Analysis of xx-ph-00000921-H208-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7.....6.7...8...5.......5..9..6....4.3..9......2..1.7.8..5......4...2.....1.3. initial

Autosolve

position: 98.7.....6.7...8...5.......5..9..6....4.3..9......2..1.7.8..5......4...2.....1.3. 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: 0:00:47.107272

The following important HDP chains were detected:

* DIS # G3: 2,7 # E9: 2,9 => CTR => E9: 5,6,7
* PRF # G3: 2,7 + E9: 5,6,7 # F8: 3,9 => SOL
* STA # G3: 2,7 + E9: 5,6,7 + F8: 3,9
* CNT   2 HDP CHAINS /  73 HYP OPENED

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

Details

Positions

98.7.....6.7...8...5.......5..9..6....4.3..9......2..1.7.8..5......4...2.....1.3. initial
98.7.....6.7...8...5.......5..9..6....4.3..9......2..1.7.8..5......4...2.....1.3. autosolve
982765413637214859451398267513987624824136795796452381179823546368549172245671938 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
G5: 2,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E4,D5: 1.. / E4 = 1  =>  3 pairs (_) / D5 = 1  =>  3 pairs (_)
H4,G5: 2.. / H4 = 2  =>  9 pairs (_) / G5 = 2  =>  1 pairs (_)
I4,G6: 3.. / I4 = 3  =>  3 pairs (_) / G6 = 3  =>  3 pairs (_)
B2,A3: 4.. / B2 = 4  =>  1 pairs (_) / A3 = 4  =>  3 pairs (_)
F4,D6: 4.. / F4 = 4  =>  2 pairs (_) / D6 = 4  =>  3 pairs (_)
B2,B9: 4.. / B2 = 4  =>  1 pairs (_) / B9 = 4  =>  3 pairs (_)
I5,H6: 5.. / I5 = 5  =>  2 pairs (_) / H6 = 5  =>  3 pairs (_)
C8,C9: 5.. / C8 = 5  =>  2 pairs (_) / C9 = 5  =>  2 pairs (_)
A5,A6: 7.. / A5 = 7  =>  3 pairs (_) / A6 = 7  =>  2 pairs (_)
F8,E9: 7.. / F8 = 7  =>  3 pairs (_) / E9 = 7  =>  3 pairs (_)
E3,F3: 8.. / E3 = 8  =>  2 pairs (_) / F3 = 8  =>  2 pairs (_)
H8,I9: 8.. / H8 = 8  =>  2 pairs (_) / I9 = 8  =>  3 pairs (_)
B6,C6: 9.. / B6 = 9  =>  1 pairs (_) / C6 = 9  =>  2 pairs (_)
* DURATION: 0:00:08.726124  START: 07:05:39.127442  END: 07:05:47.853566 2020-11-23
* CP COUNT: (13)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:46.625094  START: 07:05:52.952239  END: 07:06:39.577333 2020-11-23
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00000921-H208-base-pr-002.dot
* REASONING
* DIS # G3: 2,7 # E9: 2,9 => CTR => E9: 5,6,7
* PRF # G3: 2,7 + E9: 5,6,7 # F8: 3,9 => SOL
* STA # G3: 2,7 + E9: 5,6,7 + F8: 3,9
* CNT   2 HDP CHAINS /  73 HYP OPENED

Header Info

921;H208;GP;22;11.30;11.30;7.90

Solution

position: 982765413637214859451398267513987624824136795796452381179823546368549172245671938 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 # H4: 2,7 => UNS
* INC # H4: 4,8 => UNS
* INC # A5: 2,7 => UNS
* INC # A5: 1,8 => UNS
* INC # G3: 2,7 => UNS
* INC # G3: 1,3,4,9 => UNS
* CNT   6 HDP CHAINS /   6 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # H4: 2,7 => UNS
* INC # H4: 4,8 => UNS
* INC # A5: 2,7 => UNS
* INC # A5: 1,8 => UNS
* INC # G3: 2,7 => UNS
* INC # G3: 1,3,4,9 => UNS
* CNT   6 HDP CHAINS /   6 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # H4: 2,7 => UNS
* INC # H4: 4,8 => UNS
* INC # A5: 2,7 => UNS
* INC # A5: 1,8 => UNS
* INC # G3: 2,7 => UNS
* INC # G3: 1,3,4,9 => UNS
* INC # H4: 2,7 # H3: 2,7 => UNS
* INC # H4: 2,7 # H3: 1,4,6 => UNS
* INC # H4: 2,7 # A5: 2,7 => UNS
* INC # H4: 2,7 # A5: 1,8 => UNS
* INC # H4: 2,7 # G3: 2,7 => UNS
* INC # H4: 2,7 # G3: 1,3,4,9 => UNS
* INC # H4: 2,7 # H6: 5,8 => UNS
* INC # H4: 2,7 # H6: 4 => UNS
* INC # H4: 2,7 # F5: 5,8 => UNS
* INC # H4: 2,7 # F5: 6,7 => UNS
* INC # H4: 2,7 # I4: 3,4 => UNS
* INC # H4: 2,7 # I4: 8 => UNS
* INC # H4: 2,7 # G1: 3,4 => UNS
* INC # H4: 2,7 # G3: 3,4 => UNS
* INC # H4: 2,7 => UNS
* INC # H4: 4,8 # D5: 1,6 => UNS
* INC # H4: 4,8 # D5: 5 => UNS
* INC # H4: 4,8 # B8: 1,6 => UNS
* INC # H4: 4,8 # B8: 3,9 => UNS
* INC # H4: 4,8 # I4: 4,8 => UNS
* INC # H4: 4,8 # H6: 4,8 => UNS
* INC # H4: 4,8 # F4: 4,8 => UNS
* INC # H4: 4,8 # F4: 7 => UNS
* INC # H4: 4,8 => UNS
* INC # A5: 2,7 # D5: 1,6 => UNS
* INC # A5: 2,7 # D5: 5 => UNS
* INC # A5: 2,7 # B8: 1,6 => UNS
* INC # A5: 2,7 # B8: 3,9 => UNS
* INC # A5: 2,7 # H4: 2,7 => UNS
* INC # A5: 2,7 # H4: 4,8 => UNS
* INC # A5: 2,7 # G3: 2,7 => UNS
* INC # A5: 2,7 # G3: 1,3,4,9 => UNS
* INC # A5: 2,7 # H6: 5,8 => UNS
* INC # A5: 2,7 # H6: 4,7 => UNS
* INC # A5: 2,7 # F5: 5,8 => UNS
* INC # A5: 2,7 # F5: 6 => UNS
* INC # A5: 2,7 => UNS
* INC # A5: 1,8 # C4: 1,8 => UNS
* INC # A5: 1,8 # C4: 2,3 => UNS
* INC # A5: 1,8 # A8: 1,8 => UNS
* INC # A5: 1,8 # A8: 3 => UNS
* INC # A5: 1,8 # H4: 2,7 => UNS
* INC # A5: 1,8 # H4: 4,8 => UNS
* INC # A5: 1,8 # G3: 2,7 => UNS
* INC # A5: 1,8 # G3: 1,3,4,9 => UNS
* INC # A5: 1,8 # I4: 3,4 => UNS
* INC # A5: 1,8 # I4: 7,8 => UNS
* INC # A5: 1,8 # G1: 3,4 => UNS
* INC # A5: 1,8 # G3: 3,4 => UNS
* INC # A5: 1,8 => UNS
* INC # G3: 2,7 # H3: 2,7 => UNS
* INC # G3: 2,7 # H3: 1,4,6 => UNS
* INC # G3: 2,7 # H4: 2,7 => UNS
* INC # G3: 2,7 # H4: 4,8 => UNS
* INC # G3: 2,7 # A5: 2,7 => UNS
* INC # G3: 2,7 # A5: 1,8 => UNS
* INC # G3: 2,7 # I4: 3,4 => UNS
* INC # G3: 2,7 # I4: 7,8 => UNS
* INC # G3: 2,7 # G1: 3,4 => UNS
* INC # G3: 2,7 # G1: 1 => UNS
* DIS # G3: 2,7 # E9: 2,9 => CTR => E9: 5,6,7
* INC # G3: 2,7 + E9: 5,6,7 # C7: 2,9 => UNS
* INC # G3: 2,7 + E9: 5,6,7 # C7: 1,3 => UNS
* INC # G3: 2,7 + E9: 5,6,7 # E2: 2,9 => UNS
* INC # G3: 2,7 + E9: 5,6,7 # E3: 2,9 => UNS
* PRF # G3: 2,7 + E9: 5,6,7 # F8: 3,9 => SOL
* STA # G3: 2,7 + E9: 5,6,7 + F8: 3,9
* CNT  72 HDP CHAINS /  73 HYP OPENED