Analysis of xx-ph-00035966-12_05-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7.....6...8.7....7..5...4..3...2...6.4.9.......1..4.6...4.3...9.5.8.....2....1 initial

Autosolve

position: 98.7.....6...8.7....7..5...4..3...2...6.4.9.......1..4.6...4.3...9.5.8.....2....1 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: 0:00:32.800703

The following important HDP chains were detected:

* DIS # A5: 5,8 # B5: 2,7 => CTR => B5: 1,3
* PRF # A5: 5,8 + B5: 1,3 # I7: 2,5 => SOL
* STA # A5: 5,8 + B5: 1,3 + I7: 2,5
* CNT   2 HDP CHAINS /  64 HYP OPENED

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

Details

Positions

98.7.....6...8.7....7..5...4..3...2...6.4.9.......1..4.6...4.3...9.5.8.....2....1 initial
98.7.....6...8.7....7..5...4..3...2...6.4.9.......1..4.6...4.3...9.5.8.....2....1 autosolve
981723456653489712247615389495367128816542973732891564168974235329156847574238691 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (3)
D5: 5,8
D8: 1,6
G7: 2,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G4,H5: 1.. / G4 = 1  =>  4 pairs (_) / H5 = 1  =>  4 pairs (_)
F5,E6: 2.. / F5 = 2  =>  5 pairs (_) / E6 = 2  =>  4 pairs (_)
I5,G6: 3.. / I5 = 3  =>  4 pairs (_) / G6 = 3  =>  3 pairs (_)
D2,D3: 4.. / D2 = 4  =>  3 pairs (_) / D3 = 4  =>  4 pairs (_)
B8,H8: 4.. / B8 = 4  =>  4 pairs (_) / H8 = 4  =>  4 pairs (_)
D5,D6: 5.. / D5 = 5  =>  2 pairs (_) / D6 = 5  =>  5 pairs (_)
H3,I3: 8.. / H3 = 8  =>  3 pairs (_) / I3 = 8  =>  3 pairs (_)
D7,F9: 8.. / D7 = 8  =>  3 pairs (_) / F9 = 8  =>  6 pairs (_)
B4,B6: 9.. / B4 = 9  =>  4 pairs (_) / B6 = 9  =>  3 pairs (_)
I7,H9: 9.. / I7 = 9  =>  5 pairs (_) / H9 = 9  =>  3 pairs (_)
* DURATION: 0:00:05.491031  START: 23:11:38.694381  END: 23:11:44.185412 2020-12-16
* CP COUNT: (10)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:32.419363  START: 23:11:53.245925  END: 23:12:25.665288 2020-12-16
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00035966-12_05-base-pr-002.dot
* REASONING
* DIS # A5: 5,8 # B5: 2,7 => CTR => B5: 1,3
* PRF # A5: 5,8 + B5: 1,3 # I7: 2,5 => SOL
* STA # A5: 5,8 + B5: 1,3 + I7: 2,5
* CNT   2 HDP CHAINS /  64 HYP OPENED

Header Info

35966;12_05;GP;24;11.30;11.30;10.60

Solution

position: 981723456653489712247615389495367128816542973732891564168974235329156847574238691 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 # D6: 5,8 => UNS
* INC # D6: 6,9 => UNS
* INC # A5: 5,8 => UNS
* INC # H5: 5,8 => UNS
* INC # I5: 5,8 => UNS
* INC # D3: 1,6 => UNS
* INC # D3: 4,9 => UNS
* INC # I7: 2,5 => UNS
* INC # I7: 7,9 => UNS
* INC # A7: 2,5 => UNS
* INC # C7: 2,5 => UNS
* INC # G1: 2,5 => UNS
* INC # G1: 1,3,4,6 => UNS
* CNT  13 HDP CHAINS /  13 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D6: 5,8 => UNS
* INC # D6: 6,9 => UNS
* INC # A5: 5,8 => UNS
* INC # H5: 5,8 => UNS
* INC # I5: 5,8 => UNS
* INC # D3: 1,6 => UNS
* INC # D3: 4,9 => UNS
* INC # I7: 2,5 => UNS
* INC # I7: 7,9 => UNS
* INC # A7: 2,5 => UNS
* INC # C7: 2,5 => UNS
* INC # G1: 2,5 => UNS
* INC # G1: 1,3,4,6 => UNS
* CNT  13 HDP CHAINS /  13 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # D6: 5,8 => UNS
* INC # D6: 6,9 => UNS
* INC # A5: 5,8 => UNS
* INC # H5: 5,8 => UNS
* INC # I5: 5,8 => UNS
* INC # D3: 1,6 => UNS
* INC # D3: 4,9 => UNS
* INC # I7: 2,5 => UNS
* INC # I7: 7,9 => UNS
* INC # A7: 2,5 => UNS
* INC # C7: 2,5 => UNS
* INC # G1: 2,5 => UNS
* INC # G1: 1,3,4,6 => UNS
* INC # D6: 5,8 # A5: 5,8 => UNS
* INC # D6: 5,8 # H5: 5,8 => UNS
* INC # D6: 5,8 # I5: 5,8 => UNS
* INC # D6: 5,8 # E6: 2,7 => UNS
* INC # D6: 5,8 # E6: 6,9 => UNS
* INC # D6: 5,8 # A5: 2,7 => UNS
* INC # D6: 5,8 # B5: 2,7 => UNS
* INC # D6: 5,8 # A6: 5,8 => UNS
* INC # D6: 5,8 # C6: 5,8 => UNS
* INC # D6: 5,8 # H6: 5,8 => UNS
* INC # D6: 5,8 # E7: 1,9 => UNS
* INC # D6: 5,8 # E7: 7 => UNS
* INC # D6: 5,8 # D2: 1,9 => UNS
* INC # D6: 5,8 # D3: 1,9 => UNS
* INC # D6: 5,8 # D3: 1,6 => UNS
* INC # D6: 5,8 # D3: 4,9 => UNS
* INC # D6: 5,8 # I7: 2,5 => UNS
* INC # D6: 5,8 # I7: 7,9 => UNS
* INC # D6: 5,8 # A7: 2,5 => UNS
* INC # D6: 5,8 # C7: 2,5 => UNS
* INC # D6: 5,8 # G1: 2,5 => UNS
* INC # D6: 5,8 # G1: 1,3,4,6 => UNS
* INC # D6: 5,8 => UNS
* INC # D6: 6,9 # E4: 6,9 => UNS
* INC # D6: 6,9 # F4: 6,9 => UNS
* INC # D6: 6,9 # E6: 6,9 => UNS
* INC # D6: 6,9 # D3: 6,9 => UNS
* INC # D6: 6,9 # D3: 1,4 => UNS
* INC # D6: 6,9 # D3: 1,6 => UNS
* INC # D6: 6,9 # D3: 4,9 => UNS
* INC # D6: 6,9 # I7: 2,5 => UNS
* INC # D6: 6,9 # I7: 7,9 => UNS
* INC # D6: 6,9 # A7: 2,5 => UNS
* INC # D6: 6,9 # C7: 2,5 => UNS
* INC # D6: 6,9 # G1: 2,5 => UNS
* INC # D6: 6,9 # G1: 1,3,4,6 => UNS
* INC # D6: 6,9 => UNS
* INC # A5: 5,8 # C4: 5,8 => UNS
* INC # A5: 5,8 # A6: 5,8 => UNS
* INC # A5: 5,8 # C6: 5,8 => UNS
* INC # A5: 5,8 # A7: 5,8 => UNS
* INC # A5: 5,8 # A9: 5,8 => UNS
* INC # A5: 5,8 # D6: 5,8 => UNS
* INC # A5: 5,8 # D6: 6,9 => UNS
* INC # A5: 5,8 # E6: 2,7 => UNS
* INC # A5: 5,8 # E6: 6,9 => UNS
* DIS # A5: 5,8 # B5: 2,7 => CTR => B5: 1,3
* INC # A5: 5,8 + B5: 1,3 # D3: 1,6 => UNS
* INC # A5: 5,8 + B5: 1,3 # D3: 4,9 => UNS
* PRF # A5: 5,8 + B5: 1,3 # I7: 2,5 => SOL
* STA # A5: 5,8 + B5: 1,3 + I7: 2,5
* CNT  63 HDP CHAINS /  64 HYP OPENED