Analysis of xx-ph-00016392-Kz1_b-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7.....65....7....7.6....4...3..2...56..8.......1..3..98..6......2..1......6..4 initial

Autosolve

position: 98.7.....65....7....7.6....4...3..2...56..8.......1..3..98..6......2..1......6..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: 0:00:47.680270

The following important HDP chains were detected:

* DIS # F4: 5,9 # A9: 1,3 => CTR => A9: 2,5,7,8
* DIS # F4: 5,9 + A9: 2,5,7,8 # D3: 5,9 => CTR => D3: 1,2,3
* DIS # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 # F8: 5,9 => CTR => F8: 3,4,7
* DIS # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 + F8: 3,4,7 # H9: 3,9 => CTR => H9: 5,7,8
* PRF # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 + F8: 3,4,7 + H9: 5,7,8 # G9: 2 => SOL
* STA # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 + F8: 3,4,7 + H9: 5,7,8 + G9: 2
* CNT   5 HDP CHAINS /  36 HYP OPENED

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

Details

Positions

98.7.....65....7....7.6....4...3..2...56..8.......1..3..98..6......2..1......6..4 initial
98.7.....65....7....7.6....4...3..2...56..8.......1..3..98..6......2..1......6..4 autosolve
982753461653148792147269358478935126315672849296481573529814637864327915731596284 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
D4: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F5,D6: 2.. / F5 = 2  =>  1 pairs (_) / D6 = 2  =>  9 pairs (_)
I7,G9: 2.. / I7 = 2  =>  1 pairs (_) / G9 = 2  =>  2 pairs (_)
A5,B5: 3.. / A5 = 3  =>  2 pairs (_) / B5 = 3  =>  1 pairs (_)
H1,I1: 6.. / H1 = 6  =>  2 pairs (_) / I1 = 6  =>  2 pairs (_)
I4,H6: 6.. / I4 = 6  =>  2 pairs (_) / H6 = 6  =>  2 pairs (_)
B8,C8: 6.. / B8 = 6  =>  1 pairs (_) / C8 = 6  =>  3 pairs (_)
H1,H6: 6.. / H1 = 6  =>  2 pairs (_) / H6 = 6  =>  2 pairs (_)
I1,I4: 6.. / I1 = 6  =>  2 pairs (_) / I4 = 6  =>  2 pairs (_)
F4,E6: 8.. / F4 = 8  =>  2 pairs (_) / E6 = 8  =>  3 pairs (_)
I8,H9: 8.. / I8 = 8  =>  1 pairs (_) / H9 = 8  =>  1 pairs (_)
C4,F4: 8.. / C4 = 8  =>  3 pairs (_) / F4 = 8  =>  2 pairs (_)
E2,E6: 8.. / E2 = 8  =>  2 pairs (_) / E6 = 8  =>  3 pairs (_)
* DURATION: 0:00:08.507145  START: 11:52:36.472044  END: 11:52:44.979189 2020-10-19
* CP COUNT: (12)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:47.508855  START: 11:52:52.608052  END: 11:53:40.116907 2020-10-19
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00016392-Kz1_b-base-pr-002.dot
* REASONING
* DIS # F4: 5,9 # A9: 1,3 => CTR => A9: 2,5,7,8
* DIS # F4: 5,9 + A9: 2,5,7,8 # D3: 5,9 => CTR => D3: 1,2,3
* DIS # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 # F8: 5,9 => CTR => F8: 3,4,7
* DIS # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 + F8: 3,4,7 # H9: 3,9 => CTR => H9: 5,7,8
* PRF # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 + F8: 3,4,7 + H9: 5,7,8 # G9: 2 => SOL
* STA # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 + F8: 3,4,7 + H9: 5,7,8 + G9: 2
* CNT   5 HDP CHAINS /  36 HYP OPENED

Header Info

16392;Kz1 b;GP;23;11.40;11.40;10.30

Solution

position: 982753461653148792147269358478935126315672849296481573529814637864327915731596284 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 # F4: 5,9 => UNS
* INC # D6: 5,9 => UNS
* INC # E6: 5,9 => UNS
* INC # G4: 5,9 => UNS
* INC # I4: 5,9 => UNS
* INC # D3: 5,9 => UNS
* INC # D8: 5,9 => UNS
* INC # D9: 5,9 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F4: 5,9 => UNS
* INC # D6: 5,9 => UNS
* INC # E6: 5,9 => UNS
* INC # G4: 5,9 => UNS
* INC # I4: 5,9 => UNS
* INC # D3: 5,9 => UNS
* INC # D8: 5,9 => UNS
* INC # D9: 5,9 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # F4: 5,9 => UNS
* INC # D6: 5,9 => UNS
* INC # E6: 5,9 => UNS
* INC # G4: 5,9 => UNS
* INC # I4: 5,9 => UNS
* INC # D3: 5,9 => UNS
* INC # D8: 5,9 => UNS
* INC # D9: 5,9 => UNS
* INC # F4: 5,9 # B8: 6,7 => UNS
* INC # F4: 5,9 # B8: 3,4 => UNS
* INC # F4: 5,9 # A3: 1,3 => UNS
* INC # F4: 5,9 # A7: 1,3 => UNS
* DIS # F4: 5,9 # A9: 1,3 => CTR => A9: 2,5,7,8
* INC # F4: 5,9 + A9: 2,5,7,8 # A3: 1,3 => UNS
* INC # F4: 5,9 + A9: 2,5,7,8 # A7: 1,3 => UNS
* INC # F4: 5,9 + A9: 2,5,7,8 # B3: 1,3 => UNS
* INC # F4: 5,9 + A9: 2,5,7,8 # B7: 1,3 => UNS
* INC # F4: 5,9 + A9: 2,5,7,8 # B9: 1,3 => UNS
* INC # F4: 5,9 + A9: 2,5,7,8 # A7: 2,7 => UNS
* INC # F4: 5,9 + A9: 2,5,7,8 # A9: 2,7 => UNS
* DIS # F4: 5,9 + A9: 2,5,7,8 # D3: 5,9 => CTR => D3: 1,2,3
* INC # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 # D8: 5,9 => UNS
* INC # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 # D9: 5,9 => UNS
* INC # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 # D8: 5,9 => UNS
* INC # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 # D9: 5,9 => UNS
* INC # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 # F3: 5,9 => UNS
* DIS # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 # F8: 5,9 => CTR => F8: 3,4,7
* INC # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 + F8: 3,4,7 # F3: 5,9 => UNS
* INC # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 + F8: 3,4,7 # F3: 3,4,8 => UNS
* INC # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 + F8: 3,4,7 # F3: 5,9 => UNS
* INC # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 + F8: 3,4,7 # F3: 3,4,8 => UNS
* INC # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 + F8: 3,4,7 # G9: 3,9 => UNS
* DIS # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 + F8: 3,4,7 # H9: 3,9 => CTR => H9: 5,7,8
* INC # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 + F8: 3,4,7 + H9: 5,7,8 # G9: 3,9 => UNS
* PRF # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 + F8: 3,4,7 + H9: 5,7,8 # G9: 2 => SOL
* STA # F4: 5,9 + A9: 2,5,7,8 + D3: 1,2,3 + F8: 3,4,7 + H9: 5,7,8 + G9: 2
* CNT  35 HDP CHAINS /  36 HYP OPENED