Analysis of zz-www.sudokuoftheday.co.uk-20060504-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: ...5.6..8...41..57.2.......582...3......9.8....6..3..5.......4.1...876.9.6....... initial

Autosolve

position: ...5.6..86..41..57.25......582...39.....958....68.3..5.......4.154.876.9.6.....8. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C2: 3,9 => CTR => C2: 8
* DIS # D3: 3,7 => CTR => D3: 9
* DIS # F2: 8,9 => CTR => F2: 2
* DIS # A3: 8,9 => CTR => A3: 4,7
* PRF # E1: 7 => SOL
* PRF # G1: 2,9 => SOL
* DIS # F2: 8 => CTR => F2: 2,9
* DIS # F9: 2,9 => CTR => F9: 1,4
* DIS # I5: 4 => CTR => I5: 2,6
* PRF # D7: 2,6 => SOL
* DIS # G6: 1 => CTR => G6: 2,4
* DIS # E9: 2,4 => CTR => E9: 3,5
* DIS # I5: 4,6 => CTR => I5: 2
* PRF # I5: 2 => SOL
* DIS # E4: 7 => CTR => E4: 4,6
* PRF # I3: 4,6 => SOL
* DIS # I3: 3 => CTR => I3: 4,6
* DIS # H5: 6 => CTR => H5: 1,7
* PRF # D7: 2,3 => SOL
* DIS # E7: 2,3 => CTR => E7: 5,6
* DIS # D9: 2,3 => CTR => D9: 1,9
* DIS # E9: 2,3 => CTR => E9: 4,5
* CNT  22 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 # C2: 3,9 => CTR => C2: 8
* DIS C2: 8 # D3: 3,7 => CTR => D3: 9
* DIS C2: 8 + D3: 9 # H5: 7 => CTR => H5: 1,6
* DIS C2: 8 + D3: 9 + H5: 1,6 # I5: 4 => CTR => I5: 2,6
* PRF C2: 8 + D3: 9 + H5: 1,6 + I5: 2,6 # D7: 2,6 => SOL
* STA C2: 8 + D3: 9 + H5: 1,6 + I5: 2,6 + D7: 2,6
* CNT   5 HDP CHAINS /   8 HYP OPENED

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

Details

Positions

...5.6..8...41..57.2.......582...3......9.8....6..3..5.......4.1...876.9.6....... initial
...5.6..86..41..57.25......582...39.....958....68.3..5.......4.154.876.9.6.....8. autosolve
491576238638412957725938164582741396347695812916823475873269541154387629269154783 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
B2: 3,9
E3: 3,7
F3: 8,9
H1: 2,3
G2: 2,9
H3: 1,6
F4: 1,4
D5: 2,6
E6: 2,4
I4: 4,6
H6: 1,7
D8: 2,3
G7: 5,7
H8: 2,3
G9: 5,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,C1: 1.. / B1 = 1  => 19 pairs (_) / C1 = 1  => 16 pairs (_)
G3,H3: 1.. / G3 = 1  => 19 pairs (_) / H3 = 1  =>  0 pairs (X)
D4,F4: 1.. / D4 = 1  =>  0 pairs (X) / F4 = 1  => 16 pairs (_)
I7,I9: 1.. / I7 = 1  => 18 pairs (_) / I9 = 1  => 16 pairs (_)
C1,C5: 1.. / C1 = 1  => 16 pairs (_) / C5 = 1  => 19 pairs (_)
G3,G6: 1.. / G3 = 1  => 19 pairs (_) / G6 = 1  =>  0 pairs (X)
E1,F2: 2.. / E1 = 2  =>  0 pairs (X) / F2 = 2  => 21 pairs (_)
D5,E6: 2.. / D5 = 2  =>  0 pairs (X) / E6 = 2  =>  0 pairs (_)
I5,G6: 2.. / I5 = 2  =>  0 pairs (*) / G6 = 2  =>  0 pairs (X)
A7,A9: 2.. / A7 = 2  =>  0 pairs (X) / A9 = 2  => 16 pairs (_)
F2,G2: 2.. / F2 = 2  => 21 pairs (_) / G2 = 2  =>  0 pairs (X)
D5,I5: 2.. / D5 = 2  =>  0 pairs (X) / I5 = 2  =>  0 pairs (_)
E6,G6: 2.. / E6 = 2  =>  0 pairs (*) / G6 = 2  =>  0 pairs (X)
D8,H8: 2.. / D8 = 2  =>  0 pairs (X) / H8 = 2  =>  0 pairs (_)
H1,H8: 2.. / H1 = 2  =>  0 pairs (X) / H8 = 2  =>  0 pairs (_)
B2,C2: 3.. / B2 = 3  => 16 pairs (_) / C2 = 3  =>  0 pairs (X)
H1,I3: 3.. / H1 = 3  =>  0 pairs (*) / I3 = 3  =>  0 pairs (X)
E1,H1: 3.. / E1 = 3  =>  0 pairs (X) / H1 = 3  =>  0 pairs (_)
D8,H8: 3.. / D8 = 3  =>  0 pairs (*) / H8 = 3  =>  0 pairs (X)
H1,H8: 3.. / H1 = 3  =>  0 pairs (*) / H8 = 3  =>  0 pairs (X)
E9,F9: 4.. / E9 = 4  =>  0 pairs (X) / F9 = 4  => 16 pairs (_)
F4,F9: 4.. / F4 = 4  =>  0 pairs (X) / F9 = 4  => 16 pairs (_)
E7,E9: 5.. / E7 = 5  =>  0 pairs (X) / E9 = 5  => 15 pairs (_)
G7,G9: 5.. / G7 = 5  => 15 pairs (_) / G9 = 5  =>  0 pairs (X)
E7,G7: 5.. / E7 = 5  =>  0 pairs (X) / G7 = 5  => 15 pairs (_)
E9,G9: 5.. / E9 = 5  => 15 pairs (_) / G9 = 5  =>  0 pairs (X)
H3,I3: 6.. / H3 = 6  => 19 pairs (_) / I3 = 6  =>  0 pairs (X)
D7,E7: 6.. / D7 = 6  =>  0 pairs (X) / E7 = 6  => 17 pairs (_)
E4,E7: 6.. / E4 = 6  =>  0 pairs (X) / E7 = 6  => 17 pairs (_)
H3,H5: 6.. / H3 = 6  => 19 pairs (_) / H5 = 6  =>  0 pairs (X)
D4,E4: 7.. / D4 = 7  => 17 pairs (_) / E4 = 7  =>  0 pairs (X)
H5,H6: 7.. / H5 = 7  => 22 pairs (_) / H6 = 7  => 16 pairs (_)
G7,G9: 7.. / G7 = 7  =>  0 pairs (X) / G9 = 7  => 15 pairs (_)
D3,D4: 7.. / D3 = 7  =>  0 pairs (X) / D4 = 7  => 17 pairs (_)
C2,A3: 8.. / C2 = 8  => 17 pairs (_) / A3 = 8  =>  0 pairs (X)
F2,F3: 8.. / F2 = 8  =>  0 pairs (X) / F3 = 8  => 17 pairs (_)
A7,C7: 8.. / A7 = 8  => 17 pairs (_) / C7 = 8  =>  0 pairs (X)
C2,F2: 8.. / C2 = 8  => 17 pairs (_) / F2 = 8  =>  0 pairs (X)
A3,F3: 8.. / A3 = 8  =>  0 pairs (X) / F3 = 8  => 17 pairs (_)
A3,A7: 8.. / A3 = 8  =>  0 pairs (X) / A7 = 8  => 17 pairs (_)
C2,C7: 8.. / C2 = 8  => 17 pairs (_) / C7 = 8  =>  0 pairs (X)
A6,B6: 9.. / A6 = 9  => 16 pairs (_) / B6 = 9  => 22 pairs (_)
* DURATION: 0:00:48.047567  START: 22:53:20.259977  END: 22:54:08.307544 2019-04-30
* CP COUNT: (42)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,D5,D8,E3,E6,F3,F4,G2,G7,G9,H1,H3,H6,H8,I4)
* ...5.6..86..41..57.25......582...39.....958....68.3..5.......4.154.876.9.6.....8.
* PAIR B2: 3,9 BLK 1
C2: 3,9,8                                # reduction candidate for 3,9
C2: 3,9 => CTR
* ...5.6..86..418257825..9...582...39.....958.2..6823..5..8....4.154.87629.6.....8.
C2: 8                                    # 17 pairs
* PAIR B2: 3,9 COL B
B7: 3,9,7                                # reduction candidate for 3,9
B7: 7                                    # 17 pairs
B7: 3,9                                  # 17 pairs
* PAIR E3: 3,7 BLK 2
E1: 3,7,2                                # reduction candidate for 3,7
E1: 3,7                                  # 21 pairs
D3: 3,7,9                                # reduction candidate for 3,7
D3: 3,7 => CTR
* ...526.386..41.257.25......582...39....2958....68.3..5.......4.154.876.9.6.....8.
D3: 9                                    # 21 pairs
* PAIR F3: 8,9 BLK 2
F2: 8,9,2                                # reduction candidate for 8,9
F2: 8,9 => CTR
* ...526.386..41.257.25......582...39....2958....6843175.......4.154387629.6..5478.
F2: 2                                    # 21 pairs
* PAIR F3: 8,9 ROW 3
A3: 8,9,4,7                              # reduction candidate for 8,9
A3: 8,9 => CTR
* ...5.69386..41.257.25......582...39.....958.2..6823..5.......4.154.876.9.6.....8.
A3: 4,7                                  # 19 pairs
* PAIR H1: 2,3 ROW 1
E1: 2,3,7                                # reduction candidate for 2,3
E1: 7 => SOLVED
* 491576238638412957725938164582741396347695812916823475873269541154387629269154783
E1: 2,3                                  # 17 pairs
* PAIR G2: 2,9 BLK 3
G1: 2,9,4                                # reduction candidate for 2,9
G1: 2,9 => SOLVED
* 491576238638412957725938164582741396347695812916823475873269541154387629269154783
G1: 4                                    # 23 pairs
* PAIR G2: 2,9 ROW 2
F2: 2,9,8                                # reduction candidate for 2,9
F2: 8 => CTR
* ...526.386..418257825..9...582...39....2958....6843175..8....4.154387629.6..5478.
F2: 2,9                                  # 17 pairs
* PAIR H3: 1,6 COL H
H5: 1,6,7                                # reduction candidate for 1,6
H5: 7                                    # 22 pairs
H5: 1,6                                  # 16 pairs
* PAIR F4: 1,4 COL F
F9: 1,4,2,9                              # reduction candidate for 1,4
F9: 2,9 => CTR
* ...5.6..86..41..57.25......582..4396...6958.2..68234.5....61.4.154.876.9.6.....8.
F9: 1,4                                  # 17 pairs
* PAIR D5: 2,6 ROW 5
I5: 2,6,4                                # reduction candidate for 2,6
I5: 4 => CTR
* ...5.6..86..41..57.25......582...39....295864..68.3..5.......4.154.876.9.6.....8.
I5: 2,6                                  # 19 pairs
* PAIR D5: 2,6 COL D
D7: 2,6,1,3,9                            # reduction candidate for 2,6
D7: 2,6 => SOLVED
* 491576238638412957725938164582741396347695812916823475873269541154387629269154783
D7: 1,3,9                                # 17 pairs
* PAIR E6: 2,4 ROW 6
G6: 2,4,1                                # reduction candidate for 2,4
G6: 1 => CTR
* ...5.6..86..41..57.25......582...39.....958.2..6823175.......4.154.87629.6.....8.
G6: 2,4                                  # 19 pairs
* PAIR E6: 2,4 COL E
E9: 2,4,3,5                              # reduction candidate for 2,4
E9: 2,4 => CTR
* ...5.6..86..41..57.25......582.6.394...2958.6..68432.5...65.74.154387629.6....58.
E9: 3,5                                  # 17 pairs
* PAIR I4: 4,6 BLK 6
I5: 4,6,2                                # reduction candidate for 4,6
I5: 4,6 => CTR
* ...5.6..86..41..57.25......582...39....2958....68432.5.......4.154387629.6.....8.
I5: 2 => SOLVED
* 491576238638412957725938164582741396347695812916823475873269541154387629269154783
* PAIR I4: 4,6 ROW 4
E4: 4,6,7                                # reduction candidate for 4,6
E4: 7 => CTR
* ...5.6..86..41..57.2573....582.71394....958....68432.5....6.54.154.876.9.6..5478.
E4: 4,6                                  # 17 pairs
* PAIR I4: 4,6 COL I
I3: 4,6,3                                # reduction candidate for 4,6
I3: 4,6 => SOLVED
* 491576238638412957725938164582741396347695812916823475873269541154387629269154783
I3: 3 => CTR
* ...536.286..412957.25.781635827.139.....958....68.32.58....9.4.1542876392693.4781
* PAIR H6: 1,7 BLK 6
H5: 1,7,6                                # reduction candidate for 1,7
H5: 6 => CTR
* ...5.6..86..41..57.25....16582...394...29586...68.3.75.......4.154.876.9.6.....8.
H5: 1,7                                  # 19 pairs
* PAIR H6: 1,7 ROW 6
B6: 1,7,4,9                              # reduction candidate for 1,7
B6: 1,7                                  # 21 pairs
B6: 4,9                                  # 17 pairs
* PAIR D8: 2,3 BLK 8
D7: 2,3,1,6,9                            # reduction candidate for 2,3
D7: 2,3 => SOLVED
* 491576238638412957725938164582741396347695812916823475873269541154387629269154783
D7: 1,6,9                                # 15 pairs
E7: 2,3,5,6                              # reduction candidate for 2,3
E7: 2,3 => CTR
* ...5.6..86..41..57.25......582.6.394...2958.6..68432.5...6..54.154387629.6.....8.
E7: 5,6                                  # 16 pairs
D9: 2,3,1,9                              # reduction candidate for 2,3
D9: 2,3 => CTR
* ...5.6..86..412957.25..8...582...39....6958.2..6823..5.......4.154.876.9.6.....8.
D9: 1,9                                  # 16 pairs
E9: 2,3,4,5                              # reduction candidate for 2,3
E9: 2,3 => CTR
* ...5.6..86..41..57.25......582.61394...2958.6..68432.5...65.741154387629.6...458.
E9: 4,5                                  # 16 pairs
* PAIR H8: 2,3 BLK 9
I7: 2,3,1                                # reduction candidate for 2,3
I7: 2,3                                  # 16 pairs
I9: 2,3,1                                # reduction candidate for 2,3
I9: 2,3                                  # 18 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060504-absurd-base-pr-000.dot
* REASONING
* DIS # C2: 3,9 => CTR => C2: 8
* DIS # D3: 3,7 => CTR => D3: 9
* DIS # F2: 8,9 => CTR => F2: 2
* DIS # A3: 8,9 => CTR => A3: 4,7
* PRF # E1: 7 => SOL
* PRF # G1: 2,9 => SOL
* DIS # F2: 8 => CTR => F2: 2,9
* DIS # F9: 2,9 => CTR => F9: 1,4
* DIS # I5: 4 => CTR => I5: 2,6
* PRF # D7: 2,6 => SOL
* DIS # G6: 1 => CTR => G6: 2,4
* DIS # E9: 2,4 => CTR => E9: 3,5
* DIS # I5: 4,6 => CTR => I5: 2
* PRF # I5: 2 => SOL
* DIS # E4: 7 => CTR => E4: 4,6
* PRF # I3: 4,6 => SOL
* DIS # I3: 3 => CTR => I3: 4,6
* DIS # H5: 6 => CTR => H5: 1,7
* PRF # D7: 2,3 => SOL
* DIS # E7: 2,3 => CTR => E7: 5,6
* DIS # D9: 2,3 => CTR => D9: 1,9
* DIS # E9: 2,3 => CTR => E9: 4,5
* CNT  22 HDP CHAINS /  49 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,D5,D8,E3,E6,F3,F4,G2,G7,G9,H1,H3,H6,H8,I4)
* ...5.6..86..41..57.25......582...39.....958....68.3..5.......4.154.876.9.6.....8.
* PAIR B2: 3,9 BLK 1
C2: 3,9,8                                # reduction candidate for 3,9
C2: 3,9 => CTR
* ...5.6..86..418257825..9...582...39.....958.2..6823..5..8....4.154.87629.6.....8.
* PAIR E3: 3,7 BLK 2
E1: 3,7,2                                # reduction candidate for 3,7
E1: 3,7                                  # 21 pairs
D3: 3,7,9                                # reduction candidate for 3,7
D3: 3,7 => CTR
* ...5.6..8638419257.25..8...582...39.3...958.2..6823..58....2.4.15438762926.....8.
* RESTART
* PAIR H3: 1,6 COL H
H5: 1,6,7                                # reduction candidate for 1,6
H5: 7 => CTR
* 9.7536.286384129574259781635827.139.341.9587.7968.3215873.29541154.876.9269.5478.
* PAIR RESTART
* PAIR D5: 2,6 ROW 5
I5: 2,6,4                                # reduction candidate for 2,6
I5: 4 => CTR
* ..15.6..8638412957.259.8...5827.139.3.7295864..68.3.75873..954.154.876.9269.5478.
* PAIR D5: 2,6 COL D
D7: 2,6,1                                # reduction candidate for 2,6
D7: 2,6 => SOLVED
* 491576238638412957725938164582741396347695812916823475873269541154387629269154783
* DURATION: 0:00:08.336363  START: 22:54:40.202013  END: 22:54:48.538376 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060504-absurd-base-pr-001.dot
* REASONING
* DIS # C2: 3,9 => CTR => C2: 8
* DIS C2: 8 # D3: 3,7 => CTR => D3: 9
* DIS C2: 8 + D3: 9 # H5: 7 => CTR => H5: 1,6
* DIS C2: 8 + D3: 9 + H5: 1,6 # I5: 4 => CTR => I5: 2,6
* PRF C2: 8 + D3: 9 + H5: 1,6 + I5: 2,6 # D7: 2,6 => SOL
* STA C2: 8 + D3: 9 + H5: 1,6 + I5: 2,6 + D7: 2,6
* CNT   5 HDP CHAINS /   8 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060504, absurd

Solution

position: 491576238638412957725938164582741396347695812916823475873269541154387629269154783 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 # C2: 3,9 => CTR => C2: 8
* INC # C2: 8 => UNS
* INC # B7: 3,9 => UNS
* INC # B7: 7 => UNS
* INC # E1: 3,7 => UNS
* DIS # D3: 3,7 => CTR => D3: 9
* INC # D3: 9 => UNS
* DIS # F2: 8,9 => CTR => F2: 2
* INC # F2: 2 => UNS
* DIS # A3: 8,9 => CTR => A3: 4,7
* INC # A3: 4,7 => UNS
* INC # E1: 2,3 => UNS
* PRF # E1: 7 => SOL
* PRF # G1: 2,9 => SOL
* INC # G1: 4 => UNS
* INC # F2: 2,9 => UNS
* DIS # F2: 8 => CTR => F2: 2,9
* INC # H5: 1,6 => UNS
* INC # H5: 7 => UNS
* INC # F9: 1,4 => UNS
* DIS # F9: 2,9 => CTR => F9: 1,4
* INC # I5: 2,6 => UNS
* DIS # I5: 4 => CTR => I5: 2,6
* PRF # D7: 2,6 => SOL
* INC # D7: 1,3,9 => UNS
* INC # G6: 2,4 => UNS
* DIS # G6: 1 => CTR => G6: 2,4
* DIS # E9: 2,4 => CTR => E9: 3,5
* INC # E9: 3,5 => UNS
* DIS # I5: 4,6 => CTR => I5: 2
* PRF # I5: 2 => SOL
* INC # E4: 4,6 => UNS
* DIS # E4: 7 => CTR => E4: 4,6
* PRF # I3: 4,6 => SOL
* DIS # I3: 3 => CTR => I3: 4,6
* INC # H5: 1,7 => UNS
* DIS # H5: 6 => CTR => H5: 1,7
* INC # B6: 1,7 => UNS
* INC # B6: 4,9 => UNS
* PRF # D7: 2,3 => SOL
* INC # D7: 1,6,9 => UNS
* DIS # E7: 2,3 => CTR => E7: 5,6
* INC # E7: 5,6 => UNS
* DIS # D9: 2,3 => CTR => D9: 1,9
* INC # D9: 1,9 => UNS
* DIS # E9: 2,3 => CTR => E9: 4,5
* INC # E9: 4,5 => UNS
* INC # I7: 2,3 => UNS
* INC # I9: 2,3 => UNS
* CNT  49 HDP CHAINS /  49 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # C2: 3,9 => CTR => C2: 8
* INC C2: 8 # E1: 3,7 => UNS
* DIS C2: 8 # D3: 3,7 => CTR => D3: 9
* INC C2: 8 + D3: 9 # H5: 1,6 => UNS
* DIS C2: 8 + D3: 9 # H5: 7 => CTR => H5: 1,6
* INC C2: 8 + D3: 9 + H5: 1,6 # I5: 2,6 => UNS
* DIS C2: 8 + D3: 9 + H5: 1,6 # I5: 4 => CTR => I5: 2,6
* PRF C2: 8 + D3: 9 + H5: 1,6 + I5: 2,6 # D7: 2,6 => SOL
* STA C2: 8 + D3: 9 + H5: 1,6 + I5: 2,6 + D7: 2,6
* CNT   8 HDP CHAINS /   8 HYP OPENED