Analysis of xx-ph-00052146-12_10-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7.....6...8.9....5..4...7...3.....3.8..7.......2.1..9.6..3....4....2.........5 initial

Autosolve

position: 98.7.....64..8.9....5..4...7...3.....3.8..7......72.13.9.6..3....4....2.........5 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: 0:00:21.655800

The following important HDP chains were detected:

* DIS # B4: 5,6 # C2: 1,2 => CTR => C2: 3,7
* DIS # B4: 5,6 + C2: 3,7 # D3: 1,2 => CTR => D3: 3,9
* DIS # B4: 5,6 + C2: 3,7 + D3: 3,9 # E3: 1,2 => CTR => E3: 6,9
* DIS # B4: 5,6 + C2: 3,7 + D3: 3,9 + E3: 6,9 # I3: 1,2 => CTR => I3: 6,7,8
* PRF # B4: 5,6 + C2: 3,7 + D3: 3,9 + E3: 6,9 + I3: 6,7,8 # A9: 1,2 => SOL
* STA # B4: 5,6 + C2: 3,7 + D3: 3,9 + E3: 6,9 + I3: 6,7,8 + A9: 1,2
* CNT   5 HDP CHAINS /  19 HYP OPENED

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

Details

Positions

98.7.....6...8.9....5..4...7...3.....3.8..7.......2.1..9.6..3....4....2.........5 initial
98.7.....64..8.9....5..4...7...3.....3.8..7......72.13.9.6..3....4....2.........5 autosolve
983715246647283951125964837752136489431859762869472513598621374314597628276348195 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
B6: 5,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A5,A6: 4.. / A5 = 4  =>  2 pairs (_) / A6 = 4  =>  2 pairs (_)
C2,B3: 7.. / C2 = 7  =>  4 pairs (_) / B3 = 7  =>  1 pairs (_)
D3,E3: 9.. / D3 = 9  =>  2 pairs (_) / E3 = 9  =>  2 pairs (_)
I8,H9: 9.. / I8 = 9  =>  2 pairs (_) / H9 = 9  =>  1 pairs (_)
C6,D6: 9.. / C6 = 9  =>  2 pairs (_) / D6 = 9  =>  5 pairs (_)
* DURATION: 0:00:03.502792  START: 10:08:30.084407  END: 10:08:33.587199 2020-12-20
* CP COUNT: (5)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:21.555051  START: 10:08:38.701216  END: 10:09:00.256267 2020-12-20
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00052146-12_10-base-pr-002.dot
* REASONING
* DIS # B4: 5,6 # C2: 1,2 => CTR => C2: 3,7
* DIS # B4: 5,6 + C2: 3,7 # D3: 1,2 => CTR => D3: 3,9
* DIS # B4: 5,6 + C2: 3,7 + D3: 3,9 # E3: 1,2 => CTR => E3: 6,9
* DIS # B4: 5,6 + C2: 3,7 + D3: 3,9 + E3: 6,9 # I3: 1,2 => CTR => I3: 6,7,8
* PRF # B4: 5,6 + C2: 3,7 + D3: 3,9 + E3: 6,9 + I3: 6,7,8 # A9: 1,2 => SOL
* STA # B4: 5,6 + C2: 3,7 + D3: 3,9 + E3: 6,9 + I3: 6,7,8 + A9: 1,2
* CNT   5 HDP CHAINS /  19 HYP OPENED

Header Info

52146;12_10;GP;21;11.30;1.20;1.20

Solution

position: 983715246647283951125964837752136489431859762869472513598621374314597628276348195 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 # B4: 5,6 => UNS
* INC # B4: 1,2 => UNS
* INC # G6: 5,6 => UNS
* INC # G6: 4,8 => UNS
* INC # B8: 5,6 => UNS
* INC # B8: 1,7 => UNS
* CNT   6 HDP CHAINS /   6 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B4: 5,6 => UNS
* INC # B4: 1,2 => UNS
* INC # G6: 5,6 => UNS
* INC # G6: 4,8 => UNS
* INC # B8: 5,6 => UNS
* INC # B8: 1,7 => UNS
* CNT   6 HDP CHAINS /   6 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B4: 5,6 => UNS
* INC # B4: 1,2 => UNS
* INC # G6: 5,6 => UNS
* INC # G6: 4,8 => UNS
* INC # B8: 5,6 => UNS
* INC # B8: 1,7 => UNS
* INC # B4: 5,6 # C1: 1,2 => UNS
* DIS # B4: 5,6 # C2: 1,2 => CTR => C2: 3,7
* INC # B4: 5,6 + C2: 3,7 # B3: 1,2 => UNS
* DIS # B4: 5,6 + C2: 3,7 # D3: 1,2 => CTR => D3: 3,9
* DIS # B4: 5,6 + C2: 3,7 + D3: 3,9 # E3: 1,2 => CTR => E3: 6,9
* INC # B4: 5,6 + C2: 3,7 + D3: 3,9 + E3: 6,9 # G3: 1,2 => UNS
* DIS # B4: 5,6 + C2: 3,7 + D3: 3,9 + E3: 6,9 # I3: 1,2 => CTR => I3: 6,7,8
* INC # B4: 5,6 + C2: 3,7 + D3: 3,9 + E3: 6,9 + I3: 6,7,8 # G3: 1,2 => UNS
* INC # B4: 5,6 + C2: 3,7 + D3: 3,9 + E3: 6,9 + I3: 6,7,8 # G3: 6,8 => UNS
* INC # B4: 5,6 + C2: 3,7 + D3: 3,9 + E3: 6,9 + I3: 6,7,8 # A5: 1,2 => UNS
* INC # B4: 5,6 + C2: 3,7 + D3: 3,9 + E3: 6,9 + I3: 6,7,8 # A7: 1,2 => UNS
* PRF # B4: 5,6 + C2: 3,7 + D3: 3,9 + E3: 6,9 + I3: 6,7,8 # A9: 1,2 => SOL
* STA # B4: 5,6 + C2: 3,7 + D3: 3,9 + E3: 6,9 + I3: 6,7,8 + A9: 1,2
* CNT  18 HDP CHAINS /  19 HYP OPENED