Analysis of xx-top500-004-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 72.61.........2..5.......9..15...2.....93...........4.3..8...........1..9........ initial

Autosolve

position: 729615384.3..92.1515.3...92.15..62392.793.5616935218473.185.9265..2.91739.21.3458 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C2: 4,8 => CTR => C2: 6
* PRF # C2: 6 => SOL
* PRF # C2: 4,6 => SOL
* DIS # C2: 8 => CTR => C2: 4,6
* PRF # E3: 4,7 => SOL
* DIS # E3: 8 => CTR => E3: 4,7
* DIS # F3: 4,7 => CTR => F3: 8
* PRF # F3: 8 => SOL
* PRF # E4: 4,8 => SOL
* DIS # E4: 7 => CTR => E4: 4,8
* DIS # B8: 4,8 => CTR => B8: 6
* PRF # B8: 6 => SOL
* DIS # E4: 4,7 => CTR => E4: 8
* PRF # E4: 8 => SOL
* PRF # E4: 4,8 => SOL
* DIS # E4: 7 => CTR => E4: 4,8
* PRF # F3: 4,8 => SOL
* DIS # F3: 7 => CTR => F3: 4,8
* DIS # B8: 4,8 => CTR => B8: 6
* PRF # B8: 6 => SOL
* DIS # C2: 4,8 => CTR => C2: 6
* PRF # C2: 6 => SOL
* DIS # F3: 4,7 => CTR => F3: 8
* PRF # F3: 8 => SOL
* PRF # B8: 4,6 => SOL
* DIS # B8: 8 => CTR => B8: 4,6
* CNT  26 HDP CHAINS /  26 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 # C2: 4,8 => CTR => C2: 6
* PRF C2: 6 => SOL
* STA C2: 6
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

72.61.........2..5.......9..15...2.....93...........4.3..8...........1..9........ initial
729615384.3..92.1515.3...92.15..62392.793.5616935218473.185.9265..2.91739.21.3458 autosolve
729615384836492715154378692415786239287934561693521847341857926568249173972163458 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
A2: 4,8
C3: 4,6
D2: 4,7
G2: 6,7
G3: 6,7
A4: 4,8
B5: 4,8
D4: 4,7
F5: 4,8
B7: 4,7
C8: 4,8
B9: 6,7
F7: 4,7
E8: 4,6
E9: 6,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A4,B5: 4.. / A4 = 4  =>  0 pairs (*) / B5 = 4  =>  0 pairs (X)
F7,E8: 4.. / F7 = 4  =>  0 pairs (X) / E8 = 4  =>  0 pairs (_)
B5,F5: 4.. / B5 = 4  =>  0 pairs (X) / F5 = 4  =>  0 pairs (_)
B7,F7: 4.. / B7 = 4  =>  0 pairs (*) / F7 = 4  =>  0 pairs (X)
A2,A4: 4.. / A2 = 4  =>  0 pairs (X) / A4 = 4  =>  0 pairs (_)
D2,D4: 4.. / D2 = 4  =>  0 pairs (*) / D4 = 4  =>  0 pairs (X)
C2,C3: 6.. / C2 = 6  =>  0 pairs (*) / C3 = 6  =>  0 pairs (X)
G2,G3: 6.. / G2 = 6  =>  0 pairs (X) / G3 = 6  =>  0 pairs (_)
B8,B9: 6.. / B8 = 6  =>  0 pairs (*) / B9 = 6  =>  0 pairs (X)
E8,E9: 6.. / E8 = 6  =>  0 pairs (X) / E9 = 6  =>  0 pairs (_)
C2,G2: 6.. / C2 = 6  =>  0 pairs (*) / G2 = 6  =>  0 pairs (X)
C3,G3: 6.. / C3 = 6  =>  0 pairs (X) / G3 = 6  =>  0 pairs (_)
B8,E8: 6.. / B8 = 6  =>  0 pairs (*) / E8 = 6  =>  0 pairs (X)
B9,E9: 6.. / B9 = 6  =>  0 pairs (X) / E9 = 6  =>  0 pairs (_)
G2,G3: 7.. / G2 = 7  =>  0 pairs (*) / G3 = 7  =>  0 pairs (X)
D4,E4: 7.. / D4 = 7  =>  0 pairs (*) / E4 = 7  =>  0 pairs (X)
B7,B9: 7.. / B7 = 7  =>  0 pairs (X) / B9 = 7  =>  0 pairs (_)
F7,E9: 7.. / F7 = 7  =>  0 pairs (*) / E9 = 7  =>  0 pairs (X)
D2,G2: 7.. / D2 = 7  =>  0 pairs (X) / G2 = 7  =>  0 pairs (_)
B7,F7: 7.. / B7 = 7  =>  0 pairs (X) / F7 = 7  =>  0 pairs (_)
B9,E9: 7.. / B9 = 7  =>  0 pairs (*) / E9 = 7  =>  0 pairs (X)
D2,D4: 7.. / D2 = 7  =>  0 pairs (X) / D4 = 7  =>  0 pairs (_)
F3,F7: 7.. / F3 = 7  =>  0 pairs (X) / F7 = 7  =>  0 pairs (_)
A2,C2: 8.. / A2 = 8  =>  0 pairs (*) / C2 = 8  =>  0 pairs (X)
E3,F3: 8.. / E3 = 8  =>  0 pairs (X) / F3 = 8  =>  0 pairs (_)
A4,B5: 8.. / A4 = 8  =>  0 pairs (X) / B5 = 8  =>  0 pairs (_)
E4,F5: 8.. / E4 = 8  =>  0 pairs (*) / F5 = 8  =>  0 pairs (X)
B8,C8: 8.. / B8 = 8  =>  0 pairs (X) / C8 = 8  =>  0 pairs (_)
A4,E4: 8.. / A4 = 8  =>  0 pairs (X) / E4 = 8  =>  0 pairs (_)
B5,F5: 8.. / B5 = 8  =>  0 pairs (*) / F5 = 8  =>  0 pairs (X)
A2,A4: 8.. / A2 = 8  =>  0 pairs (*) / A4 = 8  =>  0 pairs (X)
B5,B8: 8.. / B5 = 8  =>  0 pairs (*) / B8 = 8  =>  0 pairs (X)
C2,C8: 8.. / C2 = 8  =>  0 pairs (X) / C8 = 8  =>  0 pairs (_)
E3,E4: 8.. / E3 = 8  =>  0 pairs (X) / E4 = 8  =>  0 pairs (_)
F3,F5: 8.. / F3 = 8  =>  0 pairs (*) / F5 = 8  =>  0 pairs (X)
* DURATION: 0:01:09.152032  START: 02:42:52.742070  END: 02:44:01.894102 2017-05-04
* CP COUNT: (35)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B5,B7,B9,C3,C8,D2,D4,E8,E9,F5,F7,G2,G3)
* 729615384.3..92.1515.3...92.15..62392.793.5616935218473.185.9265..2.91739.21.3458
* PAIR A2: 4,8 BLK 1
C2: 4,8,6                                # reduction candidate for 4,8
C2: 4,8 => CTR
* 729615384.34792615156384792.15..62392.793.5616935218473.18579265..249173972163458
C2: 6 => SOLVED
* 729615384836492715154378692415786239287934561693521847341857926568249173972163458
* PAIR C3: 4,6 BLK 1
C2: 4,6,8                                # reduction candidate for 4,6
C2: 4,6 => SOLVED
* 729615384836492715154378692415786239287934561693521847341857926568249173972163458
C2: 8 => CTR
* 729615384.38.926151563..792815..62392479385616935218473.185.9265..2.91739.21.3458
* PAIR D2: 4,7 BLK 2
E3: 4,7,8                                # reduction candidate for 4,7
E3: 4,7 => SOLVED
* 729615384836492715154378692415786239287934561693521847341857926568249173972163458
E3: 8 => CTR
* 729615384.3..92.1515.38..92815..6239247938561693521847371854926584269173962173458
F3: 4,7,8                                # reduction candidate for 4,7
F3: 4,7 => CTR
* 729615384.3..92.1515.38..92815..6239247938561693521847371854926584269173962173458
F3: 8 => SOLVED
* 729615384836492715154378692415786239287934561693521847341857926568249173972163458
* PAIR A4: 4,8 ROW 4
E4: 4,8,7                                # reduction candidate for 4,8
E4: 4,8 => SOLVED
* 729615384836492715154378692415786239287934561693521847341857926568249173972163458
E4: 7 => CTR
* 729615384.3..92.1515.38..928154762392479385616935218473.185.9265..2.91739.21.3458
* PAIR B5: 4,8 COL B
B8: 4,8,6                                # reduction candidate for 4,8
B8: 4,8 => CTR
* 729615384.3..92.1515.3.7692.157.62392.7938561693521847371854926584269173962173458
B8: 6 => SOLVED
* 729615384836492715154378692415786239287934561693521847341857926568249173972163458
* PAIR D4: 4,7 BLK 5
E4: 4,7,8                                # reduction candidate for 4,7
E4: 4,7 => CTR
* 729615384.3..92.1515.38..92815..6239247938561693521847371854926584269173962173458
E4: 8 => SOLVED
* 729615384836492715154378692415786239287934561693521847341857926568249173972163458
* PAIR F5: 4,8 BLK 5
E4: 4,8,7                                # reduction candidate for 4,8
E4: 4,8 => SOLVED
* 729615384836492715154378692415786239287934561693521847341857926568249173972163458
E4: 7 => CTR
* 729615384.3..92.1515.38..928154762392479385616935218473.185.9265..2.91739.21.3458
* PAIR F5: 4,8 COL F
F3: 4,8,7                                # reduction candidate for 4,8
F3: 4,8 => SOLVED
* 729615384836492715154378692415786239287934561693521847341857926568249173972163458
F3: 7 => CTR
* 729615384.3..92.1515.3876928157462392479385616935218473718549265842.91739.21.3458
* PAIR C8: 4,8 BLK 7
B8: 4,8,6                                # reduction candidate for 4,8
B8: 4,8 => CTR
* 729615384.3..92.1515.3.7692.157.62392.7938561693521847371854926584269173962173458
B8: 6 => SOLVED
* 729615384836492715154378692415786239287934561693521847341857926568249173972163458
* PAIR C8: 4,8 COL C
C2: 4,8,6                                # reduction candidate for 4,8
C2: 4,8 => CTR
* 729615384.34792615156384792.15..62392.793.5616935218473.18579265..249173972163458
C2: 6 => SOLVED
* 729615384836492715154378692415786239287934561693521847341857926568249173972163458
* PAIR F7: 4,7 COL F
F3: 4,7,8                                # reduction candidate for 4,7
F3: 4,7 => CTR
* 729615384.3..92.1515.38..92815..6239247938561693521847371854926584269173962173458
F3: 8 => SOLVED
* 729615384836492715154378692415786239287934561693521847341857926568249173972163458
* PAIR E8: 4,6 ROW 8
B8: 4,6,8                                # reduction candidate for 4,6
B8: 4,6 => SOLVED
* 729615384836492715154378692415786239287934561693521847341857926568249173972163458
B8: 8 => CTR
* 729615384438792.1515.3...92.15..62392.793.5616935218473.185.926584269173962173458
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-004-base-pr-000.dot
* REASONING
* DIS # C2: 4,8 => CTR => C2: 6
* PRF # C2: 6 => SOL
* PRF # C2: 4,6 => SOL
* DIS # C2: 8 => CTR => C2: 4,6
* PRF # E3: 4,7 => SOL
* DIS # E3: 8 => CTR => E3: 4,7
* DIS # F3: 4,7 => CTR => F3: 8
* PRF # F3: 8 => SOL
* PRF # E4: 4,8 => SOL
* DIS # E4: 7 => CTR => E4: 4,8
* DIS # B8: 4,8 => CTR => B8: 6
* PRF # B8: 6 => SOL
* DIS # E4: 4,7 => CTR => E4: 8
* PRF # E4: 8 => SOL
* PRF # E4: 4,8 => SOL
* DIS # E4: 7 => CTR => E4: 4,8
* PRF # F3: 4,8 => SOL
* DIS # F3: 7 => CTR => F3: 4,8
* DIS # B8: 4,8 => CTR => B8: 6
* PRF # B8: 6 => SOL
* DIS # C2: 4,8 => CTR => C2: 6
* PRF # C2: 6 => SOL
* DIS # F3: 4,7 => CTR => F3: 8
* PRF # F3: 8 => SOL
* PRF # B8: 4,6 => SOL
* DIS # B8: 8 => CTR => B8: 4,6
* CNT  26 HDP CHAINS /  26 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B5,B7,B9,C3,C8,D2,D4,E8,E9,F5,F7,G2,G3)
* 729615384.3..92.1515.3...92.15..62392.793.5616935218473.185.9265..2.91739.21.3458
* PAIR A2: 4,8 BLK 1
C2: 4,8,6                                # reduction candidate for 4,8
C2: 4,8 => CTR
* 729615384.34792615156384792.15..62392.793.5616935218473.18579265..249173972163458
C2: 6 => SOLVED
* 729615384836492715154378692415786239287934561693521847341857926568249173972163458
* DURATION: 0:00:03.168214  START: 02:44:37.084637  END: 02:44:40.252851 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-004-base-pr-001.dot
* REASONING
* DIS # C2: 4,8 => CTR => C2: 6
* PRF C2: 6 => SOL
* STA C2: 6
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 004

solution: 729615384836492715154378692415786239287934561693521847341857926568249173972163458
info: 1305     FNBWY    S8.f     37567

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

Solution

position: 729615384836492715154378692415786239287934561693521847341857926568249173972163458 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 # C2: 4,8 => CTR => C2: 6
* PRF # C2: 6 => SOL
* PRF # C2: 4,6 => SOL
* DIS # C2: 8 => CTR => C2: 4,6
* PRF # E3: 4,7 => SOL
* DIS # E3: 8 => CTR => E3: 4,7
* DIS # F3: 4,7 => CTR => F3: 8
* PRF # F3: 8 => SOL
* PRF # E4: 4,8 => SOL
* DIS # E4: 7 => CTR => E4: 4,8
* DIS # B8: 4,8 => CTR => B8: 6
* PRF # B8: 6 => SOL
* DIS # E4: 4,7 => CTR => E4: 8
* PRF # E4: 8 => SOL
* PRF # E4: 4,8 => SOL
* DIS # E4: 7 => CTR => E4: 4,8
* PRF # F3: 4,8 => SOL
* DIS # F3: 7 => CTR => F3: 4,8
* DIS # B8: 4,8 => CTR => B8: 6
* PRF # B8: 6 => SOL
* DIS # C2: 4,8 => CTR => C2: 6
* PRF # C2: 6 => SOL
* DIS # F3: 4,7 => CTR => F3: 8
* PRF # F3: 8 => SOL
* PRF # B8: 4,6 => SOL
* DIS # B8: 8 => CTR => B8: 4,6
* CNT  26 HDP CHAINS /  26 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # C2: 4,8 => CTR => C2: 6
* PRF C2: 6 => SOL
* STA C2: 6
* CNT   2 HDP CHAINS /   1 HYP OPENED