Analysis of zz-www.sudokuoftheday.co.uk-20060607-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: ....8...1..5.9.7......1739.4....1.....2......37..4...8.2....54...34..6..5.4.36... initial

Autosolve

position: ..7.8...1..5.9.78.....1739.4....1.....2......37..4...8.2..7.5437.34..6..5.4.368.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A3: 6,8 => CTR => A3: 2
* DIS # B3: 6,8 => CTR => B3: 4
* PRF # C4: 6,8 => SOL
* DIS # C4: 9 => CTR => C4: 6,8
* DIS # C7: 6,8 => CTR => C7: 1,9
* DIS # I3: 2,4 => CTR => I3: 5,6
* DIS # A5: 1,6 => CTR => A5: 8,9
* DIS # C7: 1,6 => CTR => C7: 8,9
* PRF # C7: 8,9 => SOL
* DIS # E4: 5,6 => CTR => E4: 2
* PRF # E4: 2 => SOL
* PRF # H5: 5,6 => SOL
* DIS # I5: 5,6 => CTR => I5: 4,7
* DIS # A7: 1,9 => CTR => A7: 6,8
* DIS # B8: 1,9 => CTR => B8: 8
* DIS # D9: 2 => CTR => D9: 1,9
* PRF # B5: 1,9 => SOL
* DIS # D7: 8,9 => CTR => D7: 1
* PRF # D7: 1 => SOL
* DIS # F8: 8,9 => CTR => F8: 2,5
* DIS # A7: 8,9 => CTR => A7: 1,6
* PRF # C7: 8,9 => SOL
* DIS # C7: 1,6 => CTR => C7: 8,9
* DIS # F8: 8,9 => CTR => F8: 2,5
* DIS # E4: 6 => CTR => E4: 2,5
* PRF # F8: 2,9 => SOL
* CNT  26 HDP CHAINS /  54 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: 6,8 => CTR => A3: 2
* DIS A3: 2 # B3: 6,8 => CTR => B3: 4
* PRF A3: 2 + B3: 4 # I2: 6 => SOL
* STA A3: 2 + B3: 4 + I2: 6
* CNT   3 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

....8...1..5.9.7......1739.4....1.....2......37..4...8.2....54...34..6..5.4.36... initial
..7.8...1..5.9.78.....1739.4....1.....2......37..4...8.2..7.5437.34..6..5.4.368.. autosolve
967385421135294786248617395456821937892763154371549268629178543783452619514936872 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (12)
C3: 6,8
G1: 2,4
C6: 1,6
E5: 5,6
F5: 3,8
G4: 2,9
G6: 1,2
B9: 1,9
F7: 8,9
E8: 2,5
H8: 1,2
I8: 2,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A2,B2: 1.. / A2 = 1  => 12 pairs (_) / B2 = 1  =>  0 pairs (X)
G5,G6: 1.. / G5 = 1  =>  0 pairs (*) / G6 = 1  =>  0 pairs (X)
D7,D9: 1.. / D7 = 1  =>  0 pairs (*) / D9 = 1  =>  0 pairs (X)
H8,H9: 1.. / H8 = 1  => 13 pairs (_) / H9 = 1  =>  0 pairs (X)
C6,G6: 1.. / C6 = 1  =>  0 pairs (*) / G6 = 1  =>  0 pairs (X)
B8,H8: 1.. / B8 = 1  =>  0 pairs (X) / H8 = 1  => 13 pairs (_)
C6,C7: 1.. / C6 = 1  =>  0 pairs (*) / C7 = 1  =>  0 pairs (X)
E4,E8: 2.. / E4 = 2  =>  0 pairs (*) / E8 = 2  =>  0 pairs (X)
B1,B2: 3.. / B1 = 3  => 12 pairs (_) / B2 = 3  => 14 pairs (_)
H4,H5: 3.. / H4 = 3  => 13 pairs (_) / H5 = 3  =>  0 pairs (X)
D4,H4: 3.. / D4 = 3  =>  0 pairs (X) / H4 = 3  => 13 pairs (_)
F1,F2: 4.. / F1 = 4  =>  0 pairs (X) / F2 = 4  => 13 pairs (_)
G5,I5: 4.. / G5 = 4  =>  0 pairs (X) / I5 = 4  => 14 pairs (_)
B3,I3: 4.. / B3 = 4  => 12 pairs (_) / I3 = 4  =>  0 pairs (X)
G1,G5: 4.. / G1 = 4  => 14 pairs (_) / G5 = 4  =>  0 pairs (X)
H1,I3: 5.. / H1 = 5  =>  0 pairs (X) / I3 = 5  => 14 pairs (_)
B4,B5: 5.. / B4 = 5  => 13 pairs (_) / B5 = 5  => 17 pairs (_)
E8,F8: 5.. / E8 = 5  =>  0 pairs (*) / F8 = 5  =>  0 pairs (X)
D3,I3: 5.. / D3 = 5  =>  0 pairs (X) / I3 = 5  => 14 pairs (_)
E4,E5: 6.. / E4 = 6  =>  0 pairs (X) / E5 = 6  => 12 pairs (_)
A7,C7: 6.. / A7 = 6  => 15 pairs (_) / C7 = 6  =>  0 pairs (X)
C6,H6: 6.. / C6 = 6  =>  0 pairs (X) / H6 = 6  =>  0 pairs (_)
D4,D5: 7.. / D4 = 7  => 13 pairs (_) / D5 = 7  => 13 pairs (_)
H9,I9: 7.. / H9 = 7  => 15 pairs (_) / I9 = 7  => 18 pairs (_)
B8,F8: 8.. / B8 = 8  => 13 pairs (_) / F8 = 8  =>  0 pairs (X)
A1,B1: 9.. / A1 = 9  => 12 pairs (_) / B1 = 9  =>  0 pairs (X)
D6,F6: 9.. / D6 = 9  => 15 pairs (_) / F6 = 9  => 18 pairs (_)
G4,G5: 9.. / G4 = 9  =>  0 pairs (*) / G5 = 9  =>  0 pairs (X)
I8,I9: 9.. / I8 = 9  => 13 pairs (_) / I9 = 9  =>  0 pairs (X)
C4,C7: 9.. / C4 = 9  =>  0 pairs (X) / C7 = 9  =>  0 pairs (_)
* DURATION: 0:00:32.024987  START: 23:41:19.765466  END: 23:41:51.790453 2019-04-30
* CP COUNT: (30)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,C3,C6,E5,E8,F5,F7,G1,G4,G6,H8,I8)
* ..7.8...1..5.9.78.....1739.4....1.....2......37..4...8.2..7.5437.34..6..5.4.368..
* PAIR C3: 6,8 BLK 1
A3: 6,8,2                                # reduction candidate for 6,8
A3: 6,8 => CTR
* 2976834.1..5.94786.4..1739.4...219..9.2.6.1.4371.4.268.29.7854378345.61.514.368..
A3: 2                                    # 15 pairs
B3: 6,8,4                                # reduction candidate for 6,8
B3: 6,8 => CTR
* 9.7.8.251..5.9.786...5173944.9..1.....2...4..37..4.1.8.21.7.5437.34..61.5941368..
B3: 4                                    # 12 pairs
* PAIR C3: 6,8 COL C
C4: 6,8,9                                # reduction candidate for 6,8
C4: 6,8 => SOLVED
* 967385421135294786248617395456821937892763154371549268629178543783452619514936872
C4: 9 => CTR
* 9.758.4.1..5.9478.248617395459861237812753964376.4.158621978543783425619594136872
C7: 6,8,1,9                              # reduction candidate for 6,8
C7: 6,8 => CTR
* ..7.8...1..5.9.78.....1739.4.9..12....2...9.4371.4...8.2..7.5437.34..6..5.4.368..
C7: 1,9                                  # 17 pairs
* PAIR G1: 2,4 BLK 3
I2: 2,4,6                                # reduction candidate for 2,4
I2: 2,4                                  # 15 pairs
I3: 2,4,5,6                              # reduction candidate for 2,4
I3: 2,4 => CTR
* ..768..51..5.9.786...51739.4...219....2.6....37.945..8.29.78543783459612514236879
I3: 5,6                                  # 13 pairs
* PAIR G1: 2,4 ROW 1
F1: 2,4,3,5                              # reduction candidate for 2,4
F1: 3,5                                  # 18 pairs
F1: 2,4                                  # 16 pairs
* PAIR C6: 1,6 BLK 4
A5: 1,6,8,9                              # reduction candidate for 1,6
A5: 1,6 => CTR
* 9.7.8...11.5.9.78.2.8.1739.4.9..12....2......37..4...8.2..7.5437.34..6..5.4.368..
A5: 8,9                                  # 13 pairs
B5: 1,6,5,8,9                            # reduction candidate for 1,6
B5: 1,6                                  # 16 pairs
* PAIR C6: 1,6 COL C
C7: 1,6,8,9                              # reduction candidate for 1,6
C7: 1,6 => CTR
* 9.758.4.1..5.9478.248617395459861237812753964376.4.158621978543783425619594136872
C7: 8,9 => SOLVED
* 967385421135294786248617395456821937892763154371549268629178543783452619514936872
* PAIR E5: 5,6 BLK 5
E4: 5,6,2                                # reduction candidate for 5,6
E4: 5,6 => CTR
* 9.758...1..5.9.78.....173954.98.1237812753964376.4.158621978543783425619594136872
E4: 2 => SOLVED
* 967385421135294786248617395456821937892763154371549268629178543783452619514936872
* PAIR E5: 5,6 ROW 5
B5: 5,6,1,8,9                            # reduction candidate for 5,6
B5: 5,6                                  # 18 pairs
H5: 5,6,3,7                              # reduction candidate for 5,6
H5: 5,6 => SOLVED
* 967385421135294786248617395456821937892763154371549268629178543783452619514936872
H5: 3,7                                  # 13 pairs
I5: 5,6,4,7                              # reduction candidate for 5,6
I5: 5,6 => CTR
* 9.7.8.2.1..5.9.78.....1739.4.9..1.....2...4..37..4.1.8.21.7.5437.34..61.5941368..
I5: 4,7                                  # 13 pairs
* PAIR F5: 3,8 BLK 5
D4: 3,8,7                                # reduction candidate for 3,8
D4: 3,8                                  # 13 pairs
D5: 3,8,7                                # reduction candidate for 3,8
D5: 3,8                                  # 13 pairs
* PAIR B9: 1,9 BLK 7
A7: 1,9,6,8                              # reduction candidate for 1,9
A7: 1,9 => CTR
* ..7.8...1..5.9.78...8.1739.4.98.12378.27.39.4371.4...8.26.7.5437834..61.5.4.368..
A7: 6,8                                  # 13 pairs
C7: 1,9,6,8                              # reduction candidate for 1,9
C7: 1,9                                  # 17 pairs
B8: 1,9,8                                # reduction candidate for 1,9
B8: 1,9 => CTR
* ..7.8...1..5.9.78.....1739.4.9.21.....2..3...37..4...8.2..795437.34586..5.42368..
B8: 8                                    # 13 pairs
* PAIR B9: 1,9 ROW 9
D9: 1,9,2                                # reduction candidate for 1,9
D9: 2 => CTR
* ..7.8.4211.5.9.78.....1739.4...219....2.6....371945268.29178543783459612514236879
D9: 1,9                                  # 15 pairs
* PAIR B9: 1,9 COL B
B5: 1,9,5,6,8                            # reduction candidate for 1,9
B5: 1,9 => SOLVED
* 967385421135294786248617395456821937892763154371549268629178543783452619514936872
B5: 5,6,8                                # 15 pairs
* PAIR F7: 8,9 BLK 8
D7: 8,9,1                                # reduction candidate for 8,9
D7: 8,9 => CTR
* 9.7582461..5.9478..48.1739.4.98.12378127.39.4376.4.158621978543783425619594136872
D7: 1 => SOLVED
* 967385421135294786248617395456821937892763154371549268629178543783452619514936872
F8: 8,9,2,5                              # reduction candidate for 8,9
F8: 8,9 => CTR
* ..7.8...11.5.9278.2.8.1739.4.6821937892763154371945268629178543783459612514236879
F8: 2,5                                  # 15 pairs
* PAIR F7: 8,9 ROW 7
A7: 8,9,1,6                              # reduction candidate for 8,9
A7: 8,9 => CTR
* ..7.8...1..5.9.78...8.1739.4.9..12....2...9.4371.4...8.2617.5437.34..6..5.4.368..
A7: 1,6                                  # 13 pairs
C7: 8,9,1,6                              # reduction candidate for 8,9
C7: 8,9 => SOLVED
* 967385421135294786248617395456821937892763154371549268629178543783452619514936872
C7: 1,6 => CTR
* 9.758.4.1..5.9478.248617395459861237812753964376.4.158621978543783425619594136872
* PAIR E8: 2,5 BLK 8
F8: 2,5,8,9                              # reduction candidate for 2,5
F8: 8,9 => CTR
* ..7.8...11.5.9278.2.8.1739.4.6821937892763154371945268629178543783459612514236879
F8: 2,5                                  # 15 pairs
* PAIR E8: 2,5 COL E
E4: 2,5,6                                # reduction candidate for 2,5
E4: 6 => CTR
* 9.758...1..5.9.78..48617395459861237812753964376.4.158621978543783425619594136872
E4: 2,5                                  # 12 pairs
* PAIR H8: 1,2 BLK 9
H9: 1,2,7                                # reduction candidate for 1,2
H9: 1,2                                  # 18 pairs
H9: 7                                    # 15 pairs
* PAIR I8: 2,9 BLK 9
I9: 2,9,7                                # reduction candidate for 2,9
I9: 7                                    # 18 pairs
I9: 2,9                                  # 15 pairs
* PAIR I8: 2,9 ROW 8
F8: 2,9,5,8                              # reduction candidate for 2,9
F8: 2,9 => SOLVED
* 967385421135294786248617395456821937892763154371549268629178543783452619514936872
F8: 5,8                                  # 13 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060607-absurd-base-pr-000.dot
* REASONING
* DIS # A3: 6,8 => CTR => A3: 2
* DIS # B3: 6,8 => CTR => B3: 4
* PRF # C4: 6,8 => SOL
* DIS # C4: 9 => CTR => C4: 6,8
* DIS # C7: 6,8 => CTR => C7: 1,9
* DIS # I3: 2,4 => CTR => I3: 5,6
* DIS # A5: 1,6 => CTR => A5: 8,9
* DIS # C7: 1,6 => CTR => C7: 8,9
* PRF # C7: 8,9 => SOL
* DIS # E4: 5,6 => CTR => E4: 2
* PRF # E4: 2 => SOL
* PRF # H5: 5,6 => SOL
* DIS # I5: 5,6 => CTR => I5: 4,7
* DIS # A7: 1,9 => CTR => A7: 6,8
* DIS # B8: 1,9 => CTR => B8: 8
* DIS # D9: 2 => CTR => D9: 1,9
* PRF # B5: 1,9 => SOL
* DIS # D7: 8,9 => CTR => D7: 1
* PRF # D7: 1 => SOL
* DIS # F8: 8,9 => CTR => F8: 2,5
* DIS # A7: 8,9 => CTR => A7: 1,6
* PRF # C7: 8,9 => SOL
* DIS # C7: 1,6 => CTR => C7: 8,9
* DIS # F8: 8,9 => CTR => F8: 2,5
* DIS # E4: 6 => CTR => E4: 2,5
* PRF # F8: 2,9 => SOL
* CNT  26 HDP CHAINS /  54 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,C3,C6,E5,E8,F5,F7,G1,G4,G6,H8,I8)
* ..7.8...1..5.9.78.....1739.4....1.....2......37..4...8.2..7.5437.34..6..5.4.368..
* PAIR C3: 6,8 BLK 1
A3: 6,8,2                                # reduction candidate for 6,8
A3: 6,8 => CTR
* 2976834.1..5.94786.4..1739.4...219..9.2.6.1.4371.4.268.29.7854378345.61.514.368..
B3: 6,8,4                                # reduction candidate for 6,8
B3: 6,8 => CTR
* 9.7.8.251..5.9.7862..5173944.9..1.....2...4..37..4.1.8.21.7.5437.34..61.5941368..
* PAIR G1: 2,4 BLK 3
I2: 2,4,6                                # reduction candidate for 2,4
I2: 6 => SOLVED
* 967385421135294786248617395456821937892763154371549268629178543783452619514936872
* DURATION: 0:00:03.865210  START: 23:42:27.780060  END: 23:42:31.645270 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060607-absurd-base-pr-001.dot
* REASONING
* DIS # A3: 6,8 => CTR => A3: 2
* DIS A3: 2 # B3: 6,8 => CTR => B3: 4
* PRF A3: 2 + B3: 4 # I2: 6 => SOL
* STA A3: 2 + B3: 4 + I2: 6
* CNT   3 HDP CHAINS /   4 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060607, absurd

Solution

position: 967385421135294786248617395456821937892763154371549268629178543783452619514936872 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 # A3: 6,8 => CTR => A3: 2
* INC # A3: 2 => UNS
* DIS # B3: 6,8 => CTR => B3: 4
* INC # B3: 4 => UNS
* PRF # C4: 6,8 => SOL
* DIS # C4: 9 => CTR => C4: 6,8
* DIS # C7: 6,8 => CTR => C7: 1,9
* INC # C7: 1,9 => UNS
* INC # I2: 2,4 => UNS
* DIS # I3: 2,4 => CTR => I3: 5,6
* INC # I3: 5,6 => UNS
* INC # F1: 2,4 => UNS
* INC # F1: 3,5 => UNS
* DIS # A5: 1,6 => CTR => A5: 8,9
* INC # A5: 8,9 => UNS
* INC # B5: 1,6 => UNS
* DIS # C7: 1,6 => CTR => C7: 8,9
* PRF # C7: 8,9 => SOL
* DIS # E4: 5,6 => CTR => E4: 2
* PRF # E4: 2 => SOL
* INC # B5: 5,6 => UNS
* PRF # H5: 5,6 => SOL
* INC # H5: 3,7 => UNS
* DIS # I5: 5,6 => CTR => I5: 4,7
* INC # I5: 4,7 => UNS
* INC # D4: 3,8 => UNS
* INC # D5: 3,8 => UNS
* DIS # A7: 1,9 => CTR => A7: 6,8
* INC # A7: 6,8 => UNS
* INC # C7: 1,9 => UNS
* DIS # B8: 1,9 => CTR => B8: 8
* INC # B8: 8 => UNS
* INC # D9: 1,9 => UNS
* DIS # D9: 2 => CTR => D9: 1,9
* PRF # B5: 1,9 => SOL
* INC # B5: 5,6,8 => UNS
* DIS # D7: 8,9 => CTR => D7: 1
* PRF # D7: 1 => SOL
* DIS # F8: 8,9 => CTR => F8: 2,5
* INC # F8: 2,5 => UNS
* DIS # A7: 8,9 => CTR => A7: 1,6
* INC # A7: 1,6 => UNS
* PRF # C7: 8,9 => SOL
* DIS # C7: 1,6 => CTR => C7: 8,9
* INC # F8: 2,5 => UNS
* DIS # F8: 8,9 => CTR => F8: 2,5
* INC # E4: 2,5 => UNS
* DIS # E4: 6 => CTR => E4: 2,5
* INC # H9: 1,2 => UNS
* INC # H9: 7 => UNS
* INC # I9: 2,9 => UNS
* INC # I9: 7 => UNS
* PRF # F8: 2,9 => SOL
* INC # F8: 5,8 => UNS
* CNT  54 HDP CHAINS /  54 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A3: 6,8 => CTR => A3: 2
* DIS A3: 2 # B3: 6,8 => CTR => B3: 4
* INC A3: 2 + B3: 4 # I2: 2,4 => UNS
* PRF A3: 2 + B3: 4 # I2: 6 => SOL
* STA A3: 2 + B3: 4 + I2: 6
* CNT   4 HDP CHAINS /   4 HYP OPENED