Analysis of xx-ph-00014015-kz0-base.sdk

Contents

Original Sudoku
Autosolve
Pair Reduction Variants
Details
Solution
Appendix: Full HDP Chains

Original Sudoku

level: hard

position: 98.76....75....6....6.......4..3..9...78..5.......2..1..85..9......1..2......4..3 initial

Autosolve

position: 98.76....75....6....6.......4..3..9...78..5.......2..1..85..9......1..2......4..3 autosolve

Pair Reduction Variants

Pair Reduction Analysis

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

Pair Reduction

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

Deep Pair Reduction

Time used: 0:00:26.927473

The following important HDP chains were detected:

* DIS # F5: 9 # A4: 2,5 => CTR => A4: 6,8
* DIS # F5: 9 + A4: 6,8 # C6: 5 => CTR => C6: 3,9
* DIS # F5: 9 + A4: 6,8 + C6: 3,9 # I4: 2,6 => CTR => I4: 7,8
* PRF # F5: 9 + A4: 6,8 + C6: 3,9 + I4: 7,8 # E9: 2,7 => SOL
* STA # F5: 9 + A4: 6,8 + C6: 3,9 + I4: 7,8 + E9: 2,7
* CNT   4 HDP CHAINS /  35 HYP OPENED

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

Details

Positions

`98.76....75....6....6.......4..3..9...78..5.......2..1..85..9......1..2......4..3`	initial
`98.76....75....6....6.......4..3..9...78..5.......2..1..85..9......1..2......4..3`	autosolve
`984761352751283649236495187645137298127849536893652471378526914469318725512974863`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
D4: 1,6
F4: 5,7
E5: 4,9
E6: 5,7
E7: 2,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D4,F5: 1.. / D4 = 1  =>  6 pairs (_) / F5 = 1  =>  8 pairs (_)
E5,D6: 4.. / E5 = 4  =>  7 pairs (_) / D6 = 4  =>  5 pairs (_)
F4,E6: 5.. / F4 = 5  =>  6 pairs (_) / E6 = 5  =>  6 pairs (_)
I8,H9: 5.. / I8 = 5  =>  6 pairs (_) / H9 = 5  =>  5 pairs (_)
E3,E6: 5.. / E3 = 5  =>  6 pairs (_) / E6 = 5  =>  6 pairs (_)
F4,E6: 7.. / F4 = 7  =>  6 pairs (_) / E6 = 7  =>  6 pairs (_)
A4,A6: 8.. / A4 = 8  =>  6 pairs (_) / A6 = 8  =>  5 pairs (_)
F8,E9: 8.. / F8 = 8  =>  6 pairs (_) / E9 = 8  =>  6 pairs (_)
I2,I3: 9.. / I2 = 9  =>  5 pairs (_) / I3 = 9  =>  5 pairs (_)
* DURATION: 0:00:06.169346  START: 20:07:40.422660  END: 20:07:46.592006 2020-12-02
* CP COUNT: (9)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:26.738581  START: 20:07:56.971091  END: 20:08:23.709672 2020-12-02
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00014015-kz0-base-pr-002.dot
* REASONING
* DIS # F5: 9 # A4: 2,5 => CTR => A4: 6,8
* DIS # F5: 9 + A4: 6,8 # C6: 5 => CTR => C6: 3,9
* DIS # F5: 9 + A4: 6,8 + C6: 3,9 # I4: 2,6 => CTR => I4: 7,8
* PRF # F5: 9 + A4: 6,8 + C6: 3,9 + I4: 7,8 # E9: 2,7 => SOL
* STA # F5: 9 + A4: 6,8 + C6: 3,9 + I4: 7,8 + E9: 2,7
* CNT   4 HDP CHAINS /  35 HYP OPENED

Header Info

14015;kz0;GP;23;11.30;11.30;3.40

Solution

position: 984761352751283649236495187645137298127849536893652471378526914469318725512974863 solved

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 # F5: 1,6 => UNS
* INC # F5: 9 => UNS
* INC # A4: 1,6 => UNS
* INC # A4: 2,5,8 => UNS
* INC # D6: 4,9 => UNS
* INC # D6: 6 => UNS
* INC # E2: 4,9 => UNS
* INC # E3: 4,9 => UNS
* INC # E9: 2,7 => UNS
* INC # E9: 8,9 => UNS
* INC # B7: 2,7 => UNS
* INC # B7: 1,3,6 => UNS
* CNT  12 HDP CHAINS /  12 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F5: 1,6 => UNS
* INC # F5: 9 => UNS
* INC # A4: 1,6 => UNS
* INC # A4: 2,5,8 => UNS
* INC # D6: 4,9 => UNS
* INC # D6: 6 => UNS
* INC # E2: 4,9 => UNS
* INC # E3: 4,9 => UNS
* INC # E9: 2,7 => UNS
* INC # E9: 8,9 => UNS
* INC # B7: 2,7 => UNS
* INC # B7: 1,3,6 => UNS
* CNT  12 HDP CHAINS /  12 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # F5: 1,6 => UNS
* INC # F5: 9 => UNS
* INC # A4: 1,6 => UNS
* INC # A4: 2,5,8 => UNS
* INC # D6: 4,9 => UNS
* INC # D6: 6 => UNS
* INC # E2: 4,9 => UNS
* INC # E3: 4,9 => UNS
* INC # E9: 2,7 => UNS
* INC # E9: 8,9 => UNS
* INC # B7: 2,7 => UNS
* INC # B7: 1,3,6 => UNS
* INC # F5: 1,6 # A4: 1,6 => UNS
* INC # F5: 1,6 # A4: 2,5,8 => UNS
* INC # F5: 1,6 # E2: 4,9 => UNS
* INC # F5: 1,6 # E3: 4,9 => UNS
* INC # F5: 1,6 # A5: 1,6 => UNS
* INC # F5: 1,6 # B5: 1,6 => UNS
* INC # F5: 1,6 # D2: 4,9 => UNS
* INC # F5: 1,6 # D3: 4,9 => UNS
* INC # F5: 1,6 # E9: 2,7 => UNS
* INC # F5: 1,6 # E9: 8,9 => UNS
* INC # F5: 1,6 # B7: 2,7 => UNS
* INC # F5: 1,6 # B7: 1,3,6 => UNS
* INC # F5: 1,6 => UNS
* DIS # F5: 9 # A4: 2,5 => CTR => A4: 6,8
* INC # F5: 9 + A4: 6,8 # C9: 2,5 => UNS
* INC # F5: 9 + A4: 6,8 # C9: 1,9 => UNS
* INC # F5: 9 + A4: 6,8 # C6: 3,9 => UNS
* DIS # F5: 9 + A4: 6,8 # C6: 5 => CTR => C6: 3,9
* INC # F5: 9 + A4: 6,8 + C6: 3,9 # B8: 3,9 => UNS
* INC # F5: 9 + A4: 6,8 + C6: 3,9 # B8: 6,7 => UNS
* DIS # F5: 9 + A4: 6,8 + C6: 3,9 # I4: 2,6 => CTR => I4: 7,8
* PRF # F5: 9 + A4: 6,8 + C6: 3,9 + I4: 7,8 # E9: 2,7 => SOL
* STA # F5: 9 + A4: 6,8 + C6: 3,9 + I4: 7,8 + E9: 2,7
* CNT  34 HDP CHAINS /  35 HYP OPENED