Analysis of xx-ph-00057065-12_10-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7..6..7...5......4..9.7.4....7.3...3.2.5......1..6..4...8.9...92....6......1.. initial

Autosolve

position: 98.7..6..7...5......4..9.7.4....7.3...3.2.5......1..6..4...8.9...92....6......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: 0:00:20.963865

The following important HDP chains were detected:

* DIS # F1: 3,4 # E9: 3,4 => CTR => E9: 6,7,9
* PRF # F1: 3,4 + E9: 6,7,9 # F9: 3,4 => SOL
* STA # F1: 3,4 + E9: 6,7,9 + F9: 3,4
* CNT   2 HDP CHAINS /  27 HYP OPENED

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

Details

Positions

98.7..6..7...5......4..9.7.4....7.3...3.2.5......1..6..4...8.9...92....6......1.. initial
98.7..6..7...5......4..9.7.4....7.3...3.2.5......1..6..4...8.9...92....6......1.. autosolve
982734615736152948514689372465897231193426587827315469241568793379241856658973124 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (2)
E1: 3,4
F5: 4,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D7,F8: 1.. / D7 = 1  =>  4 pairs (_) / F8 = 1  =>  2 pairs (_)
F1,F2: 2.. / F1 = 2  =>  3 pairs (_) / F2 = 2  =>  3 pairs (_)
D6,F6: 3.. / D6 = 3  =>  3 pairs (_) / F6 = 3  =>  2 pairs (_)
B5,I5: 7.. / B5 = 7  =>  2 pairs (_) / I5 = 7  =>  2 pairs (_)
E3,E4: 8.. / E3 = 8  =>  4 pairs (_) / E4 = 8  =>  4 pairs (_)
G2,I2: 9.. / G2 = 9  =>  3 pairs (_) / I2 = 9  =>  2 pairs (_)
D9,E9: 9.. / D9 = 9  =>  6 pairs (_) / E9 = 9  =>  3 pairs (_)
E4,E9: 9.. / E4 = 9  =>  6 pairs (_) / E9 = 9  =>  3 pairs (_)
* DURATION: 0:00:04.767372  START: 02:19:40.585606  END: 02:19:45.352978 2020-12-21
* CP COUNT: (8)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:20.791562  START: 02:19:53.475574  END: 02:20:14.267136 2020-12-21
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00057065-12_10-base-pr-002.dot
* REASONING
* DIS # F1: 3,4 # E9: 3,4 => CTR => E9: 6,7,9
* PRF # F1: 3,4 + E9: 6,7,9 # F9: 3,4 => SOL
* STA # F1: 3,4 + E9: 6,7,9 + F9: 3,4
* CNT   2 HDP CHAINS /  27 HYP OPENED

Header Info

57065;12_10;GP;24;11.30;11.30;11.00

Solution

position: 982734615736152948514689372465897231193426587827315469241568793379241856658973124 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 # F1: 3,4 => UNS
* INC # D2: 3,4 => UNS
* INC # F2: 3,4 => UNS
* INC # I1: 3,4 => UNS
* INC # I1: 1,2,5 => UNS
* INC # E8: 3,4 => UNS
* INC # E9: 3,4 => UNS
* INC # D5: 4,6 => UNS
* INC # D5: 8,9 => UNS
* INC # F2: 4,6 => UNS
* INC # F9: 4,6 => UNS
* CNT  11 HDP CHAINS /  11 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F1: 3,4 => UNS
* INC # D2: 3,4 => UNS
* INC # F2: 3,4 => UNS
* INC # I1: 3,4 => UNS
* INC # I1: 1,2,5 => UNS
* INC # E8: 3,4 => UNS
* INC # E9: 3,4 => UNS
* INC # D5: 4,6 => UNS
* INC # D5: 8,9 => UNS
* INC # F2: 4,6 => UNS
* INC # F9: 4,6 => UNS
* CNT  11 HDP CHAINS /  11 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # F1: 3,4 => UNS
* INC # D2: 3,4 => UNS
* INC # F2: 3,4 => UNS
* INC # I1: 3,4 => UNS
* INC # I1: 1,2,5 => UNS
* INC # E8: 3,4 => UNS
* INC # E9: 3,4 => UNS
* INC # D5: 4,6 => UNS
* INC # D5: 8,9 => UNS
* INC # F2: 4,6 => UNS
* INC # F9: 4,6 => UNS
* INC # F1: 3,4 # B2: 1,6 => UNS
* INC # F1: 3,4 # A3: 1,6 => UNS
* INC # F1: 3,4 # B3: 1,6 => UNS
* INC # F1: 3,4 # D2: 1,6 => UNS
* INC # F1: 3,4 # D2: 8 => UNS
* INC # F1: 3,4 # C4: 1,6 => UNS
* INC # F1: 3,4 # C7: 1,6 => UNS
* INC # F1: 3,4 # E8: 3,4 => UNS
* DIS # F1: 3,4 # E9: 3,4 => CTR => E9: 6,7,9
* INC # F1: 3,4 + E9: 6,7,9 # E8: 3,4 => UNS
* INC # F1: 3,4 + E9: 6,7,9 # E8: 7 => UNS
* INC # F1: 3,4 + E9: 6,7,9 # E8: 3,4 => UNS
* INC # F1: 3,4 + E9: 6,7,9 # E8: 7 => UNS
* INC # F1: 3,4 + E9: 6,7,9 # F6: 3,4 => UNS
* PRF # F1: 3,4 + E9: 6,7,9 # F9: 3,4 => SOL
* STA # F1: 3,4 + E9: 6,7,9 + F9: 3,4
* CNT  26 HDP CHAINS /  27 HYP OPENED