Analysis of xx-ph-00012398-kz0-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7.....76....9....5......4...5..3...68..7.......2..1..95..8......18.2......3..4 initial

Autosolve

position: 98.7.....76....9....5......4...5..3...68..7.......2..1..95..8......18.2......3..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: 0:00:23.673341

The following important HDP chains were detected:

* DIS # I4: 2,6 # A5: 3,5 => CTR => A5: 1,2
* DIS # I4: 2,6 + A5: 1,2 # B5: 3,5 => CTR => B5: 1,2
* DIS # I4: 2,6 + A5: 1,2 + B5: 1,2 # A8: 3,5 => CTR => A8: 6
* DIS # I4: 2,6 + A5: 1,2 + B5: 1,2 + A8: 6 # C8: 4 => CTR => C8: 3,7
* DIS # I4: 2,6 + A5: 1,2 + B5: 1,2 + A8: 6 + C8: 3,7 # B6: 9 => CTR => B6: 3,7
* DIS # I4: 2,6 + A5: 1,2 + B5: 1,2 + A8: 6 + C8: 3,7 + B6: 3,7 # G1: 2,6 => CTR => G1: 1,3,5
* PRF # I4: 2,6 + A5: 1,2 + B5: 1,2 + A8: 6 + C8: 3,7 + B6: 3,7 + G1: 1,3,5 # G3: 2,6 => SOL
* STA # I4: 2,6 + A5: 1,2 + B5: 1,2 + A8: 6 + C8: 3,7 + B6: 3,7 + G1: 1,3,5 + G3: 2,6
* CNT   7 HDP CHAINS /  19 HYP OPENED

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

Details

Positions

98.7.....76....9....5......4...5..3...68..7.......2..1..95..8......18.2......3..4 initial
98.7.....76....9....5......4...5..3...68..7.......2..1..95..8......18.2......3..4 autosolve
982765143764381952135249678498157236216834795573692481349526817657418329821973564 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
G4: 2,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F1,F2: 5.. / F1 = 5  =>  2 pairs (_) / F2 = 5  =>  1 pairs (_)
H3,I3: 7.. / H3 = 7  =>  2 pairs (_) / I3 = 7  =>  2 pairs (_)
F4,E6: 7.. / F4 = 7  =>  2 pairs (_) / E6 = 7  =>  7 pairs (_)
F4,F7: 7.. / F4 = 7  =>  2 pairs (_) / F7 = 7  =>  7 pairs (_)
E2,E3: 8.. / E2 = 8  =>  3 pairs (_) / E3 = 8  =>  1 pairs (_)
I4,H6: 8.. / I4 = 8  =>  1 pairs (_) / H6 = 8  =>  3 pairs (_)
A9,C9: 8.. / A9 = 8  =>  2 pairs (_) / C9 = 8  =>  2 pairs (_)
C4,I4: 8.. / C4 = 8  =>  3 pairs (_) / I4 = 8  =>  1 pairs (_)
A6,A9: 8.. / A6 = 8  =>  2 pairs (_) / A9 = 8  =>  2 pairs (_)
I8,H9: 9.. / I8 = 9  =>  3 pairs (_) / H9 = 9  =>  4 pairs (_)
D8,I8: 9.. / D8 = 9  =>  4 pairs (_) / I8 = 9  =>  3 pairs (_)
* DURATION: 0:00:06.505406  START: 07:49:48.637597  END: 07:49:55.143003 2020-12-02
* CP COUNT: (11)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:23.556466  START: 07:49:58.334799  END: 07:50:21.891265 2020-12-02
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00012398-kz0-base-pr-002.dot
* REASONING
* DIS # I4: 2,6 # A5: 3,5 => CTR => A5: 1,2
* DIS # I4: 2,6 + A5: 1,2 # B5: 3,5 => CTR => B5: 1,2
* DIS # I4: 2,6 + A5: 1,2 + B5: 1,2 # A8: 3,5 => CTR => A8: 6
* DIS # I4: 2,6 + A5: 1,2 + B5: 1,2 + A8: 6 # C8: 4 => CTR => C8: 3,7
* DIS # I4: 2,6 + A5: 1,2 + B5: 1,2 + A8: 6 + C8: 3,7 # B6: 9 => CTR => B6: 3,7
* DIS # I4: 2,6 + A5: 1,2 + B5: 1,2 + A8: 6 + C8: 3,7 + B6: 3,7 # G1: 2,6 => CTR => G1: 1,3,5
* PRF # I4: 2,6 + A5: 1,2 + B5: 1,2 + A8: 6 + C8: 3,7 + B6: 3,7 + G1: 1,3,5 # G3: 2,6 => SOL
* STA # I4: 2,6 + A5: 1,2 + B5: 1,2 + A8: 6 + C8: 3,7 + B6: 3,7 + G1: 1,3,5 + G3: 2,6
* CNT   7 HDP CHAINS /  19 HYP OPENED

Header Info

12398;kz0;GP;23;11.30;11.30;10.90

Solution

position: 982765143764381952135249678498157236216834795573692481349526817657418329821973564 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: 2,6 => UNS
* INC # I4: 8,9 => UNS
* INC # G1: 2,6 => UNS
* INC # G3: 2,6 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # I4: 2,6 => UNS
* INC # I4: 8,9 => UNS
* INC # G1: 2,6 => UNS
* INC # G3: 2,6 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # I4: 2,6 => UNS
* INC # I4: 8,9 => UNS
* INC # G1: 2,6 => UNS
* INC # G3: 2,6 => UNS
* DIS # I4: 2,6 # A5: 3,5 => CTR => A5: 1,2
* DIS # I4: 2,6 + A5: 1,2 # B5: 3,5 => CTR => B5: 1,2
* INC # I4: 2,6 + A5: 1,2 + B5: 1,2 # B6: 3,5 => UNS
* INC # I4: 2,6 + A5: 1,2 + B5: 1,2 # B6: 3,5 => UNS
* INC # I4: 2,6 + A5: 1,2 + B5: 1,2 # B6: 7,9 => UNS
* DIS # I4: 2,6 + A5: 1,2 + B5: 1,2 # A8: 3,5 => CTR => A8: 6
* INC # I4: 2,6 + A5: 1,2 + B5: 1,2 + A8: 6 # B6: 3,7 => UNS
* INC # I4: 2,6 + A5: 1,2 + B5: 1,2 + A8: 6 # B6: 9 => UNS
* INC # I4: 2,6 + A5: 1,2 + B5: 1,2 + A8: 6 # C8: 3,7 => UNS
* DIS # I4: 2,6 + A5: 1,2 + B5: 1,2 + A8: 6 # C8: 4 => CTR => C8: 3,7
* INC # I4: 2,6 + A5: 1,2 + B5: 1,2 + A8: 6 + C8: 3,7 # B6: 3,7 => UNS
* DIS # I4: 2,6 + A5: 1,2 + B5: 1,2 + A8: 6 + C8: 3,7 # B6: 9 => CTR => B6: 3,7
* DIS # I4: 2,6 + A5: 1,2 + B5: 1,2 + A8: 6 + C8: 3,7 + B6: 3,7 # G1: 2,6 => CTR => G1: 1,3,5
* PRF # I4: 2,6 + A5: 1,2 + B5: 1,2 + A8: 6 + C8: 3,7 + B6: 3,7 + G1: 1,3,5 # G3: 2,6 => SOL
* STA # I4: 2,6 + A5: 1,2 + B5: 1,2 + A8: 6 + C8: 3,7 + B6: 3,7 + G1: 1,3,5 + G3: 2,6
* CNT  18 HDP CHAINS /  19 HYP OPENED