Analysis of xx-top500-198-base.sdk

Contents

Original Sudoku
Autosolve
Pair Reduction Variants
- Pair Reduction Analysis
- Pair Reduction
Details
Solution
Appendix: Full HDP Chains
- A1. Pair Reduction Analysis
- A2. Pair Reduction

Original Sudoku

level: medium

position: .6.7.1...5......3..............3...24..8......7....1..3.2.6.......4...8.......7.. initial

Autosolve

position: 8637.12.451428..37729.43.18...134872431872.6.278...143382.674.11.742.386.4.31872. autosolve

Pair Reduction Variants

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # F6: 6,9 => SOL
* DIS # F6: 5 => CTR => F6: 6,9
* PRF # D6: 5,6 => SOL
* DIS # D6: 9 => CTR => D6: 5,6
* PRF # D6: 5,9 => SOL
* DIS # D6: 6 => CTR => D6: 5,9
* DIS # F6: 5,9 => CTR => F6: 6
* PRF # F6: 6 => SOL
* PRF # D6: 5,9 => SOL
* DIS # D6: 6 => CTR => D6: 5,9
* DIS # F6: 5,9 => CTR => F6: 6
* PRF # F6: 6 => SOL
* CNT  12 HDP CHAINS /  12 HYP OPENED

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

Pair Reduction

The following important HDP chains were detected:

* PRF # F6: 6,9 => SOL
* STA F6: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

`.6.7.1...5......3..............3...24..8......7....1..3.2.6.......4...8.......7..`	initial
`8637.12.451428..37729.43.18...134872431872.6.278...143382.674.11.742.386.4.31872.`	autosolve
`863751294514289637729643518956134872431872965278596143382967451197425386645318729`	solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (19)
E1: 5,9
F2: 6,9
D3: 5,6
H1: 5,9
G2: 6,9
G3: 5,6
A4: 6,9
B4: 5,9
C4: 5,6
E6: 5,9
G5: 5,9
I5: 5,9
B8: 5,9
A9: 6,9
C9: 5,6
D7: 5,9
F8: 5,9
H7: 5,9
I9: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E1,D3: 5.. / E1 = 5  =>  0 pairs (*) / D3 = 5  =>  0 pairs (X)
H1,G3: 5.. / H1 = 5  =>  0 pairs (X) / G3 = 5  =>  0 pairs (_)
B4,C4: 5.. / B4 = 5  =>  0 pairs (*) / C4 = 5  =>  0 pairs (X)
G5,I5: 5.. / G5 = 5  =>  0 pairs (X) / I5 = 5  =>  0 pairs (_)
B8,C9: 5.. / B8 = 5  =>  0 pairs (X) / C9 = 5  =>  0 pairs (_)
D7,F8: 5.. / D7 = 5  =>  0 pairs (X) / F8 = 5  =>  0 pairs (_)
H7,I9: 5.. / H7 = 5  =>  0 pairs (*) / I9 = 5  =>  0 pairs (X)
E1,H1: 5.. / E1 = 5  =>  0 pairs (*) / H1 = 5  =>  0 pairs (X)
D3,G3: 5.. / D3 = 5  =>  0 pairs (X) / G3 = 5  =>  0 pairs (_)
D7,H7: 5.. / D7 = 5  =>  0 pairs (X) / H7 = 5  =>  0 pairs (_)
B8,F8: 5.. / B8 = 5  =>  0 pairs (X) / F8 = 5  =>  0 pairs (_)
C9,I9: 5.. / C9 = 5  =>  0 pairs (*) / I9 = 5  =>  0 pairs (X)
B4,B8: 5.. / B4 = 5  =>  0 pairs (*) / B8 = 5  =>  0 pairs (X)
C4,C9: 5.. / C4 = 5  =>  0 pairs (X) / C9 = 5  =>  0 pairs (_)
E1,E6: 5.. / E1 = 5  =>  0 pairs (*) / E6 = 5  =>  0 pairs (X)
F6,F8: 5.. / F6 = 5  =>  0 pairs (X) / F8 = 5  =>  0 pairs (_)
G3,G5: 5.. / G3 = 5  =>  0 pairs (*) / G5 = 5  =>  0 pairs (X)
H1,H7: 5.. / H1 = 5  =>  0 pairs (X) / H7 = 5  =>  0 pairs (_)
I5,I9: 5.. / I5 = 5  =>  0 pairs (*) / I9 = 5  =>  0 pairs (X)
F2,D3: 6.. / F2 = 6  =>  0 pairs (X) / D3 = 6  =>  0 pairs (_)
G2,G3: 6.. / G2 = 6  =>  0 pairs (*) / G3 = 6  =>  0 pairs (X)
A4,C4: 6.. / A4 = 6  =>  0 pairs (X) / C4 = 6  =>  0 pairs (_)
D6,F6: 6.. / D6 = 6  =>  0 pairs (X) / F6 = 6  =>  0 pairs (_)
A9,C9: 6.. / A9 = 6  =>  0 pairs (*) / C9 = 6  =>  0 pairs (X)
F2,G2: 6.. / F2 = 6  =>  0 pairs (X) / G2 = 6  =>  0 pairs (_)
D3,G3: 6.. / D3 = 6  =>  0 pairs (*) / G3 = 6  =>  0 pairs (X)
A4,A9: 6.. / A4 = 6  =>  0 pairs (X) / A9 = 6  =>  0 pairs (_)
C4,C9: 6.. / C4 = 6  =>  0 pairs (*) / C9 = 6  =>  0 pairs (X)
D3,D6: 6.. / D3 = 6  =>  0 pairs (*) / D6 = 6  =>  0 pairs (X)
F2,F6: 6.. / F2 = 6  =>  0 pairs (X) / F6 = 6  =>  0 pairs (_)
E1,F2: 9.. / E1 = 9  =>  0 pairs (X) / F2 = 9  =>  0 pairs (_)
H1,G2: 9.. / H1 = 9  =>  0 pairs (*) / G2 = 9  =>  0 pairs (X)
A4,B4: 9.. / A4 = 9  =>  0 pairs (*) / B4 = 9  =>  0 pairs (X)
G5,I5: 9.. / G5 = 9  =>  0 pairs (*) / I5 = 9  =>  0 pairs (X)
B8,A9: 9.. / B8 = 9  =>  0 pairs (*) / A9 = 9  =>  0 pairs (X)
D7,F8: 9.. / D7 = 9  =>  0 pairs (*) / F8 = 9  =>  0 pairs (X)
H7,I9: 9.. / H7 = 9  =>  0 pairs (X) / I9 = 9  =>  0 pairs (_)
E1,H1: 9.. / E1 = 9  =>  0 pairs (X) / H1 = 9  =>  0 pairs (_)
F2,G2: 9.. / F2 = 9  =>  0 pairs (*) / G2 = 9  =>  0 pairs (X)
D7,H7: 9.. / D7 = 9  =>  0 pairs (*) / H7 = 9  =>  0 pairs (X)
B8,F8: 9.. / B8 = 9  =>  0 pairs (*) / F8 = 9  =>  0 pairs (X)
A9,I9: 9.. / A9 = 9  =>  0 pairs (X) / I9 = 9  =>  0 pairs (_)
A4,A9: 9.. / A4 = 9  =>  0 pairs (*) / A9 = 9  =>  0 pairs (X)
B4,B8: 9.. / B4 = 9  =>  0 pairs (X) / B8 = 9  =>  0 pairs (_)
D6,D7: 9.. / D6 = 9  =>  0 pairs (X) / D7 = 9  =>  0 pairs (_)
E1,E6: 9.. / E1 = 9  =>  0 pairs (X) / E6 = 9  =>  0 pairs (_)
G2,G5: 9.. / G2 = 9  =>  0 pairs (X) / G5 = 9  =>  0 pairs (_)
H1,H7: 9.. / H1 = 9  =>  0 pairs (*) / H7 = 9  =>  0 pairs (X)
I5,I9: 9.. / I5 = 9  =>  0 pairs (X) / I9 = 9  =>  0 pairs (_)
* DURATION: 0:01:35.180084  START: 09:29:59.371794  END: 09:31:34.551878 2017-05-04
* CP COUNT: (49)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B4,B8,C4,C9,D3,D7,E1,E6,F2,F8,G2,G3,G5,H1,H7,I5,I9)
* 8637.12.451428..37729.43.18...134872431872.6.278...143382.674.11.742.386.4.31872.
* PAIR F2: 6,9 COL F
F6: 6,9,5                                # reduction candidate for 6,9
F6: 6,9 => SOLVED
* 863751294514289637729643518956134872431872965278596143382967451197425386645318729
F6: 5 => CTR
* 8637.12.4514286937729543618...1348724318725692786..143382.674.11.742.386.4.31872.
* PAIR D3: 5,6 COL D
D6: 5,6,9                                # reduction candidate for 5,6
D6: 5,6 => SOLVED
* 863751294514289637729643518956134872431872965278596143382967451197425386645318729
D6: 9 => CTR
* 8637.12.451428..37729643518...13487243187296527895.143382.674.11.742.386.4.31872.
* PAIR E6: 5,9 BLK 5
D6: 5,9,6                                # reduction candidate for 5,9
D6: 5,9 => SOLVED
* 863751294514289637729643518956134872431872965278596143382967451197425386645318729
D6: 6 => CTR
* 8637.12.451428..37729.43.18...134872431872.6.2786..143382967451197425386645318729
F6: 5,9,6                                # reduction candidate for 5,9
F6: 5,9 => CTR
* 8637.12.4514286937729543618...1348724318725692786591433829674.11.742.386.4.31872.
F6: 6 => SOLVED
* 863751294514289637729643518956134872431872965278596143382967451197425386645318729
* PAIR D7: 5,9 COL D
D6: 5,9,6                                # reduction candidate for 5,9
D6: 5,9 => SOLVED
* 863751294514289637729643518956134872431872965278596143382967451197425386645318729
D6: 6 => CTR
* 8637.12.451428..37729.43.18...134872431872.6.2786..143382967451197425386645318729
* PAIR F8: 5,9 COL F
F6: 5,9,6                                # reduction candidate for 5,9
F6: 5,9 => CTR
* 8637.12.4514286937729543618...1348724318725692786591433829674.11.742.386.4.31872.
F6: 6 => SOLVED
* 863751294514289637729643518956134872431872965278596143382967451197425386645318729
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-198-base-pr-000.dot
* REASONING
* PRF # F6: 6,9 => SOL
* DIS # F6: 5 => CTR => F6: 6,9
* PRF # D6: 5,6 => SOL
* DIS # D6: 9 => CTR => D6: 5,6
* PRF # D6: 5,9 => SOL
* DIS # D6: 6 => CTR => D6: 5,9
* DIS # F6: 5,9 => CTR => F6: 6
* PRF # F6: 6 => SOL
* PRF # D6: 5,9 => SOL
* DIS # D6: 6 => CTR => D6: 5,9
* DIS # F6: 5,9 => CTR => F6: 6
* PRF # F6: 6 => SOL
* CNT  12 HDP CHAINS /  12 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B4,B8,C4,C9,D3,D7,E1,E6,F2,F8,G2,G3,G5,H1,H7,I5,I9)
* 8637.12.451428..37729.43.18...134872431872.6.278...143382.674.11.742.386.4.31872.
* PAIR F2: 6,9 COL F
F6: 6,9,5                                # reduction candidate for 6,9
F6: 6,9 => SOLVED
* 863751294514289637729643518956134872431872965278596143382967451197425386645318729
* DURATION: 0:00:02.135026  START: 09:31:51.969550  END: 09:31:54.104576 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-198-base-pr-001.dot
* REASONING
* PRF # F6: 6,9 => SOL
* STA F6: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 198

solution: 863751294514289637729643518956134872431872965278596143382967451197425386645318729
info: 1882     FNBTHWX  S8.f     21596

http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/

Solution

position: 863751294514289637729643518956134872431872965278596143382967451197425386645318729 solved

See section Pair Reduction for the HDP chains leading to this result.

Appendix: Full HDP Chains

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* PRF # F6: 6,9 => SOL
* DIS # F6: 5 => CTR => F6: 6,9
* PRF # D6: 5,6 => SOL
* DIS # D6: 9 => CTR => D6: 5,6
* PRF # D6: 5,9 => SOL
* DIS # D6: 6 => CTR => D6: 5,9
* DIS # F6: 5,9 => CTR => F6: 6
* PRF # F6: 6 => SOL
* PRF # D6: 5,9 => SOL
* DIS # D6: 6 => CTR => D6: 5,9
* DIS # F6: 5,9 => CTR => F6: 6
* PRF # F6: 6 => SOL
* CNT  12 HDP CHAINS /  12 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # F6: 6,9 => SOL
* STA F6: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED