Analysis of zz-www.sudokuoftheday.co.uk-20060419-absurd-base.sdk

Contents

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

level: medium

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

position: .56.4..124..1...6...3.6.8.4..7.5....9..3..1.......6..8..4..32..5.9.....32...9...1 initial

Autosolve

position: .56.493124.213..6...3.6.8.4..7.51.3.9.53..1..3.1..6..8..4..32..5.9.....3238.9...1 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B2: 9 => CTR => B2: 7,8
* DIS # B3: 1,7 => CTR => B3: 9
* DIS # A7: 1,7 => CTR => A7: 6
* PRF # F2: 5 => SOL
* DIS # B4: 6,8 => CTR => B4: 2,4
* DIS # B5: 2,4 => CTR => B5: 6,8
* DIS # D6: 2,4 => CTR => D6: 7,9
* DIS # F5: 2,7 => CTR => F5: 4,8
* DIS # D6: 2,7 => CTR => D6: 4,9
* PRF # G4: 6,9 => SOL
* DIS # I7: 6,9 => CTR => I7: 5,7
* CNT  11 HDP CHAINS /  34 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: 9 => CTR => B2: 7,8
* PRF B2: 7,8 # F2: 5 => SOL
* STA B2: 7,8 + F2: 5
* CNT   2 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

.56.4..124..1...6...3.6.8.4..7.5....9..3..1.......6..8..4..32..5.9.....32...9...1 initial
.56.493124.213..6...3.6.8.4..7.51.3.9.53..1..3.1..6..8..4..32..5.9.....3238.9...1 autosolve
756849312482135769193267854827451936965328147341976528614783295579612483238594671 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
A1: 7,8
A3: 1,7
D1: 7,8
A4: 6,8
B6: 2,4
E6: 2,7
I4: 6,9
I5: 6,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A3,B3: 1.. / A3 = 1  =>  9 pairs (_) / B3 = 1  =>  0 pairs (X)
E7,E8: 1.. / E7 = 1  => 13 pairs (_) / E8 = 1  => 11 pairs (_)
B8,E8: 1.. / B8 = 1  => 13 pairs (_) / E8 = 1  => 11 pairs (_)
A3,A7: 1.. / A3 = 1  =>  9 pairs (_) / A7 = 1  =>  0 pairs (X)
D3,F3: 2.. / D3 = 2  => 11 pairs (_) / F3 = 2  =>  9 pairs (_)
H5,H6: 2.. / H5 = 2  =>  9 pairs (_) / H6 = 2  => 10 pairs (_)
B4,D4: 2.. / B4 = 2  =>  8 pairs (_) / D4 = 2  => 21 pairs (_)
G6,H6: 5.. / G6 = 5  =>  9 pairs (_) / H6 = 5  => 15 pairs (_)
I2,I7: 5.. / I2 = 5  => 13 pairs (_) / I7 = 5  => 13 pairs (_)
B5,I5: 6.. / B5 = 6  => 13 pairs (_) / I5 = 6  =>  0 pairs (X)
D9,G9: 6.. / D9 = 6  =>  8 pairs (_) / G9 = 6  => 10 pairs (_)
A4,A7: 6.. / A4 = 6  =>  0 pairs (X) / A7 = 6  => 10 pairs (_)
A1,D1: 7.. / A1 = 7  => 10 pairs (_) / D1 = 7  =>  0 pairs (X)
A1,B2: 8.. / A1 = 8  =>  0 pairs (X) / B2 = 8  => 10 pairs (_)
D1,F2: 8.. / D1 = 8  => 10 pairs (_) / F2 = 8  =>  0 pairs (X)
H7,H8: 8.. / H7 = 8  =>  0 pairs (X) / H8 = 8  =>  8 pairs (_)
A1,D1: 8.. / A1 = 8  =>  0 pairs (X) / D1 = 8  => 10 pairs (_)
B2,F2: 8.. / B2 = 8  => 10 pairs (_) / F2 = 8  =>  0 pairs (X)
A1,A4: 8.. / A1 = 8  =>  0 pairs (X) / A4 = 8  => 10 pairs (_)
B2,B3: 9.. / B2 = 9  =>  0 pairs (X) / B3 = 9  => 10 pairs (_)
D4,D6: 9.. / D4 = 9  =>  0 pairs (X) / D6 = 9  =>  8 pairs (_)
H7,I7: 9.. / H7 = 9  => 10 pairs (_) / I7 = 9  =>  0 pairs (X)
B3,H3: 9.. / B3 = 9  => 10 pairs (_) / H3 = 9  =>  0 pairs (X)
* DURATION: 0:00:23.828857  START: 22:30:02.177550  END: 22:30:26.006407 2019-04-30
* CP COUNT: (23)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A4,B6,D1,E6,I4,I5)
* .56.493124.213..6...3.6.8.4..7.51.3.9.53..1..3.1..6..8..4..32..5.9.....3238.9...1
* PAIR A1: 7,8 BLK 1
B2: 7,8,9                                # reduction candidate for 7,8
B2: 9 => CTR
* 856749312492138.6...3.6.8946.7.51.399.53..1.63.19.6..8..4..32..5.9.....3238.9...1
B2: 7,8                                  # 10 pairs
* PAIR A3: 1,7 BLK 1
B3: 1,7,9                                # reduction candidate for 1,7
B3: 1,7 => CTR
* 856749312492138.65..3.6.8946.7.51.3.9.53..1..3.1..6..8..4..32.95.9.....3238.9...1
B3: 9                                    # 10 pairs
* PAIR A3: 1,7 COL A
A7: 1,7,6                                # reduction candidate for 1,7
A7: 1,7 => CTR
* 8567493124.2138965.93.6.8746.7.514399.53.41263419267587.4..329.5.9....83238.9...1
A7: 6                                    # 10 pairs
* PAIR D1: 7,8 BLK 2
F2: 7,8,5                                # reduction candidate for 7,8
F2: 5 => SOLVED
* 756849312482135769193267854827451936965328147341976528614783295579612483238594671
F2: 7,8                                  # 12 pairs
* PAIR D1: 7,8 COL D
D7: 7,8,5,6                              # reduction candidate for 7,8
D7: 7,8                                  # 15 pairs
D8: 7,8,2,4,6                            # reduction candidate for 7,8
D8: 7,8                                  # 11 pairs
* PAIR A4: 6,8 BLK 4
B4: 6,8,2,4                              # reduction candidate for 6,8
B4: 6,8 => CTR
* .56.493124.213.96..93.62854..72514399253841.63.1976528..4..329.5.9.2..83238.9..41
B4: 2,4                                  # 10 pairs
B5: 6,8,2,4                              # reduction candidate for 6,8
B5: 6,8                                  # 10 pairs
* PAIR B6: 2,4 BLK 4
B4: 2,4,6,8                              # reduction candidate for 2,4
B4: 2,4                                  # 10 pairs
B5: 2,4,6,8                              # reduction candidate for 2,4
B5: 2,4 => CTR
* .56.493124.2138965193.6.874.872514399.53.41.63419.6..8..4..329.5.94...83238.9..41
B5: 6,8                                  # 10 pairs
* PAIR B6: 2,4 ROW 6
D6: 2,4,7,9                              # reduction candidate for 2,4
D6: 2,4 => CTR
* 75684931248213.965193562874827951436965384127341276598674.13289519.28..3238.9...1
D6: 7,9                                  #  9 pairs
H6: 2,4,5,7,9                            # reduction candidate for 2,4
H6: 2,4                                  # 11 pairs
* PAIR E6: 2,7 BLK 5
E5: 2,7,8                                # reduction candidate for 2,7
E5: 2,7                                  # 14 pairs
F5: 2,7,4,8                              # reduction candidate for 2,7
F5: 2,7 => CTR
* .56.4931248213..6..93.6.8.4827451.3.96538.1473419765286.4.13295519.28473238.9...1
F5: 4,8                                  #  9 pairs
D6: 2,7,4,9                              # reduction candidate for 2,7
D6: 2,7 => CTR
* 75684931248213.965193.62874827951436965384127341..65986.45.32895.9..8..3238.9...1
D6: 4,9                                  #  9 pairs
* PAIR E6: 2,7 ROW 6
H6: 2,7,4,5,9                            # reduction candidate for 2,7
H6: 4,5,9                                #  9 pairs
H6: 2,7                                  #  9 pairs
* PAIR E6: 2,7 COL E
E8: 2,7,1,8                              # reduction candidate for 2,7
E8: 2,7                                  # 14 pairs
E8: 1,8                                  # 10 pairs
* PAIR I4: 6,9 BLK 6
G4: 6,9,4                                # reduction candidate for 6,9
G4: 6,9 => SOLVED
* 756849312482135769193267854827451936965328147341976528614783295579612483238594671
G4: 4                                    # 10 pairs
* PAIR I4: 6,9 COL I
I7: 6,9,5,7                              # reduction candidate for 6,9
I7: 6,9 => CTR
* 756849312482137965193.6.8748.79514369653.4127341..65986.4..32.95.9..8.43238495..1
I7: 5,7                                  # 12 pairs
* PAIR I5: 6,7 COL I
I7: 6,7,5,9                              # reduction candidate for 6,7
I7: 6,7                                  # 20 pairs
I7: 5,9                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060419-absurd-base-pr-000.dot
* REASONING
* DIS # B2: 9 => CTR => B2: 7,8
* DIS # B3: 1,7 => CTR => B3: 9
* DIS # A7: 1,7 => CTR => A7: 6
* PRF # F2: 5 => SOL
* DIS # B4: 6,8 => CTR => B4: 2,4
* DIS # B5: 2,4 => CTR => B5: 6,8
* DIS # D6: 2,4 => CTR => D6: 7,9
* DIS # F5: 2,7 => CTR => F5: 4,8
* DIS # D6: 2,7 => CTR => D6: 4,9
* PRF # G4: 6,9 => SOL
* DIS # I7: 6,9 => CTR => I7: 5,7
* CNT  11 HDP CHAINS /  34 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,A4,B6,D1,E6,I4,I5)
* .56.493124.213..6...3.6.8.4..7.51.3.9.53..1..3.1..6..8..4..32..5.9.....3238.9...1
* PAIR A1: 7,8 BLK 1
B2: 7,8,9                                # reduction candidate for 7,8
B2: 9 => CTR
* 856749312492138.6...3.6.8946.7.51.399.53..1.63.19.6..8..4..32..5.9.....3238.9...1
* PAIR D1: 7,8 BLK 2
F2: 7,8,5                                # reduction candidate for 7,8
F2: 5 => SOLVED
* 756849312482135769193267854827451936965328147341976528614783295579612483238594671
* DURATION: 0:00:03.327231  START: 22:30:46.165748  END: 22:30:49.492979 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060419-absurd-base-pr-001.dot
* REASONING
* DIS # B2: 9 => CTR => B2: 7,8
* PRF B2: 7,8 # F2: 5 => SOL
* STA B2: 7,8 + F2: 5
* CNT   2 HDP CHAINS /   4 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060419, absurd

Solution

position: 756849312482135769193267854827451936965328147341976528614783295579612483238594671 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 # B2: 7,8 => UNS
* DIS # B2: 9 => CTR => B2: 7,8
* DIS # B3: 1,7 => CTR => B3: 9
* INC # B3: 9 => UNS
* DIS # A7: 1,7 => CTR => A7: 6
* INC # A7: 6 => UNS
* INC # F2: 7,8 => UNS
* PRF # F2: 5 => SOL
* INC # D7: 7,8 => UNS
* INC # D8: 7,8 => UNS
* DIS # B4: 6,8 => CTR => B4: 2,4
* INC # B4: 2,4 => UNS
* INC # B5: 6,8 => UNS
* INC # B4: 2,4 => UNS
* DIS # B5: 2,4 => CTR => B5: 6,8
* INC # B5: 6,8 => UNS
* DIS # D6: 2,4 => CTR => D6: 7,9
* INC # D6: 7,9 => UNS
* INC # H6: 2,4 => UNS
* INC # E5: 2,7 => UNS
* DIS # F5: 2,7 => CTR => F5: 4,8
* INC # F5: 4,8 => UNS
* DIS # D6: 2,7 => CTR => D6: 4,9
* INC # D6: 4,9 => UNS
* INC # H6: 2,7 => UNS
* INC # H6: 4,5,9 => UNS
* INC # E8: 2,7 => UNS
* INC # E8: 1,8 => UNS
* PRF # G4: 6,9 => SOL
* INC # G4: 4 => UNS
* DIS # I7: 6,9 => CTR => I7: 5,7
* INC # I7: 5,7 => UNS
* INC # I7: 6,7 => UNS
* INC # I7: 5,9 => UNS
* CNT  34 HDP CHAINS /  34 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 7,8 => UNS
* DIS # B2: 9 => CTR => B2: 7,8
* INC B2: 7,8 # F2: 7,8 => UNS
* PRF B2: 7,8 # F2: 5 => SOL
* STA B2: 7,8 + F2: 5
* CNT   4 HDP CHAINS /   4 HYP OPENED