Analysis of xx-top500-195-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 6...2...........41....8.......5..2........36..17.......5.1.7...3.....8.....4..... initial

Autosolve

position: 6...21..........411...84......5.921.5...1236.217.......5.1.7...3.12..8.....4.81.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # I4: 4,8 => CTR => I4: 7
* PRF # I4: 7 => SOL
* DIS # A7: 9 => CTR => A7: 4,8
* PRF # I4: 4,7 => SOL
* DIS # I4: 8 => CTR => I4: 4,7
* PRF # I5: 7,8 => SOL
* DIS # I5: 4 => CTR => I5: 7,8
* DIS # D6: 3,6 => CTR => D6: 8
* PRF # D6: 8 => SOL
* DIS # F2: 3,6 => CTR => F2: 5
* PRF # B8: 7,9 => SOL
* DIS # B9: 7,9 => CTR => B9: 2,6
* DIS # A2: 8 => CTR => A2: 7,9
* DIS # I8: 5,6 => CTR => I8: 4,9
* DIS # F2: 3 => CTR => F2: 5,6
* CNT  15 HDP CHAINS /  28 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 # I4: 4,8 => CTR => I4: 7
* PRF I4: 7 => SOL
* STA I4: 7
* CNT   2 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

6...2...........41....8.......5..2........36..17.......5.1.7...3.....8.....4..... initial
6...21..........411...84......5.921.5...1236.217.......5.1.7...3.12..8.....4.81.. autosolve
674921583982375641135684792863549217549712368217863459458137926391256874726498135 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
A4: 4,8
B4: 3,6
C4: 3,6
E4: 4,7
D5: 7,8
E6: 4,6
F6: 3,6
A9: 7,9
F8: 5,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B2,C2: 2.. / B2 = 2  =>  0 pairs (X) / C2 = 2  => 10 pairs (_)
H3,I3: 2.. / H3 = 2  => 10 pairs (_) / I3 = 2  => 10 pairs (_)
B2,B9: 2.. / B2 = 2  =>  0 pairs (X) / B9 = 2  => 10 pairs (_)
B4,C4: 3.. / B4 = 3  =>  9 pairs (_) / C4 = 3  =>  8 pairs (_)
D6,F6: 3.. / D6 = 3  =>  0 pairs (X) / F6 = 3  => 10 pairs (_)
E7,E9: 3.. / E7 = 3  => 10 pairs (_) / E9 = 3  => 11 pairs (_)
F2,F6: 3.. / F2 = 3  =>  0 pairs (X) / F6 = 3  => 10 pairs (_)
B1,C1: 4.. / B1 = 4  =>  0 pairs (X) / C1 = 4  => 10 pairs (_)
E4,E6: 4.. / E4 = 4  =>  0 pairs (*) / E6 = 4  =>  0 pairs (X)
B8,I8: 4.. / B8 = 4  =>  0 pairs (X) / I8 = 4  =>  0 pairs (_)
A4,A7: 4.. / A4 = 4  =>  0 pairs (X) / A7 = 4  =>  0 pairs (_)
G6,G7: 4.. / G6 = 4  =>  0 pairs (*) / G7 = 4  =>  0 pairs (X)
C1,C3: 5.. / C1 = 5  =>  0 pairs (X) / C3 = 5  =>  9 pairs (_)
E2,F2: 5.. / E2 = 5  =>  0 pairs (X) / F2 = 5  => 11 pairs (_)
F2,F8: 5.. / F2 = 5  => 11 pairs (_) / F8 = 5  =>  0 pairs (X)
B4,C4: 6.. / B4 = 6  =>  8 pairs (_) / C4 = 6  =>  9 pairs (_)
E4,D5: 7.. / E4 = 7  =>  0 pairs (X) / D5 = 7  =>  0 pairs (_)
I4,I5: 7.. / I4 = 7  =>  0 pairs (*) / I5 = 7  =>  0 pairs (X)
H8,H9: 7.. / H8 = 7  =>  9 pairs (_) / H9 = 7  =>  0 pairs (X)
E4,I4: 7.. / E4 = 7  =>  0 pairs (X) / I4 = 7  =>  0 pairs (_)
D5,I5: 7.. / D5 = 7  =>  0 pairs (*) / I5 = 7  =>  0 pairs (X)
B8,H8: 7.. / B8 = 7  =>  0 pairs (X) / H8 = 7  =>  9 pairs (_)
A2,A9: 7.. / A2 = 7  =>  0 pairs (X) / A9 = 7  =>  9 pairs (_)
E2,E4: 7.. / E2 = 7  =>  0 pairs (*) / E4 = 7  =>  0 pairs (X)
H1,I1: 8.. / H1 = 8  => 10 pairs (_) / I1 = 8  =>  0 pairs (X)
D5,D6: 8.. / D5 = 8  =>  0 pairs (X) / D6 = 8  =>  0 pairs (_)
A7,C7: 8.. / A7 = 8  =>  0 pairs (X) / C7 = 8  => 11 pairs (_)
A4,I4: 8.. / A4 = 8  =>  0 pairs (*) / I4 = 8  =>  0 pairs (X)
B2,B5: 8.. / B2 = 8  => 14 pairs (_) / B5 = 8  =>  0 pairs (X)
H1,H6: 8.. / H1 = 8  => 10 pairs (_) / H6 = 8  =>  0 pairs (X)
B5,C5: 9.. / B5 = 9  => 15 pairs (_) / C5 = 9  => 12 pairs (_)
* DURATION: 0:00:50.306642  START: 09:24:47.238453  END: 09:25:37.545095 2017-05-04
* CP COUNT: (31)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B4,C4,D5,E4,E6,F6,F8)
* 6...21..........411...84......5.921.5...1236.217.......5.1.7...3.12..8.....4.81..
* PAIR A4: 4,8 BLK 4
B5: 4,8,9                                # reduction candidate for 4,8
B5: 4,8                                  # 12 pairs
C5: 4,8,9                                # reduction candidate for 4,8
C5: 4,8                                  # 15 pairs
* PAIR A4: 4,8 ROW 4
I4: 4,8,7                                # reduction candidate for 4,8
I4: 4,8 => CTR
* 6...21..........411...84......57921.5..812367217.4.....5.1.74..3412..87....4.81..
I4: 7 => SOLVED
* 674921583982375641135684792863549217549712368217863459458137926391256874726498135
* PAIR A4: 4,8 COL A
A7: 4,8,9                                # reduction candidate for 4,8
A7: 9 => CTR
* 6...21..........411...84...4..5792185...1236.217.......5.1.7...3.12..8.....4.81..
A7: 4,8                                  # 14 pairs
* PAIR E4: 4,7 ROW 4
I4: 4,7,8                                # reduction candidate for 4,7
I4: 4,7 => SOLVED
* 674921583982375641135684792863549217549712368217863459458137926391256874726498135
I4: 8 => CTR
* 6...21..........411...84......5792185..812367217.4.....5.1.74..3412..87....4.81..
* PAIR D5: 7,8 ROW 5
I5: 7,8,4                                # reduction candidate for 7,8
I5: 7,8 => SOLVED
* 674921583982375641135684792863549217549712368217863459458137926391256874726498135
I5: 4 => CTR
* 6...21..........411...84......5.92175..71236421784.....5.1.7...3.12..8.....4.81..
* PAIR F6: 3,6 BLK 5
D6: 3,6,8                                # reduction candidate for 3,6
D6: 3,6 => CTR
* 6...21....82....411...84...8..5792145..812367217.4....4581.7...3.12..8...2.4.81..
D6: 8 => SOLVED
* 674921583982375641135684792863549217549712368217863459458137926391256874726498135
* PAIR F6: 3,6 COL F
F2: 3,6,5                                # reduction candidate for 3,6
F2: 3,6 => CTR
* 6...21.......5..411...84......57921.5..812367217.4.....5.1.74..3412.587....4.81..
F2: 5                                    # 11 pairs
* PAIR A9: 7,9 BLK 7
B8: 7,9,4,6                              # reduction candidate for 7,9
B8: 7,9 => SOLVED
* 674921583982375641135684792863549217549712368217863459458137926391256874726498135
B8: 4,6                                  # 10 pairs
B9: 7,9,2,6                              # reduction candidate for 7,9
B9: 7,9 => CTR
* 6...21....2.....411...84......5.921.589712364217.......5.1.7...3.12..8.....4.81..
B9: 2,6                                  # 10 pairs
* PAIR A9: 7,9 ROW 9
H9: 7,9,2,3,5                            # reduction candidate for 7,9
H9: 7,9                                  # 14 pairs
H9: 2,3,5                                #  9 pairs
* PAIR A9: 7,9 COL A
A2: 7,9,8                                # reduction candidate for 7,9
A2: 8 => CTR
* 6...21...8......411...84...4..5792185...1236.217.......5.1.7...3.12..8.....4.81..
A2: 7,9                                  # 14 pairs
* PAIR F8: 5,6 BLK 8
E8: 5,6,9                                # reduction candidate for 5,6
E8: 5,6                                  # 14 pairs
E9: 5,6,3,9                              # reduction candidate for 5,6
E9: 5,6                                  # 12 pairs
* PAIR F8: 5,6 ROW 8
I8: 5,6,4,9                              # reduction candidate for 5,6
I8: 5,6 => CTR
* 6.4.21..........411.5.84...4..5792185...1236.217.......5.1.7...3412..87....4.81..
I8: 4,9                                  # 10 pairs
* PAIR F8: 5,6 COL F
F2: 5,6,3                                # reduction candidate for 5,6
F2: 3 => CTR
* 6...21.......53.411...84......57921.5..812367217346....5.1.74..3412.587....4.81..
F2: 5,6                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-195-base-pr-000.dot
* REASONING
* DIS # I4: 4,8 => CTR => I4: 7
* PRF # I4: 7 => SOL
* DIS # A7: 9 => CTR => A7: 4,8
* PRF # I4: 4,7 => SOL
* DIS # I4: 8 => CTR => I4: 4,7
* PRF # I5: 7,8 => SOL
* DIS # I5: 4 => CTR => I5: 7,8
* DIS # D6: 3,6 => CTR => D6: 8
* PRF # D6: 8 => SOL
* DIS # F2: 3,6 => CTR => F2: 5
* PRF # B8: 7,9 => SOL
* DIS # B9: 7,9 => CTR => B9: 2,6
* DIS # A2: 8 => CTR => A2: 7,9
* DIS # I8: 5,6 => CTR => I8: 4,9
* DIS # F2: 3 => CTR => F2: 5,6
* CNT  15 HDP CHAINS /  28 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B4,C4,D5,E4,E6,F6,F8)
* 6...21..........411...84......5.921.5...1236.217.......5.1.7...3.12..8.....4.81..
* PAIR A4: 4,8 BLK 4
B5: 4,8,9                                # reduction candidate for 4,8
B5: 4,8                                  # 12 pairs
C5: 4,8,9                                # reduction candidate for 4,8
C5: 4,8                                  # 15 pairs
* PAIR A4: 4,8 ROW 4
I4: 4,8,7                                # reduction candidate for 4,8
I4: 4,8 => CTR
* 6...21..........411...84......57921.5..812367217.4.....5.1.74..3412..87....4.81..
I4: 7 => SOLVED
* 674921583982375641135684792863549217549712368217863459458137926391256874726498135
* DURATION: 0:00:04.999004  START: 09:26:04.446184  END: 09:26:09.445188 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-195-base-pr-001.dot
* REASONING
* DIS # I4: 4,8 => CTR => I4: 7
* PRF I4: 7 => SOL
* STA I4: 7
* CNT   2 HDP CHAINS /   3 HYP OPENED

Header Info

Top 500 Minimum 17 195

solution: 674921583982375641135684792863549217549712368217863459458137926391256874726498135
info: 1880     FNBHWY   S8.f     34518

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

Solution

position: 674921583982375641135684792863549217549712368217863459458137926391256874726498135 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:

* INC # B5: 4,8 => UNS
* INC # C5: 4,8 => UNS
* DIS # I4: 4,8 => CTR => I4: 7
* PRF # I4: 7 => SOL
* INC # A7: 4,8 => UNS
* DIS # A7: 9 => CTR => A7: 4,8
* PRF # I4: 4,7 => SOL
* DIS # I4: 8 => CTR => I4: 4,7
* PRF # I5: 7,8 => SOL
* DIS # I5: 4 => CTR => I5: 7,8
* DIS # D6: 3,6 => CTR => D6: 8
* PRF # D6: 8 => SOL
* DIS # F2: 3,6 => CTR => F2: 5
* INC # F2: 5 => UNS
* PRF # B8: 7,9 => SOL
* INC # B8: 4,6 => UNS
* DIS # B9: 7,9 => CTR => B9: 2,6
* INC # B9: 2,6 => UNS
* INC # H9: 7,9 => UNS
* INC # H9: 2,3,5 => UNS
* INC # A2: 7,9 => UNS
* DIS # A2: 8 => CTR => A2: 7,9
* INC # E8: 5,6 => UNS
* INC # E9: 5,6 => UNS
* DIS # I8: 5,6 => CTR => I8: 4,9
* INC # I8: 4,9 => UNS
* INC # F2: 5,6 => UNS
* DIS # F2: 3 => CTR => F2: 5,6
* CNT  28 HDP CHAINS /  28 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B5: 4,8 => UNS
* INC # C5: 4,8 => UNS
* DIS # I4: 4,8 => CTR => I4: 7
* PRF I4: 7 => SOL
* STA I4: 7
* CNT   4 HDP CHAINS /   3 HYP OPENED