Analysis of xx-ph-01001706-13_07-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7..6..75..6..8...6......4...3...8..89...6.........2.1...5.....789..5...56...7. initial

Autosolve

position: 98.7..6..75..6..8...6......4...3...8..89...6.........2.1..75.....789..5...56...7. 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: 0:00:51.479235

The following important HDP chains were detected:

* DIS # G4: 1,9 # D2: 1,4 => CTR => D2: 2,3
* DIS # G4: 1,9 + D2: 2,3 # D3: 3 => CTR => D3: 1,4
* DIS # G4: 1,9 + D2: 2,3 + D3: 1,4 # G6: 3,4 => CTR => G6: 5,7
* DIS # G4: 1,9 + D2: 2,3 + D3: 1,4 + G6: 5,7 # H1: 3,4 => CTR => H1: 1,2
* PRF # G4: 1,9 + D2: 2,3 + D3: 1,4 + G6: 5,7 + H1: 1,2 # F2: 2,3 => SOL
* STA # G4: 1,9 + D2: 2,3 + D3: 1,4 + G6: 5,7 + H1: 1,2 + F2: 2,3
* CNT   5 HDP CHAINS /  45 HYP OPENED

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

Details

Positions

98.7..6..75..6..8...6......4...3...8..89...6.........2.1...5.....789..5...56...7. initial
98.7..6..75..6..8...6......4...3...8..89...6.........2.1..75.....789..5...56...7. autosolve
981754623754362189326189547472536918138927465569418732613275894247891356895643271 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
H4: 1,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A5,A6: 5.. / A5 = 5  =>  1 pairs (_) / A6 = 5  =>  2 pairs (_)
E1,I1: 5.. / E1 = 5  =>  4 pairs (_) / I1 = 5  =>  1 pairs (_)
D4,G4: 5.. / D4 = 5  =>  2 pairs (_) / G4 = 5  =>  4 pairs (_)
F4,F6: 6.. / F4 = 6  =>  1 pairs (_) / F6 = 6  =>  1 pairs (_)
I7,I8: 6.. / I7 = 6  =>  1 pairs (_) / I8 = 6  =>  2 pairs (_)
B4,F4: 6.. / B4 = 6  =>  1 pairs (_) / F4 = 6  =>  1 pairs (_)
A7,I7: 6.. / A7 = 6  =>  2 pairs (_) / I7 = 6  =>  1 pairs (_)
G3,I3: 7.. / G3 = 7  =>  5 pairs (_) / I3 = 7  =>  1 pairs (_)
I3,I5: 7.. / I3 = 7  =>  1 pairs (_) / I5 = 7  =>  5 pairs (_)
E3,F3: 8.. / E3 = 8  =>  2 pairs (_) / F3 = 8  =>  1 pairs (_)
E6,F6: 8.. / E6 = 8  =>  1 pairs (_) / F6 = 8  =>  2 pairs (_)
A7,A9: 8.. / A7 = 8  =>  2 pairs (_) / A9 = 8  =>  1 pairs (_)
G7,G9: 8.. / G7 = 8  =>  1 pairs (_) / G9 = 8  =>  2 pairs (_)
A7,G7: 8.. / A7 = 8  =>  2 pairs (_) / G7 = 8  =>  1 pairs (_)
A9,G9: 8.. / A9 = 8  =>  1 pairs (_) / G9 = 8  =>  2 pairs (_)
E3,E6: 8.. / E3 = 8  =>  2 pairs (_) / E6 = 8  =>  1 pairs (_)
F3,F6: 8.. / F3 = 8  =>  1 pairs (_) / F6 = 8  =>  2 pairs (_)
F2,F3: 9.. / F2 = 9  =>  1 pairs (_) / F3 = 9  =>  2 pairs (_)
C7,B9: 9.. / C7 = 9  =>  4 pairs (_) / B9 = 9  =>  1 pairs (_)
* DURATION: 0:00:13.714031  START: 02:24:48.048806  END: 02:25:01.762837 2021-01-09
* CP COUNT: (19)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:51.291684  START: 02:25:07.552925  END: 02:25:58.844609 2021-01-09
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-01001706-13_07-base-pr-002.dot
* REASONING
* DIS # G4: 1,9 # D2: 1,4 => CTR => D2: 2,3
* DIS # G4: 1,9 + D2: 2,3 # D3: 3 => CTR => D3: 1,4
* DIS # G4: 1,9 + D2: 2,3 + D3: 1,4 # G6: 3,4 => CTR => G6: 5,7
* DIS # G4: 1,9 + D2: 2,3 + D3: 1,4 + G6: 5,7 # H1: 3,4 => CTR => H1: 1,2
* PRF # G4: 1,9 + D2: 2,3 + D3: 1,4 + G6: 5,7 + H1: 1,2 # F2: 2,3 => SOL
* STA # G4: 1,9 + D2: 2,3 + D3: 1,4 + G6: 5,7 + H1: 1,2 + F2: 2,3
* CNT   5 HDP CHAINS /  45 HYP OPENED

Header Info

1001706;13_07;GP;25;11.30;1.20;1.20

Solution

position: 981754623754362189326189547472536918138927465569418732613275894247891356895643271 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 # G4: 1,9 => UNS
* INC # G6: 1,9 => UNS
* INC # H6: 1,9 => UNS
* INC # C4: 1,9 => UNS
* INC # C4: 2 => UNS
* INC # H3: 1,9 => UNS
* INC # H3: 2,3,4 => UNS
* CNT   7 HDP CHAINS /   7 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G4: 1,9 => UNS
* INC # G6: 1,9 => UNS
* INC # H6: 1,9 => UNS
* INC # C4: 1,9 => UNS
* INC # C4: 2 => UNS
* INC # H3: 1,9 => UNS
* INC # H3: 2,3,4 => UNS
* CNT   7 HDP CHAINS /   7 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # G4: 1,9 => UNS
* INC # G6: 1,9 => UNS
* INC # H6: 1,9 => UNS
* INC # C4: 1,9 => UNS
* INC # C4: 2 => UNS
* INC # H3: 1,9 => UNS
* INC # H3: 2,3,4 => UNS
* INC # G4: 1,9 # B6: 6,7 => UNS
* INC # G4: 1,9 # B6: 3,9 => UNS
* INC # G4: 1,9 # B6: 3,7 => UNS
* INC # G4: 1,9 # B6: 6,9 => UNS
* INC # G4: 1,9 # G5: 3,7 => UNS
* INC # G4: 1,9 # I5: 3,7 => UNS
* INC # G4: 1,9 # F6: 6,7 => UNS
* INC # G4: 1,9 # F6: 1,4,8 => UNS
* INC # G4: 1,9 # E5: 1,4 => UNS
* INC # G4: 1,9 # F5: 1,4 => UNS
* INC # G4: 1,9 # E6: 1,4 => UNS
* INC # G4: 1,9 # F6: 1,4 => UNS
* DIS # G4: 1,9 # D2: 1,4 => CTR => D2: 2,3
* INC # G4: 1,9 + D2: 2,3 # D3: 1,4 => UNS
* INC # G4: 1,9 + D2: 2,3 # D3: 1,4 => UNS
* DIS # G4: 1,9 + D2: 2,3 # D3: 3 => CTR => D3: 1,4
* INC # G4: 1,9 + D2: 2,3 + D3: 1,4 # E5: 1,4 => UNS
* INC # G4: 1,9 + D2: 2,3 + D3: 1,4 # F5: 1,4 => UNS
* INC # G4: 1,9 + D2: 2,3 + D3: 1,4 # E6: 1,4 => UNS
* INC # G4: 1,9 + D2: 2,3 + D3: 1,4 # F6: 1,4 => UNS
* INC # G4: 1,9 + D2: 2,3 + D3: 1,4 # G2: 1,9 => UNS
* INC # G4: 1,9 + D2: 2,3 + D3: 1,4 # G3: 1,9 => UNS
* INC # G4: 1,9 + D2: 2,3 + D3: 1,4 # G9: 1,9 => UNS
* INC # G4: 1,9 + D2: 2,3 + D3: 1,4 # H3: 1,9 => UNS
* INC # G4: 1,9 + D2: 2,3 + D3: 1,4 # H3: 3,4 => UNS
* INC # G4: 1,9 + D2: 2,3 + D3: 1,4 # G5: 3,4 => UNS
* INC # G4: 1,9 + D2: 2,3 + D3: 1,4 # I5: 3,4 => UNS
* DIS # G4: 1,9 + D2: 2,3 + D3: 1,4 # G6: 3,4 => CTR => G6: 5,7
* DIS # G4: 1,9 + D2: 2,3 + D3: 1,4 + G6: 5,7 # H1: 3,4 => CTR => H1: 1,2
* INC # G4: 1,9 + D2: 2,3 + D3: 1,4 + G6: 5,7 + H1: 1,2 # H3: 3,4 => UNS
* INC # G4: 1,9 + D2: 2,3 + D3: 1,4 + G6: 5,7 + H1: 1,2 # H7: 3,4 => UNS
* INC # G4: 1,9 + D2: 2,3 + D3: 1,4 + G6: 5,7 + H1: 1,2 # G5: 3,4 => UNS
* INC # G4: 1,9 + D2: 2,3 + D3: 1,4 + G6: 5,7 + H1: 1,2 # I5: 3,4 => UNS
* INC # G4: 1,9 + D2: 2,3 + D3: 1,4 + G6: 5,7 + H1: 1,2 # H3: 3,4 => UNS
* INC # G4: 1,9 + D2: 2,3 + D3: 1,4 + G6: 5,7 + H1: 1,2 # H7: 3,4 => UNS
* INC # G4: 1,9 + D2: 2,3 + D3: 1,4 + G6: 5,7 + H1: 1,2 # F1: 2,3 => UNS
* PRF # G4: 1,9 + D2: 2,3 + D3: 1,4 + G6: 5,7 + H1: 1,2 # F2: 2,3 => SOL
* STA # G4: 1,9 + D2: 2,3 + D3: 1,4 + G6: 5,7 + H1: 1,2 + F2: 2,3
* CNT  44 HDP CHAINS /  45 HYP OPENED