Analysis of xx-ph-00060697-12_10-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 9876..5..4..9..6...3.....8.8...6..5....8...96.....48..5..4..9....2....7......1... initial

Autosolve

position: 9876..5..4..9..6...3.....898...6..5....8...96.....48..5..4..9....2....7......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: 0:00:37.011164

The following important HDP chains were detected:

* DIS # C3: 1,5 # E3: 1,5 => CTR => E3: 2,4,7
* PRF # C3: 1,5 + E3: 2,4,7 # F4: 2,3 => SOL
* STA # C3: 1,5 + E3: 2,4,7 + F4: 2,3
* CNT   2 HDP CHAINS /  69 HYP OPENED

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

Details

Positions

9876..5..4..9..6...3.....8.8...6..5....8...96.....48..5..4..9....2....7......1... initial
9876..5..4..9..6...3.....898...6..5....8...96.....48..5..4..9....2....7......1... autosolve
987613542421958637635247189893162754214875396756394821578426913162539478349781265 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (3)
C2: 1,5
F1: 2,3
D8: 3,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B2,A3: 2.. / B2 = 2  =>  5 pairs (_) / A3 = 2  =>  6 pairs (_)
E1,E3: 4.. / E1 = 4  => 10 pairs (_) / E3 = 4  =>  3 pairs (_)
E3,G3: 4.. / E3 = 4  =>  3 pairs (_) / G3 = 4  => 10 pairs (_)
H1,H9: 4.. / H1 = 4  =>  3 pairs (_) / H9 = 4  =>  8 pairs (_)
I8,I9: 5.. / I8 = 5  =>  6 pairs (_) / I9 = 5  =>  3 pairs (_)
A3,C3: 6.. / A3 = 6  =>  8 pairs (_) / C3 = 6  =>  4 pairs (_)
F7,F8: 6.. / F7 = 6  =>  5 pairs (_) / F8 = 6  =>  4 pairs (_)
H7,H9: 6.. / H7 = 6  =>  5 pairs (_) / H9 = 6  =>  4 pairs (_)
I2,G3: 7.. / I2 = 7  =>  3 pairs (_) / G3 = 7  =>  7 pairs (_)
E2,F2: 8.. / E2 = 8  =>  5 pairs (_) / F2 = 8  =>  3 pairs (_)
C7,C9: 8.. / C7 = 8  =>  5 pairs (_) / C9 = 8  =>  5 pairs (_)
F4,E6: 9.. / F4 = 9  =>  3 pairs (_) / E6 = 9  =>  5 pairs (_)
F4,F8: 9.. / F4 = 9  =>  3 pairs (_) / F8 = 9  =>  5 pairs (_)
* DURATION: 0:00:08.583537  START: 12:07:18.450031  END: 12:07:27.033568 2020-12-21
* CP COUNT: (13)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:36.610983  START: 12:07:44.164924  END: 12:08:20.775907 2020-12-21
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00060697-12_10-base-pr-002.dot
* REASONING
* DIS # C3: 1,5 # E3: 1,5 => CTR => E3: 2,4,7
* PRF # C3: 1,5 + E3: 2,4,7 # F4: 2,3 => SOL
* STA # C3: 1,5 + E3: 2,4,7 + F4: 2,3
* CNT   2 HDP CHAINS /  69 HYP OPENED

Header Info

60697;12_10;GP;24;11.30;1.20;1.20

Solution

position: 987613542421958637635247189893162754214875396756394821578426913162539478349781265 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 # B2: 1,5 => UNS
* INC # C3: 1,5 => UNS
* INC # E2: 1,5 => UNS
* INC # E2: 2,3,7,8 => UNS
* INC # C5: 1,5 => UNS
* INC # C6: 1,5 => UNS
* INC # E1: 2,3 => UNS
* INC # E2: 2,3 => UNS
* INC # F2: 2,3 => UNS
* INC # H1: 2,3 => UNS
* INC # I1: 2,3 => UNS
* INC # F4: 2,3 => UNS
* INC # F5: 2,3 => UNS
* INC # F7: 2,3 => UNS
* INC # E8: 3,5 => UNS
* INC # F8: 3,5 => UNS
* INC # D9: 3,5 => UNS
* INC # E9: 3,5 => UNS
* INC # I8: 3,5 => UNS
* INC # I8: 1,4,8 => UNS
* INC # D6: 3,5 => UNS
* INC # D6: 1,2,7 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 1,5 => UNS
* INC # C3: 1,5 => UNS
* INC # E2: 1,5 => UNS
* INC # E2: 2,3,7,8 => UNS
* INC # C5: 1,5 => UNS
* INC # C6: 1,5 => UNS
* INC # E1: 2,3 => UNS
* INC # E2: 2,3 => UNS
* INC # F2: 2,3 => UNS
* INC # H1: 2,3 => UNS
* INC # I1: 2,3 => UNS
* INC # F4: 2,3 => UNS
* INC # F5: 2,3 => UNS
* INC # F7: 2,3 => UNS
* INC # E8: 3,5 => UNS
* INC # F8: 3,5 => UNS
* INC # D9: 3,5 => UNS
* INC # E9: 3,5 => UNS
* INC # I8: 3,5 => UNS
* INC # I8: 1,4,8 => UNS
* INC # D6: 3,5 => UNS
* INC # D6: 1,2,7 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 1,5 => UNS
* INC # C3: 1,5 => UNS
* INC # E2: 1,5 => UNS
* INC # E2: 2,3,7,8 => UNS
* INC # C5: 1,5 => UNS
* INC # C6: 1,5 => UNS
* INC # E1: 2,3 => UNS
* INC # E2: 2,3 => UNS
* INC # F2: 2,3 => UNS
* INC # H1: 2,3 => UNS
* INC # I1: 2,3 => UNS
* INC # F4: 2,3 => UNS
* INC # F5: 2,3 => UNS
* INC # F7: 2,3 => UNS
* INC # E8: 3,5 => UNS
* INC # F8: 3,5 => UNS
* INC # D9: 3,5 => UNS
* INC # E9: 3,5 => UNS
* INC # I8: 3,5 => UNS
* INC # I8: 1,4,8 => UNS
* INC # D6: 3,5 => UNS
* INC # D6: 1,2,7 => UNS
* INC # B2: 1,5 # B5: 1,5 => UNS
* INC # B2: 1,5 # B6: 1,5 => UNS
* INC # B2: 1,5 # C5: 1,5 => UNS
* INC # B2: 1,5 # C6: 1,5 => UNS
* INC # B2: 1,5 # E1: 2,3 => UNS
* INC # B2: 1,5 # E2: 2,3 => UNS
* INC # B2: 1,5 # F2: 2,3 => UNS
* INC # B2: 1,5 # H1: 2,3 => UNS
* INC # B2: 1,5 # I1: 2,3 => UNS
* INC # B2: 1,5 # F4: 2,3 => UNS
* INC # B2: 1,5 # F5: 2,3 => UNS
* INC # B2: 1,5 # F7: 2,3 => UNS
* INC # B2: 1,5 # D3: 5,7 => UNS
* INC # B2: 1,5 # E3: 5,7 => UNS
* INC # B2: 1,5 # F5: 5,7 => UNS
* INC # B2: 1,5 # F5: 2,3 => UNS
* INC # B2: 1,5 # H1: 2,3 => UNS
* INC # B2: 1,5 # I1: 2,3 => UNS
* INC # B2: 1,5 # I2: 2,3 => UNS
* INC # B2: 1,5 # E2: 2,3 => UNS
* INC # B2: 1,5 # F2: 2,3 => UNS
* INC # B2: 1,5 # H6: 2,3 => UNS
* INC # B2: 1,5 # H7: 2,3 => UNS
* INC # B2: 1,5 # H9: 2,3 => UNS
* INC # B2: 1,5 # E8: 3,5 => UNS
* INC # B2: 1,5 # F8: 3,5 => UNS
* INC # B2: 1,5 # D9: 3,5 => UNS
* INC # B2: 1,5 # E9: 3,5 => UNS
* INC # B2: 1,5 # I8: 3,5 => UNS
* INC # B2: 1,5 # I8: 1,4,8 => UNS
* INC # B2: 1,5 # D6: 3,5 => UNS
* INC # B2: 1,5 # D6: 1,2,7 => UNS
* INC # B2: 1,5 => UNS
* INC # C3: 1,5 # E2: 1,5 => UNS
* INC # C3: 1,5 # E2: 3,7,8 => UNS
* INC # C3: 1,5 # D3: 1,5 => UNS
* DIS # C3: 1,5 # E3: 1,5 => CTR => E3: 2,4,7
* INC # C3: 1,5 + E3: 2,4,7 # D3: 1,5 => UNS
* INC # C3: 1,5 + E3: 2,4,7 # D3: 2,7 => UNS
* INC # C3: 1,5 + E3: 2,4,7 # D3: 1,5 => UNS
* INC # C3: 1,5 + E3: 2,4,7 # D3: 2,7 => UNS
* INC # C3: 1,5 + E3: 2,4,7 # E1: 2,3 => UNS
* INC # C3: 1,5 + E3: 2,4,7 # E1: 1,4 => UNS
* INC # C3: 1,5 + E3: 2,4,7 # H1: 2,3 => UNS
* INC # C3: 1,5 + E3: 2,4,7 # I1: 2,3 => UNS
* PRF # C3: 1,5 + E3: 2,4,7 # F4: 2,3 => SOL
* STA # C3: 1,5 + E3: 2,4,7 + F4: 2,3
* CNT  68 HDP CHAINS /  69 HYP OPENED