Analysis of zz-www.sudokuoftheday.co.uk-20190430-absurd-base.sdk

Contents

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

level: medium

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

position: ..92.8....359..2..4..7.....15..9......4..5.39....8...5..7....1......6..45.3....76 initial

Autosolve

position: ..92.8....359..2..4..7.....15..9......4..5.3939..8...5..7....1.....76..45.3....76 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B1: 6,7 => CTR => B1: 1
* DIS # A5: 6,7 => CTR => A5: 2,8
* PRF # F6: 1,4 => SOL
* DIS # F9: 1,4 => CTR => F9: 2,9
* DIS # E3: 1,3 => CTR => E3: 5,6
* DIS # I3: 8 => CTR => I3: 1,3
* DIS # A5: 2,6 => CTR => A5: 7,8
* DIS # B5: 2,6 => CTR => B5: 7,8
* DIS # C3: 2,6 => CTR => C3: 1,8
* DIS # G5: 8 => CTR => G5: 1,6
* DIS # F6: 1,2 => CTR => F6: 4,7
* DIS # E9: 4 => CTR => E9: 1,2
* DIS # G7: 8,9 => CTR => G7: 3,5
* DIS # G8: 8,9 => CTR => G8: 3,5
* DIS # G3: 8,9 => CTR => G3: 3,5,6
* CNT  15 HDP CHAINS /  42 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 # B1: 6,7 => CTR => B1: 1
* DIS B1: 1 # A2: 8 => CTR => A2: 6,7
* DIS B1: 1 + A2: 6,7 # C4: 8 => CTR => C4: 2,6
* PRF B1: 1 + A2: 6,7 + C4: 2,6 # E1: 4,6 => SOL
* STA B1: 1 + A2: 6,7 + C4: 2,6 + E1: 4,6
* CNT   4 HDP CHAINS /   9 HYP OPENED

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

Details

Positions

..92.8....359..2..4..7.....15..9......4..5.39....8...5..7....1......6..45.3....76 initial
..92.8....359..2..4..7.....15..9......4..5.3939..8...5..7....1.....76..45.3....76 autosolve
719268453635941287428753691156397842874625139392184765267439518981576324543812976 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
A1: 6,7
F2: 1,4
F3: 1,3
C6: 2,6
D5: 1,6
E5: 1,2
G9: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G5,G6: 1.. / G5 = 1  => 20 pairs (_) / G6 = 1  => 11 pairs (_)
C3,C8: 1.. / C3 = 1  =>  0 pairs (X) / C8 = 1  =>  8 pairs (_)
B3,C3: 2.. / B3 = 2  =>  9 pairs (_) / C3 = 2  =>  0 pairs (X)
I7,H8: 2.. / I7 = 2  =>  9 pairs (_) / H8 = 2  => 16 pairs (_)
I4,I7: 2.. / I4 = 2  => 16 pairs (_) / I7 = 2  =>  9 pairs (_)
D4,F4: 3.. / D4 = 3  =>  8 pairs (_) / F4 = 3  =>  0 pairs (X)
D8,G8: 3.. / D8 = 3  =>  0 pairs (X) / G8 = 3  =>  8 pairs (_)
B7,B9: 4.. / B7 = 4  =>  0 pairs (X) / B9 = 4  => 12 pairs (_)
E1,E3: 5.. / E1 = 5  =>  0 pairs (X) / E3 = 5  =>  7 pairs (_)
D7,D8: 5.. / D7 = 5  =>  7 pairs (_) / D8 = 5  =>  8 pairs (_)
D7,G7: 5.. / D7 = 5  =>  7 pairs (_) / G7 = 5  =>  8 pairs (_)
A7,B7: 6.. / A7 = 6  =>  0 pairs (X) / B7 = 6  => 13 pairs (_)
A5,B5: 7.. / A5 = 7  =>  0 pairs (X) / B5 = 7  =>  8 pairs (_)
F4,F6: 7.. / F4 = 7  =>  0 pairs (*) / F6 = 7  =>  0 pairs (X)
A2,I2: 7.. / A2 = 7  => 20 pairs (_) / I2 = 7  => 11 pairs (_)
F6,G6: 7.. / F6 = 7  =>  7 pairs (_) / G6 = 7  =>  0 pairs (*)
B1,B5: 7.. / B1 = 7  =>  0 pairs (X) / B5 = 7  =>  8 pairs (_)
G3,H3: 9.. / G3 = 9  =>  0 pairs (X) / H3 = 9  =>  7 pairs (_)
A7,A8: 9.. / A7 = 9  =>  0 pairs (X) / A8 = 9  =>  7 pairs (_)
F7,F9: 9.. / F7 = 9  =>  6 pairs (_) / F9 = 9  =>  0 pairs (X)
F9,G9: 9.. / F9 = 9  =>  0 pairs (X) / G9 = 9  =>  6 pairs (_)
H3,H8: 9.. / H3 = 9  =>  7 pairs (_) / H8 = 9  =>  0 pairs (X)
* DURATION: 0:00:19.711048  START: 05:42:36.610627  END: 05:42:56.321675 2019-05-01
* CP COUNT: (22)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C6,D5,E5,F2,F3,G9)
* ..92.8....359..2..4..7.....15..9......4..5.3939..8...5..7....1.....76..45.3....76
* PAIR A1: 6,7 BLK 1
B1: 6,7,1                                # reduction candidate for 6,7
B1: 6,7 => CTR
* ..92.8..38359..2..4..7.3..815.39......4..5.3939..8...5..7.3..12....763.45.3....76
B1: 1                                    #  9 pairs
A2: 6,7,8                                # reduction candidate for 6,7
A2: 6,7                                  # 20 pairs
* PAIR A1: 6,7 ROW 1
G1: 6,7,3,4,5                            # reduction candidate for 6,7
G1: 6,7                                  # 15 pairs
G1: 3,4,5                                #  8 pairs
* PAIR A1: 6,7 COL A
A5: 6,7,2,8                              # reduction candidate for 6,7
A5: 6,7 => CTR
* .192.8..38359..2.7426753..115839...267412583939268.145267439518981576324543....76
A5: 2,8                                  #  9 pairs
* PAIR F2: 1,4 BLK 2
E1: 1,4,3,5,6                            # reduction candidate for 1,4
E1: 1,4                                  # 11 pairs
E2: 1,4,6                                # reduction candidate for 1,4
E2: 1,4                                  # 14 pairs
* PAIR F2: 1,4 COL F
F6: 1,4,2,7                              # reduction candidate for 1,4
F6: 1,4 => SOLVED
* 719268453635941287428753691156397842874625139392184765267439518981576324543812976
F6: 2,7                                  #  8 pairs
F9: 1,4,2,9                              # reduction candidate for 1,4
F9: 1,4 => CTR
* ..92.87537359.124848.7...9.158392..7..4615839396487125..7.395129..5763845.3124976
F9: 2,9                                  #  8 pairs
* PAIR F3: 1,3 BLK 2
E1: 1,3,4,5,6                            # reduction candidate for 1,3
E1: 1,3                                  # 19 pairs
E3: 1,3,5,6                              # reduction candidate for 1,3
E3: 1,3 => CTR
* ..9258....359642814..7....315..9......4..5.3939..8...5..7.3..1.....763.45.3.4..76
E3: 5,6                                  #  8 pairs
* PAIR F3: 1,3 ROW 3
I3: 1,3,8                                # reduction candidate for 1,3
I3: 8 => CTR
* .792.8.518359..2.74.17...9815..93782.84..5.3939..87..5..75..8139183765245.38..976
I3: 1,3                                  # 11 pairs
* PAIR C6: 2,6 BLK 4
C4: 2,6,8                                # reduction candidate for 2,6
C4: 2,6                                  # 20 pairs
A5: 2,6,7,8                              # reduction candidate for 2,6
A5: 2,6 => CTR
* ..924875373596124848.75.69.158.92467274615839396487125..7..9.129...76.845.3124976
A5: 7,8                                  # 20 pairs
B5: 2,6,7,8                              # reduction candidate for 2,6
B5: 2,6 => CTR
* 6792.8...8359..2.74..7...98158.9.7.27.4..583939648.1.5..7....1.....76..45.3...976
B5: 7,8                                  #  8 pairs
* PAIR C6: 2,6 ROW 6
H6: 2,6,4                                # reduction candidate for 2,6
H6: 4                                    # 21 pairs
H6: 2,6                                  #  9 pairs
* PAIR C6: 2,6 COL C
C3: 2,6,1,8                              # reduction candidate for 2,6
C3: 2,6 => CTR
* ..924875373596124848275.69.158.92467274615839396487125..7..9.12921.76.845.3124976
C3: 1,8                                  # 12 pairs
* PAIR D5: 1,6 BLK 5
D6: 1,6,4                                # reduction candidate for 1,6
D6: 1,6                                  # 18 pairs
D6: 4                                    # 12 pairs
* PAIR D5: 1,6 ROW 5
G5: 1,6,8                                # reduction candidate for 1,6
G5: 8 => CTR
* ..924875373596124848.75.69.158.92467274615839396487125..7..9.129...76.845.3124976
G5: 1,6                                  # 20 pairs
* PAIR E5: 1,2 BLK 5
F6: 1,2,4,7                              # reduction candidate for 1,2
F6: 1,2 => CTR
* .192.8..3.359142.7462753..1158397..27.462513939.4817.5.47.3..1...1.763.45.314..76
F6: 4,7                                  #  8 pairs
* PAIR E5: 1,2 COL E
E9: 1,2,4                                # reduction candidate for 1,2
E9: 4 => CTR
* 7.92.8...8359.42674..7...9.15..9....274.15.3939..8...5647....1.9...76..45.3.4..76
E9: 1,2                                  # 10 pairs
* PAIR G9: 8,9 BLK 9
G7: 8,9,3,5                              # reduction candidate for 8,9
G7: 8,9 => CTR
* ..92.8.5..359..2..42.75.69.15..93..2..462513939218746526754.8139..376524543812976
G7: 3,5                                  #  8 pairs
G8: 8,9,3,5                              # reduction candidate for 8,9
G8: 8,9 => CTR
* ..92.8....359..2..4..7.1.9.15..93.....4.25.3939..87..5..7549312...376.545.38.2976
G8: 3,5                                  #  8 pairs
H8: 8,9,2,5                              # reduction candidate for 8,9
H8: 8,9                                  # 14 pairs
* PAIR G9: 8,9 COL G
G3: 8,9,3,5,6                            # reduction candidate for 8,9
G3: 8,9 => CTR
* ..92.8....359..2..42.7..89.15..9......4.25.3939..8...5.67..9.1.9.8.76.24543812976
G3: 3,5,6                                #  7 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190430-absurd-base-pr-000.dot
* REASONING
* DIS # B1: 6,7 => CTR => B1: 1
* DIS # A5: 6,7 => CTR => A5: 2,8
* PRF # F6: 1,4 => SOL
* DIS # F9: 1,4 => CTR => F9: 2,9
* DIS # E3: 1,3 => CTR => E3: 5,6
* DIS # I3: 8 => CTR => I3: 1,3
* DIS # A5: 2,6 => CTR => A5: 7,8
* DIS # B5: 2,6 => CTR => B5: 7,8
* DIS # C3: 2,6 => CTR => C3: 1,8
* DIS # G5: 8 => CTR => G5: 1,6
* DIS # F6: 1,2 => CTR => F6: 4,7
* DIS # E9: 4 => CTR => E9: 1,2
* DIS # G7: 8,9 => CTR => G7: 3,5
* DIS # G8: 8,9 => CTR => G8: 3,5
* DIS # G3: 8,9 => CTR => G3: 3,5,6
* CNT  15 HDP CHAINS /  42 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C6,D5,E5,F2,F3,G9)
* ..92.8....359..2..4..7.....15..9......4..5.3939..8...5..7....1.....76..45.3....76
* PAIR A1: 6,7 BLK 1
B1: 6,7,1                                # reduction candidate for 6,7
B1: 6,7 => CTR
* ..92.8..38359..2..4..7.3..815.39......4..5.3939..8...5..7.3..12....763.45.3....76
A2: 6,7,8                                # reduction candidate for 6,7
A2: 6,7                                  # 20 pairs
* RESTART
* PAIR A1: 6,7 BLK 1
A2: 6,7,8                                # reduction candidate for 6,7
A2: 8 => CTR
* 7192.8..38359..2.74..7....1158.9...2.74..583939..8.1.5..7....18..1.76.245.3...976
* PAIR A1: 6,7 ROW 1
G1: 6,7,3,4,5                            # reduction candidate for 6,7
G1: 6,7                                  # 25 pairs
G1: 3,4,5                                # 21 pairs
* PAIR C6: 2,6 BLK 4
C4: 2,6,8                                # reduction candidate for 2,6
C4: 8 => CTR
* .192.8....359..2..4..7.....158.9....274.1583939648...5.67....1...1.76..4543....76

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,A2,D4,D8,E2,E7,F2,F3,F6,G1,G6,G8,H2,H4,I1,I3,I7)
* .192.8.5..359..2..42875.69.156.9...287462513939218..65267..9.1.981.76.24543812976
* PAIR E2: 4,6 BLK 2
E1: 4,6,3                                # reduction candidate for 4,6
E1: 4,6 => SOLVED
* 719268453635941287428753691156397842874625139392184765267439518981576324543812976
* DURATION: 0:00:07.218837  START: 05:43:18.725820  END: 05:43:25.944657 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190430-absurd-base-pr-001.dot
* REASONING
* DIS # B1: 6,7 => CTR => B1: 1
* DIS B1: 1 # A2: 8 => CTR => A2: 6,7
* DIS B1: 1 + A2: 6,7 # C4: 8 => CTR => C4: 2,6
* PRF B1: 1 + A2: 6,7 + C4: 2,6 # E1: 4,6 => SOL
* STA B1: 1 + A2: 6,7 + C4: 2,6 + E1: 4,6
* CNT   4 HDP CHAINS /   9 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190430, absurd

Solution

position: 719268453635941287428753691156397842874625139392184765267439518981576324543812976 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 # B1: 6,7 => CTR => B1: 1
* INC # B1: 1 => UNS
* INC # A2: 6,7 => UNS
* INC # G1: 6,7 => UNS
* INC # G1: 3,4,5 => UNS
* DIS # A5: 6,7 => CTR => A5: 2,8
* INC # A5: 2,8 => UNS
* INC # E1: 1,4 => UNS
* INC # E2: 1,4 => UNS
* PRF # F6: 1,4 => SOL
* INC # F6: 2,7 => UNS
* DIS # F9: 1,4 => CTR => F9: 2,9
* INC # F9: 2,9 => UNS
* INC # E1: 1,3 => UNS
* DIS # E3: 1,3 => CTR => E3: 5,6
* INC # E3: 5,6 => UNS
* INC # I3: 1,3 => UNS
* DIS # I3: 8 => CTR => I3: 1,3
* INC # C4: 2,6 => UNS
* DIS # A5: 2,6 => CTR => A5: 7,8
* INC # A5: 7,8 => UNS
* DIS # B5: 2,6 => CTR => B5: 7,8
* INC # B5: 7,8 => UNS
* INC # H6: 2,6 => UNS
* INC # H6: 4 => UNS
* DIS # C3: 2,6 => CTR => C3: 1,8
* INC # C3: 1,8 => UNS
* INC # D6: 1,6 => UNS
* INC # D6: 4 => UNS
* INC # G5: 1,6 => UNS
* DIS # G5: 8 => CTR => G5: 1,6
* DIS # F6: 1,2 => CTR => F6: 4,7
* INC # F6: 4,7 => UNS
* INC # E9: 1,2 => UNS
* DIS # E9: 4 => CTR => E9: 1,2
* DIS # G7: 8,9 => CTR => G7: 3,5
* INC # G7: 3,5 => UNS
* DIS # G8: 8,9 => CTR => G8: 3,5
* INC # G8: 3,5 => UNS
* INC # H8: 8,9 => UNS
* DIS # G3: 8,9 => CTR => G3: 3,5,6
* INC # G3: 3,5,6 => UNS
* CNT  42 HDP CHAINS /  42 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B1: 6,7 => CTR => B1: 1
* INC B1: 1 # A2: 6,7 => UNS
* INC B1: 1 # A2: 6,7 => UNS
* DIS B1: 1 # A2: 8 => CTR => A2: 6,7
* INC B1: 1 + A2: 6,7 # G1: 6,7 => UNS
* INC B1: 1 + A2: 6,7 # G1: 3,4,5 => UNS
* INC B1: 1 + A2: 6,7 # C4: 2,6 => UNS
* DIS B1: 1 + A2: 6,7 # C4: 8 => CTR => C4: 2,6
* PRF B1: 1 + A2: 6,7 + C4: 2,6 # E1: 4,6 => SOL
* STA B1: 1 + A2: 6,7 + C4: 2,6 + E1: 4,6
* CNT   9 HDP CHAINS /   9 HYP OPENED