: 8
* PRF # B1: 8 => SOL
* DIS # F4: 6,8 => CTR => F4: 1,7
* INC # F4: 1,7 => UNS
* DIS # E5: 6,8 => CTR => E5: 2,5
* PRF # E5: 2,5 => SOL
* DIS # B4: 6,8 => CTR => B4: 4
* PRF # B4: 4 => SOL
* DIS # E9: 6,8 => CTR => E9: 3,5
* INC # E9: 3,5 => UNS
* PRF # E5: 5,8 => SOL
* DIS # E5: 2,6 => CTR => E5: 5,8
* PRF # D7: 5,8 => SOL
* DIS # D7: 3 => CTR => D7: 5,8
* DIS # D9: 5,8 => CTR => D9: 3,4,7
* INC # D9: 3,4,7 => UNS
* INC # C6: 1,2 => UNS
* DIS # C6: 5 => CTR => C6: 1,2
* DIS # F8: 2,4 => CTR => F8: 6
* PRF # F8: 6 => SOL
* DIS # D9: 4,5 => CTR => D9: 3,7,8
* INC # D9: 3,7,8 => UNS
* DIS # E9: 5,6 => CTR => E9: 3,8
* PRF # E9: 3,8 => SOL
* CNT  48 HDP CHAINS /  48 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B2: 4,8 => CTR => B2: 3,9
* DIS B2: 3,9 # C2: 4,8 => CTR => C2: 3,9
* PRF B2: 3,9 + C2: 3,9 => SOL
* STA B2: 3,9 + C2: 3,9
* CNT   3 HDP CHAINS /   2 HYP OPENED