Analysis of zz-www.sudokuoftheday.co.uk-20060813-absurd-base.sdk

Contents

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

level: medium

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

position: ..95..326.....21..56.......2....8..749....218..8.1.5....68..4..7..12..8.....4...1 initial

Autosolve

position: 1.95..3263....21..562..18..2.1..8..749....2186.821.5..9168..4.27..12..8.82..4.7.1 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B1: 4 => CTR => B1: 7,8
* DIS # F6: 4,7 => CTR => F6: 3,9
* DIS # H3: 4,9 => CTR => H3: 7
* DIS # C5: 7 => CTR => C5: 3,5
* DIS # E4: 9 => CTR => E4: 3,5
* DIS # B8: 4 => CTR => B8: 3,5
* DIS # F6: 3,7 => CTR => F6: 4,9
* DIS # H4: 3,4 => CTR => H4: 6,9
* DIS # C8: 3,5 => CTR => C8: 4
* DIS # C5: 7 => CTR => C5: 3,5
* CNT  10 HDP CHAINS /  49 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: 4 => CTR => B1: 7,8
* DIS B1: 7,8 # E2: 6,9 => CTR => E2: 7,8
* DIS B1: 7,8 + E2: 7,8 # E4: 9 => CTR => E4: 3,5
* PRF B1: 7,8 + E2: 7,8 + E4: 3,5 # F9: 3,5 => SOL
* STA B1: 7,8 + E2: 7,8 + E4: 3,5 + F9: 3,5
* CNT   4 HDP CHAINS /  13 HYP OPENED

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

Details

Positions

..95..326.....21..56.......2....8..749....218..8.1.5....68..4..7..12..8.....4...1 initial
1.95..3263....21..562..18..2.1..8..749....2186.821.5..9168..4.27..12..8.82..4.7.1 autosolve
189574326347682159562391874251438697493765218678219543916857432734126985825943761 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
C2: 4,7
E1: 7,8
F1: 4,7
I3: 4,9
B4: 3,5
B6: 3,7
G4: 6,9
C9: 3,5
H7: 3,5
G8: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D3,E3: 3.. / D3 = 3  => 15 pairs (_) / E3 = 3  => 12 pairs (_)
I6,I8: 3.. / I6 = 3  => 17 pairs (_) / I8 = 3  => 19 pairs (_)
D4,F6: 4.. / D4 = 4  => 11 pairs (_) / F6 = 4  =>  0 pairs (X)
B8,C8: 4.. / B8 = 4  =>  0 pairs (X) / C8 = 4  => 13 pairs (_)
B1,F1: 4.. / B1 = 4  =>  0 pairs (X) / F1 = 4  => 11 pairs (_)
D4,H4: 4.. / D4 = 4  => 11 pairs (_) / H4 = 4  =>  0 pairs (X)
C2,C8: 4.. / C2 = 4  =>  0 pairs (X) / C8 = 4  => 13 pairs (_)
F1,F6: 4.. / F1 = 4  => 11 pairs (_) / F6 = 4  =>  0 pairs (X)
H2,I2: 5.. / H2 = 5  => 20 pairs (_) / I2 = 5  => 11 pairs (_)
B4,C5: 5.. / B4 = 5  => 12 pairs (_) / C5 = 5  => 23 pairs (_)
B4,E4: 5.. / B4 = 5  => 12 pairs (_) / E4 = 5  => 23 pairs (_)
B4,B8: 5.. / B4 = 5  => 12 pairs (_) / B8 = 5  => 23 pairs (_)
I2,I8: 5.. / I2 = 5  => 11 pairs (_) / I8 = 5  => 20 pairs (_)
D2,E2: 6.. / D2 = 6  => 12 pairs (_) / E2 = 6  => 10 pairs (_)
G4,H4: 6.. / G4 = 6  => 10 pairs (_) / H4 = 6  => 10 pairs (_)
G8,H9: 6.. / G8 = 6  => 10 pairs (_) / H9 = 6  => 10 pairs (_)
F8,G8: 6.. / F8 = 6  => 10 pairs (_) / G8 = 6  => 10 pairs (_)
E2,E5: 6.. / E2 = 6  => 10 pairs (_) / E5 = 6  => 12 pairs (_)
G4,G8: 6.. / G4 = 6  => 10 pairs (_) / G8 = 6  => 10 pairs (_)
H4,H9: 6.. / H4 = 6  => 10 pairs (_) / H9 = 6  => 10 pairs (_)
H2,H3: 7.. / H2 = 7  =>  0 pairs (X) / H3 = 7  => 11 pairs (_)
C5,B6: 7.. / C5 = 7  =>  0 pairs (X) / B6 = 7  => 13 pairs (_)
E7,F7: 7.. / E7 = 7  => 13 pairs (_) / F7 = 7  => 16 pairs (_)
B6,F6: 7.. / B6 = 7  => 13 pairs (_) / F6 = 7  =>  0 pairs (X)
C2,C5: 7.. / C2 = 7  => 13 pairs (_) / C5 = 7  =>  0 pairs (X)
B1,B2: 8.. / B1 = 8  => 16 pairs (_) / B2 = 8  => 10 pairs (_)
E1,E2: 8.. / E1 = 8  => 10 pairs (_) / E2 = 8  => 16 pairs (_)
B1,E1: 8.. / B1 = 8  => 16 pairs (_) / E1 = 8  => 10 pairs (_)
B2,E2: 8.. / B2 = 8  => 10 pairs (_) / E2 = 8  => 16 pairs (_)
G4,G8: 9.. / G4 = 9  => 10 pairs (_) / G8 = 9  => 10 pairs (_)
* DURATION: 0:00:35.210777  START: 01:45:45.641972  END: 01:46:20.852749 2019-05-01
* CP COUNT: (30)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B6,C2,C9,E1,F1,G4,G8,H7,I3)
* 1.95..3263....21..562..18..2.1..8..749....2186.821.5..9168..4.27..12..8.82..4.7.1
* PAIR C2: 4,7 BLK 1
B1: 4,7,8                                # reduction candidate for 4,7
B1: 4,7                                  # 10 pairs
B2: 4,7,8                                # reduction candidate for 4,7
B2: 4,7                                  # 16 pairs
* PAIR C2: 4,7 ROW 2
D2: 4,7,6,9                              # reduction candidate for 4,7
D2: 4,7                                  # 15 pairs
H2: 4,7,5,9                              # reduction candidate for 4,7
H2: 4,7                                  # 15 pairs
* PAIR E1: 7,8 BLK 2
E2: 7,8,6,9                              # reduction candidate for 7,8
E2: 7,8                                  # 16 pairs
E2: 6,9                                  # 11 pairs
* PAIR E1: 7,8 ROW 1
B1: 7,8,4                                # reduction candidate for 7,8
B1: 4 => CTR
* 1495873263876921545624318792.19586474957632186782145..91687.4.27.412..8.82..4.761
B1: 7,8                                  # 11 pairs
* PAIR F1: 4,7 BLK 2
D2: 4,7,6,9                              # reduction candidate for 4,7
D2: 4,7                                  # 15 pairs
D3: 4,7,3,9                              # reduction candidate for 4,7
D3: 4,7                                  # 16 pairs
* PAIR F1: 4,7 ROW 1
B1: 4,7,8                                # reduction candidate for 4,7
B1: 8                                    # 16 pairs
B1: 4,7                                  # 10 pairs
* PAIR F1: 4,7 COL F
F6: 4,7,3,9                              # reduction candidate for 4,7
F6: 4,7 => CTR
* 1.95..3263....21..562.318..2.1..86.749...32186.821.5..9168.54327.3126985825349761
F6: 3,9                                  # 16 pairs
* PAIR I3: 4,9 BLK 3
H2: 4,9,5,7                              # reduction candidate for 4,9
H2: 4,9                                  # 13 pairs
I2: 4,9,5                                # reduction candidate for 4,9
I2: 4,9                                  # 20 pairs
H3: 4,9,7                                # reduction candidate for 4,9
H3: 4,9 => CTR
* 179584326384..21755627318..2514986374973562186382175..916873452745129.83823.4.7.1
H3: 7                                    # 11 pairs
* PAIR I3: 4,9 ROW 3
D3: 4,9,3,7                              # reduction candidate for 4,9
D3: 4,9                                  # 13 pairs
D3: 3,7                                  # 12 pairs
* PAIR I3: 4,9 COL I
I6: 4,9,3                                # reduction candidate for 4,9
I6: 4,9                                  # 19 pairs
I6: 3                                    # 17 pairs
* PAIR B4: 3,5 BLK 4
C5: 3,5,7                                # reduction candidate for 3,5
C5: 7 => CTR
* 179584326384..21.5562..18..251498637497.5.2186382175..916873452745126.83823.4.7.1
C5: 3,5                                  # 13 pairs
* PAIR B4: 3,5 ROW 4
E4: 3,5,9                                # reduction candidate for 3,5
E4: 9 => CTR
* 1.95..3263....21..562.318..25149863749....2186.821.5..9168..4527..12698.825349761
E4: 3,5                                  # 18 pairs
* PAIR B4: 3,5 COL B
B8: 3,5,4                                # reduction candidate for 3,5
B8: 4 => CTR
* 179584326384..21.5562..18..251498637497.5.2186382175..916873452745126.83823.4.7.1
B8: 3,5                                  # 13 pairs
* PAIR B6: 3,7 BLK 4
C5: 3,7,5                                # reduction candidate for 3,7
C5: 5                                    # 23 pairs
C5: 3,7                                  # 12 pairs
* PAIR B6: 3,7 ROW 6
F6: 3,7,4,9                              # reduction candidate for 3,7
F6: 3,7 => CTR
* 1.95.43263....21..562..18..2.149863749....2186.821.5..9168..4527..126983823.4.7.1
F6: 4,9                                  # 14 pairs
* PAIR G4: 6,9 BLK 6
H4: 6,9,3,4                              # reduction candidate for 6,9
H4: 3,4 => CTR
* 1.95..3263....21..562.318..2.1..86.749....2186.821.5..9168..4327..126985825349761
H4: 6,9                                  # 14 pairs
* PAIR C9: 3,5 BLK 7
B8: 3,5,4                                # reduction candidate for 3,5
B8: 3,5                                  # 13 pairs
C8: 3,5,4                                # reduction candidate for 3,5
C8: 3,5 => CTR
* 179584326384..21.5562..18..251498637497.5.2186382175..916873452745126.83823.4.7.1
C8: 4                                    # 13 pairs
* PAIR C9: 3,5 ROW 9
F9: 3,5,6,9                              # reduction candidate for 3,5
F9: 3,5                                  # 15 pairs
H9: 3,5,6,9                              # reduction candidate for 3,5
H9: 3,5                                  # 10 pairs
* PAIR C9: 3,5 COL C
C5: 3,5,7                                # reduction candidate for 3,5
C5: 7 => CTR
* 179584326384..21.5562..18..251498637497.5.2186382175..916873452745126.83823.4.7.1
C5: 3,5                                  # 13 pairs
* PAIR H7: 3,5 BLK 9
I8: 3,5,9                                # reduction candidate for 3,5
I8: 3,5                                  # 13 pairs
H9: 3,5,6,9                              # reduction candidate for 3,5
H9: 3,5                                  # 10 pairs
* PAIR H7: 3,5 ROW 7
E7: 3,5,7                                # reduction candidate for 3,5
E7: 3,5                                  # 16 pairs
F7: 3,5,7                                # reduction candidate for 3,5
F7: 3,5                                  # 13 pairs
* PAIR G8: 6,9 BLK 9
H9: 6,9,3,5                              # reduction candidate for 6,9
H9: 6,9                                  # 13 pairs
H9: 3,5                                  # 10 pairs
* PAIR G8: 6,9 ROW 8
F8: 6,9,3,5                              # reduction candidate for 6,9
F8: 6,9                                  # 13 pairs
F8: 3,5                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060813-absurd-base-pr-000.dot
* REASONING
* DIS # B1: 4 => CTR => B1: 7,8
* DIS # F6: 4,7 => CTR => F6: 3,9
* DIS # H3: 4,9 => CTR => H3: 7
* DIS # C5: 7 => CTR => C5: 3,5
* DIS # E4: 9 => CTR => E4: 3,5
* DIS # B8: 4 => CTR => B8: 3,5
* DIS # F6: 3,7 => CTR => F6: 4,9
* DIS # H4: 3,4 => CTR => H4: 6,9
* DIS # C8: 3,5 => CTR => C8: 4
* DIS # C5: 7 => CTR => C5: 3,5
* CNT  10 HDP CHAINS /  49 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B6,C2,C9,E1,F1,G4,G8,H7,I3)
* 1.95..3263....21..562..18..2.1..8..749....2186.821.5..9168..4.27..12..8.82..4.7.1
* PAIR C2: 4,7 BLK 1
B1: 4,7,8                                # reduction candidate for 4,7
B1: 4,7                                  # 10 pairs
B2: 4,7,8                                # reduction candidate for 4,7
B2: 4,7                                  # 16 pairs
* PAIR C2: 4,7 ROW 2
D2: 4,7,6,9                              # reduction candidate for 4,7
D2: 4,7                                  # 15 pairs
H2: 4,7,5,9                              # reduction candidate for 4,7
H2: 4,7                                  # 15 pairs
* PAIR E1: 7,8 BLK 2
E2: 7,8,6,9                              # reduction candidate for 7,8
E2: 7,8                                  # 16 pairs
E2: 6,9                                  # 11 pairs
* PAIR E1: 7,8 ROW 1
B1: 7,8,4                                # reduction candidate for 7,8
B1: 4 => CTR
* 1495873263876921545624318792.19586474957632186782145..91687.4.27.412..8.82..4.761
* PAIR RESTART
* PAIR E1: 7,8 BLK 2
E2: 7,8,6,9                              # reduction candidate for 7,8
E2: 6,9 => CTR
* 179584326384..21.5562..18..251498637497.5.2186382175..916873452745126.83823.4.7.1
* PAIR B4: 3,5 ROW 4
E4: 3,5,9                                # reduction candidate for 3,5
E4: 9 => CTR
* 1895743263476821..562..18742514986374937652186782135499168.74.27.412..8.82..4.7.1
* PAIR RESTART
* PAIR C9: 3,5 ROW 9
F9: 3,5,6                                # reduction candidate for 3,5
F9: 3,5 => SOLVED
* 189574326347682159562391874251438697493765218678219543916857432734126985825943761
* DURATION: 0:00:09.954893  START: 01:46:52.000587  END: 01:47:01.955480 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060813-absurd-base-pr-001.dot
* REASONING
* DIS # B1: 4 => CTR => B1: 7,8
* DIS B1: 7,8 # E2: 6,9 => CTR => E2: 7,8
* DIS B1: 7,8 + E2: 7,8 # E4: 9 => CTR => E4: 3,5
* PRF B1: 7,8 + E2: 7,8 + E4: 3,5 # F9: 3,5 => SOL
* STA B1: 7,8 + E2: 7,8 + E4: 3,5 + F9: 3,5
* CNT   4 HDP CHAINS /  13 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060813, absurd

Solution

position: 189574326347682159562391874251438697493765218678219543916857432734126985825943761 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 # B1: 4,7 => UNS
* INC # B2: 4,7 => UNS
* INC # D2: 4,7 => UNS
* INC # H2: 4,7 => UNS
* INC # E2: 7,8 => UNS
* INC # E2: 6,9 => UNS
* INC # B1: 7,8 => UNS
* DIS # B1: 4 => CTR => B1: 7,8
* INC # D2: 4,7 => UNS
* INC # D3: 4,7 => UNS
* INC # B1: 4,7 => UNS
* INC # B1: 8 => UNS
* DIS # F6: 4,7 => CTR => F6: 3,9
* INC # F6: 3,9 => UNS
* INC # H2: 4,9 => UNS
* INC # I2: 4,9 => UNS
* DIS # H3: 4,9 => CTR => H3: 7
* INC # H3: 7 => UNS
* INC # D3: 4,9 => UNS
* INC # D3: 3,7 => UNS
* INC # I6: 4,9 => UNS
* INC # I6: 3 => UNS
* INC # C5: 3,5 => UNS
* DIS # C5: 7 => CTR => C5: 3,5
* INC # E4: 3,5 => UNS
* DIS # E4: 9 => CTR => E4: 3,5
* INC # B8: 3,5 => UNS
* DIS # B8: 4 => CTR => B8: 3,5
* INC # C5: 3,7 => UNS
* INC # C5: 5 => UNS
* DIS # F6: 3,7 => CTR => F6: 4,9
* INC # F6: 4,9 => UNS
* INC # H4: 6,9 => UNS
* DIS # H4: 3,4 => CTR => H4: 6,9
* INC # B8: 3,5 => UNS
* DIS # C8: 3,5 => CTR => C8: 4
* INC # C8: 4 => UNS
* INC # F9: 3,5 => UNS
* INC # H9: 3,5 => UNS
* INC # C5: 3,5 => UNS
* DIS # C5: 7 => CTR => C5: 3,5
* INC # I8: 3,5 => UNS
* INC # H9: 3,5 => UNS
* INC # E7: 3,5 => UNS
* INC # F7: 3,5 => UNS
* INC # H9: 6,9 => UNS
* INC # H9: 3,5 => UNS
* INC # F8: 6,9 => UNS
* INC # F8: 3,5 => UNS
* CNT  49 HDP CHAINS /  49 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 4,7 => UNS
* INC # B2: 4,7 => UNS
* INC # D2: 4,7 => UNS
* INC # H2: 4,7 => UNS
* INC # E2: 7,8 => UNS
* INC # E2: 6,9 => UNS
* INC # B1: 7,8 => UNS
* DIS # B1: 4 => CTR => B1: 7,8
* INC B1: 7,8 # E2: 7,8 => UNS
* DIS B1: 7,8 # E2: 6,9 => CTR => E2: 7,8
* INC B1: 7,8 + E2: 7,8 # E4: 3,5 => UNS
* DIS B1: 7,8 + E2: 7,8 # E4: 9 => CTR => E4: 3,5
* PRF B1: 7,8 + E2: 7,8 + E4: 3,5 # F9: 3,5 => SOL
* STA B1: 7,8 + E2: 7,8 + E4: 3,5 + F9: 3,5
* CNT  13 HDP CHAINS /  13 HYP OPENED