Analysis of xx-ph-02345674-2019_05_01-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7.....6...9.5....4..3...5..6..7...6.........3..2.1..7.9..8......1...2.....7..4 initial

Autosolve

position: 98.7.....63..9.5....4..3...5..6..7...6.........3..2.1..7.9..8......1..72.....7..4 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: 0:00:32.475513

The following important HDP chains were detected:

* DIS # B4: 4,9 # H4: 4,9 => CTR => H4: 2,3,8
* DIS # B4: 4,9 + H4: 2,3,8 # C9: 1,2 => CTR => C9: 6,8,9
* PRF # B4: 1,2 # B8: 5 => SOL
* STA # B4: 1,2 + B8: 5
* CNT   3 HDP CHAINS /  55 HYP OPENED

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

Details

Positions

98.7.....6...9.5....4..3...5..6..7...6.........3..2.1..7.9..8......1...2.....7..4 initial
98.7.....63..9.5....4..3...5..6..7...6.........3..2.1..7.9..8......1..72.....7..4 autosolve
985726431632194587714853296529631748167489325843572619271945863456318972398267154 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
B6: 4,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I7,G9: 1.. / I7 = 1  =>  3 pairs (_) / G9 = 1  =>  1 pairs (_)
C1,B3: 5.. / C1 = 5  =>  2 pairs (_) / B3 = 5  =>  5 pairs (_)
G6,I6: 6.. / G6 = 6  =>  2 pairs (_) / I6 = 6  =>  5 pairs (_)
C2,A3: 7.. / C2 = 7  =>  4 pairs (_) / A3 = 7  =>  3 pairs (_)
I2,I3: 7.. / I2 = 7  =>  3 pairs (_) / I3 = 7  =>  4 pairs (_)
E5,E6: 7.. / E5 = 7  =>  4 pairs (_) / E6 = 7  =>  2 pairs (_)
C2,I2: 7.. / C2 = 7  =>  4 pairs (_) / I2 = 7  =>  3 pairs (_)
A3,I3: 7.. / A3 = 7  =>  3 pairs (_) / I3 = 7  =>  4 pairs (_)
A6,E6: 7.. / A6 = 7  =>  4 pairs (_) / E6 = 7  =>  2 pairs (_)
C2,C5: 7.. / C2 = 7  =>  4 pairs (_) / C5 = 7  =>  3 pairs (_)
F4,F5: 9.. / F4 = 9  =>  2 pairs (_) / F5 = 9  =>  1 pairs (_)
* DURATION: 0:00:07.243125  START: 14:00:34.917184  END: 14:00:42.160309 2020-09-23
* CP COUNT: (11)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:32.317100  START: 14:00:46.758658  END: 14:01:19.075758 2020-09-23
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-02345674-2019_05_01-base-pr-002.dot
* REASONING
* DIS # B4: 4,9 # H4: 4,9 => CTR => H4: 2,3,8
* DIS # B4: 4,9 + H4: 2,3,8 # C9: 1,2 => CTR => C9: 6,8,9
* PRF # B4: 1,2 # B8: 5 => SOL
* STA # B4: 1,2 + B8: 5
* CNT   3 HDP CHAINS /  55 HYP OPENED

Header Info

2345674;2019_05_01;PAQ;22;11.60;1.20;1.20

Solution

position: 985726431632194587714853296529631748167489325843572619271945863456318972398267154 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: 4,9 => UNS
* INC # B4: 1,2 => UNS
* INC # G6: 4,9 => UNS
* INC # G6: 6 => UNS
* INC # B8: 4,9 => UNS
* INC # B8: 5 => UNS
* CNT   6 HDP CHAINS /   6 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B4: 4,9 => UNS
* INC # B4: 1,2 => UNS
* INC # G6: 4,9 => UNS
* INC # G6: 6 => UNS
* INC # B8: 4,9 => UNS
* INC # B8: 5 => UNS
* CNT   6 HDP CHAINS /   6 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B4: 4,9 => UNS
* INC # B4: 1,2 => UNS
* INC # G6: 4,9 => UNS
* INC # G6: 6 => UNS
* INC # B8: 4,9 => UNS
* INC # B8: 5 => UNS
* INC # B4: 4,9 # C2: 1,2 => UNS
* INC # B4: 4,9 # A3: 1,2 => UNS
* INC # B4: 4,9 # D3: 1,2 => UNS
* INC # B4: 4,9 # G3: 1,2 => UNS
* INC # B4: 4,9 # F4: 4,9 => UNS
* DIS # B4: 4,9 # H4: 4,9 => CTR => H4: 2,3,8
* INC # B4: 4,9 + H4: 2,3,8 # F4: 4,9 => UNS
* INC # B4: 4,9 + H4: 2,3,8 # F4: 1,8 => UNS
* INC # B4: 4,9 + H4: 2,3,8 # F4: 4,9 => UNS
* INC # B4: 4,9 + H4: 2,3,8 # F4: 1,8 => UNS
* INC # B4: 4,9 + H4: 2,3,8 # A5: 7,8 => UNS
* INC # B4: 4,9 + H4: 2,3,8 # C5: 7,8 => UNS
* INC # B4: 4,9 + H4: 2,3,8 # E6: 7,8 => UNS
* INC # B4: 4,9 + H4: 2,3,8 # E6: 4,5 => UNS
* INC # B4: 4,9 + H4: 2,3,8 # G6: 4,9 => UNS
* INC # B4: 4,9 + H4: 2,3,8 # G6: 6 => UNS
* INC # B4: 4,9 + H4: 2,3,8 # A7: 1,2 => UNS
* INC # B4: 4,9 + H4: 2,3,8 # C7: 1,2 => UNS
* INC # B4: 4,9 + H4: 2,3,8 # A9: 1,2 => UNS
* DIS # B4: 4,9 + H4: 2,3,8 # C9: 1,2 => CTR => C9: 6,8,9
* INC # B4: 4,9 + H4: 2,3,8 + C9: 6,8,9 # A7: 1,2 => UNS
* INC # B4: 4,9 + H4: 2,3,8 + C9: 6,8,9 # C7: 1,2 => UNS
* INC # B4: 4,9 + H4: 2,3,8 + C9: 6,8,9 # A9: 1,2 => UNS
* INC # B4: 4,9 + H4: 2,3,8 + C9: 6,8,9 # C2: 1,2 => UNS
* INC # B4: 4,9 + H4: 2,3,8 + C9: 6,8,9 # A3: 1,2 => UNS
* INC # B4: 4,9 + H4: 2,3,8 + C9: 6,8,9 # D3: 1,2 => UNS
* INC # B4: 4,9 + H4: 2,3,8 + C9: 6,8,9 # G3: 1,2 => UNS
* INC # B4: 4,9 + H4: 2,3,8 + C9: 6,8,9 # F4: 4,9 => UNS
* INC # B4: 4,9 + H4: 2,3,8 + C9: 6,8,9 # F4: 1,8 => UNS
* INC # B4: 4,9 + H4: 2,3,8 + C9: 6,8,9 # A5: 7,8 => UNS
* INC # B4: 4,9 + H4: 2,3,8 + C9: 6,8,9 # C5: 7,8 => UNS
* INC # B4: 4,9 + H4: 2,3,8 + C9: 6,8,9 # E6: 7,8 => UNS
* INC # B4: 4,9 + H4: 2,3,8 + C9: 6,8,9 # E6: 4,5 => UNS
* INC # B4: 4,9 + H4: 2,3,8 + C9: 6,8,9 # G6: 4,9 => UNS
* INC # B4: 4,9 + H4: 2,3,8 + C9: 6,8,9 # G6: 6 => UNS
* INC # B4: 4,9 + H4: 2,3,8 + C9: 6,8,9 # A7: 1,2 => UNS
* INC # B4: 4,9 + H4: 2,3,8 + C9: 6,8,9 # C7: 1,2 => UNS
* INC # B4: 4,9 + H4: 2,3,8 + C9: 6,8,9 # A9: 1,2 => UNS
* INC # B4: 4,9 + H4: 2,3,8 + C9: 6,8,9 => UNS
* INC # B4: 1,2 # C4: 1,2 => UNS
* INC # B4: 1,2 # A5: 1,2 => UNS
* INC # B4: 1,2 # C5: 1,2 => UNS
* INC # B4: 1,2 # B3: 1,2 => UNS
* INC # B4: 1,2 # B9: 1,2 => UNS
* INC # B4: 1,2 # G6: 4,9 => UNS
* INC # B4: 1,2 # G6: 6 => UNS
* INC # B4: 1,2 # B8: 4,9 => UNS
* PRF # B4: 1,2 # B8: 5 => SOL
* STA # B4: 1,2 + B8: 5
* CNT  54 HDP CHAINS /  55 HYP OPENED