Analysis of xx-ph-02210326-2018_12_06-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7..6..7.........54.3....6..8..2...1.....4...5.........2.7..8....1..5......89.2 initial

Autosolve

position: 98.7..6..7...8.....54.3....6..8..2...1.....4...5.........2.7..8....1..5......89.2 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: 0:00:46.833957

The following important HDP chains were detected:

* DIS # C1: 1,2 # C8: 3,6 => CTR => C8: 2,7,8,9
* DIS # F3: 1,2 # F2: 1,2 => CTR => F2: 4,5,9
* DIS # H3: 1,2 # D6: 6,9 => CTR => D6: 1,3,4
* DIS # H3: 1,2 + D6: 1,3,4 # F5: 6,9 => CTR => F5: 2,3,5
* PRF # H3: 1,2 + D6: 1,3,4 + F5: 2,3,5 # F6: 6,9 => SOL
* STA # H3: 1,2 + D6: 1,3,4 + F5: 2,3,5 + F6: 6,9
* CNT   5 HDP CHAINS /  86 HYP OPENED

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

Details

Positions

98.7..6..7.........54.3....6..8..2...1.....4...5.........2.7..8....1..5......89.2 initial
98.7..6..7...8.....54.3....6..8..2...1.....4...5.........2.7..8....1..5......89.2 autosolve
983724615762581493154936827639845271817362549425179386546297138298613754371458962 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
A3: 1,2

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A7,A9: 5.. / A7 = 5  =>  1 pairs (_) / A9 = 5  =>  3 pairs (_)
A7,E7: 5.. / A7 = 5  =>  1 pairs (_) / E7 = 5  =>  3 pairs (_)
G2,G5: 5.. / G2 = 5  =>  1 pairs (_) / G5 = 5  =>  1 pairs (_)
B2,C2: 6.. / B2 = 6  =>  2 pairs (_) / C2 = 6  =>  2 pairs (_)
D3,F3: 6.. / D3 = 6  =>  1 pairs (_) / F3 = 6  =>  2 pairs (_)
G3,H3: 8.. / G3 = 8  =>  1 pairs (_) / H3 = 8  =>  2 pairs (_)
A8,C8: 8.. / A8 = 8  =>  2 pairs (_) / C8 = 8  =>  1 pairs (_)
C5,C8: 8.. / C5 = 8  =>  2 pairs (_) / C8 = 8  =>  1 pairs (_)
H3,H6: 8.. / H3 = 8  =>  2 pairs (_) / H6 = 8  =>  1 pairs (_)
* DURATION: 0:00:06.047989  START: 21:46:16.557780  END: 21:46:22.605769 2020-09-23
* CP COUNT: (9)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:46.545819  START: 21:46:26.290098  END: 21:47:12.835917 2020-09-23
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-02210326-2018_12_06-base-pr-002.dot
* REASONING
* DIS # C1: 1,2 # C8: 3,6 => CTR => C8: 2,7,8,9
* DIS # F3: 1,2 # F2: 1,2 => CTR => F2: 4,5,9
* DIS # H3: 1,2 # D6: 6,9 => CTR => D6: 1,3,4
* DIS # H3: 1,2 + D6: 1,3,4 # F5: 6,9 => CTR => F5: 2,3,5
* PRF # H3: 1,2 + D6: 1,3,4 + F5: 2,3,5 # F6: 6,9 => SOL
* STA # H3: 1,2 + D6: 1,3,4 + F5: 2,3,5 + F6: 6,9
* CNT   5 HDP CHAINS /  86 HYP OPENED

Header Info

2210326;2018_12_06;PAQ;22;11.60;1.20;1.20

Solution

position: 983724615762581493154936827639845271817362549425179386546297138298613754371458962 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 # C1: 1,2 => UNS
* INC # C2: 1,2 => UNS
* INC # F3: 1,2 => UNS
* INC # H3: 1,2 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 1,2 => UNS
* INC # C2: 1,2 => UNS
* INC # F3: 1,2 => UNS
* INC # H3: 1,2 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 1,2 => UNS
* INC # C2: 1,2 => UNS
* INC # F3: 1,2 => UNS
* INC # H3: 1,2 => UNS
* INC # C1: 1,2 # F1: 1,2 => UNS
* INC # C1: 1,2 # H1: 1,2 => UNS
* INC # C1: 1,2 # B7: 3,6 => UNS
* INC # C1: 1,2 # B8: 3,6 => UNS
* INC # C1: 1,2 # B9: 3,6 => UNS
* INC # C1: 1,2 # C7: 3,6 => UNS
* DIS # C1: 1,2 # C8: 3,6 => CTR => C8: 2,7,8,9
* INC # C1: 1,2 + C8: 2,7,8,9 # C9: 3,6 => UNS
* INC # C1: 1,2 + C8: 2,7,8,9 # C7: 3,6 => UNS
* INC # C1: 1,2 + C8: 2,7,8,9 # C9: 3,6 => UNS
* INC # C1: 1,2 + C8: 2,7,8,9 # F3: 1,2 => UNS
* INC # C1: 1,2 + C8: 2,7,8,9 # H3: 1,2 => UNS
* INC # C1: 1,2 + C8: 2,7,8,9 # F1: 1,2 => UNS
* INC # C1: 1,2 + C8: 2,7,8,9 # H1: 1,2 => UNS
* INC # C1: 1,2 + C8: 2,7,8,9 # B7: 3,6 => UNS
* INC # C1: 1,2 + C8: 2,7,8,9 # B8: 3,6 => UNS
* INC # C1: 1,2 + C8: 2,7,8,9 # B9: 3,6 => UNS
* INC # C1: 1,2 + C8: 2,7,8,9 # C7: 3,6 => UNS
* INC # C1: 1,2 + C8: 2,7,8,9 # C9: 3,6 => UNS
* INC # C1: 1,2 + C8: 2,7,8,9 # F3: 1,2 => UNS
* INC # C1: 1,2 + C8: 2,7,8,9 # H3: 1,2 => UNS
* INC # C1: 1,2 + C8: 2,7,8,9 => UNS
* INC # C2: 1,2 # F2: 1,2 => UNS
* INC # C2: 1,2 # H2: 1,2 => UNS
* INC # C2: 1,2 # F3: 1,2 => UNS
* INC # C2: 1,2 # H3: 1,2 => UNS
* INC # C2: 1,2 # H2: 1,2 => UNS
* INC # C2: 1,2 # H3: 1,2 => UNS
* INC # C2: 1,2 # F1: 1,2 => UNS
* INC # C2: 1,2 # F1: 4,5 => UNS
* INC # C2: 1,2 # B4: 7,9 => UNS
* INC # C2: 1,2 # C5: 7,9 => UNS
* INC # C2: 1,2 # B6: 7,9 => UNS
* INC # C2: 1,2 # E4: 7,9 => UNS
* INC # C2: 1,2 # H4: 7,9 => UNS
* INC # C2: 1,2 # I4: 7,9 => UNS
* INC # C2: 1,2 # C8: 7,9 => UNS
* INC # C2: 1,2 # C8: 2,6,8 => UNS
* INC # C2: 1,2 => UNS
* INC # F3: 1,2 # C1: 1,2 => UNS
* INC # F3: 1,2 # C2: 1,2 => UNS
* INC # F3: 1,2 # F1: 1,2 => UNS
* DIS # F3: 1,2 # F2: 1,2 => CTR => F2: 4,5,9
* INC # F3: 1,2 + F2: 4,5,9 # F1: 1,2 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # F1: 4,5 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # F6: 1,2 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # F6: 3,4,6,9 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # H3: 7,8 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # H3: 9 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # G5: 7,8 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # G6: 7,8 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # H3: 7,9 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # H3: 8 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # I4: 7,9 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # I5: 7,9 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # I6: 7,9 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # C1: 1,2 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # C2: 1,2 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # F1: 1,2 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # F1: 4,5 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # F6: 1,2 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # F6: 3,4,6,9 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # H3: 7,8 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # H3: 9 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # G5: 7,8 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # G6: 7,8 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # H3: 7,9 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # H3: 8 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # I4: 7,9 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # I5: 7,9 => UNS
* INC # F3: 1,2 + F2: 4,5,9 # I6: 7,9 => UNS
* INC # F3: 1,2 + F2: 4,5,9 => UNS
* INC # H3: 1,2 # C1: 1,2 => UNS
* INC # H3: 1,2 # C2: 1,2 => UNS
* INC # H3: 1,2 # D5: 6,9 => UNS
* DIS # H3: 1,2 # D6: 6,9 => CTR => D6: 1,3,4
* INC # H3: 1,2 + D6: 1,3,4 # D8: 6,9 => UNS
* INC # H3: 1,2 + D6: 1,3,4 # D5: 6,9 => UNS
* INC # H3: 1,2 + D6: 1,3,4 # D8: 6,9 => UNS
* DIS # H3: 1,2 + D6: 1,3,4 # F5: 6,9 => CTR => F5: 2,3,5
* PRF # H3: 1,2 + D6: 1,3,4 + F5: 2,3,5 # F6: 6,9 => SOL
* STA # H3: 1,2 + D6: 1,3,4 + F5: 2,3,5 + F6: 6,9
* CNT  85 HDP CHAINS /  86 HYP OPENED