Analysis of xx-ph-00001640-H309-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7.....6.....7....7.5....4....3.8...58..6......2...1..86..9......1...3.....4.2. initial

Autosolve

position: 98.7.....65....7....7.5....4....3.8...58..6..8...2...1..86..9......1...3.....4.2. 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: 0:00:38.755211

The following important HDP chains were detected:

* DIS # I4: 2,5 # B4: 1,9 => CTR => B4: 6,7
* DIS # I4: 2,5 + B4: 6,7 # H6: 3,4 => CTR => H6: 7,9
* DIS # I4: 2,5 + B4: 6,7 + H6: 7,9 # H5: 7,9 => CTR => H5: 3,4
* DIS # I4: 2,5 + B4: 6,7 + H6: 7,9 + H5: 3,4 # E9: 3,7 => CTR => E9: 8,9
* PRF # I4: 2,5 + B4: 6,7 + H6: 7,9 + H5: 3,4 + E9: 8,9 # E4: 9 => SOL
* STA # I4: 2,5 + B4: 6,7 + H6: 7,9 + H5: 3,4 + E9: 8,9 + E4: 9
* CNT   5 HDP CHAINS /  40 HYP OPENED

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

Details

Positions

98.7.....6.....7....7.5....4....3.8...58..6......2...1..86..9......1...3.....4.2. initial
98.7.....65....7....7.5....4....3.8...58..6..8...2...1..86..9......1...3.....4.2. autosolve
984761352651239748327458196476193285215847639893526471538672914742915863169384527 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (2)
G4: 2,5
E7: 3,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D4,F5: 1.. / D4 = 1  =>  4 pairs (_) / F5 = 1  =>  4 pairs (_)
H7,G9: 1.. / H7 = 1  =>  3 pairs (_) / G9 = 1  =>  2 pairs (_)
E5,D6: 4.. / E5 = 4  =>  4 pairs (_) / D6 = 4  =>  4 pairs (_)
E4,F6: 6.. / E4 = 6  =>  3 pairs (_) / F6 = 6  =>  7 pairs (_)
H8,I9: 6.. / H8 = 6  =>  2 pairs (_) / I9 = 6  =>  2 pairs (_)
E1,E4: 6.. / E1 = 6  =>  7 pairs (_) / E4 = 6  =>  3 pairs (_)
F8,E9: 8.. / F8 = 8  =>  3 pairs (_) / E9 = 8  =>  3 pairs (_)
F8,G8: 8.. / F8 = 8  =>  3 pairs (_) / G8 = 8  =>  3 pairs (_)
E2,E9: 8.. / E2 = 8  =>  3 pairs (_) / E9 = 8  =>  3 pairs (_)
* DURATION: 0:00:05.920934  START: 05:57:11.057607  END: 05:57:16.978541 2020-11-30
* CP COUNT: (9)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:38.524753  START: 05:57:23.739411  END: 05:58:02.264164 2020-11-30
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00001640-H309-base-pr-002.dot
* REASONING
* DIS # I4: 2,5 # B4: 1,9 => CTR => B4: 6,7
* DIS # I4: 2,5 + B4: 6,7 # H6: 3,4 => CTR => H6: 7,9
* DIS # I4: 2,5 + B4: 6,7 + H6: 7,9 # H5: 7,9 => CTR => H5: 3,4
* DIS # I4: 2,5 + B4: 6,7 + H6: 7,9 + H5: 3,4 # E9: 3,7 => CTR => E9: 8,9
* PRF # I4: 2,5 + B4: 6,7 + H6: 7,9 + H5: 3,4 + E9: 8,9 # E4: 9 => SOL
* STA # I4: 2,5 + B4: 6,7 + H6: 7,9 + H5: 3,4 + E9: 8,9 + E4: 9
* CNT   5 HDP CHAINS /  40 HYP OPENED

Header Info

1640;H309;GP;22;11.30;1.20;1.20

Solution

position: 984761352651239748327458196476193285215847639893526471538672914742915863169384527 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 # I4: 2,5 => UNS
* INC # I4: 7,9 => UNS
* INC # G1: 2,5 => UNS
* INC # G1: 1,3,4 => UNS
* INC # E9: 3,7 => UNS
* INC # E9: 8,9 => UNS
* INC # A7: 3,7 => UNS
* INC # B7: 3,7 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # I4: 2,5 => UNS
* INC # I4: 7,9 => UNS
* INC # G1: 2,5 => UNS
* INC # G1: 1,3,4 => UNS
* INC # E9: 3,7 => UNS
* INC # E9: 8,9 => UNS
* INC # A7: 3,7 => UNS
* INC # B7: 3,7 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # I4: 2,5 => UNS
* INC # I4: 7,9 => UNS
* INC # G1: 2,5 => UNS
* INC # G1: 1,3,4 => UNS
* INC # E9: 3,7 => UNS
* INC # E9: 8,9 => UNS
* INC # A7: 3,7 => UNS
* INC # B7: 3,7 => UNS
* INC # I4: 2,5 # F5: 1,9 => UNS
* INC # I4: 2,5 # F5: 7 => UNS
* DIS # I4: 2,5 # B4: 1,9 => CTR => B4: 6,7
* INC # I4: 2,5 + B4: 6,7 # C4: 1,9 => UNS
* INC # I4: 2,5 + B4: 6,7 # C4: 1,9 => UNS
* INC # I4: 2,5 + B4: 6,7 # C4: 6 => UNS
* INC # I4: 2,5 + B4: 6,7 # D2: 1,9 => UNS
* INC # I4: 2,5 + B4: 6,7 # D3: 1,9 => UNS
* INC # I4: 2,5 + B4: 6,7 # F5: 1,9 => UNS
* INC # I4: 2,5 + B4: 6,7 # F5: 7 => UNS
* INC # I4: 2,5 + B4: 6,7 # C4: 1,9 => UNS
* INC # I4: 2,5 + B4: 6,7 # C4: 6 => UNS
* INC # I4: 2,5 + B4: 6,7 # D2: 1,9 => UNS
* INC # I4: 2,5 + B4: 6,7 # D3: 1,9 => UNS
* INC # I4: 2,5 + B4: 6,7 # G1: 2,5 => UNS
* INC # I4: 2,5 + B4: 6,7 # G1: 1,3,4 => UNS
* INC # I4: 2,5 + B4: 6,7 # I1: 2,5 => UNS
* INC # I4: 2,5 + B4: 6,7 # I1: 4,6 => UNS
* INC # I4: 2,5 + B4: 6,7 # H5: 3,4 => UNS
* DIS # I4: 2,5 + B4: 6,7 # H6: 3,4 => CTR => H6: 7,9
* INC # I4: 2,5 + B4: 6,7 + H6: 7,9 # H5: 3,4 => UNS
* DIS # I4: 2,5 + B4: 6,7 + H6: 7,9 # H5: 7,9 => CTR => H5: 3,4
* INC # I4: 2,5 + B4: 6,7 + H6: 7,9 + H5: 3,4 # G1: 3,4 => UNS
* INC # I4: 2,5 + B4: 6,7 + H6: 7,9 + H5: 3,4 # G3: 3,4 => UNS
* DIS # I4: 2,5 + B4: 6,7 + H6: 7,9 + H5: 3,4 # E9: 3,7 => CTR => E9: 8,9
* INC # I4: 2,5 + B4: 6,7 + H6: 7,9 + H5: 3,4 + E9: 8,9 # A7: 3,7 => UNS
* INC # I4: 2,5 + B4: 6,7 + H6: 7,9 + H5: 3,4 + E9: 8,9 # B7: 3,7 => UNS
* INC # I4: 2,5 + B4: 6,7 + H6: 7,9 + H5: 3,4 + E9: 8,9 # B6: 6,7 => UNS
* INC # I4: 2,5 + B4: 6,7 + H6: 7,9 + H5: 3,4 + E9: 8,9 # B6: 3,9 => UNS
* INC # I4: 2,5 + B4: 6,7 + H6: 7,9 + H5: 3,4 + E9: 8,9 # E4: 6,7 => UNS
* PRF # I4: 2,5 + B4: 6,7 + H6: 7,9 + H5: 3,4 + E9: 8,9 # E4: 9 => SOL
* STA # I4: 2,5 + B4: 6,7 + H6: 7,9 + H5: 3,4 + E9: 8,9 + E4: 9
* CNT  39 HDP CHAINS /  40 HYP OPENED