Analysis of xx-top500-323-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .7.....614...3..............68....9.2.1..........4.3.....8.6...5.....2.....1..... initial

Autosolve

position: .73....614...3.............368....9.241..........4.3.....8.6...5.....2.....1..... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B2: 8,9 => CTR => B2: 1,2,5
* DIS # A3: 8,9 => CTR => A3: 1,6
* DIS # F1: 8,9 => CTR => F1: 2,4,5
* PRF # G1: 8,9 => SOL
* DIS # A9: 8,9 => CTR => A9: 6,7
* PRF # A7: 7,9 => SOL
* DIS # A7: 1 => CTR => A7: 7,9
* DIS # A9: 7,9 => CTR => A9: 6,8
* DIS # C6: 7 => CTR => C6: 5,9
* PRF # B2: 5,9 => SOL
* PRF # I6: 8 => SOL
* PRF # C8: 7,9 => SOL
* DIS # I8: 7,9 => CTR => I8: 3,4,6,8
* DIS # E3: 7,9 => CTR => E3: 1,5,6,8
* DIS # E5: 7,9 => CTR => E5: 5,6,8
* CNT  15 HDP CHAINS /  38 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 # B2: 8,9 => CTR => B2: 1,2,5
* DIS B2: 1,2,5 # A3: 8,9 => CTR => A3: 1,6
* PRF B2: 1,2,5 + A3: 1,6 # B3: 1,2,5 => SOL
* STA B2: 1,2,5 + A3: 1,6 + B3: 1,2,5
* CNT   3 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

.7.....614...3..............68....9.2.1..........4.3.....8.6...5.....2.....1..... initial
.73....614...3.............368....9.241..........4.3.....8.6...5.....2.....1..... autosolve
873254961456931827129768543368517492241389675795642318932876154517493286684125739 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
A1: 8,9
A6: 7,9
B6: 5,9
D6: 2,6
E8: 7,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G4,H6: 1.. / G4 = 1  =>  0 pairs (X) / H6 = 1  =>  0 pairs (_)
B2,F2: 1.. / B2 = 1  =>  0 pairs (X) / F2 = 1  =>  0 pairs (_)
F6,H6: 1.. / F6 = 1  =>  0 pairs (X) / H6 = 1  =>  0 pairs (_)
B8,H8: 1.. / B8 = 1  =>  0 pairs (*) / H8 = 1  =>  0 pairs (X)
A3,A7: 1.. / A3 = 1  =>  0 pairs (*) / A7 = 1  =>  0 pairs (X)
E3,E4: 1.. / E3 = 1  =>  0 pairs (X) / E4 = 1  =>  0 pairs (_)
G4,G7: 1.. / G4 = 1  =>  0 pairs (X) / G7 = 1  =>  0 pairs (_)
H3,I3: 3.. / H3 = 3  =>  5 pairs (_) / I3 = 3  =>  5 pairs (_)
D5,F5: 3.. / D5 = 3  =>  5 pairs (_) / F5 = 3  =>  5 pairs (_)
D5,D8: 3.. / D5 = 3  =>  5 pairs (_) / D8 = 3  =>  5 pairs (_)
G4,I4: 4.. / G4 = 4  =>  0 pairs (*) / I4 = 4  =>  0 pairs (X)
B6,C6: 5.. / B6 = 5  =>  5 pairs (_) / C6 = 5  =>  4 pairs (_)
C2,D2: 6.. / C2 = 6  =>  0 pairs (*) / D2 = 6  =>  0 pairs (X)
D6,I6: 6.. / D6 = 6  =>  0 pairs (*) / I6 = 6  =>  0 pairs (X)
C8,I8: 6.. / C8 = 6  =>  0 pairs (X) / I8 = 6  =>  0 pairs (_)
A3,A9: 6.. / A3 = 6  =>  0 pairs (X) / A9 = 6  =>  0 pairs (_)
E3,E5: 6.. / E3 = 6  =>  0 pairs (*) / E5 = 6  =>  0 pairs (X)
G5,G9: 6.. / G5 = 6  =>  0 pairs (*) / G9 = 6  =>  0 pairs (X)
A6,C6: 7.. / A6 = 7  =>  6 pairs (_) / C6 = 7  =>  0 pairs (X)
* DURATION: 0:00:30.284020  START: 13:56:42.990070  END: 13:57:13.274090 2017-05-04
* CP COUNT: (19)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B6,D6,E8)
* .73....614...3.............368....9.241..........4.3.....8.6...5.....2.....1.....
* PAIR A1: 8,9 BLK 1
B2: 8,9,1,2,5                            # reduction candidate for 8,9
B2: 8,9 => CTR
* 8732549614967318251259687..368517492241389657.5.642318.3.8.61..51.4.328668.1.5...
B2: 1,2,5                                #  5 pairs
A3: 8,9,1,6                              # reduction candidate for 8,9
A3: 8,9 => CTR
* .73....614...3.............368...194241...6..7..6413..1..8.6...5.....2166..1.....
A3: 1,6                                  #  6 pairs
B3: 8,9,1,2,5                            # reduction candidate for 8,9
B3: 8,9                                  #  7 pairs
* PAIR A1: 8,9 ROW 1
E1: 8,9,2,5                              # reduction candidate for 8,9
E1: 8,9                                  #  7 pairs
F1: 8,9,2,4,5                            # reduction candidate for 8,9
F1: 8,9 => CTR
* 8732594614.67318..1..468...36851..9.2419836.....642318.3.8.61..51.3..28668.1.....
F1: 2,4,5                                #  5 pairs
G1: 8,9,4,5                              # reduction candidate for 8,9
G1: 8,9 => SOLVED
* 873254961456931827129768543368517492241389675795642318932876154517493286684125739
G1: 4,5                                  #  6 pairs
* PAIR A1: 8,9 COL A
A9: 8,9,6,7                              # reduction candidate for 8,9
A9: 8,9 => CTR
* .73....614..63....6........368...19.241.6.......24.3.61..8.6...5.6...21....1..6..
A9: 6,7                                  #  6 pairs
* PAIR A6: 7,9 BLK 4
C6: 7,9,5                                # reduction candidate for 7,9
C6: 7,9                                  #  5 pairs
C6: 5                                    #  4 pairs
* PAIR A6: 7,9 COL A
A7: 7,9,1                                # reduction candidate for 7,9
A7: 7,9 => SOLVED
* 873254961456931827129768543368517492241389675795642318932876154517493286684125739
A7: 1 => CTR
* .73....6141..3........1....368...194241.68......2413..1..8.6...5.....21....1.....
A9: 7,9,6,8                              # reduction candidate for 7,9
A9: 7,9 => CTR
* 873....614..63....6...8....368.1..92241.6.......2483.61..8.6...5.6...21....1..6..
A9: 6,8                                  #  6 pairs
* PAIR B6: 5,9 BLK 4
C6: 5,9,7                                # reduction candidate for 5,9
C6: 7 => CTR
* 8732549614.6.318..1.5.687..368.1.4922413896..95764231873.8.61..51947328668.1.5...
C6: 5,9                                  #  6 pairs
* PAIR B6: 5,9 COL B
B2: 5,9,1,2,8                            # reduction candidate for 5,9
B2: 5,9 => SOLVED
* 873254961456931827129768543368517492241389675795642318932876154517493286684125739
B2: 1,2,8                                #  5 pairs
B3: 5,9,1,2,8                            # reduction candidate for 5,9
B3: 5,9                                  #  6 pairs
* PAIR D6: 2,6 ROW 6
I6: 2,6,8                                # reduction candidate for 2,6
I6: 8 => SOLVED
* 873254961456931827129768543368517492241389675795642318932876154517493286684125739
I6: 2,6                                  #  8 pairs
* PAIR E8: 7,9 BLK 8
E7: 7,9,2,5                              # reduction candidate for 7,9
E7: 7,9                                  # 12 pairs
D8: 7,9,3,4                              # reduction candidate for 7,9
D8: 7,9                                  # 15 pairs
F8: 7,9,3,4                              # reduction candidate for 7,9
F8: 7,9                                  # 14 pairs
E9: 7,9,2,5                              # reduction candidate for 7,9
E9: 7,9                                  # 12 pairs
F9: 7,9,2,3,4,5                          # reduction candidate for 7,9
F9: 7,9                                  # 13 pairs
* PAIR E8: 7,9 ROW 8
C8: 7,9,4,6                              # reduction candidate for 7,9
C8: 7,9 => SOLVED
* 873254961456931827129768543368517492241389675795642318932876154517493286684125739
C8: 4,6                                  #  6 pairs
I8: 7,9,3,4,6,8                          # reduction candidate for 7,9
I8: 7,9 => CTR
* .73....614..63....6........368...19.241.6.......24.3.61..8.6...5.6...21....1..6..
I8: 3,4,6,8                              #  5 pairs
* PAIR E8: 7,9 COL E
E3: 7,9,1,5,6,8                          # reduction candidate for 7,9
E3: 7,9 => CTR
* .73....614...3.............368.1..9.241.6.......248316...8.61..516...2.....1..6..
E3: 1,5,6,8                              #  5 pairs
E5: 7,9,5,6,8                            # reduction candidate for 7,9
E5: 7,9 => CTR
* .73.8..614.6.3........6....368.1..9.241..........4.31....8.61..51....2..68.1.....
E5: 5,6,8                                #  7 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-323-base-pr-000.dot
* REASONING
* DIS # B2: 8,9 => CTR => B2: 1,2,5
* DIS # A3: 8,9 => CTR => A3: 1,6
* DIS # F1: 8,9 => CTR => F1: 2,4,5
* PRF # G1: 8,9 => SOL
* DIS # A9: 8,9 => CTR => A9: 6,7
* PRF # A7: 7,9 => SOL
* DIS # A7: 1 => CTR => A7: 7,9
* DIS # A9: 7,9 => CTR => A9: 6,8
* DIS # C6: 7 => CTR => C6: 5,9
* PRF # B2: 5,9 => SOL
* PRF # I6: 8 => SOL
* PRF # C8: 7,9 => SOL
* DIS # I8: 7,9 => CTR => I8: 3,4,6,8
* DIS # E3: 7,9 => CTR => E3: 1,5,6,8
* DIS # E5: 7,9 => CTR => E5: 5,6,8
* CNT  15 HDP CHAINS /  38 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B6,D6,E8)
* .73....614...3.............368....9.241..........4.3.....8.6...5.....2.....1.....
* PAIR A1: 8,9 BLK 1
B2: 8,9,1,2,5                            # reduction candidate for 8,9
B2: 8,9 => CTR
* 8732549614967318251259687..368517492241389657.5.642318.3.8.61..51.4.328668.1.5...
A3: 8,9,1,6                              # reduction candidate for 8,9
A3: 8,9 => CTR
* .73....614...3.............368...194241...6..7..6413..1..8.6...5.....2166..1.....
B3: 8,9,1,2,5                            # reduction candidate for 8,9
B3: 8,9                                  #  7 pairs
* RESTART
* PAIR A1: 8,9 BLK 1
B3: 8,9,1,2,5                            # reduction candidate for 8,9
B3: 1,2,5 => SOLVED
* 873254961456931827129768543368517492241389675795642318932876154517493286684125739
* DURATION: 0:00:05.916081  START: 13:57:41.145624  END: 13:57:47.061705 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-323-base-pr-001.dot
* REASONING
* DIS # B2: 8,9 => CTR => B2: 1,2,5
* DIS B2: 1,2,5 # A3: 8,9 => CTR => A3: 1,6
* PRF B2: 1,2,5 + A3: 1,6 # B3: 1,2,5 => SOL
* STA B2: 1,2,5 + A3: 1,6 + B3: 1,2,5
* CNT   3 HDP CHAINS /   5 HYP OPENED

Header Info

Top 500 Minimum 17 323

solution: 873254961456931827129768543368517492241389675795642318932876154517493286684125739
info: 2931     FNBTHWY  S8.f     22108

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

Solution

position: 873254961456931827129768543368517492241389675795642318932876154517493286684125739 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 # B2: 8,9 => CTR => B2: 1,2,5
* INC # B2: 1,2,5 => UNS
* DIS # A3: 8,9 => CTR => A3: 1,6
* INC # A3: 1,6 => UNS
* INC # B3: 8,9 => UNS
* INC # E1: 8,9 => UNS
* DIS # F1: 8,9 => CTR => F1: 2,4,5
* INC # F1: 2,4,5 => UNS
* PRF # G1: 8,9 => SOL
* INC # G1: 4,5 => UNS
* DIS # A9: 8,9 => CTR => A9: 6,7
* INC # A9: 6,7 => UNS
* INC # C6: 7,9 => UNS
* INC # C6: 5 => UNS
* PRF # A7: 7,9 => SOL
* DIS # A7: 1 => CTR => A7: 7,9
* DIS # A9: 7,9 => CTR => A9: 6,8
* INC # A9: 6,8 => UNS
* INC # C6: 5,9 => UNS
* DIS # C6: 7 => CTR => C6: 5,9
* PRF # B2: 5,9 => SOL
* INC # B2: 1,2,8 => UNS
* INC # B3: 5,9 => UNS
* INC # I6: 2,6 => UNS
* PRF # I6: 8 => SOL
* INC # E7: 7,9 => UNS
* INC # D8: 7,9 => UNS
* INC # F8: 7,9 => UNS
* INC # E9: 7,9 => UNS
* INC # F9: 7,9 => UNS
* PRF # C8: 7,9 => SOL
* INC # C8: 4,6 => UNS
* DIS # I8: 7,9 => CTR => I8: 3,4,6,8
* INC # I8: 3,4,6,8 => UNS
* DIS # E3: 7,9 => CTR => E3: 1,5,6,8
* INC # E3: 1,5,6,8 => UNS
* DIS # E5: 7,9 => CTR => E5: 5,6,8
* INC # E5: 5,6,8 => UNS
* CNT  38 HDP CHAINS /  38 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B2: 8,9 => CTR => B2: 1,2,5
* DIS B2: 1,2,5 # A3: 8,9 => CTR => A3: 1,6
* INC B2: 1,2,5 + A3: 1,6 # B3: 8,9 => UNS
* INC B2: 1,2,5 + A3: 1,6 # B3: 8,9 => UNS
* PRF B2: 1,2,5 + A3: 1,6 # B3: 1,2,5 => SOL
* STA B2: 1,2,5 + A3: 1,6 + B3: 1,2,5
* CNT   5 HDP CHAINS /   5 HYP OPENED