Analysis of zz-www.sudokuoftheday.co.uk-20060526-absurd-base.sdk

Contents

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

level: medium

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

position: .6...9.3.....7....4.3...792....8..2.98.4.65..3.51......1............41.7..9.1..6. initial

Autosolve

position: .6..4983..9..7....453861792....8..2.98.4.65..3.51......1............41.7..9.1..6. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # I2: 1,5 => CTR => I2: 4,6
* DIS # I2: 1,5 => CTR => I2: 4,6
* DIS # G6: 9 => CTR => G6: 4,6
* DIS # C4: 4,7 => CTR => C4: 1,6
* PRF # B6: 4,7 => SOL
* DIS # B6: 2 => CTR => B6: 4,7
* DIS # B9: 4,7 => CTR => B9: 2,3
* PRF # B9: 2,3 => SOL
* DIS # E7: 2,3 => CTR => E7: 5
* PRF # E8: 2,9 => SOL
* DIS # B6: 4 => CTR => B6: 2,7
* DIS # F9: 2,7 => CTR => F9: 3,8
* DIS # C5: 1,7 => CTR => C5: 2
* PRF # C5: 2 => SOL
* DIS # I4: 4,9 => CTR => I4: 1,3
* PRF # B9: 2,3 => SOL
* DIS # B9: 4,7 => CTR => B9: 2,3
* DIS # D8: 2,3 => CTR => D8: 6,9
* DIS # I7: 5,8 => CTR => I7: 3,4,9
* DIS # I9: 5,8 => CTR => I9: 3,4
* CNT  20 HDP CHAINS /  41 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 # I2: 1,5 => CTR => I2: 4,6
* DIS I2: 4,6 # G6: 9 => CTR => G6: 4,6
* DIS I2: 4,6 + G6: 4,6 # C4: 4,7 => CTR => C4: 1,6
* DIS I2: 4,6 + G6: 4,6 + C4: 1,6 # E7: 2,3 => CTR => E7: 5
* PRF I2: 4,6 + G6: 4,6 + C4: 1,6 + E7: 5 # F7: 3 => SOL
* STA I2: 4,6 + G6: 4,6 + C4: 1,6 + E7: 5 + F7: 3
* CNT   5 HDP CHAINS /  10 HYP OPENED

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

Details

Positions

.6...9.3.....7....4.3...792....8..2.98.4.65..3.51......1............41.7..9.1..6. initial
.6..4983..9..7....453861792....8..2.98.4.65..3.51......1............41.7..9.1..6. autosolve
167249835298375416453861792641587923982436571375192648714653289836924157529718364 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
D1: 2,5
I1: 1,5
G2: 4,6
B4: 4,7
E5: 2,3
E6: 2,9
F6: 2,7
H5: 1,7
I5: 1,3
B8: 2,3
H8: 5,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H2,H5: 1.. / H2 = 1  => 18 pairs (_) / H5 = 1  =>  0 pairs (X)
C5,B6: 2.. / C5 = 2  =>  0 pairs (*) / B6 = 2  =>  0 pairs (X)
G7,G9: 2.. / G7 = 2  => 13 pairs (_) / G9 = 2  => 12 pairs (_)
C5,E5: 2.. / C5 = 2  =>  0 pairs (*) / E5 = 2  =>  0 pairs (X)
D2,F2: 3.. / D2 = 3  => 13 pairs (_) / F2 = 3  => 13 pairs (_)
B8,B9: 3.. / B8 = 3  => 10 pairs (_) / B9 = 3  =>  0 pairs (X)
E5,I5: 3.. / E5 = 3  =>  0 pairs (*) / I5 = 3  =>  0 pairs (X)
C7,B9: 4.. / C7 = 4  => 18 pairs (_) / B9 = 4  =>  0 pairs (X)
C4,C7: 4.. / C4 = 4  =>  0 pairs (X) / C7 = 4  => 18 pairs (_)
D4,F4: 5.. / D4 = 5  => 20 pairs (_) / F4 = 5  => 12 pairs (_)
E7,E8: 5.. / E7 = 5  => 12 pairs (_) / E8 = 5  =>  0 pairs (X)
D1,I1: 5.. / D1 = 5  =>  0 pairs (X) / I1 = 5  => 17 pairs (_)
A9,I9: 5.. / A9 = 5  => 11 pairs (_) / I9 = 5  =>  0 pairs (X)
F2,F4: 5.. / F2 = 5  => 20 pairs (_) / F4 = 5  => 12 pairs (_)
G2,I2: 6.. / G2 = 6  =>  0 pairs (X) / I2 = 6  => 13 pairs (_)
A4,C4: 6.. / A4 = 6  => 13 pairs (_) / C4 = 6  =>  0 pairs (X)
G6,I6: 6.. / G6 = 6  => 13 pairs (_) / I6 = 6  =>  0 pairs (X)
D7,D8: 6.. / D7 = 6  => 11 pairs (_) / D8 = 6  =>  0 pairs (X)
G2,G6: 6.. / G2 = 6  =>  0 pairs (X) / G6 = 6  => 13 pairs (_)
I2,I6: 6.. / I2 = 6  => 13 pairs (_) / I6 = 6  =>  0 pairs (X)
A1,C1: 7.. / A1 = 7  =>  0 pairs (X) / C1 = 7  => 17 pairs (_)
H5,H6: 7.. / H5 = 7  => 18 pairs (_) / H6 = 7  =>  0 pairs (X)
C5,H5: 7.. / C5 = 7  =>  0 pairs (X) / H5 = 7  => 18 pairs (_)
A2,C2: 8.. / A2 = 8  => 14 pairs (_) / C2 = 8  => 13 pairs (_)
H6,I6: 8.. / H6 = 8  =>  0 pairs (X) / I6 = 8  => 13 pairs (_)
F7,F9: 8.. / F7 = 8  =>  0 pairs (X) / F9 = 8  => 11 pairs (_)
D4,E6: 9.. / D4 = 9  =>  0 pairs (X) / E6 = 9  => 13 pairs (_)
D8,E8: 9.. / D8 = 9  => 13 pairs (_) / E8 = 9  =>  0 pairs (X)
G7,I7: 9.. / G7 = 9  =>  0 pairs (X) / I7 = 9  => 11 pairs (_)
D4,D8: 9.. / D4 = 9  =>  0 pairs (X) / D8 = 9  => 13 pairs (_)
E6,E8: 9.. / E6 = 9  => 13 pairs (_) / E8 = 9  =>  0 pairs (X)
* DURATION: 0:00:31.256117  START: 23:25:31.415522  END: 23:26:02.671639 2019-04-30
* CP COUNT: (31)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B8,D1,E5,E6,F6,G2,H5,H8,I1,I5)
* .6..4983..9..7....453861792....8..2.98.4.65..3.51......1............41.7..9.1..6.
* PAIR D1: 2,5 BLK 2
D2: 2,5,3                                # reduction candidate for 2,5
D2: 2,5                                  # 13 pairs
F2: 2,5,3                                # reduction candidate for 2,5
F2: 2,5                                  # 13 pairs
* PAIR I1: 1,5 BLK 3
H2: 1,5,4                                # reduction candidate for 1,5
H2: 1,5                                  # 13 pairs
I2: 1,5,4,6                              # reduction candidate for 1,5
I2: 1,5 => CTR
* .6..4983..9..7.64.453861792....8..2.98.4.65133.51...7..1............41.7..9.1..6.
I2: 4,6                                  # 13 pairs
* PAIR G2: 4,6 BLK 3
I2: 4,6,1,5                              # reduction candidate for 4,6
I2: 1,5 => CTR
* .6..4983..9..7.64.453861792....8..2.98.4.65133.51...7..1............41.7..9.1..6.
I2: 4,6                                  # 13 pairs
* PAIR G2: 4,6 COL G
G6: 4,6,9                                # reduction candidate for 4,6
G6: 9 => CTR
* .6..4983..9..7.6..453861792...985.2.98.4365.13.5127986.1..58.49....94157549.1..68
G6: 4,6                                  # 14 pairs
* PAIR B4: 4,7 BLK 4
C4: 4,7,1,6                              # reduction candidate for 4,7
C4: 4,7 => CTR
* 167249835.9..7..1.453861792674.8.921981426573325197.48.1.63.4.9.3.954187..9.1..6.
C4: 1,6                                  # 18 pairs
B6: 4,7,2                                # reduction candidate for 4,7
B6: 4,7 => SOLVED
* 167249835298375416453861792641587923982436571375192648714653289836924157529718364
B6: 2 => CTR
* .6..4983..9..7..1.453861792.74.8.921981426573325197.48.1.63.25..3.954187..971.36.
* PAIR B4: 4,7 COL B
B9: 4,7,2,3                              # reduction candidate for 4,7
B9: 4,7 => CTR
* .6..4983..9..7..1.453861792.74.8.921981426573325197.48.1.63.25..3.954187..971.36.
B9: 2,3 => SOLVED
* 167249835298375416453861792641587923982436571375192648714653289836924157529718364
* PAIR E5: 2,3 COL E
E7: 2,3,5                                # reduction candidate for 2,3
E7: 2,3 => CTR
* .6..4983..9..7.4.6453861792....8..2.98.4265.3325197648.1.63..5..3.9541875.9718.6.
E7: 5                                    # 12 pairs
E8: 2,3,5,9                              # reduction candidate for 2,3
E8: 2,3                                  # 16 pairs
* PAIR E6: 2,9 COL E
E8: 2,9,3,5                              # reduction candidate for 2,9
E8: 2,9 => SOLVED
* 167249835298375416453861792641587923982436571375192648714653289836924157529718364
E8: 3,5                                  # 14 pairs
* PAIR F6: 2,7 ROW 6
B6: 2,7,4                                # reduction candidate for 2,7
B6: 4 => CTR
* .6..4983..9..7....453861792....8..2.9824365713451.7.8..14....5......41.7..9.1..6.
B6: 2,7                                  # 21 pairs
* PAIR F6: 2,7 COL F
F7: 2,7,3,8                              # reduction candidate for 2,7
F7: 2,7                                  # 15 pairs
F9: 2,7,3,8                              # reduction candidate for 2,7
F9: 2,7 => CTR
* .6..4983..9..7....453861792.74.8..2.98.4.657.325197.8..1...8.4..3.9.4157549712.6.
F9: 3,8                                  # 12 pairs
* PAIR H5: 1,7 ROW 5
C5: 1,7,2                                # reduction candidate for 1,7
C5: 1,7 => CTR
* .6..4983..9..7....453861792....8..2.98.426573325197.48.1.63..5..3.9541875.9718.6.
C5: 2 => SOLVED
* 167249835298375416453861792641587923982436571375192648714653289836924157529718364
* PAIR I5: 1,3 BLK 6
I4: 1,3,4,9                              # reduction candidate for 1,3
I4: 4,9 => CTR
* .67249835.9..7.416453861792.41.8.3299824365713751926487146.3......9.41.75.9.18.64
I4: 1,3                                  # 23 pairs
* PAIR B8: 2,3 BLK 7
B9: 2,3,4,7                              # reduction candidate for 2,3
B9: 2,3 => SOLVED
* 167249835298375416453861792641587923982436571375192648714653289836924157529718364
B9: 4,7 => CTR
* .6..4983..9..7..1.453861792.74.8.921981426573325197.48.1.63.25..3.954187..971.36.
* PAIR B8: 2,3 ROW 8
D8: 2,3,6,9                              # reduction candidate for 2,3
D8: 2,3 => CTR
* .6..49835.9.573.1.453861792.7.985.2.982436571345127.8..1465........941.7..971..6.
D8: 6,9                                  # 12 pairs
E8: 2,3,5,9                              # reduction candidate for 2,3
E8: 2,3                                  # 16 pairs
* PAIR H8: 5,8 BLK 9
H7: 5,8,4                                # reduction candidate for 5,8
H7: 5,8                                  # 19 pairs
I7: 5,8,3,4,9                            # reduction candidate for 5,8
I7: 5,8 => CTR
* .6..49835.9..7..1.453861792.74.8532.98.4365.13.51......1....94..3...41.7549718263
I7: 3,4,9                                # 11 pairs
I9: 5,8,3,4                              # reduction candidate for 5,8
I9: 5,8 => CTR
* .6..4983..9..7..1.453861792674.8..2198142657.325197.8..1.....4..3.9.415754971..68
I9: 3,4                                  # 12 pairs
* PAIR H8: 5,8 ROW 8
A8: 5,8,2,6                              # reduction candidate for 5,8
A8: 5,8                                  # 14 pairs
A8: 2,6                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060526-absurd-base-pr-000.dot
* REASONING
* DIS # I2: 1,5 => CTR => I2: 4,6
* DIS # I2: 1,5 => CTR => I2: 4,6
* DIS # G6: 9 => CTR => G6: 4,6
* DIS # C4: 4,7 => CTR => C4: 1,6
* PRF # B6: 4,7 => SOL
* DIS # B6: 2 => CTR => B6: 4,7
* DIS # B9: 4,7 => CTR => B9: 2,3
* PRF # B9: 2,3 => SOL
* DIS # E7: 2,3 => CTR => E7: 5
* PRF # E8: 2,9 => SOL
* DIS # B6: 4 => CTR => B6: 2,7
* DIS # F9: 2,7 => CTR => F9: 3,8
* DIS # C5: 1,7 => CTR => C5: 2
* PRF # C5: 2 => SOL
* DIS # I4: 4,9 => CTR => I4: 1,3
* PRF # B9: 2,3 => SOL
* DIS # B9: 4,7 => CTR => B9: 2,3
* DIS # D8: 2,3 => CTR => D8: 6,9
* DIS # I7: 5,8 => CTR => I7: 3,4,9
* DIS # I9: 5,8 => CTR => I9: 3,4
* CNT  20 HDP CHAINS /  41 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B8,D1,E5,E6,F6,G2,H5,H8,I1,I5)
* .6..4983..9..7....453861792....8..2.98.4.65..3.51......1............41.7..9.1..6.
* PAIR D1: 2,5 BLK 2
D2: 2,5,3                                # reduction candidate for 2,5
D2: 2,5                                  # 13 pairs
F2: 2,5,3                                # reduction candidate for 2,5
F2: 2,5                                  # 13 pairs
* PAIR I1: 1,5 BLK 3
H2: 1,5,4                                # reduction candidate for 1,5
H2: 1,5                                  # 13 pairs
I2: 1,5,4,6                              # reduction candidate for 1,5
I2: 1,5 => CTR
* .6..4983..9..7.64.453861792....8..2.98.4.65133.51...7..1............41.7..9.1..6.
* RESTART
* PAIR G2: 4,6 COL G
G6: 4,6,9                                # reduction candidate for 4,6
G6: 9 => CTR
* .6..49835.9..7.614453861792...985.2.98.4365713.5127986.1..58.49....94157549.1..68
* PAIR RESTART
* PAIR B4: 4,7 BLK 4
C4: 4,7,1,6                              # reduction candidate for 4,7
C4: 4,7 => CTR
* 167249835.9..7..1.453861792674.8.921981426573325197.4..1......9.3.954187..9.1..6.
* PAIR E5: 2,3 COL E
E7: 2,3,5                                # reduction candidate for 2,3
E7: 2,3 => CTR
* 167249835.98.7.416453861792.4..8..2.98.4.657.3.519.6488146.7.5..3.954187579318264
* RESTART
* PAIR RESTART
* PAIR F6: 2,7 COL F
F7: 2,7,3                                # reduction candidate for 2,7
F7: 3 => SOLVED
* 167249835298375416453861792641587923982436571375192648714653289836924157529718364
* DURATION: 0:00:07.723203  START: 23:26:27.993395  END: 23:26:35.716598 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060526-absurd-base-pr-001.dot
* REASONING
* DIS # I2: 1,5 => CTR => I2: 4,6
* DIS I2: 4,6 # G6: 9 => CTR => G6: 4,6
* DIS I2: 4,6 + G6: 4,6 # C4: 4,7 => CTR => C4: 1,6
* DIS I2: 4,6 + G6: 4,6 + C4: 1,6 # E7: 2,3 => CTR => E7: 5
* PRF I2: 4,6 + G6: 4,6 + C4: 1,6 + E7: 5 # F7: 3 => SOL
* STA I2: 4,6 + G6: 4,6 + C4: 1,6 + E7: 5 + F7: 3
* CNT   5 HDP CHAINS /  10 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060526, absurd

Solution

position: 167249835298375416453861792641587923982436571375192648714653289836924157529718364 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 # D2: 2,5 => UNS
* INC # F2: 2,5 => UNS
* INC # H2: 1,5 => UNS
* DIS # I2: 1,5 => CTR => I2: 4,6
* INC # I2: 4,6 => UNS
* INC # I2: 4,6 => UNS
* DIS # I2: 1,5 => CTR => I2: 4,6
* INC # G6: 4,6 => UNS
* DIS # G6: 9 => CTR => G6: 4,6
* DIS # C4: 4,7 => CTR => C4: 1,6
* INC # C4: 1,6 => UNS
* PRF # B6: 4,7 => SOL
* DIS # B6: 2 => CTR => B6: 4,7
* DIS # B9: 4,7 => CTR => B9: 2,3
* PRF # B9: 2,3 => SOL
* DIS # E7: 2,3 => CTR => E7: 5
* INC # E7: 5 => UNS
* INC # E8: 2,3 => UNS
* PRF # E8: 2,9 => SOL
* INC # E8: 3,5 => UNS
* INC # B6: 2,7 => UNS
* DIS # B6: 4 => CTR => B6: 2,7
* INC # F7: 2,7 => UNS
* DIS # F9: 2,7 => CTR => F9: 3,8
* INC # F9: 3,8 => UNS
* DIS # C5: 1,7 => CTR => C5: 2
* PRF # C5: 2 => SOL
* INC # I4: 1,3 => UNS
* DIS # I4: 4,9 => CTR => I4: 1,3
* PRF # B9: 2,3 => SOL
* DIS # B9: 4,7 => CTR => B9: 2,3
* DIS # D8: 2,3 => CTR => D8: 6,9
* INC # D8: 6,9 => UNS
* INC # E8: 2,3 => UNS
* INC # H7: 5,8 => UNS
* DIS # I7: 5,8 => CTR => I7: 3,4,9
* INC # I7: 3,4,9 => UNS
* DIS # I9: 5,8 => CTR => I9: 3,4
* INC # I9: 3,4 => UNS
* INC # A8: 5,8 => UNS
* INC # A8: 2,6 => UNS
* CNT  41 HDP CHAINS /  41 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D2: 2,5 => UNS
* INC # F2: 2,5 => UNS
* INC # H2: 1,5 => UNS
* DIS # I2: 1,5 => CTR => I2: 4,6
* INC I2: 4,6 # G6: 4,6 => UNS
* DIS I2: 4,6 # G6: 9 => CTR => G6: 4,6
* DIS I2: 4,6 + G6: 4,6 # C4: 4,7 => CTR => C4: 1,6
* DIS I2: 4,6 + G6: 4,6 + C4: 1,6 # E7: 2,3 => CTR => E7: 5
* INC I2: 4,6 + G6: 4,6 + C4: 1,6 + E7: 5 # F7: 2,7 => UNS
* PRF I2: 4,6 + G6: 4,6 + C4: 1,6 + E7: 5 # F7: 3 => SOL
* STA I2: 4,6 + G6: 4,6 + C4: 1,6 + E7: 5 + F7: 3
* CNT  10 HDP CHAINS /  10 HYP OPENED