Analysis of xx-top500-135-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 7.6.4.2..........13........2......4....1.9......6......1.8......89............53. initial

Autosolve

position: 75634128994826.3.1321.9846.29..831468641.97.313.6.489.6138..9.458943.61.472916538 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # F7: 5,7 => SOL
* DIS # F7: 2 => CTR => F7: 5,7
* PRF # E6: 5,7 => SOL
* DIS # E6: 2 => CTR => E6: 5,7
* PRF # E6: 5,7 => SOL
* DIS # E6: 2 => CTR => E6: 5,7
* DIS # E6: 2,5 => CTR => E6: 7
* PRF # E6: 7 => SOL
* DIS # E6: 2,5 => CTR => E6: 7
* PRF # E6: 7 => SOL
* PRF # F7: 5,7 => SOL
* DIS # F7: 2 => CTR => F7: 5,7
* PRF # E6: 5,7 => SOL
* DIS # E6: 2 => CTR => E6: 5,7
* PRF # F7: 2,7 => SOL
* DIS # F7: 5 => CTR => F7: 2,7
* PRF # F7: 2,7 => SOL
* DIS # F7: 5 => CTR => F7: 2,7
* CNT  18 HDP CHAINS /  18 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # F7: 5,7 => SOL
* STA F7: 5,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

7.6.4.2..........13........2......4....1.9......6......1.8......89............53. initial
75634128994826.3.1321.9846.29..831468641.97.313.6.489.6138..9.458943.61.472916538 autosolve
756341289948265371321798465297583146864129753135674892613857924589432617472916538 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
F2: 5,7
D3: 5,7
H2: 5,7
I3: 5,7
C4: 5,7
C6: 5,7
D4: 5,7
E5: 2,5
H5: 2,5
I6: 2,5
E7: 5,7
F8: 2,7
H7: 2,7
I8: 2,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E5,E6: 2.. / E5 = 2  =>  0 pairs (*) / E6 = 2  =>  0 pairs (X)
H5,I6: 2.. / H5 = 2  =>  0 pairs (X) / I6 = 2  =>  0 pairs (_)
F7,F8: 2.. / F7 = 2  =>  0 pairs (X) / F8 = 2  =>  0 pairs (_)
H7,I8: 2.. / H7 = 2  =>  0 pairs (*) / I8 = 2  =>  0 pairs (X)
E5,H5: 2.. / E5 = 2  =>  0 pairs (*) / H5 = 2  =>  0 pairs (X)
E6,I6: 2.. / E6 = 2  =>  0 pairs (X) / I6 = 2  =>  0 pairs (_)
F7,H7: 2.. / F7 = 2  =>  0 pairs (X) / H7 = 2  =>  0 pairs (_)
F8,I8: 2.. / F8 = 2  =>  0 pairs (*) / I8 = 2  =>  0 pairs (X)
H5,H7: 2.. / H5 = 2  =>  0 pairs (X) / H7 = 2  =>  0 pairs (_)
I6,I8: 2.. / I6 = 2  =>  0 pairs (*) / I8 = 2  =>  0 pairs (X)
F2,D3: 5.. / F2 = 5  =>  0 pairs (*) / D3 = 5  =>  0 pairs (X)
H2,I3: 5.. / H2 = 5  =>  0 pairs (X) / I3 = 5  =>  0 pairs (_)
C4,C6: 5.. / C4 = 5  =>  0 pairs (X) / C6 = 5  =>  0 pairs (_)
H5,I6: 5.. / H5 = 5  =>  0 pairs (*) / I6 = 5  =>  0 pairs (X)
E7,F7: 5.. / E7 = 5  =>  0 pairs (*) / F7 = 5  =>  0 pairs (X)
F2,H2: 5.. / F2 = 5  =>  0 pairs (*) / H2 = 5  =>  0 pairs (X)
D3,I3: 5.. / D3 = 5  =>  0 pairs (X) / I3 = 5  =>  0 pairs (_)
C4,D4: 5.. / C4 = 5  =>  0 pairs (X) / D4 = 5  =>  0 pairs (_)
E5,H5: 5.. / E5 = 5  =>  0 pairs (X) / H5 = 5  =>  0 pairs (_)
D3,D4: 5.. / D3 = 5  =>  0 pairs (X) / D4 = 5  =>  0 pairs (_)
F2,F7: 5.. / F2 = 5  =>  0 pairs (*) / F7 = 5  =>  0 pairs (X)
H2,H5: 5.. / H2 = 5  =>  0 pairs (X) / H5 = 5  =>  0 pairs (_)
I3,I6: 5.. / I3 = 5  =>  0 pairs (*) / I6 = 5  =>  0 pairs (X)
F2,D3: 7.. / F2 = 7  =>  0 pairs (X) / D3 = 7  =>  0 pairs (_)
H2,I3: 7.. / H2 = 7  =>  0 pairs (*) / I3 = 7  =>  0 pairs (X)
C4,C6: 7.. / C4 = 7  =>  0 pairs (*) / C6 = 7  =>  0 pairs (X)
D4,E6: 7.. / D4 = 7  =>  0 pairs (X) / E6 = 7  =>  0 pairs (_)
H7,I8: 7.. / H7 = 7  =>  0 pairs (X) / I8 = 7  =>  0 pairs (_)
F2,H2: 7.. / F2 = 7  =>  0 pairs (X) / H2 = 7  =>  0 pairs (_)
D3,I3: 7.. / D3 = 7  =>  0 pairs (*) / I3 = 7  =>  0 pairs (X)
C4,D4: 7.. / C4 = 7  =>  0 pairs (*) / D4 = 7  =>  0 pairs (X)
C6,E6: 7.. / C6 = 7  =>  0 pairs (X) / E6 = 7  =>  0 pairs (_)
F8,I8: 7.. / F8 = 7  =>  0 pairs (X) / I8 = 7  =>  0 pairs (_)
D3,D4: 7.. / D3 = 7  =>  0 pairs (*) / D4 = 7  =>  0 pairs (X)
E6,E7: 7.. / E6 = 7  =>  0 pairs (*) / E7 = 7  =>  0 pairs (X)
H2,H7: 7.. / H2 = 7  =>  0 pairs (*) / H7 = 7  =>  0 pairs (X)
I3,I8: 7.. / I3 = 7  =>  0 pairs (X) / I8 = 7  =>  0 pairs (_)
* DURATION: 0:01:03.279883  START: 07:21:41.125379  END: 07:22:44.405262 2017-05-04
* CP COUNT: (37)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C4,C6,D3,D4,E5,E7,F2,F8,H2,H5,H7,I3,I6,I8)
* 75634128994826.3.1321.9846.29..831468641.97.313.6.489.6138..9.458943.61.472916538
* PAIR F2: 5,7 COL F
F7: 5,7,2                                # reduction candidate for 5,7
F7: 5,7 => SOLVED
* 756341289948265371321798465297583146864129753135674892613857924589432617472916538
F7: 2 => CTR
* 7563412899482653713217984652975831468641297.313.6.489.6138..9.458943.61.472916538
* PAIR C6: 5,7 ROW 6
E6: 5,7,2                                # reduction candidate for 5,7
E6: 5,7 => SOLVED
* 756341289948265371321798465297583146864129753135674892613857924589432617472916538
E6: 2 => CTR
* 75634128994826.3.1321.9846.29.78314686415972313762489561387.9.458943.61.472916538
* PAIR D4: 5,7 BLK 5
E6: 5,7,2                                # reduction candidate for 5,7
E6: 5,7 => SOLVED
* 756341289948265371321798465297583146864129753135674892613857924589432617472916538
E6: 2 => CTR
* 75634128994826.3.1321.9846.29.78314686415972313762489561387.9.458943.61.472916538
* PAIR E5: 2,5 BLK 5
E6: 2,5,7                                # reduction candidate for 2,5
E6: 2,5 => CTR
* 75634128994826.3.1321.9846.29.7831468641.97.31376.489.61387592458943.61.472916538
E6: 7 => SOLVED
* 756341289948265371321798465297583146864129753135674892613857924589432617472916538
* PAIR I6: 2,5 ROW 6
E6: 2,5,7                                # reduction candidate for 2,5
E6: 2,5 => CTR
* 75634128994826.3.1321.9846.29.7831468641.97.31376.489.61387592458943.61.472916538
E6: 7 => SOLVED
* 756341289948265371321798465297583146864129753135674892613857924589432617472916538
* PAIR E7: 5,7 BLK 8
F7: 5,7,2                                # reduction candidate for 5,7
F7: 5,7 => SOLVED
* 756341289948265371321798465297583146864129753135674892613857924589432617472916538
F7: 2 => CTR
* 7563412899482653713217984652975831468641297.313.6.489.6138..9.458943.61.472916538
* PAIR E7: 5,7 COL E
E6: 5,7,2                                # reduction candidate for 5,7
E6: 5,7 => SOLVED
* 756341289948265371321798465297583146864129753135674892613857924589432617472916538
E6: 2 => CTR
* 75634128994826.3.1321.9846.29.78314686415972313762489561387.9.458943.61.472916538
* PAIR F8: 2,7 BLK 8
F7: 2,7,5                                # reduction candidate for 2,7
F7: 2,7 => SOLVED
* 756341289948265371321798465297583146864129753135674892613857924589432617472916538
F7: 5 => CTR
* 75634128994826.3.1321.9846.29..831468641.97.313.6.489.6138.5924589432617472916538
* PAIR H7: 2,7 ROW 7
F7: 2,7,5                                # reduction candidate for 2,7
F7: 2,7 => SOLVED
* 756341289948265371321798465297583146864129753135674892613857924589432617472916538
F7: 5 => CTR
* 75634128994826.3.1321.9846.29..831468641.97.313.6.489.6138.5924589432617472916538
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-135-base-pr-000.dot
* REASONING
* PRF # F7: 5,7 => SOL
* DIS # F7: 2 => CTR => F7: 5,7
* PRF # E6: 5,7 => SOL
* DIS # E6: 2 => CTR => E6: 5,7
* PRF # E6: 5,7 => SOL
* DIS # E6: 2 => CTR => E6: 5,7
* DIS # E6: 2,5 => CTR => E6: 7
* PRF # E6: 7 => SOL
* DIS # E6: 2,5 => CTR => E6: 7
* PRF # E6: 7 => SOL
* PRF # F7: 5,7 => SOL
* DIS # F7: 2 => CTR => F7: 5,7
* PRF # E6: 5,7 => SOL
* DIS # E6: 2 => CTR => E6: 5,7
* PRF # F7: 2,7 => SOL
* DIS # F7: 5 => CTR => F7: 2,7
* PRF # F7: 2,7 => SOL
* DIS # F7: 5 => CTR => F7: 2,7
* CNT  18 HDP CHAINS /  18 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C4,C6,D3,D4,E5,E7,F2,F8,H2,H5,H7,I3,I6,I8)
* 75634128994826.3.1321.9846.29..831468641.97.313.6.489.6138..9.458943.61.472916538
* PAIR F2: 5,7 COL F
F7: 5,7,2                                # reduction candidate for 5,7
F7: 5,7 => SOLVED
* 756341289948265371321798465297583146864129753135674892613857924589432617472916538
* DURATION: 0:00:01.920241  START: 07:23:05.242506  END: 07:23:07.162747 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-135-base-pr-001.dot
* REASONING
* PRF # F7: 5,7 => SOL
* STA F7: 5,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 135

solution: 756341289948265371321798465297583146864129753135674892613857924589432617472916538
info: 1812     FNBWX    S8.f     37411

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

Solution

position: 756341289948265371321798465297583146864129753135674892613857924589432617472916538 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:

* PRF # F7: 5,7 => SOL
* DIS # F7: 2 => CTR => F7: 5,7
* PRF # E6: 5,7 => SOL
* DIS # E6: 2 => CTR => E6: 5,7
* PRF # E6: 5,7 => SOL
* DIS # E6: 2 => CTR => E6: 5,7
* DIS # E6: 2,5 => CTR => E6: 7
* PRF # E6: 7 => SOL
* DIS # E6: 2,5 => CTR => E6: 7
* PRF # E6: 7 => SOL
* PRF # F7: 5,7 => SOL
* DIS # F7: 2 => CTR => F7: 5,7
* PRF # E6: 5,7 => SOL
* DIS # E6: 2 => CTR => E6: 5,7
* PRF # F7: 2,7 => SOL
* DIS # F7: 5 => CTR => F7: 2,7
* PRF # F7: 2,7 => SOL
* DIS # F7: 5 => CTR => F7: 2,7
* CNT  18 HDP CHAINS /  18 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # F7: 5,7 => SOL
* STA F7: 5,7
* CNT   1 HDP CHAINS /   1 HYP OPENED