Analysis of xx-top500-175-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 3.....56....7.1....4.......2......815.7.3..............814.........5.3........... initial

Autosolve

position: 31928456782576143974639512823457..815.71382..1.8.42753.81423.75.7285.31..53.178.2 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A8: 6,9 => SOL
* DIS # A8: 4 => CTR => A8: 6,9
* DIS # A9: 6,9 => CTR => A9: 4
* PRF # A9: 4 => SOL
* PRF # A8: 6,9 => SOL
* DIS # A8: 4 => CTR => A8: 6,9
* DIS # A9: 6,9 => CTR => A9: 4
* PRF # A9: 4 => SOL
* PRF # A8: 4,6 => SOL
* DIS # A8: 9 => CTR => A8: 4,6
* PRF # A9: 4,9 => SOL
* DIS # A9: 6 => CTR => A9: 4,9
* CNT  12 HDP CHAINS /  12 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 # A8: 6,9 => SOL
* STA A8: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

3.....56....7.1....4.......2......815.7.3..............814.........5.3........... initial
31928456782576143974639512823457..815.71382..1.8.42753.81423.75.7285.31..53.178.2 autosolve
319284567825761439746395128234576981597138246168942753981423675672859314453617892 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
B5: 6,9
B6: 6,9
F4: 6,9
D6: 6,9
G4: 6,9
H5: 4,9
I5: 4,6
A7: 6,9
F8: 6,9
D9: 6,9
G7: 6,9
I8: 4,6
H9: 4,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H5,I5: 4.. / H5 = 4  =>  0 pairs (*) / I5 = 4  =>  0 pairs (X)
A8,A9: 4.. / A8 = 4  =>  0 pairs (X) / A9 = 4  =>  0 pairs (_)
I8,H9: 4.. / I8 = 4  =>  0 pairs (*) / H9 = 4  =>  0 pairs (X)
A8,I8: 4.. / A8 = 4  =>  0 pairs (X) / I8 = 4  =>  0 pairs (_)
A9,H9: 4.. / A9 = 4  =>  0 pairs (*) / H9 = 4  =>  0 pairs (X)
H5,H9: 4.. / H5 = 4  =>  0 pairs (*) / H9 = 4  =>  0 pairs (X)
I5,I8: 4.. / I5 = 4  =>  0 pairs (X) / I8 = 4  =>  0 pairs (_)
B5,B6: 6.. / B5 = 6  =>  0 pairs (X) / B6 = 6  =>  0 pairs (_)
F4,D6: 6.. / F4 = 6  =>  0 pairs (*) / D6 = 6  =>  0 pairs (X)
G4,I5: 6.. / G4 = 6  =>  0 pairs (X) / I5 = 6  =>  0 pairs (_)
F8,D9: 6.. / F8 = 6  =>  0 pairs (X) / D9 = 6  =>  0 pairs (_)
G7,I8: 6.. / G7 = 6  =>  0 pairs (*) / I8 = 6  =>  0 pairs (X)
F4,G4: 6.. / F4 = 6  =>  0 pairs (*) / G4 = 6  =>  0 pairs (X)
B5,I5: 6.. / B5 = 6  =>  0 pairs (X) / I5 = 6  =>  0 pairs (_)
B6,D6: 6.. / B6 = 6  =>  0 pairs (*) / D6 = 6  =>  0 pairs (X)
A7,G7: 6.. / A7 = 6  =>  0 pairs (X) / G7 = 6  =>  0 pairs (_)
A9,D9: 6.. / A9 = 6  =>  0 pairs (X) / D9 = 6  =>  0 pairs (_)
D6,D9: 6.. / D6 = 6  =>  0 pairs (X) / D9 = 6  =>  0 pairs (_)
F4,F8: 6.. / F4 = 6  =>  0 pairs (*) / F8 = 6  =>  0 pairs (X)
G4,G7: 6.. / G4 = 6  =>  0 pairs (X) / G7 = 6  =>  0 pairs (_)
I5,I8: 6.. / I5 = 6  =>  0 pairs (*) / I8 = 6  =>  0 pairs (X)
B5,B6: 9.. / B5 = 9  =>  0 pairs (*) / B6 = 9  =>  0 pairs (X)
F4,D6: 9.. / F4 = 9  =>  0 pairs (X) / D6 = 9  =>  0 pairs (_)
G4,H5: 9.. / G4 = 9  =>  0 pairs (*) / H5 = 9  =>  0 pairs (X)
F8,D9: 9.. / F8 = 9  =>  0 pairs (*) / D9 = 9  =>  0 pairs (X)
G7,H9: 9.. / G7 = 9  =>  0 pairs (X) / H9 = 9  =>  0 pairs (_)
F4,G4: 9.. / F4 = 9  =>  0 pairs (X) / G4 = 9  =>  0 pairs (_)
B5,H5: 9.. / B5 = 9  =>  0 pairs (*) / H5 = 9  =>  0 pairs (X)
B6,D6: 9.. / B6 = 9  =>  0 pairs (X) / D6 = 9  =>  0 pairs (_)
A7,G7: 9.. / A7 = 9  =>  0 pairs (*) / G7 = 9  =>  0 pairs (X)
A8,F8: 9.. / A8 = 9  =>  0 pairs (X) / F8 = 9  =>  0 pairs (_)
D6,D9: 9.. / D6 = 9  =>  0 pairs (*) / D9 = 9  =>  0 pairs (X)
F4,F8: 9.. / F4 = 9  =>  0 pairs (X) / F8 = 9  =>  0 pairs (_)
G4,G7: 9.. / G4 = 9  =>  0 pairs (*) / G7 = 9  =>  0 pairs (X)
H5,H9: 9.. / H5 = 9  =>  0 pairs (X) / H9 = 9  =>  0 pairs (_)
* DURATION: 0:01:03.273762  START: 08:41:23.696240  END: 08:42:26.970002 2017-05-04
* CP COUNT: (35)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B5,B6,D6,D9,F4,F8,G4,G7,H5,H9,I5,I8)
* 31928456782576143974639512823457..815.71382..1.8.42753.81423.75.7285.31..53.178.2
* PAIR A7: 6,9 BLK 7
A8: 6,9,4                                # reduction candidate for 6,9
A8: 6,9 => SOLVED
* 319284567825761439746395128234576981597138246168942753981423675672859314453617892
A8: 4 => CTR
* 31928456782576143974639512823457..815.71382..1.8.42753.81423.75472859316.53617842
A9: 6,9,4                                # reduction candidate for 6,9
A9: 6,9 => CTR
* 31928456782576143974639512823457..815.71382..1.8.42753.81423.75472859316.53617842
A9: 4 => SOLVED
* 319284567825761439746395128234576981597138246168942753981423675672859314453617892
* PAIR F8: 6,9 ROW 8
A8: 6,9,4                                # reduction candidate for 6,9
A8: 6,9 => SOLVED
* 319284567825761439746395128234576981597138246168942753981423675672859314453617892
A8: 4 => CTR
* 31928456782576143974639512823457..815.71382..1.8.42753.81423.75472859316.53617842
* PAIR D9: 6,9 ROW 9
A9: 6,9,4                                # reduction candidate for 6,9
A9: 6,9 => CTR
* 31928456782576143974639512823457..815.71382..1.8.42753.81423.75472859316.53617842
A9: 4 => SOLVED
* 319284567825761439746395128234576981597138246168942753981423675672859314453617892
* PAIR I8: 4,6 ROW 8
A8: 4,6,9                                # reduction candidate for 4,6
A8: 4,6 => SOLVED
* 319284567825761439746395128234576981597138246168942753981423675672859314453617892
A8: 9 => CTR
* 31928456782576143974639512823457..815.71382..1.8.42753.81423.75972856314.53.178.2
* PAIR H9: 4,9 ROW 9
A9: 4,9,6                                # reduction candidate for 4,9
A9: 4,9 => SOLVED
* 319284567825761439746395128234576981597138246168942753981423675672859314453617892
A9: 6 => CTR
* 31928456782576143974639512823457..815.71382..1.8.42753.81423.75472859316.53.178.2
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-175-base-pr-000.dot
* REASONING
* PRF # A8: 6,9 => SOL
* DIS # A8: 4 => CTR => A8: 6,9
* DIS # A9: 6,9 => CTR => A9: 4
* PRF # A9: 4 => SOL
* PRF # A8: 6,9 => SOL
* DIS # A8: 4 => CTR => A8: 6,9
* DIS # A9: 6,9 => CTR => A9: 4
* PRF # A9: 4 => SOL
* PRF # A8: 4,6 => SOL
* DIS # A8: 9 => CTR => A8: 4,6
* PRF # A9: 4,9 => SOL
* DIS # A9: 6 => CTR => A9: 4,9
* CNT  12 HDP CHAINS /  12 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B5,B6,D6,D9,F4,F8,G4,G7,H5,H9,I5,I8)
* 31928456782576143974639512823457..815.71382..1.8.42753.81423.75.7285.31..53.178.2
* PAIR A7: 6,9 BLK 7
A8: 6,9,4                                # reduction candidate for 6,9
A8: 6,9 => SOLVED
* 319284567825761439746395128234576981597138246168942753981423675672859314453617892
* DURATION: 0:00:02.085842  START: 08:42:42.508550  END: 08:42:44.594392 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-175-base-pr-001.dot
* REASONING
* PRF # A8: 6,9 => SOL
* STA A8: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 175

solution: 319284567825761439746395128234576981597138246168942753981423675672859314453617892
info: 1827     FNTWX    S8.f     28928

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

Solution

position: 319284567825761439746395128234576981597138246168942753981423675672859314453617892 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 # A8: 6,9 => SOL
* DIS # A8: 4 => CTR => A8: 6,9
* DIS # A9: 6,9 => CTR => A9: 4
* PRF # A9: 4 => SOL
* PRF # A8: 6,9 => SOL
* DIS # A8: 4 => CTR => A8: 6,9
* DIS # A9: 6,9 => CTR => A9: 4
* PRF # A9: 4 => SOL
* PRF # A8: 4,6 => SOL
* DIS # A8: 9 => CTR => A8: 4,6
* PRF # A9: 4,9 => SOL
* DIS # A9: 6 => CTR => A9: 4,9
* CNT  12 HDP CHAINS /  12 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # A8: 6,9 => SOL
* STA A8: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED