Analysis of xx-top500-006-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ....15..97.....4.............389.7...5..........7...........32.1......5..9.6..... initial

Autosolve

position: 3...156797.59..4139.13..582.1389.765.571.329...975.13..765.932113....956592631847 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B1: 4,8 => CTR => B1: 2
* PRF # B1: 2 => SOL
* DIS # E2: 8 => CTR => E2: 2,6
* DIS # E3: 4,6 => CTR => E3: 7
* PRF # B1: 2,4 => SOL
* DIS # B1: 8 => CTR => B1: 2,4
* DIS # E2: 6,8 => CTR => E2: 2
* PRF # E2: 2 => SOL
* DIS # A5: 6 => CTR => A5: 4,8
* DIS # B1: 4,8 => CTR => B1: 2
* PRF # B1: 2 => SOL
* PRF # A5: 4,6 => SOL
* DIS # A5: 8 => CTR => A5: 4,6
* DIS # E3: 4,6 => CTR => E3: 7
* DIS # A5: 6 => CTR => A5: 4,8
* DIS # A5: 6 => CTR => A5: 4,8
* PRF # E8: 4,8 => SOL
* DIS # F8: 4,8 => CTR => F8: 7
* PRF # E8: 4,8 => SOL
* DIS # F8: 4,8 => CTR => F8: 7
* DIS # E8: 2,4 => CTR => E8: 7,8
* PRF # E8: 7,8 => SOL
* CNT  22 HDP CHAINS /  33 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # B1: 4,8 => CTR => B1: 2
* PRF B1: 2 => SOL
* STA B1: 2
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

....15..97.....4.............389.7...5..........7...........32.1......5..9.6..... initial
3...156797.59..4139.13..582.1389.765.571.329...975.13..765.932113....956592631847 autosolve
328415679765928413941376582213894765457163298689752134876549321134287956592631847 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (17)
C1: 4,8
B2: 2,6
B3: 4,6
D1: 2,4
F2: 6,8
A4: 2,4
A6: 2,6
B6: 4,8
F4: 2,4
E5: 4,6
F6: 2,6
I5: 4,8
I6: 4,8
A7: 4,8
C8: 4,8
E7: 4,8
D8: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,B2: 2.. / B1 = 2  =>  0 pairs (*) / B2 = 2  =>  0 pairs (X)
D1,E2: 2.. / D1 = 2  =>  0 pairs (X) / E2 = 2  =>  0 pairs (_)
A4,A6: 2.. / A4 = 2  => 17 pairs (_) / A6 = 2  =>  0 pairs (X)
F4,F6: 2.. / F4 = 2  =>  0 pairs (X) / F6 = 2  => 17 pairs (_)
D8,E8: 2.. / D8 = 2  =>  0 pairs (*) / E8 = 2  =>  0 pairs (X)
B1,D1: 2.. / B1 = 2  =>  0 pairs (*) / D1 = 2  =>  0 pairs (X)
B2,E2: 2.. / B2 = 2  =>  0 pairs (X) / E2 = 2  =>  0 pairs (_)
A4,F4: 2.. / A4 = 2  => 17 pairs (_) / F4 = 2  =>  0 pairs (X)
A6,F6: 2.. / A6 = 2  =>  0 pairs (X) / F6 = 2  => 17 pairs (_)
D1,D8: 2.. / D1 = 2  =>  0 pairs (X) / D8 = 2  =>  0 pairs (_)
E2,E8: 2.. / E2 = 2  =>  0 pairs (*) / E8 = 2  =>  0 pairs (X)
F4,E5: 4.. / F4 = 4  => 17 pairs (_) / E5 = 4  =>  0 pairs (X)
I5,I6: 4.. / I5 = 4  =>  0 pairs (X) / I6 = 4  =>  0 pairs (_)
A7,C8: 4.. / A7 = 4  =>  0 pairs (X) / C8 = 4  =>  0 pairs (_)
A4,F4: 4.. / A4 = 4  =>  0 pairs (X) / F4 = 4  => 17 pairs (_)
B6,I6: 4.. / B6 = 4  =>  0 pairs (X) / I6 = 4  =>  0 pairs (_)
A7,E7: 4.. / A7 = 4  =>  0 pairs (X) / E7 = 4  =>  0 pairs (_)
C1,C8: 4.. / C1 = 4  =>  0 pairs (X) / C8 = 4  =>  0 pairs (_)
D1,D8: 4.. / D1 = 4  =>  0 pairs (*) / D8 = 4  =>  0 pairs (X)
B2,B3: 6.. / B2 = 6  =>  0 pairs (*) / B3 = 6  =>  0 pairs (X)
A5,A6: 6.. / A5 = 6  =>  0 pairs (X) / A6 = 6  => 17 pairs (_)
E5,F6: 6.. / E5 = 6  => 17 pairs (_) / F6 = 6  =>  0 pairs (X)
A5,E5: 6.. / A5 = 6  =>  0 pairs (X) / E5 = 6  => 17 pairs (_)
A6,F6: 6.. / A6 = 6  => 17 pairs (_) / F6 = 6  =>  0 pairs (X)
E3,F3: 7.. / E3 = 7  => 18 pairs (_) / F3 = 7  =>  0 pairs (X)
E8,F8: 7.. / E8 = 7  =>  0 pairs (X) / F8 = 7  => 18 pairs (_)
E3,E8: 7.. / E3 = 7  => 18 pairs (_) / E8 = 7  =>  0 pairs (X)
F3,F8: 7.. / F3 = 7  =>  0 pairs (X) / F8 = 7  => 18 pairs (_)
B1,C1: 8.. / B1 = 8  =>  0 pairs (X) / C1 = 8  =>  0 pairs (_)
E2,F2: 8.. / E2 = 8  =>  0 pairs (X) / F2 = 8  => 18 pairs (_)
A5,B6: 8.. / A5 = 8  =>  0 pairs (X) / B6 = 8  =>  0 pairs (_)
I5,I6: 8.. / I5 = 8  =>  0 pairs (*) / I6 = 8  =>  0 pairs (X)
A7,C8: 8.. / A7 = 8  =>  0 pairs (*) / C8 = 8  =>  0 pairs (X)
A5,I5: 8.. / A5 = 8  =>  0 pairs (X) / I5 = 8  =>  0 pairs (_)
B6,I6: 8.. / B6 = 8  =>  0 pairs (*) / I6 = 8  =>  0 pairs (X)
A7,E7: 8.. / A7 = 8  =>  0 pairs (*) / E7 = 8  =>  0 pairs (X)
A5,A7: 8.. / A5 = 8  =>  0 pairs (X) / A7 = 8  =>  0 pairs (_)
B1,B6: 8.. / B1 = 8  =>  0 pairs (X) / B6 = 8  =>  0 pairs (_)
C1,C8: 8.. / C1 = 8  =>  0 pairs (*) / C8 = 8  =>  0 pairs (X)
F2,F8: 8.. / F2 = 8  => 18 pairs (_) / F8 = 8  =>  0 pairs (X)
* DURATION: 0:01:16.070416  START: 02:46:48.845961  END: 02:48:04.916377 2017-05-04
* CP COUNT: (40)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A7,B2,B3,B6,C1,C8,D1,D8,E5,E7,F2,F4,F6,I5,I6)
* 3...156797.59..4139.13..582.1389.765.571.329...975.13..765.932113....956592631847
* PAIR C1: 4,8 BLK 1
B1: 4,8,2                                # reduction candidate for 4,8
B1: 4,8 => CTR
* 3.42156797259.8413961374582413892765.5714329828975.13..765.932113.427956592631847
B1: 2 => SOLVED
* 328415679765928413941376582213894765457163298689752134876549321134287956592631847
* PAIR B2: 2,6 ROW 2
E2: 2,6,8                                # reduction candidate for 2,6
E2: 8 => CTR
* 3..2156797259864139613..582.1389.765.5716329.6.975213.87654932113....956592631847
E2: 2,6                                  # 18 pairs
* PAIR B3: 4,6 ROW 3
E3: 4,6,7                                # reduction candidate for 4,6
E3: 4,6 => CTR
* 3...156797.59284139.1367582.1389.7656571432982.975.13..765.932113..7.956592631847
E3: 7                                    # 18 pairs
F3: 4,6,7                                # reduction candidate for 4,6
F3: 4,6                                  # 18 pairs
* PAIR D1: 2,4 ROW 1
B1: 2,4,8                                # reduction candidate for 2,4
B1: 2,4 => SOLVED
* 328415679765928413941376582213894765457163298689752134876549321134287956592631847
B1: 8 => CTR
* 3842156797259..4139613..582.1389.76585716329464975213847658932113....956592631847
* PAIR F2: 6,8 BLK 2
E2: 6,8,2                                # reduction candidate for 6,8
E2: 6,8 => CTR
* 3.42156797259.8413961374582413892765.5714329828975.13..765.932113.427956592631847
E2: 2 => SOLVED
* 328415679765928413941376582213894765457163298689752134876549321134287956592631847
* PAIR B6: 4,8 BLK 4
A5: 4,8,6                                # reduction candidate for 4,8
A5: 6 => CTR
* 3...156797.59..4139.13..582.1389.7656571432982.975.13..765.932113....956592631847
A5: 4,8                                  # 17 pairs
* PAIR B6: 4,8 COL B
B1: 4,8,2                                # reduction candidate for 4,8
B1: 4,8 => CTR
* 3.42156797259.8413961374582413892765.5714329828975.13..765.932113.427956592631847
B1: 2 => SOLVED
* 328415679765928413941376582213894765457163298689752134876549321134287956592631847
* PAIR E5: 4,6 ROW 5
A5: 4,6,8                                # reduction candidate for 4,6
A5: 4,6 => SOLVED
* 328415679765928413941376582213894765457163298689752134876549321134287956592631847
A5: 8 => CTR
* 3842156797.59..4139.13..582.1389.765857163294649752138476589321138...956592631847
* PAIR E5: 4,6 COL E
E3: 4,6,7                                # reduction candidate for 4,6
E3: 4,6 => CTR
* 3...156797.59284139.1367582.1389.7656571432982.975.13..765.932113..7.956592631847
E3: 7                                    # 18 pairs
* PAIR I5: 4,8 ROW 5
A5: 4,8,6                                # reduction candidate for 4,8
A5: 6 => CTR
* 3...156797.59..4139.13..582.1389.7656571432982.975.13..765.932113....956592631847
A5: 4,8                                  # 17 pairs
* PAIR A7: 4,8 COL A
A5: 4,8,6                                # reduction candidate for 4,8
A5: 6 => CTR
* 3...156797.59..4139.13..582.1389.7656571432982.975.13..765.932113....956592631847
A5: 4,8                                  # 17 pairs
* PAIR C8: 4,8 ROW 8
E8: 4,8,2,7                              # reduction candidate for 4,8
E8: 4,8 => SOLVED
* 328415679765928413941376582213894765457163298689752134876549321134287956592631847
E8: 2,7                                  # 18 pairs
F8: 4,8,7                                # reduction candidate for 4,8
F8: 4,8 => CTR
* 3...156797.59284139.1367582.1389.7656571432982.975.13..765.932113..7.956592631847
F8: 7                                    # 18 pairs
* PAIR E7: 4,8 BLK 8
E8: 4,8,2,7                              # reduction candidate for 4,8
E8: 4,8 => SOLVED
* 328415679765928413941376582213894765457163298689752134876549321134287956592631847
E8: 2,7                                  # 18 pairs
F8: 4,8,7                                # reduction candidate for 4,8
F8: 4,8 => CTR
* 3...156797.59284139.1367582.1389.7656571432982.975.13..765.932113..7.956592631847
F8: 7                                    # 18 pairs
* PAIR D8: 2,4 BLK 8
E8: 2,4,7,8                              # reduction candidate for 2,4
E8: 2,4 => CTR
* 38421567972596841396137458241389.765.571.329...975.13..76589321138..7956592631847
E8: 7,8 => SOLVED
* 328415679765928413941376582213894765457163298689752134876549321134287956592631847
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-006-base-pr-000.dot
* REASONING
* DIS # B1: 4,8 => CTR => B1: 2
* PRF # B1: 2 => SOL
* DIS # E2: 8 => CTR => E2: 2,6
* DIS # E3: 4,6 => CTR => E3: 7
* PRF # B1: 2,4 => SOL
* DIS # B1: 8 => CTR => B1: 2,4
* DIS # E2: 6,8 => CTR => E2: 2
* PRF # E2: 2 => SOL
* DIS # A5: 6 => CTR => A5: 4,8
* DIS # B1: 4,8 => CTR => B1: 2
* PRF # B1: 2 => SOL
* PRF # A5: 4,6 => SOL
* DIS # A5: 8 => CTR => A5: 4,6
* DIS # E3: 4,6 => CTR => E3: 7
* DIS # A5: 6 => CTR => A5: 4,8
* DIS # A5: 6 => CTR => A5: 4,8
* PRF # E8: 4,8 => SOL
* DIS # F8: 4,8 => CTR => F8: 7
* PRF # E8: 4,8 => SOL
* DIS # F8: 4,8 => CTR => F8: 7
* DIS # E8: 2,4 => CTR => E8: 7,8
* PRF # E8: 7,8 => SOL
* CNT  22 HDP CHAINS /  33 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A7,B2,B3,B6,C1,C8,D1,D8,E5,E7,F2,F4,F6,I5,I6)
* 3...156797.59..4139.13..582.1389.765.571.329...975.13..765.932113....956592631847
* PAIR C1: 4,8 BLK 1
B1: 4,8,2                                # reduction candidate for 4,8
B1: 4,8 => CTR
* 3.42156797259.8413961374582413892765.5714329828975.13..765.932113.427956592631847
B1: 2 => SOLVED
* 328415679765928413941376582213894765457163298689752134876549321134287956592631847
* DURATION: 0:00:03.090000  START: 02:48:42.156669  END: 02:48:45.246669 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-006-base-pr-001.dot
* REASONING
* DIS # B1: 4,8 => CTR => B1: 2
* PRF B1: 2 => SOL
* STA B1: 2
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 006

solution: 328415679765928413941376582213894765457163298689752134876549321134287956592631847
info: 1306     FNBTWXY  S8.f     40669

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

Solution

position: 328415679765928413941376582213894765457163298689752134876549321134287956592631847 solved
Solution

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:

* DIS # B1: 4,8 => CTR => B1: 2
* PRF # B1: 2 => SOL
* INC # E2: 2,6 => UNS
* DIS # E2: 8 => CTR => E2: 2,6
* DIS # E3: 4,6 => CTR => E3: 7
* INC # E3: 7 => UNS
* INC # F3: 4,6 => UNS
* PRF # B1: 2,4 => SOL
* DIS # B1: 8 => CTR => B1: 2,4
* DIS # E2: 6,8 => CTR => E2: 2
* PRF # E2: 2 => SOL
* INC # A5: 4,8 => UNS
* DIS # A5: 6 => CTR => A5: 4,8
* DIS # B1: 4,8 => CTR => B1: 2
* PRF # B1: 2 => SOL
* PRF # A5: 4,6 => SOL
* DIS # A5: 8 => CTR => A5: 4,6
* DIS # E3: 4,6 => CTR => E3: 7
* INC # E3: 7 => UNS
* INC # A5: 4,8 => UNS
* DIS # A5: 6 => CTR => A5: 4,8
* INC # A5: 4,8 => UNS
* DIS # A5: 6 => CTR => A5: 4,8
* PRF # E8: 4,8 => SOL
* INC # E8: 2,7 => UNS
* DIS # F8: 4,8 => CTR => F8: 7
* INC # F8: 7 => UNS
* PRF # E8: 4,8 => SOL
* INC # E8: 2,7 => UNS
* DIS # F8: 4,8 => CTR => F8: 7
* INC # F8: 7 => UNS
* DIS # E8: 2,4 => CTR => E8: 7,8
* PRF # E8: 7,8 => SOL
* CNT  33 HDP CHAINS /  33 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B1: 4,8 => CTR => B1: 2
* PRF B1: 2 => SOL
* STA B1: 2
* CNT   2 HDP CHAINS /   1 HYP OPENED