Analysis of xx-ph-00000096-49-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ..3.5...9...1..........2....7...1.6.5........9.8.3.4.....2...7...5...8.48...4...3 initial

Autosolve

position: ..3.5...9...1..........2....7...1.6.5........9.8.3.4.....2...7...5...8.48...4...3 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: 0:00:23.368885

The following important HDP chains were detected:

* DIS # A4: 2,4 # C9: 1,6 => CTR => C9: 2,7,9
* PRF # A4: 2,4 + C9: 2,7,9 # D4: 5 => SOL
* STA # A4: 2,4 + C9: 2,7,9 + D4: 5
* CNT   2 HDP CHAINS /  22 HYP OPENED

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

Details

Positions

..3.5...9...1..........2....7...1.6.5........9.8.3.4.....2...7...5...8.48...4...3 initial
..3.5...9...1..........2....7...1.6.5........9.8.3.4.....2...7...5...8.48...4...3 autosolve
123456789457189236689372541274591368536824197918637452341268975765913824892745613 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
C4: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E7,E8: 1.. / E7 = 1  =>  2 pairs (_) / E8 = 1  =>  2 pairs (_)
E4,E5: 2.. / E4 = 2  =>  2 pairs (_) / E5 = 2  =>  2 pairs (_)
F2,D3: 3.. / F2 = 3  =>  1 pairs (_) / D3 = 3  =>  1 pairs (_)
A4,B5: 3.. / A4 = 3  =>  1 pairs (_) / B5 = 3  =>  6 pairs (_)
A4,G4: 3.. / A4 = 3  =>  1 pairs (_) / G4 = 3  =>  6 pairs (_)
D3,D8: 3.. / D3 = 3  =>  1 pairs (_) / D8 = 3  =>  1 pairs (_)
B2,B3: 5.. / B2 = 5  =>  1 pairs (_) / B3 = 5  =>  1 pairs (_)
A8,C9: 7.. / A8 = 7  =>  1 pairs (_) / C9 = 7  =>  1 pairs (_)
E7,F7: 8.. / E7 = 8  =>  3 pairs (_) / F7 = 8  =>  1 pairs (_)
* DURATION: 0:00:06.118211  START: 02:06:45.271476  END: 02:06:51.389687 2020-09-23
* CP COUNT: (9)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:23.252226  START: 02:06:56.060536  END: 02:07:19.312762 2020-09-23
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00000096-49-base-pr-002.dot
* REASONING
* DIS # A4: 2,4 # C9: 1,6 => CTR => C9: 2,7,9
* PRF # A4: 2,4 + C9: 2,7,9 # D4: 5 => SOL
* STA # A4: 2,4 + C9: 2,7,9 + D4: 5
* CNT   2 HDP CHAINS /  22 HYP OPENED

Header Info

96;49;elev;21;11.60;11.60;8.00

Solution

position: 123456789457189236689372541274591368536824197918637452341268975765913824892745613 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 # A4: 2,4 => UNS
* INC # B5: 2,4 => UNS
* INC # C5: 2,4 => UNS
* INC # C2: 2,4 => UNS
* INC # C2: 6,7,9 => UNS
* CNT   5 HDP CHAINS /   5 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A4: 2,4 => UNS
* INC # B5: 2,4 => UNS
* INC # C5: 2,4 => UNS
* INC # C2: 2,4 => UNS
* INC # C2: 6,7,9 => UNS
* CNT   5 HDP CHAINS /   5 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A4: 2,4 => UNS
* INC # B5: 2,4 => UNS
* INC # C5: 2,4 => UNS
* INC # C2: 2,4 => UNS
* INC # C2: 6,7,9 => UNS
* INC # A4: 2,4 # A1: 2,4 => UNS
* INC # A4: 2,4 # A2: 2,4 => UNS
* INC # A4: 2,4 # C2: 2,4 => UNS
* INC # A4: 2,4 # C2: 6,7,9 => UNS
* INC # A4: 2,4 # C3: 1,6 => UNS
* INC # A4: 2,4 # C7: 1,6 => UNS
* DIS # A4: 2,4 # C9: 1,6 => CTR => C9: 2,7,9
* INC # A4: 2,4 + C9: 2,7,9 # C3: 1,6 => UNS
* INC # A4: 2,4 + C9: 2,7,9 # C7: 1,6 => UNS
* INC # A4: 2,4 + C9: 2,7,9 # B1: 1,6 => UNS
* INC # A4: 2,4 + C9: 2,7,9 # B3: 1,6 => UNS
* INC # A4: 2,4 + C9: 2,7,9 # B7: 1,6 => UNS
* INC # A4: 2,4 + C9: 2,7,9 # B8: 1,6 => UNS
* INC # A4: 2,4 + C9: 2,7,9 # B9: 1,6 => UNS
* INC # A4: 2,4 + C9: 2,7,9 # D4: 8,9 => UNS
* PRF # A4: 2,4 + C9: 2,7,9 # D4: 5 => SOL
* STA # A4: 2,4 + C9: 2,7,9 + D4: 5
* CNT  21 HDP CHAINS /  22 HYP OPENED