Analysis of xx-ph-00019523-KZ1C-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7.....7...6......5..97..5.....4....43...6.....2...1.5...78....96...2.....1...3 initial

Autosolve

position: 98.7.....7...6......5..97..5.....4....43...6.....2...1.5...78....96...2.....1...3 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: 0:00:37.578366

The following important HDP chains were detected:

* DIS # G1: 1,5 # I5: 2,9 => CTR => I5: 5,7,8
* DIS # G1: 1,5 + I5: 5,7,8 # H7: 4,9 => CTR => H7: 1
* DIS # G1: 1,5 + I5: 5,7,8 + H7: 1 # H9: 7 => CTR => H9: 4,9
* DIS # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 # I4: 8 => CTR => I4: 2,9
* DIS # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 + I4: 2,9 # E5: 5,8 => CTR => E5: 7,9
* DIS # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 + I4: 2,9 + E5: 7,9 # F5: 5,8 => CTR => F5: 1
* PRF # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 + I4: 2,9 + E5: 7,9 + F5: 1 => SOL
* STA G1: 1,5
* CNT   7 HDP CHAINS /  37 HYP OPENED

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

Details

Positions

98.7.....7...6......5..97..5.....4....43...6.....2...1.5...78....96...2.....1...3 initial
98.7.....7...6......5..97..5.....4....43...6.....2...1.5...78....96...2.....1...3 autosolve
982753146743168259165249738531896472824371965697425381256937814319684527478512693 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
G8: 1,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H7,G8: 1.. / H7 = 1  =>  4 pairs (_) / G8 = 1  =>  1 pairs (_)
D6,F6: 4.. / D6 = 4  =>  2 pairs (_) / F6 = 4  =>  1 pairs (_)
F4,F6: 6.. / F4 = 6  =>  1 pairs (_) / F6 = 6  =>  5 pairs (_)
I7,G9: 6.. / I7 = 6  =>  2 pairs (_) / G9 = 6  =>  2 pairs (_)
G1,G9: 6.. / G1 = 6  =>  2 pairs (_) / G9 = 6  =>  2 pairs (_)
E4,E5: 7.. / E4 = 7  =>  1 pairs (_) / E5 = 7  =>  2 pairs (_)
I8,H9: 7.. / I8 = 7  =>  1 pairs (_) / H9 = 7  =>  2 pairs (_)
B8,I8: 7.. / B8 = 7  =>  2 pairs (_) / I8 = 7  =>  1 pairs (_)
* DURATION: 0:00:05.109388  START: 19:20:41.143340  END: 19:20:46.252728 2020-12-06
* CP COUNT: (8)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:37.393640  START: 19:20:48.202296  END: 19:21:25.595936 2020-12-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00019523-KZ1C-base-pr-002.dot
* REASONING
* DIS # G1: 1,5 # I5: 2,9 => CTR => I5: 5,7,8
* DIS # G1: 1,5 + I5: 5,7,8 # H7: 4,9 => CTR => H7: 1
* DIS # G1: 1,5 + I5: 5,7,8 + H7: 1 # H9: 7 => CTR => H9: 4,9
* DIS # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 # I4: 8 => CTR => I4: 2,9
* DIS # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 + I4: 2,9 # E5: 5,8 => CTR => E5: 7,9
* DIS # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 + I4: 2,9 + E5: 7,9 # F5: 5,8 => CTR => F5: 1
* PRF # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 + I4: 2,9 + E5: 7,9 + F5: 1 => SOL
* STA G1: 1,5
* CNT   7 HDP CHAINS /  37 HYP OPENED

Header Info

19523;KZ1C;GP;23;11.30;11.30;10.10

Solution

position: 982753146743168259165249738531896472824371965697425381256937814319684527478512693 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 # G1: 1,5 => UNS
* INC # G2: 1,5 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G1: 1,5 => UNS
* INC # G2: 1,5 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # G1: 1,5 => UNS
* INC # G2: 1,5 => UNS
* INC # G1: 1,5 # H1: 1,5 => UNS
* INC # G1: 1,5 # H2: 1,5 => UNS
* INC # G1: 1,5 # F1: 1,5 => UNS
* INC # G1: 1,5 # F1: 2,3,4 => UNS
* INC # G1: 1,5 # I4: 2,9 => UNS
* DIS # G1: 1,5 # I5: 2,9 => CTR => I5: 5,7,8
* INC # G1: 1,5 + I5: 5,7,8 # I4: 2,9 => UNS
* INC # G1: 1,5 + I5: 5,7,8 # I4: 7,8 => UNS
* INC # G1: 1,5 + I5: 5,7,8 # B5: 2,9 => UNS
* INC # G1: 1,5 + I5: 5,7,8 # B5: 1,7 => UNS
* INC # G1: 1,5 + I5: 5,7,8 # G2: 2,9 => UNS
* INC # G1: 1,5 + I5: 5,7,8 # G2: 3 => UNS
* INC # G1: 1,5 + I5: 5,7,8 # H4: 3,9 => UNS
* INC # G1: 1,5 + I5: 5,7,8 # H6: 3,9 => UNS
* INC # G1: 1,5 + I5: 5,7,8 # B6: 3,9 => UNS
* INC # G1: 1,5 + I5: 5,7,8 # B6: 6,7 => UNS
* INC # G1: 1,5 + I5: 5,7,8 # G2: 3,9 => UNS
* INC # G1: 1,5 + I5: 5,7,8 # G2: 2 => UNS
* DIS # G1: 1,5 + I5: 5,7,8 # H7: 4,9 => CTR => H7: 1
* INC # G1: 1,5 + I5: 5,7,8 + H7: 1 # H9: 4,9 => UNS
* INC # G1: 1,5 + I5: 5,7,8 + H7: 1 # H9: 4,9 => UNS
* DIS # G1: 1,5 + I5: 5,7,8 + H7: 1 # H9: 7 => CTR => H9: 4,9
* INC # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 # D7: 4,9 => UNS
* INC # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 # E7: 4,9 => UNS
* INC # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 # I2: 4,9 => UNS
* INC # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 # I2: 2,5,8 => UNS
* INC # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 # I4: 2,9 => UNS
* DIS # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 # I4: 8 => CTR => I4: 2,9
* INC # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 + I4: 2,9 # B5: 2,9 => UNS
* INC # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 + I4: 2,9 # B5: 1,7 => UNS
* INC # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 + I4: 2,9 # H6: 5,8 => UNS
* INC # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 + I4: 2,9 # H6: 7 => UNS
* DIS # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 + I4: 2,9 # E5: 5,8 => CTR => E5: 7,9
* DIS # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 + I4: 2,9 + E5: 7,9 # F5: 5,8 => CTR => F5: 1
* PRF # G1: 1,5 + I5: 5,7,8 + H7: 1 + H9: 4,9 + I4: 2,9 + E5: 7,9 + F5: 1 => SOL
* STA G1: 1,5
* CNT  37 HDP CHAINS /  37 HYP OPENED