Analysis of xx-top500-309-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ......613...54...........7..5.9..2..3.1...............7...31....8....5.9......... initial

Autosolve

position: 5..2..613613547982.2.316475.5.9.32.13.1...798...1..35.795.3182.18.7..539.3.8..1.7 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # B6: 4,7 => SOL
* DIS # B6: 6 => CTR => B6: 4,7
* PRF # C4: 4,7 => SOL
* DIS # C4: 8 => CTR => C4: 4,7
* DIS # C4: 4,8 => CTR => C4: 7
* PRF # C4: 7 => SOL
* PRF # B6: 4,6 => SOL
* DIS # B6: 7 => CTR => B6: 4,6
* PRF # E6: 6,7 => SOL
* DIS # E6: 8 => CTR => E6: 6,7
* PRF # B6: 4,6 => SOL
* DIS # B6: 7 => CTR => B6: 4,6
* DIS # C9: 4,6 => CTR => C9: 2
* PRF # C9: 2 => SOL
* PRF # C9: 2,4 => SOL
* DIS # C9: 6 => CTR => C9: 2,4
* DIS # C9: 4,6 => CTR => C9: 2
* PRF # C9: 2 => SOL
* 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 # B6: 4,7 => SOL
* STA B6: 4,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

......613...54...........7..5.9..2..3.1...............7...31....8....5.9......... initial
5..2..613613547982.2.316475.5.9.32.13.1...798...1..35.795.3182.18.7..539.3.8..1.7 autosolve
574289613613547982928316475857963241361452798249178356795631824186724539432895167 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (26)
B1: 4,7
C1: 4,7
A3: 8,9
C3: 8,9
E1: 8,9
F1: 8,9
A4: 4,8
B5: 4,6
A6: 2,9
C6: 2,9
E4: 6,7
D5: 4,6
E5: 2,5
F5: 2,5
F6: 4,8
H4: 4,6
I6: 4,6
C8: 4,6
A9: 2,4
D7: 4,6
E8: 2,6
F8: 2,4
E9: 5,9
F9: 5,9
I7: 4,6
H9: 4,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A6,C6: 2.. / A6 = 2  =>  0 pairs (*) / C6 = 2  =>  0 pairs (X)
E5,F5: 2.. / E5 = 2  =>  0 pairs (X) / F5 = 2  =>  0 pairs (_)
A9,C9: 2.. / A9 = 2  =>  0 pairs (X) / C9 = 2  =>  0 pairs (_)
E8,F8: 2.. / E8 = 2  =>  0 pairs (*) / F8 = 2  =>  0 pairs (X)
A6,A9: 2.. / A6 = 2  =>  0 pairs (*) / A9 = 2  =>  0 pairs (X)
C6,C9: 2.. / C6 = 2  =>  0 pairs (X) / C9 = 2  =>  0 pairs (_)
E5,E8: 2.. / E5 = 2  =>  0 pairs (X) / E8 = 2  =>  0 pairs (_)
F5,F8: 2.. / F5 = 2  =>  0 pairs (*) / F8 = 2  =>  0 pairs (X)
B1,C1: 4.. / B1 = 4  =>  0 pairs (X) / C1 = 4  =>  0 pairs (_)
D5,F6: 4.. / D5 = 4  =>  0 pairs (*) / F6 = 4  =>  0 pairs (X)
H4,I6: 4.. / H4 = 4  =>  0 pairs (*) / I6 = 4  =>  0 pairs (X)
D7,F8: 4.. / D7 = 4  =>  0 pairs (X) / F8 = 4  =>  0 pairs (_)
I7,H9: 4.. / I7 = 4  =>  0 pairs (*) / H9 = 4  =>  0 pairs (X)
B5,D5: 4.. / B5 = 4  =>  0 pairs (X) / D5 = 4  =>  0 pairs (_)
D7,I7: 4.. / D7 = 4  =>  0 pairs (X) / I7 = 4  =>  0 pairs (_)
C8,F8: 4.. / C8 = 4  =>  0 pairs (X) / F8 = 4  =>  0 pairs (_)
A4,A9: 4.. / A4 = 4  =>  0 pairs (X) / A9 = 4  =>  0 pairs (_)
D5,D7: 4.. / D5 = 4  =>  0 pairs (*) / D7 = 4  =>  0 pairs (X)
F6,F8: 4.. / F6 = 4  =>  0 pairs (X) / F8 = 4  =>  0 pairs (_)
H4,H9: 4.. / H4 = 4  =>  0 pairs (*) / H9 = 4  =>  0 pairs (X)
I6,I7: 4.. / I6 = 4  =>  0 pairs (X) / I7 = 4  =>  0 pairs (_)
E5,F5: 5.. / E5 = 5  =>  0 pairs (*) / F5 = 5  =>  0 pairs (X)
E9,F9: 5.. / E9 = 5  =>  0 pairs (X) / F9 = 5  =>  0 pairs (_)
E5,E9: 5.. / E5 = 5  =>  0 pairs (*) / E9 = 5  =>  0 pairs (X)
F5,F9: 5.. / F5 = 5  =>  0 pairs (X) / F9 = 5  =>  0 pairs (_)
B5,B6: 6.. / B5 = 6  =>  0 pairs (*) / B6 = 6  =>  0 pairs (X)
H4,I6: 6.. / H4 = 6  =>  0 pairs (X) / I6 = 6  =>  0 pairs (_)
C8,C9: 6.. / C8 = 6  =>  0 pairs (*) / C9 = 6  =>  0 pairs (X)
D7,E8: 6.. / D7 = 6  =>  0 pairs (*) / E8 = 6  =>  0 pairs (X)
I7,H9: 6.. / I7 = 6  =>  0 pairs (X) / H9 = 6  =>  0 pairs (_)
E4,H4: 6.. / E4 = 6  =>  0 pairs (*) / H4 = 6  =>  0 pairs (X)
B5,D5: 6.. / B5 = 6  =>  0 pairs (*) / D5 = 6  =>  0 pairs (X)
D7,I7: 6.. / D7 = 6  =>  0 pairs (*) / I7 = 6  =>  0 pairs (X)
C8,E8: 6.. / C8 = 6  =>  0 pairs (*) / E8 = 6  =>  0 pairs (X)
C9,H9: 6.. / C9 = 6  =>  0 pairs (X) / H9 = 6  =>  0 pairs (_)
D5,D7: 6.. / D5 = 6  =>  0 pairs (X) / D7 = 6  =>  0 pairs (_)
H4,H9: 6.. / H4 = 6  =>  0 pairs (X) / H9 = 6  =>  0 pairs (_)
I6,I7: 6.. / I6 = 6  =>  0 pairs (*) / I7 = 6  =>  0 pairs (X)
B1,C1: 7.. / B1 = 7  =>  0 pairs (*) / C1 = 7  =>  0 pairs (X)
C4,B6: 7.. / C4 = 7  =>  0 pairs (*) / B6 = 7  =>  0 pairs (X)
E4,E6: 7.. / E4 = 7  =>  0 pairs (X) / E6 = 7  =>  0 pairs (_)
C4,E4: 7.. / C4 = 7  =>  0 pairs (*) / E4 = 7  =>  0 pairs (X)
B6,E6: 7.. / B6 = 7  =>  0 pairs (X) / E6 = 7  =>  0 pairs (_)
B1,B6: 7.. / B1 = 7  =>  0 pairs (*) / B6 = 7  =>  0 pairs (X)
C1,C4: 7.. / C1 = 7  =>  0 pairs (X) / C4 = 7  =>  0 pairs (_)
A3,C3: 8.. / A3 = 8  =>  0 pairs (X) / C3 = 8  =>  0 pairs (_)
E1,F1: 8.. / E1 = 8  =>  0 pairs (*) / F1 = 8  =>  0 pairs (X)
A4,C4: 8.. / A4 = 8  =>  0 pairs (*) / C4 = 8  =>  0 pairs (X)
E6,F6: 8.. / E6 = 8  =>  0 pairs (X) / F6 = 8  =>  0 pairs (_)
A3,A4: 8.. / A3 = 8  =>  0 pairs (X) / A4 = 8  =>  0 pairs (_)
C3,C4: 8.. / C3 = 8  =>  0 pairs (*) / C4 = 8  =>  0 pairs (X)
E1,E6: 8.. / E1 = 8  =>  0 pairs (*) / E6 = 8  =>  0 pairs (X)
F1,F6: 8.. / F1 = 8  =>  0 pairs (X) / F6 = 8  =>  0 pairs (_)
A3,C3: 9.. / A3 = 9  =>  0 pairs (*) / C3 = 9  =>  0 pairs (X)
E1,F1: 9.. / E1 = 9  =>  0 pairs (X) / F1 = 9  =>  0 pairs (_)
A6,C6: 9.. / A6 = 9  =>  0 pairs (X) / C6 = 9  =>  0 pairs (_)
E9,F9: 9.. / E9 = 9  =>  0 pairs (*) / F9 = 9  =>  0 pairs (X)
A3,A6: 9.. / A3 = 9  =>  0 pairs (*) / A6 = 9  =>  0 pairs (X)
C3,C6: 9.. / C3 = 9  =>  0 pairs (X) / C6 = 9  =>  0 pairs (_)
E1,E9: 9.. / E1 = 9  =>  0 pairs (X) / E9 = 9  =>  0 pairs (_)
F1,F9: 9.. / F1 = 9  =>  0 pairs (*) / F9 = 9  =>  0 pairs (X)
* DURATION: 0:02:16.230547  START: 13:31:50.201395  END: 13:34:06.431942 2017-05-04
* CP COUNT: (61)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A6,A9,B1,B5,C1,C3,C6,C8,D5,D7,E1,E4,E5,E8,E9,F1,F5,F6,F8,F9,H4,H9,I6,I7)
* 5..2..613613547982.2.316475.5.9.32.13.1...798...1..35.795.3182.18.7..539.3.8..1.7
* PAIR B1: 4,7 COL B
B6: 4,7,6                                # reduction candidate for 4,7
B6: 4,7 => SOLVED
* 574289613613547982928316475857963241361452798249178356795631824186724539432895167
B6: 6 => CTR
* 5742..613613547982.2.316475.579632413.1...798...1..35.795.3182.18.7..539.3.8..1.7
* PAIR C1: 4,7 COL C
C4: 4,7,8                                # reduction candidate for 4,7
C4: 4,7 => SOLVED
* 574289613613547982928316475857963241361452798249178356795631824186724539432895167
C4: 8 => CTR
* 5.72..613613547982.2.316475.589732613.1...798.7.168354795.3182.18.7..539.3.8..1.7
* PAIR A4: 4,8 BLK 4
C4: 4,8,7                                # reduction candidate for 4,8
C4: 4,8 => CTR
* 5.72..613613547982.2.316475.5.9732613.1...798.7.168354795.3182.18.7..539.3.8..1.7
C4: 7 => SOLVED
* 574289613613547982928316475857963241361452798249178356795631824186724539432895167
* PAIR B5: 4,6 BLK 4
B6: 4,6,7                                # reduction candidate for 4,6
B6: 4,6 => SOLVED
* 574289613613547982928316475857963241361452798249178356795631824186724539432895167
B6: 7 => CTR
* 5..2..613613547982.2.316475.5.9.32.13614..798.7.1.835479563182.18.7..539.3.8..1.7
* PAIR E4: 6,7 BLK 5
E6: 6,7,8                                # reduction candidate for 6,7
E6: 6,7 => SOLVED
* 574289613613547982928316475857963241361452798249178356795631824186724539432895167
E6: 8 => CTR
* 5..2..613613547982.2.316475.5.9732613.16..798...1..35.795.3182.18.7..539.3.8..1.7
* PAIR I6: 4,6 ROW 6
B6: 4,6,7                                # reduction candidate for 4,6
B6: 4,6 => SOLVED
* 574289613613547982928316475857963241361452798249178356795631824186724539432895167
B6: 7 => CTR
* 5..2..613613547982.2.316475.5.9.32.13614..798.7.1.835479563182.18.7..539.3.8..1.7
* PAIR C8: 4,6 BLK 7
C9: 4,6,2                                # reduction candidate for 4,6
C9: 4,6 => CTR
* 5..2..613613547982.293164754589732613614..798972168354795.3182.18.7..53923.8..1.7
C9: 2 => SOLVED
* 574289613613547982928316475857963241361452798249178356795631824186724539432895167
* PAIR A9: 2,4 BLK 7
C9: 2,4,6                                # reduction candidate for 2,4
C9: 2,4 => SOLVED
* 574289613613547982928316475857963241361452798249178356795631824186724539432895167
C9: 6 => CTR
* 5..2..613613547982.293164754589732613614..798..21..35.795.3182.18.7..5392368..147
* PAIR H9: 4,6 ROW 9
C9: 4,6,2                                # reduction candidate for 4,6
C9: 4,6 => CTR
* 5..2..613613547982.293164754589732613614..798972168354795.3182.18.7..53923.8..1.7
C9: 2 => SOLVED
* 574289613613547982928316475857963241361452798249178356795631824186724539432895167
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-309-base-pr-000.dot
* REASONING
* PRF # B6: 4,7 => SOL
* DIS # B6: 6 => CTR => B6: 4,7
* PRF # C4: 4,7 => SOL
* DIS # C4: 8 => CTR => C4: 4,7
* DIS # C4: 4,8 => CTR => C4: 7
* PRF # C4: 7 => SOL
* PRF # B6: 4,6 => SOL
* DIS # B6: 7 => CTR => B6: 4,6
* PRF # E6: 6,7 => SOL
* DIS # E6: 8 => CTR => E6: 6,7
* PRF # B6: 4,6 => SOL
* DIS # B6: 7 => CTR => B6: 4,6
* DIS # C9: 4,6 => CTR => C9: 2
* PRF # C9: 2 => SOL
* PRF # C9: 2,4 => SOL
* DIS # C9: 6 => CTR => C9: 2,4
* DIS # C9: 4,6 => CTR => C9: 2
* PRF # C9: 2 => SOL
* CNT  18 HDP CHAINS /  18 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A6,A9,B1,B5,C1,C3,C6,C8,D5,D7,E1,E4,E5,E8,E9,F1,F5,F6,F8,F9,H4,H9,I6,I7)
* 5..2..613613547982.2.316475.5.9.32.13.1...798...1..35.795.3182.18.7..539.3.8..1.7
* PAIR B1: 4,7 COL B
B6: 4,7,6                                # reduction candidate for 4,7
B6: 4,7 => SOLVED
* 574289613613547982928316475857963241361452798249178356795631824186724539432895167
* DURATION: 0:00:02.498060  START: 13:34:34.944086  END: 13:34:37.442146 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-309-base-pr-001.dot
* REASONING
* PRF # B6: 4,7 => SOL
* STA B6: 4,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 309

solution: 574289613613547982928316475857963241361452798249178356795631824186724539432895167
info: 2729     FNBTHWX  S8.f     1487

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

Solution

position: 574289613613547982928316475857963241361452798249178356795631824186724539432895167 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 # B6: 4,7 => SOL
* DIS # B6: 6 => CTR => B6: 4,7
* PRF # C4: 4,7 => SOL
* DIS # C4: 8 => CTR => C4: 4,7
* DIS # C4: 4,8 => CTR => C4: 7
* PRF # C4: 7 => SOL
* PRF # B6: 4,6 => SOL
* DIS # B6: 7 => CTR => B6: 4,6
* PRF # E6: 6,7 => SOL
* DIS # E6: 8 => CTR => E6: 6,7
* PRF # B6: 4,6 => SOL
* DIS # B6: 7 => CTR => B6: 4,6
* DIS # C9: 4,6 => CTR => C9: 2
* PRF # C9: 2 => SOL
* PRF # C9: 2,4 => SOL
* DIS # C9: 6 => CTR => C9: 2,4
* DIS # C9: 4,6 => CTR => C9: 2
* PRF # C9: 2 => SOL
* CNT  18 HDP CHAINS /  18 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # B6: 4,7 => SOL
* STA B6: 4,7
* CNT   1 HDP CHAINS /   1 HYP OPENED