Analysis of xx-top500-035-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...5....2.1.....7...3........7...16....8..4..5..2.........1.3..86.......2........ initial

Autosolve

position: ...5...12.12...573.5312.8..327...1681968..4255..261739..5.1238.8613..2.723.7....1 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 6,9 => CTR => A1: 4,7
* DIS # F1: 6,9 => CTR => F1: 3,4,7
* DIS # H9: 4,9 => CTR => H9: 5
* DIS # B1: 7 => CTR => B1: 4,8
* DIS # C1: 4,8 => CTR => C1: 9
* PRF # C1: 9 => SOL
* DIS # D2: 4,9 => CTR => D2: 6
* PRF # D2: 6 => SOL
* PRF # D7: 4,9 => SOL
* DIS # D7: 6 => CTR => D7: 4,9
* DIS # A7: 4,7 => CTR => A7: 9
* PRF # A7: 9 => SOL
* DIS # B1: 4,7 => CTR => B1: 8
* DIS # A7: 7 => CTR => A7: 4,9
* DIS # E9: 4,9 => CTR => E9: 5,8
* DIS # F9: 4,9 => CTR => F9: 5,6,8
* DIS # H9: 4,9 => CTR => H9: 5
* DIS # C1: 8 => CTR => C1: 4,9
* PRF # D7: 4,6 => SOL
* DIS # D7: 9 => CTR => D7: 4,6
* PRF # F9: 6,9 => SOL
* DIS # F9: 4,5,8 => CTR => F9: 6,9
* CNT  22 HDP CHAINS /  39 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 # A1: 6,9 => CTR => A1: 4,7
* DIS A1: 4,7 # F1: 6,9 => CTR => F1: 3,4,7
* PRF A1: 4,7 + F1: 3,4,7 => SOL
* STA A1: 4,7 + F1: 3,4,7
* CNT   3 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

...5....2.1.....7...3........7...16....8..4..5..2.........1.3..86.......2........ initial
...5...12.12...573.5312.8..327...1681968..4255..261739..5.1238.8613..2.723.7....1 autosolve
789534612412698573653127894327945168196873425548261739975412386861359247234786951 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
E1: 3,7
G1: 6,9
H3: 4,9
I3: 4,6
B6: 4,8
C6: 4,8
D4: 4,9
E5: 3,7
F5: 3,7
B7: 4,7
C9: 4,9
I7: 4,6
G9: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E1,F1: 3.. / E1 = 3  => 10 pairs (_) / F1 = 3  => 13 pairs (_)
E5,F5: 3.. / E5 = 3  => 13 pairs (_) / F5 = 3  => 10 pairs (_)
E1,E5: 3.. / E1 = 3  => 10 pairs (_) / E5 = 3  => 13 pairs (_)
F1,F5: 3.. / F1 = 3  => 13 pairs (_) / F5 = 3  => 10 pairs (_)
H3,I3: 4.. / H3 = 4  =>  0 pairs (X) / I3 = 4  =>  0 pairs (_)
B6,C6: 4.. / B6 = 4  => 12 pairs (_) / C6 = 4  =>  0 pairs (X)
I3,I7: 4.. / I3 = 4  =>  0 pairs (*) / I7 = 4  =>  0 pairs (X)
E4,F4: 5.. / E4 = 5  => 15 pairs (_) / F4 = 5  => 15 pairs (_)
H8,H9: 5.. / H8 = 5  =>  0 pairs (X) / H9 = 5  => 14 pairs (_)
G1,I3: 6.. / G1 = 6  =>  0 pairs (*) / I3 = 6  =>  0 pairs (X)
D7,F9: 6.. / D7 = 6  =>  0 pairs (X) / F9 = 6  =>  0 pairs (_)
I7,G9: 6.. / I7 = 6  =>  0 pairs (*) / G9 = 6  =>  0 pairs (X)
D7,I7: 6.. / D7 = 6  =>  0 pairs (X) / I7 = 6  =>  0 pairs (_)
F9,G9: 6.. / F9 = 6  =>  0 pairs (*) / G9 = 6  =>  0 pairs (X)
D2,D7: 6.. / D2 = 6  =>  0 pairs (*) / D7 = 6  =>  0 pairs (X)
G1,G9: 6.. / G1 = 6  =>  0 pairs (*) / G9 = 6  =>  0 pairs (X)
I3,I7: 6.. / I3 = 6  =>  0 pairs (X) / I7 = 6  =>  0 pairs (_)
E5,F5: 7.. / E5 = 7  => 10 pairs (_) / F5 = 7  => 13 pairs (_)
A7,B7: 7.. / A7 = 7  =>  0 pairs (X) / B7 = 7  => 14 pairs (_)
A3,F3: 7.. / A3 = 7  => 17 pairs (_) / F3 = 7  => 11 pairs (_)
B1,B7: 7.. / B1 = 7  =>  0 pairs (X) / B7 = 7  => 14 pairs (_)
E1,E5: 7.. / E1 = 7  => 13 pairs (_) / E5 = 7  => 10 pairs (_)
B1,C1: 8.. / B1 = 8  => 12 pairs (_) / C1 = 8  =>  0 pairs (X)
E2,F2: 8.. / E2 = 8  =>  0 pairs (X) / F2 = 8  => 14 pairs (_)
B6,C6: 8.. / B6 = 8  =>  0 pairs (X) / C6 = 8  => 12 pairs (_)
E9,F9: 8.. / E9 = 8  => 14 pairs (_) / F9 = 8  =>  0 pairs (X)
B1,B6: 8.. / B1 = 8  => 12 pairs (_) / B6 = 8  =>  0 pairs (X)
C1,C6: 8.. / C1 = 8  =>  0 pairs (X) / C6 = 8  => 12 pairs (_)
E2,E9: 8.. / E2 = 8  =>  0 pairs (X) / E9 = 8  => 14 pairs (_)
F2,F9: 8.. / F2 = 8  => 14 pairs (_) / F9 = 8  =>  0 pairs (X)
G1,H3: 9.. / G1 = 9  =>  0 pairs (X) / H3 = 9  =>  0 pairs (_)
A7,C9: 9.. / A7 = 9  =>  0 pairs (*) / C9 = 9  =>  0 pairs (X)
A7,D7: 9.. / A7 = 9  =>  0 pairs (*) / D7 = 9  =>  0 pairs (X)
C1,C9: 9.. / C1 = 9  =>  0 pairs (*) / C9 = 9  =>  0 pairs (X)
G1,G9: 9.. / G1 = 9  =>  0 pairs (X) / G9 = 9  =>  0 pairs (_)
* DURATION: 0:00:59.272951  START: 03:52:07.172000  END: 03:53:06.444951 2017-05-04
* CP COUNT: (35)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,B7,C6,C9,D4,E1,E5,F5,G1,G9,H3,I3,I7)
* ...5...12.12...573.5312.8..327...1681968..4255..261739..5.1238.8613..2.723.7....1
* PAIR E1: 3,7 BLK 2
F1: 3,7,4,6,9                            # reduction candidate for 3,7
F1: 3,7                                  # 17 pairs
F1: 4,6,9                                # 11 pairs
* PAIR G1: 6,9 ROW 1
A1: 6,9,4,7                              # reduction candidate for 6,9
A1: 6,9 => CTR
* ...5...12.12...573.5312.8..327...1681968..4255..261739..5.1238.8613..2.72397..6.1
A1: 4,7                                  # 14 pairs
F1: 6,9,3,4,7                            # reduction candidate for 6,9
F1: 6,9 => CTR
* ...53..12.12...573.531278..327...1681968734255..261739..59123868613..29723.7....1
F1: 3,4,7                                # 13 pairs
* PAIR H3: 4,9 COL H
H8: 4,9,5                                # reduction candidate for 4,9
H8: 4,9                                  # 14 pairs
H9: 4,9,5                                # reduction candidate for 4,9
H9: 4,9 => CTR
* ..95..612.12...573.5312.894327...1681968..4255.82617399.5.1238.8613..25723.7....1
H9: 5                                    # 14 pairs
* PAIR B6: 4,8 COL B
B1: 4,8,7                                # reduction candidate for 4,8
B1: 7 => CTR
* .7853..12.12...573.531278..327...1681968734255842617397459123868613..29723.7....1
B1: 4,8                                  # 14 pairs
* PAIR C6: 4,8 COL C
C1: 4,8,9                                # reduction candidate for 4,8
C1: 4,8 => CTR
* ...5...12.12...573.5312.8..327...1681968..4255..261739..5.1238.8613..2.72397..6.1
C1: 9 => SOLVED
* 789534612412698573653127894327945168196873425548261739975412386861359247234786951
* PAIR D4: 4,9 BLK 5
E4: 4,9,5                                # reduction candidate for 4,9
E4: 4,9                                  # 15 pairs
F4: 4,9,5                                # reduction candidate for 4,9
F4: 4,9                                  # 15 pairs
* PAIR D4: 4,9 COL D
D2: 4,9,6                                # reduction candidate for 4,9
D2: 4,9 => CTR
* ..95...12.12...573.5312.8..327...1681968..4255..261739..56123848613..2.72347..6.1
D2: 6 => SOLVED
* 789534612412698573653127894327945168196873425548261739975412386861359247234786951
D7: 4,9,6                                # reduction candidate for 4,9
D7: 4,9 => SOLVED
* 789534612412698573653127894327945168196873425548261739975412386861359247234786951
D7: 6 => CTR
* ..95...12.12...573.5312.8..327...1681968..4255..2617399756123848613..2.72347..6.1
* PAIR F5: 3,7 COL F
F1: 3,7,4,6,9                            # reduction candidate for 3,7
F1: 3,7                                  # 17 pairs
F1: 4,6,9                                # 11 pairs
* PAIR B7: 4,7 BLK 7
A7: 4,7,9                                # reduction candidate for 4,7
A7: 4,7 => CTR
* ...5...12.12...573.5312.8..327...1681968..4255..261739..59123868613..29723.7....1
A7: 9 => SOLVED
* 789534612412698573653127894327945168196873425548261739975412386861359247234786951
* PAIR B7: 4,7 COL B
B1: 4,7,8                                # reduction candidate for 4,7
B1: 4,7 => CTR
* ..85...12.12...573.5312.8..327...1681968..425584261739..5.1238.8613..2.72397..6.1
B1: 8                                    # 12 pairs
* PAIR C9: 4,9 BLK 7
A7: 4,9,7                                # reduction candidate for 4,9
A7: 7 => CTR
* ...5...12.12...573.5312.8..327...1681968..4255..2617397459123868613..29723.7....1
A7: 4,9                                  # 14 pairs
* PAIR C9: 4,9 ROW 9
E9: 4,9,5,8                              # reduction candidate for 4,9
E9: 4,9 => CTR
* ...5..912.12.8.573.5312.846327...1681968..4255..261739..56123848613..29723.7.8651
E9: 5,8                                  # 14 pairs
F9: 4,9,5,6,8                            # reduction candidate for 4,9
F9: 4,9 => CTR
* ..95...12.12..8573.5312.8..327...1681968..4255..261739..56123848613..2.7234789651
F9: 5,6,8                                # 13 pairs
H9: 4,9,5                                # reduction candidate for 4,9
H9: 4,9 => CTR
* ..95..612.12...573.5312.894327...1681968..4255.82617399.5.1238.8613..25723.7....1
H9: 5                                    # 14 pairs
* PAIR C9: 4,9 COL C
C1: 4,9,8                                # reduction candidate for 4,9
C1: 8 => CTR
* ..85...12.12...573.5312.8..327...1681968..425584261739..5.1238.8613..2.72397..6.1
C1: 4,9                                  # 12 pairs
* PAIR I7: 4,6 ROW 7
D7: 4,6,9                                # reduction candidate for 4,6
D7: 4,6 => SOLVED
* 789534612412698573653127894327945168196873425548261739975412386861359247234786951
D7: 9 => CTR
* ...5...12.126..573.5312.8..3274..1681968..4255..261739..59123868613..29723.7....1
* PAIR G9: 6,9 ROW 9
F9: 6,9,4,5,8                            # reduction candidate for 6,9
F9: 6,9 => SOLVED
* 789534612412698573653127894327945168196873425548261739975412386861359247234786951
F9: 4,5,8 => CTR
* ..95...12.12...573.5312.8..327...1681968..4255..261739..56123848613..2.72347..6.1
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-035-base-pr-000.dot
* REASONING
* DIS # A1: 6,9 => CTR => A1: 4,7
* DIS # F1: 6,9 => CTR => F1: 3,4,7
* DIS # H9: 4,9 => CTR => H9: 5
* DIS # B1: 7 => CTR => B1: 4,8
* DIS # C1: 4,8 => CTR => C1: 9
* PRF # C1: 9 => SOL
* DIS # D2: 4,9 => CTR => D2: 6
* PRF # D2: 6 => SOL
* PRF # D7: 4,9 => SOL
* DIS # D7: 6 => CTR => D7: 4,9
* DIS # A7: 4,7 => CTR => A7: 9
* PRF # A7: 9 => SOL
* DIS # B1: 4,7 => CTR => B1: 8
* DIS # A7: 7 => CTR => A7: 4,9
* DIS # E9: 4,9 => CTR => E9: 5,8
* DIS # F9: 4,9 => CTR => F9: 5,6,8
* DIS # H9: 4,9 => CTR => H9: 5
* DIS # C1: 8 => CTR => C1: 4,9
* PRF # D7: 4,6 => SOL
* DIS # D7: 9 => CTR => D7: 4,6
* PRF # F9: 6,9 => SOL
* DIS # F9: 4,5,8 => CTR => F9: 6,9
* CNT  22 HDP CHAINS /  39 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,B7,C6,C9,D4,E1,E5,F5,G1,G9,H3,I3,I7)
* ...5...12.12...573.5312.8..327...1681968..4255..261739..5.1238.8613..2.723.7....1
* PAIR E1: 3,7 BLK 2
F1: 3,7,4,6,9                            # reduction candidate for 3,7
F1: 3,7                                  # 17 pairs
F1: 4,6,9                                # 11 pairs
* PAIR G1: 6,9 ROW 1
A1: 6,9,4,7                              # reduction candidate for 6,9
A1: 6,9 => CTR
* ...5...12.12...573.5312.8..327...1681968..4255..261739..5.1238.8613..2.72397..6.1
F1: 6,9,3,4,7                            # reduction candidate for 6,9
F1: 6,9 => CTR
* ...53..12.12...573.531278..327...1681968734255..261739..59123868613..29723.7....1
F1: 3,4,7 => SOLVED
* 789534612412698573653127894327945168196873425548261739975412386861359247234786951
* DURATION: 0:00:04.665905  START: 03:53:45.060012  END: 03:53:49.725917 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-035-base-pr-001.dot
* REASONING
* DIS # A1: 6,9 => CTR => A1: 4,7
* DIS A1: 4,7 # F1: 6,9 => CTR => F1: 3,4,7
* PRF A1: 4,7 + F1: 3,4,7 => SOL
* STA A1: 4,7 + F1: 3,4,7
* CNT   3 HDP CHAINS /   4 HYP OPENED

Header Info

Top 500 Minimum 17 035

solution: 789534612412698573653127894327945168196873425548261739975412386861359247234786951
info: 1360     FNBHWXY  S8.f     9541

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

Solution

position: 789534612412698573653127894327945168196873425548261739975412386861359247234786951 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 # F1: 3,7 => UNS
* INC # F1: 4,6,9 => UNS
* DIS # A1: 6,9 => CTR => A1: 4,7
* INC # A1: 4,7 => UNS
* DIS # F1: 6,9 => CTR => F1: 3,4,7
* INC # F1: 3,4,7 => UNS
* INC # H8: 4,9 => UNS
* DIS # H9: 4,9 => CTR => H9: 5
* INC # H9: 5 => UNS
* INC # B1: 4,8 => UNS
* DIS # B1: 7 => CTR => B1: 4,8
* DIS # C1: 4,8 => CTR => C1: 9
* PRF # C1: 9 => SOL
* INC # E4: 4,9 => UNS
* INC # F4: 4,9 => UNS
* DIS # D2: 4,9 => CTR => D2: 6
* PRF # D2: 6 => SOL
* PRF # D7: 4,9 => SOL
* DIS # D7: 6 => CTR => D7: 4,9
* INC # F1: 3,7 => UNS
* INC # F1: 4,6,9 => UNS
* DIS # A7: 4,7 => CTR => A7: 9
* PRF # A7: 9 => SOL
* DIS # B1: 4,7 => CTR => B1: 8
* INC # B1: 8 => UNS
* INC # A7: 4,9 => UNS
* DIS # A7: 7 => CTR => A7: 4,9
* DIS # E9: 4,9 => CTR => E9: 5,8
* INC # E9: 5,8 => UNS
* DIS # F9: 4,9 => CTR => F9: 5,6,8
* INC # F9: 5,6,8 => UNS
* DIS # H9: 4,9 => CTR => H9: 5
* INC # H9: 5 => UNS
* INC # C1: 4,9 => UNS
* DIS # C1: 8 => CTR => C1: 4,9
* PRF # D7: 4,6 => SOL
* DIS # D7: 9 => CTR => D7: 4,6
* PRF # F9: 6,9 => SOL
* DIS # F9: 4,5,8 => CTR => F9: 6,9
* CNT  39 HDP CHAINS /  39 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F1: 3,7 => UNS
* INC # F1: 4,6,9 => UNS
* DIS # A1: 6,9 => CTR => A1: 4,7
* DIS A1: 4,7 # F1: 6,9 => CTR => F1: 3,4,7
* PRF A1: 4,7 + F1: 3,4,7 => SOL
* STA A1: 4,7 + F1: 3,4,7
* CNT   5 HDP CHAINS /   4 HYP OPENED