Analysis of xx-ph-02237081-2019_01_07-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 9876.....5...4.8.........6.84..3...6..6...53....2..4..63..8..5..5...9.....1.....8 initial

Autosolve

position: 9876.....56..4.8.........6.84..3...6..6...53....2..48.63..8..5..58..9.....1.....8 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

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

Pair Reduction

Pair Reduction

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

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:38.007390

The following important HDP chains were detected:

* DIS # C3: 2,3 # G4: 7,9 => CTR => G4: 1,2
* DIS # C3: 2,3 + G4: 1,2 # H4: 1,2 => CTR => H4: 7,9
* DIS # C3: 2,3 + G4: 1,2 + H4: 7,9 # I2: 7,9 => CTR => I2: 2,3
* DIS # C3: 2,3 + G4: 1,2 + H4: 7,9 + I2: 2,3 # I3: 7,9 => CTR => I3: 2,3,5
* PRF # C3: 2,3 + G4: 1,2 + H4: 7,9 + I2: 2,3 + I3: 2,3,5 => SOL
* STA C3: 2,3
* CNT   5 HDP CHAINS /  46 HYP OPENED

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

Details

Positions

9876.....5...4.8.........6.84..3...6..6...53....2..4..63..8..5..5...9.....1.....8 initial
9876.....56..4.8.........6.84..3...6..6...53....2..48.63..8..5..58..9.....1.....8 autosolve
987625314563941872412378965845137296126894537379256481634782159758419623291563748 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (4)
C2: 2,3
B3: 1,2
D5: 4,8
F5: 4,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A3,B3: 1.. / A3 = 1  =>  6 pairs (_) / B3 = 1  =>  4 pairs (_)
A6,C6: 3.. / A6 = 3  =>  5 pairs (_) / C6 = 3  =>  8 pairs (_)
A3,A6: 3.. / A3 = 3  =>  8 pairs (_) / A6 = 3  =>  5 pairs (_)
A3,C3: 4.. / A3 = 4  => 12 pairs (_) / C3 = 4  =>  5 pairs (_)
H1,I1: 4.. / H1 = 4  =>  4 pairs (_) / I1 = 4  =>  5 pairs (_)
D5,F5: 4.. / D5 = 4  =>  3 pairs (_) / F5 = 4  =>  2 pairs (_)
C3,C7: 4.. / C3 = 4  =>  5 pairs (_) / C7 = 4  => 12 pairs (_)
I1,I3: 5.. / I1 = 5  =>  5 pairs (_) / I3 = 5  =>  4 pairs (_)
C4,C6: 5.. / C4 = 5  =>  8 pairs (_) / C6 = 5  =>  5 pairs (_)
E6,F6: 6.. / E6 = 6  =>  4 pairs (_) / F6 = 6  =>  4 pairs (_)
G8,G9: 6.. / G8 = 6  =>  4 pairs (_) / G9 = 6  =>  4 pairs (_)
E8,G8: 6.. / E8 = 6  =>  4 pairs (_) / G8 = 6  =>  4 pairs (_)
F6,F9: 6.. / F6 = 6  =>  4 pairs (_) / F9 = 6  =>  4 pairs (_)
D3,F3: 8.. / D3 = 8  =>  3 pairs (_) / F3 = 8  =>  2 pairs (_)
D5,F5: 8.. / D5 = 8  =>  2 pairs (_) / F5 = 8  =>  3 pairs (_)
D3,D5: 8.. / D3 = 8  =>  3 pairs (_) / D5 = 8  =>  2 pairs (_)
F3,F5: 8.. / F3 = 8  =>  2 pairs (_) / F5 = 8  =>  3 pairs (_)
C7,B9: 9.. / C7 = 9  =>  7 pairs (_) / B9 = 9  =>  9 pairs (_)
* DURATION: 0:00:15.614801  START: 16:30:06.618414  END: 16:30:22.233215 2020-10-10
* CP COUNT: (18)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:37.703349  START: 16:30:30.483591  END: 16:31:08.186940 2020-10-10
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-02237081-2019_01_07-base-pr-002.dot
* REASONING
* DIS # C3: 2,3 # G4: 7,9 => CTR => G4: 1,2
* DIS # C3: 2,3 + G4: 1,2 # H4: 1,2 => CTR => H4: 7,9
* DIS # C3: 2,3 + G4: 1,2 + H4: 7,9 # I2: 7,9 => CTR => I2: 2,3
* DIS # C3: 2,3 + G4: 1,2 + H4: 7,9 + I2: 2,3 # I3: 7,9 => CTR => I3: 2,3,5
* PRF # C3: 2,3 + G4: 1,2 + H4: 7,9 + I2: 2,3 + I3: 2,3,5 => SOL
* STA C3: 2,3
* CNT   5 HDP CHAINS /  46 HYP OPENED

Header Info

2237081;2019_01_07;PAQ;25;11.50;1.20;1.20

Solution

position: 987625314563941872412378965845137296126894537379256481634782159758419623291563748 solved
Solution

See section Deep 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 # A3: 2,3 => UNS
* INC # C3: 2,3 => UNS
* INC # F2: 2,3 => UNS
* INC # I2: 2,3 => UNS
* INC # A3: 1,2 => UNS
* INC # A3: 3,4 => UNS
* INC # B5: 1,2 => UNS
* INC # B5: 7,9 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A3: 2,3 => UNS
* INC # C3: 2,3 => UNS
* INC # F2: 2,3 => UNS
* INC # I2: 2,3 => UNS
* INC # A3: 1,2 => UNS
* INC # A3: 3,4 => UNS
* INC # B5: 1,2 => UNS
* INC # B5: 7,9 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A3: 2,3 => UNS
* INC # C3: 2,3 => UNS
* INC # F2: 2,3 => UNS
* INC # I2: 2,3 => UNS
* INC # A3: 1,2 => UNS
* INC # A3: 3,4 => UNS
* INC # B5: 1,2 => UNS
* INC # B5: 7,9 => UNS
* INC # A3: 2,3 # F2: 2,3 => UNS
* INC # A3: 2,3 # I2: 2,3 => UNS
* INC # A3: 2,3 # F3: 2,3 => UNS
* INC # A3: 2,3 # G3: 2,3 => UNS
* INC # A3: 2,3 # I3: 2,3 => UNS
* INC # A3: 2,3 # B5: 7,9 => UNS
* INC # A3: 2,3 # B5: 2 => UNS
* INC # A3: 2,3 # E6: 7,9 => UNS
* INC # A3: 2,3 # I6: 7,9 => UNS
* INC # A3: 2,3 # B9: 7,9 => UNS
* INC # A3: 2,3 # B9: 2 => UNS
* INC # A3: 2,3 # B9: 2,9 => UNS
* INC # A3: 2,3 # B9: 7 => UNS
* INC # A3: 2,3 # G7: 2,9 => UNS
* INC # A3: 2,3 # I7: 2,9 => UNS
* INC # A3: 2,3 # C4: 2,9 => UNS
* INC # A3: 2,3 # C4: 5 => UNS
* INC # A3: 2,3 => UNS
* INC # C3: 2,3 # F2: 2,3 => UNS
* INC # C3: 2,3 # I2: 2,3 => UNS
* INC # C3: 2,3 # F3: 2,3 => UNS
* INC # C3: 2,3 # G3: 2,3 => UNS
* INC # C3: 2,3 # I3: 2,3 => UNS
* INC # C3: 2,3 # D4: 5,9 => UNS
* INC # C3: 2,3 # D4: 1,7 => UNS
* INC # C3: 2,3 # E6: 5,9 => UNS
* INC # C3: 2,3 # E6: 1,6 => UNS
* INC # C3: 2,3 # D4: 7,9 => UNS
* INC # C3: 2,3 # D4: 1,5 => UNS
* INC # C3: 2,3 # E3: 7,9 => UNS
* INC # C3: 2,3 # E3: 2,5 => UNS
* DIS # C3: 2,3 # G4: 7,9 => CTR => G4: 1,2
* INC # C3: 2,3 + G4: 1,2 # H4: 7,9 => UNS
* INC # C3: 2,3 + G4: 1,2 # H4: 7,9 => UNS
* DIS # C3: 2,3 + G4: 1,2 # H4: 1,2 => CTR => H4: 7,9
* DIS # C3: 2,3 + G4: 1,2 + H4: 7,9 # I2: 7,9 => CTR => I2: 2,3
* DIS # C3: 2,3 + G4: 1,2 + H4: 7,9 + I2: 2,3 # I3: 7,9 => CTR => I3: 2,3,5
* PRF # C3: 2,3 + G4: 1,2 + H4: 7,9 + I2: 2,3 + I3: 2,3,5 => SOL
* STA C3: 2,3
* CNT  46 HDP CHAINS /  46 HYP OPENED