Analysis of zz-www.sudokuoftheday.co.uk-20190314-absurd-base.sdk

Contents

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

level: medium

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

position: 1..3...8.....62..43.4........5.7..6............85.3..14.....9.897.....3.....34..5 initial

Autosolve

position: 1..34..8.5...623.43.4......2.5.7.86.7........6.85.3..1453...9.897....43.8..934..5 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B3: 8,9 => CTR => B3: 2,6
* DIS # C1: 7,9 => CTR => C1: 2,6
* PRF # C1: 2,6 => SOL
* DIS # H3: 1,9 => CTR => H3: 2,5
* PRF # B5: 1,9 => SOL
* DIS # E5: 1,9 => CTR => E5: 2,8
* DIS # F5: 1,9 => CTR => F5: 6,8
* DIS # B4: 4,9 => CTR => B4: 1,3
* DIS # B5: 4,9 => CTR => B5: 1,3
* DIS # H6: 4,9 => CTR => H6: 2,7
* PRF # H6: 2,7 => SOL
* DIS # D5: 1,4 => CTR => D5: 2,6,8
* DIS # B4: 1,4 => CTR => B4: 3,9
* DIS # E5: 1,9 => CTR => E5: 2,8
* DIS # F5: 1,9 => CTR => F5: 6,8
* PRF # E5: 2,9 => SOL
* DIS # I5: 2 => CTR => I5: 3,9
* DIS # B4: 1,4 => CTR => B4: 3,9
* DIS # H5: 2,5 => CTR => H5: 4,9
* DIS # G3: 2,5 => CTR => G3: 1,6
* PRF # H6: 2,7 => SOL
* DIS # H6: 4,9 => CTR => H6: 2,7
* DIS # E8: 1,2 => CTR => E8: 5,8
* PRF # E5: 1,2 => SOL
* PRF # H9: 1,2 => SOL
* DIS # H3: 1,2 => CTR => H3: 5,9
* DIS # G9: 2,6 => CTR => G9: 1,7
* DIS # C8: 2,6 => CTR => C8: 1
* PRF # C8: 1 => SOL
* CNT  29 HDP CHAINS /  64 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 # B3: 8,9 => CTR => B3: 2,6
* DIS B3: 2,6 # C1: 7,9 => CTR => C1: 2,6
* PRF B3: 2,6 + C1: 2,6 => SOL
* STA B3: 2,6 + C1: 2,6
* CNT   3 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

1..3...8.....62..43.4........5.7..6............85.3..14.....9.897.....3.....34..5 initial
1..34..8.5...623.43.4......2.5.7.86.7........6.85.3..1453...9.897....43.8..934..5 autosolve
192345687587162394364789152235471869719826543648593271453617928971258436826934715 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
B2: 8,9
C2: 7,9
H2: 1,9
C5: 1,9
B6: 4,9
D4: 1,4
F4: 1,9
E6: 2,9
I4: 3,9
G5: 2,5
G6: 2,7
D7: 6,7
E7: 1,2
F7: 6,7
H7: 1,2
I8: 2,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,H2: 1.. / D2 = 1  => 15 pairs (_) / H2 = 1  =>  0 pairs (X)
E7,H7: 1.. / E7 = 1  =>  0 pairs (*) / H7 = 1  =>  0 pairs (X)
G3,G9: 1.. / G3 = 1  => 16 pairs (_) / G9 = 1  =>  0 pairs (X)
E7,H7: 2.. / E7 = 2  =>  0 pairs (X) / H7 = 2  =>  0 pairs (_)
D5,D8: 2.. / D5 = 2  =>  0 pairs (X) / D8 = 2  =>  0 pairs (_)
B4,B5: 3.. / B4 = 3  => 14 pairs (_) / B5 = 3  => 16 pairs (_)
I4,I5: 3.. / I4 = 3  => 16 pairs (_) / I5 = 3  => 14 pairs (_)
B4,I4: 3.. / B4 = 3  => 14 pairs (_) / I4 = 3  => 16 pairs (_)
B5,I5: 3.. / B5 = 3  => 16 pairs (_) / I5 = 3  => 14 pairs (_)
D4,D5: 4.. / D4 = 4  => 15 pairs (_) / D5 = 4  =>  0 pairs (X)
H5,H6: 4.. / H5 = 4  => 15 pairs (_) / H6 = 4  =>  0 pairs (X)
B4,D4: 4.. / B4 = 4  =>  0 pairs (X) / D4 = 4  => 15 pairs (_)
B6,H6: 4.. / B6 = 4  => 15 pairs (_) / H6 = 4  =>  0 pairs (X)
G5,H5: 5.. / G5 = 5  => 17 pairs (_) / H5 = 5  =>  0 pairs (X)
E8,F8: 5.. / E8 = 5  => 17 pairs (_) / F8 = 5  =>  0 pairs (X)
F1,G1: 5.. / F1 = 5  => 18 pairs (_) / G1 = 5  =>  0 pairs (X)
E3,E8: 5.. / E3 = 5  =>  0 pairs (X) / E8 = 5  => 17 pairs (_)
H3,H5: 5.. / H3 = 5  => 17 pairs (_) / H5 = 5  =>  0 pairs (X)
D5,F5: 6.. / D5 = 6  =>  0 pairs (X) / F5 = 6  => 15 pairs (_)
D7,F7: 6.. / D7 = 6  => 15 pairs (_) / F7 = 6  =>  0 pairs (X)
I8,G9: 6.. / I8 = 6  => 16 pairs (_) / G9 = 6  =>  0 pairs (X)
C8,I8: 6.. / C8 = 6  =>  0 pairs (X) / I8 = 6  => 16 pairs (_)
D5,D7: 6.. / D5 = 6  =>  0 pairs (X) / D7 = 6  => 15 pairs (_)
F5,F7: 6.. / F5 = 6  => 15 pairs (_) / F7 = 6  =>  0 pairs (X)
C1,C2: 7.. / C1 = 7  =>  0 pairs (X) / C2 = 7  => 16 pairs (_)
I1,I3: 7.. / I1 = 7  => 17 pairs (_) / I3 = 7  => 17 pairs (_)
G6,H6: 7.. / G6 = 7  => 15 pairs (_) / H6 = 7  =>  0 pairs (*)
D7,F7: 7.. / D7 = 7  =>  0 pairs (X) / F7 = 7  => 15 pairs (_)
G9,H9: 7.. / G9 = 7  =>  0 pairs (*) / H9 = 7  =>  0 pairs (X)
C2,D2: 7.. / C2 = 7  => 16 pairs (_) / D2 = 7  =>  0 pairs (X)
G6,G9: 7.. / G6 = 7  => 15 pairs (_) / G9 = 7  =>  0 pairs (*)
H6,H9: 7.. / H6 = 7  =>  0 pairs (*) / H9 = 7  =>  0 pairs (X)
B2,B3: 8.. / B2 = 8  => 16 pairs (_) / B3 = 8  =>  0 pairs (X)
B2,D2: 8.. / B2 = 8  => 16 pairs (_) / D2 = 8  =>  0 pairs (X)
* DURATION: 0:00:43.776042  START: 04:30:43.313385  END: 04:31:27.089427 2019-05-01
* CP COUNT: (34)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B6,C2,C5,D4,D7,E6,E7,F4,F7,G5,G6,H2,H7,I4,I8)
* 1..34..8.5...623.43.4......2.5.7.86.7........6.85.3..1453...9.897....43.8..934..5
* PAIR B2: 8,9 BLK 1
B3: 8,9,2,6                              # reduction candidate for 8,9
B3: 8,9 => CTR
* 1..34.58.5...623.43.4......2.5.7.86.7.....25.6.8523741453.1.9289712..4368..934175
B3: 2,6                                  # 17 pairs
* PAIR C2: 7,9 BLK 1
C1: 7,9,2,6                              # reduction candidate for 7,9
C1: 7,9 => CTR
* 1..34.58.5..1623943.4.5.12.2.547186.7.1.8.25.6.85.3..1453...91897..1543.81.934..5
C1: 2,6 => SOLVED
* 192345687587162394364789152235471869719826543648593271453617928971258436826934715
* PAIR H2: 1,9 BLK 3
H3: 1,9,2,5                              # reduction candidate for 1,9
H3: 1,9 => CTR
* 1..34..8.5...623.43.4......2.5.7.86.7.....25.698523741453.1.928971...43.8..934.75
H3: 2,5                                  # 17 pairs
* PAIR C5: 1,9 BLK 4
B4: 1,9,3,4                              # reduction candidate for 1,9
B4: 1,9                                  # 16 pairs
B5: 1,9,3,4                              # reduction candidate for 1,9
B5: 1,9 => SOLVED
* 192345687587162394364789152235471869719826543648593271453617928971258436826934715
B5: 3,4                                  # 17 pairs
* PAIR C5: 1,9 ROW 5
E5: 1,9,2,8                              # reduction candidate for 1,9
E5: 1,9 => CTR
* 1..34..8.5...623.43.4......2.547186.7.1.9....6.85237.1453.1.9.897....43.8..934..5
E5: 2,8                                  # 17 pairs
F5: 1,9,6,8                              # reduction candidate for 1,9
F5: 1,9 => CTR
* 1..34..8959786231438419.65.2.547.86.7.9681...6485237914537169289712584368..934175
F5: 6,8                                  # 17 pairs
* PAIR B6: 4,9 BLK 4
B4: 4,9,1,3                              # reduction candidate for 4,9
B4: 4,9 => CTR
* 1..34.58.5..1623943.4.5.12.2.5471863731.8....6.85.3..1453...91897..1543.81.934..5
B4: 1,3                                  # 16 pairs
B5: 4,9,1,3                              # reduction candidate for 4,9
B5: 4,9 => CTR
* 1..34.58.5..1623943.4.5.12.2354718697.1.8.2536.85.3..1453...91897..1543.81.934..5
B5: 1,3                                  # 17 pairs
* PAIR B6: 4,9 ROW 6
H6: 4,9,2,7                              # reduction candidate for 4,9
H6: 4,9 => CTR
* 1..34..8.597862314384.9.6522.5.7.86.7.9.8....648523791453.1.9289712584368..934175
H6: 2,7 => SOLVED
* 192345687587162394364789152235471869719826543648593271453617928971258436826934715
* PAIR D4: 1,4 BLK 5
D5: 1,4,2,6,8                            # reduction candidate for 1,4
D5: 1,4 => CTR
* 1..345.8959786231438479....2.5.79863739186.426485237914536179289712584368..934175
D5: 2,6,8                                # 15 pairs
* PAIR D4: 1,4 ROW 4
B4: 1,4,3,9                              # reduction candidate for 1,4
B4: 1,4 => CTR
* 1..34..89597862314384.9....215479863739.8..42648523791453.1.9289712584368..934175
B4: 3,9                                  # 16 pairs
* PAIR F4: 1,9 BLK 5
E5: 1,9,2,8                              # reduction candidate for 1,9
E5: 1,9 => CTR
* 1..34..8.5...623.43.4......2.547186.7.1.9....6.85237.1453.1.9.897....43.8..934..5
E5: 2,8                                  # 17 pairs
F5: 1,9,6,8                              # reduction candidate for 1,9
F5: 1,9 => CTR
* 1..34..8959786231438419.65.2.547.86.7.9681...6485237914537169289712584368..934175
F5: 6,8                                  # 17 pairs
* PAIR F4: 1,9 ROW 4
B4: 1,9,3,4                              # reduction candidate for 1,9
B4: 3,4                                  # 17 pairs
B4: 1,9                                  # 16 pairs
* PAIR F4: 1,9 COL F
F3: 1,9,5,7,8                            # reduction candidate for 1,9
F3: 1,9                                  # 20 pairs
F3: 5,7,8                                # 16 pairs
* PAIR E6: 2,9 BLK 5
E5: 2,9,1,8                              # reduction candidate for 2,9
E5: 2,9 => SOLVED
* 192345687587162394364789152235471869719826543648593271453617928971258436826934715
E5: 1,8                                  # 17 pairs
* PAIR E6: 2,9 ROW 6
H6: 2,9,4,7                              # reduction candidate for 2,9
H6: 4,7                                  # 17 pairs
H6: 2,9                                  # 15 pairs
* PAIR I4: 3,9 BLK 6
I5: 3,9,2                                # reduction candidate for 3,9
I5: 2 => CTR
* 1..345.8.5978623143.4......215479863739.8.542648523791453.1.9289712584368..934175
I5: 3,9                                  # 17 pairs
* PAIR I4: 3,9 ROW 4
B4: 3,9,1,4                              # reduction candidate for 3,9
B4: 1,4 => CTR
* 1..34..89597862314384.9....215479863739.8..42648523791453.1.9289712584368..934175
B4: 3,9                                  # 16 pairs
* PAIR G5: 2,5 BLK 6
H5: 2,5,4,9                              # reduction candidate for 2,5
H5: 2,5 => CTR
* 1..34..8.5...623.43.4......2.5.7.86.7........698523741453.1.928971...43.8..934.75
H5: 4,9                                  # 18 pairs
* PAIR G5: 2,5 COL G
G1: 2,5,6                                # reduction candidate for 2,5
G1: 2,5                                  # 19 pairs
G3: 2,5,1,6                              # reduction candidate for 2,5
G3: 2,5 => CTR
* 192345687587162394364....122.547.86.7........6.85.37.1453.1.928971...436826934175
G3: 1,6                                  # 17 pairs
* PAIR G6: 2,7 BLK 6
H6: 2,7,4,9                              # reduction candidate for 2,7
H6: 2,7 => SOLVED
* 192345687587162394364789152235471869719826543648593271453617928971258436826934715
H6: 4,9 => CTR
* 1..34..8.597862314384.9.6522.5.7.86.7.9.8....648523791453.1.9289712584368..934175
* PAIR G6: 2,7 COL G
G9: 2,7,1,6                              # reduction candidate for 2,7
G9: 2,7                                  # 21 pairs
G9: 1,6                                  # 17 pairs
* PAIR E7: 1,2 BLK 8
D8: 1,2,8                                # reduction candidate for 1,2
D8: 1,2                                  # 19 pairs
E8: 1,2,5,8                              # reduction candidate for 1,2
E8: 1,2 => CTR
* 1..34..8.5...623.43.4.5....2.5.7.86.7...8..5.6.8593.41453...9.897....43.8..934..5
E8: 5,8                                  # 17 pairs
* PAIR E7: 1,2 COL E
E5: 1,2,8,9                              # reduction candidate for 1,2
E5: 1,2 => SOLVED
* 192345687587162394364789152235471869719826543648593271453617928971258436826934715
E5: 8,9                                  # 17 pairs
* PAIR H7: 1,2 BLK 9
G9: 1,2,6,7                              # reduction candidate for 1,2
G9: 1,2                                  # 16 pairs
H9: 1,2,7                                # reduction candidate for 1,2
H9: 1,2 => SOLVED
* 192345687587162394364789152235471869719826543648593271453617928971258436826934715
H9: 7                                    # 15 pairs
* PAIR H7: 1,2 COL H
H3: 1,2,5,9                              # reduction candidate for 1,2
H3: 1,2 => CTR
* 1..34..8.5...623943.4......2.5.7.86.7.....25.698523741453.1.928971...43.8..934.75
H3: 5,9                                  # 17 pairs
* PAIR I8: 2,6 BLK 9
G9: 2,6,1,7                              # reduction candidate for 2,6
G9: 2,6 => CTR
* 1..345.875871623943.478.1..2.547.86.7..2.654.64859372145362791897.8..43.8..934.75
G9: 1,7                                  # 17 pairs
* PAIR I8: 2,6 ROW 8
C8: 2,6,1                                # reduction candidate for 2,6
C8: 2,6 => CTR
* 1..345.875871623943.478.1..2.547.86.7..2.654.648593..145362791897.8..43.8..934..5
C8: 1 => SOLVED
* 192345687587162394364789152235471869719826543648593271453617928971258436826934715
* PAIR I8: 2,6 COL I
I1: 2,6,7,9                              # reduction candidate for 2,6
I1: 2,6                                  # 19 pairs
I3: 2,6,7,9                              # reduction candidate for 2,6
I3: 2,6                                  # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190314-absurd-base-pr-000.dot
* REASONING
* DIS # B3: 8,9 => CTR => B3: 2,6
* DIS # C1: 7,9 => CTR => C1: 2,6
* PRF # C1: 2,6 => SOL
* DIS # H3: 1,9 => CTR => H3: 2,5
* PRF # B5: 1,9 => SOL
* DIS # E5: 1,9 => CTR => E5: 2,8
* DIS # F5: 1,9 => CTR => F5: 6,8
* DIS # B4: 4,9 => CTR => B4: 1,3
* DIS # B5: 4,9 => CTR => B5: 1,3
* DIS # H6: 4,9 => CTR => H6: 2,7
* PRF # H6: 2,7 => SOL
* DIS # D5: 1,4 => CTR => D5: 2,6,8
* DIS # B4: 1,4 => CTR => B4: 3,9
* DIS # E5: 1,9 => CTR => E5: 2,8
* DIS # F5: 1,9 => CTR => F5: 6,8
* PRF # E5: 2,9 => SOL
* DIS # I5: 2 => CTR => I5: 3,9
* DIS # B4: 1,4 => CTR => B4: 3,9
* DIS # H5: 2,5 => CTR => H5: 4,9
* DIS # G3: 2,5 => CTR => G3: 1,6
* PRF # H6: 2,7 => SOL
* DIS # H6: 4,9 => CTR => H6: 2,7
* DIS # E8: 1,2 => CTR => E8: 5,8
* PRF # E5: 1,2 => SOL
* PRF # H9: 1,2 => SOL
* DIS # H3: 1,2 => CTR => H3: 5,9
* DIS # G9: 2,6 => CTR => G9: 1,7
* DIS # C8: 2,6 => CTR => C8: 1
* PRF # C8: 1 => SOL
* CNT  29 HDP CHAINS /  64 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B6,C2,C5,D4,D7,E6,E7,F4,F7,G5,G6,H2,H7,I4,I8)
* 1..34..8.5...623.43.4......2.5.7.86.7........6.85.3..1453...9.897....43.8..934..5
* PAIR B2: 8,9 BLK 1
B3: 8,9,2,6                              # reduction candidate for 8,9
B3: 8,9 => CTR
* 1..34.58.5...623.43.4......2.5.7.86.7.....25.6.8523741453.1.9289712..4368..934175
* PAIR C2: 7,9 BLK 1
C1: 7,9,2,6                              # reduction candidate for 7,9
C1: 7,9 => CTR
* 1..34.58.58.1623943.4.5912.2.547186.7.1.862..6.85.3..1453...91897..1543.81.934..5
C1: 2,6 => SOLVED
* 192345687587162394364789152235471869719826543648593271453617928971258436826934715
* DURATION: 0:00:04.509210  START: 04:32:16.344314  END: 04:32:20.853524 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190314-absurd-base-pr-001.dot
* REASONING
* DIS # B3: 8,9 => CTR => B3: 2,6
* DIS B3: 2,6 # C1: 7,9 => CTR => C1: 2,6
* PRF B3: 2,6 + C1: 2,6 => SOL
* STA B3: 2,6 + C1: 2,6
* CNT   3 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190314, absurd

Solution

position: 192345687587162394364789152235471869719826543648593271453617928971258436826934715 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 # B3: 8,9 => CTR => B3: 2,6
* INC # B3: 2,6 => UNS
* DIS # C1: 7,9 => CTR => C1: 2,6
* PRF # C1: 2,6 => SOL
* DIS # H3: 1,9 => CTR => H3: 2,5
* INC # H3: 2,5 => UNS
* INC # B4: 1,9 => UNS
* PRF # B5: 1,9 => SOL
* INC # B5: 3,4 => UNS
* DIS # E5: 1,9 => CTR => E5: 2,8
* INC # E5: 2,8 => UNS
* DIS # F5: 1,9 => CTR => F5: 6,8
* INC # F5: 6,8 => UNS
* DIS # B4: 4,9 => CTR => B4: 1,3
* INC # B4: 1,3 => UNS
* DIS # B5: 4,9 => CTR => B5: 1,3
* INC # B5: 1,3 => UNS
* DIS # H6: 4,9 => CTR => H6: 2,7
* PRF # H6: 2,7 => SOL
* DIS # D5: 1,4 => CTR => D5: 2,6,8
* INC # D5: 2,6,8 => UNS
* DIS # B4: 1,4 => CTR => B4: 3,9
* INC # B4: 3,9 => UNS
* DIS # E5: 1,9 => CTR => E5: 2,8
* INC # E5: 2,8 => UNS
* DIS # F5: 1,9 => CTR => F5: 6,8
* INC # F5: 6,8 => UNS
* INC # B4: 1,9 => UNS
* INC # B4: 3,4 => UNS
* INC # F3: 1,9 => UNS
* INC # F3: 5,7,8 => UNS
* PRF # E5: 2,9 => SOL
* INC # E5: 1,8 => UNS
* INC # H6: 2,9 => UNS
* INC # H6: 4,7 => UNS
* INC # I5: 3,9 => UNS
* DIS # I5: 2 => CTR => I5: 3,9
* INC # B4: 3,9 => UNS
* DIS # B4: 1,4 => CTR => B4: 3,9
* DIS # H5: 2,5 => CTR => H5: 4,9
* INC # H5: 4,9 => UNS
* INC # G1: 2,5 => UNS
* DIS # G3: 2,5 => CTR => G3: 1,6
* INC # G3: 1,6 => UNS
* PRF # H6: 2,7 => SOL
* DIS # H6: 4,9 => CTR => H6: 2,7
* INC # G9: 2,7 => UNS
* INC # G9: 1,6 => UNS
* INC # D8: 1,2 => UNS
* DIS # E8: 1,2 => CTR => E8: 5,8
* INC # E8: 5,8 => UNS
* PRF # E5: 1,2 => SOL
* INC # E5: 8,9 => UNS
* INC # G9: 1,2 => UNS
* PRF # H9: 1,2 => SOL
* INC # H9: 7 => UNS
* DIS # H3: 1,2 => CTR => H3: 5,9
* INC # H3: 5,9 => UNS
* DIS # G9: 2,6 => CTR => G9: 1,7
* INC # G9: 1,7 => UNS
* DIS # C8: 2,6 => CTR => C8: 1
* PRF # C8: 1 => SOL
* INC # I1: 2,6 => UNS
* INC # I3: 2,6 => UNS
* CNT  64 HDP CHAINS /  64 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B3: 8,9 => CTR => B3: 2,6
* DIS B3: 2,6 # C1: 7,9 => CTR => C1: 2,6
* PRF B3: 2,6 + C1: 2,6 => SOL
* STA B3: 2,6 + C1: 2,6
* CNT   3 HDP CHAINS /   2 HYP OPENED