Analysis of xx-top500-480-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .5.6...7..38...............4......2.....31......5.8.........1.39..7.........4.8.. initial

Autosolve

position: .5.6...7..38...............4..9...2....431......528.........1.39..7.........4.8.7 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A2: 1,2 => CTR => A2: 6,7
* PRF # I1: 1,2 => SOL
* DIS # A9: 1,2 => CTR => A9: 3,5,6
* DIS # D3: 1,2 => CTR => D3: 3,8
* DIS # A2: 1,2 => CTR => A2: 6,7
* DIS # I2: 1,2 => CTR => I2: 4,5,6,9
* PRF # D9: 1,2 => SOL
* DIS # D9: 3 => CTR => D9: 1,2
* DIS # I4: 5 => CTR => I4: 1,8
* DIS # B8: 4,6 => CTR => B8: 1,8
* DIS # C4: 1 => CTR => C4: 3,5
* DIS # G3: 3,5 => CTR => G3: 2,4,6,9
* DIS # B7: 2,8 => CTR => B7: 4,6,7
* DIS # D3: 2,8 => CTR => D3: 1,3
* PRF # D3: 1,3 => SOL
* CNT  15 HDP CHAINS /  31 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 # A2: 1,2 => CTR => A2: 6,7
* PRF A2: 6,7 # I1: 1,2 => SOL
* STA A2: 6,7 + I1: 1,2
* CNT   2 HDP CHAINS /   6 HYP OPENED

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

Details

Positions

.5.6...7..38...............4......2.....31......5.8.........1.39..7.........4.8.. initial
.5.6...7..38...............4..9...2....431......528.........1.39..7.........4.8.7 autosolve
159684372738295614246317985413976528825431769697528431574862193981753246362149857 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
A1: 1,2
D2: 1,2
B4: 1,8
E4: 6,7
F4: 6,7
G4: 3,5
D7: 2,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E8,D9: 1.. / E8 = 1  =>  0 pairs (X) / D9 = 1  =>  0 pairs (_)
G8,I8: 2.. / G8 = 2  =>  7 pairs (_) / I8 = 2  =>  7 pairs (_)
F1,G1: 3.. / F1 = 3  =>  0 pairs (X) / G1 = 3  =>  0 pairs (_)
C4,G4: 3.. / C4 = 3  =>  0 pairs (*) / G4 = 3  =>  0 pairs (X)
C8,F8: 3.. / C8 = 3  =>  0 pairs (X) / F8 = 3  =>  0 pairs (_)
A6,A9: 3.. / A6 = 3  =>  0 pairs (X) / A9 = 3  =>  0 pairs (_)
D3,D9: 3.. / D3 = 3  =>  0 pairs (*) / D9 = 3  =>  0 pairs (X)
H3,H6: 3.. / H3 = 3  =>  0 pairs (X) / H6 = 3  =>  0 pairs (_)
E4,F4: 6.. / E4 = 6  =>  5 pairs (_) / F4 = 6  =>  6 pairs (_)
E4,F4: 7.. / E4 = 7  =>  6 pairs (_) / F4 = 7  =>  5 pairs (_)
G5,G6: 7.. / G5 = 7  =>  7 pairs (_) / G6 = 7  =>  7 pairs (_)
E1,I1: 8.. / E1 = 8  =>  0 pairs (*) / I1 = 8  =>  0 pairs (X)
B4,I4: 8.. / B4 = 8  =>  0 pairs (X) / I4 = 8  =>  0 pairs (_)
B8,E8: 8.. / B8 = 8  =>  0 pairs (*) / E8 = 8  =>  0 pairs (X)
A5,A7: 8.. / A5 = 8  =>  0 pairs (*) / A7 = 8  =>  0 pairs (X)
D3,D7: 8.. / D3 = 8  =>  0 pairs (X) / D7 = 8  =>  0 pairs (_)
H3,H5: 8.. / H3 = 8  =>  0 pairs (*) / H5 = 8  =>  0 pairs (X)
H7,H9: 9.. / H7 = 9  =>  8 pairs (_) / H9 = 9  =>  7 pairs (_)
F9,H9: 9.. / F9 = 9  =>  8 pairs (_) / H9 = 9  =>  7 pairs (_)
* DURATION: 0:00:30.930698  START: 19:04:11.683347  END: 19:04:42.614045 2017-05-04
* CP COUNT: (19)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B4,D2,D7,E4,F4,G4)
* .5.6...7..38...............4..9...2....431......528.........1.39..7.........4.8.7
* PAIR A1: 1,2 BLK 1
C1: 1,2,4,9                              # reduction candidate for 1,2
C1: 1,2                                  # 14 pairs
A2: 1,2,6,7                              # reduction candidate for 1,2
A2: 1,2 => CTR
* .5.6...7..38...............4..9...2....431.8....528...8..2..1.39..78.......14.8.7
A2: 6,7                                  #  8 pairs
A3: 1,2,6,7                              # reduction candidate for 1,2
A3: 1,2                                  # 10 pairs
B3: 1,2,4,6,7,9                          # reduction candidate for 1,2
B3: 1,2                                  # 13 pairs
C3: 1,2,4,6,7,9                          # reduction candidate for 1,2
C3: 1,2                                  # 13 pairs
* PAIR A1: 1,2 ROW 1
I1: 1,2,4,8,9                            # reduction candidate for 1,2
I1: 1,2 => SOLVED
* 159684372738295614246317985413976528825431769697528431574862193981753246362149857
I1: 4,8,9                                #  7 pairs
* PAIR A1: 1,2 COL A
A9: 1,2,3,5,6                            # reduction candidate for 1,2
A9: 1,2 => CTR
* .5.6...7..38.............3.4..9..32....431.8.3..528...8..2..1.39..78........4.8.7
A9: 3,5,6                                #  7 pairs
* PAIR D2: 1,2 BLK 2
D3: 1,2,3,8                              # reduction candidate for 1,2
D3: 1,2 => CTR
* .5.6...7..38...............41.9...288..431...3..528......8..1.398371.......34.8.7
D3: 3,8                                  #  8 pairs
* PAIR D2: 1,2 ROW 2
A2: 1,2,6,7                              # reduction candidate for 1,2
A2: 1,2 => CTR
* .5.6...7..38...............4..9...2....431.8....528...8..2..1.39..78.......14.8.7
A2: 6,7                                  #  8 pairs
I2: 1,2,4,5,6,9                          # reduction candidate for 1,2
I2: 1,2 => CTR
* .5.6...7..38...............4..9...2....431.8....528...8..2..1.39..78.......14.8.7
I2: 4,5,6,9                              #  7 pairs
* PAIR D2: 1,2 COL D
D9: 1,2,3                                # reduction candidate for 1,2
D9: 1,2 => SOLVED
* 159684372738295614246317985413976528825431769697528431574862193981753246362149857
D9: 3 => CTR
* .5.6...7..38.............3.4159..3288..431...3..528.........1.398371.......34.8.7
* PAIR B4: 1,8 ROW 4
I4: 1,8,5                                # reduction candidate for 1,8
I4: 5 => CTR
* .5.6...7..38...............4819..325...431......528...8..2..1.39..78.......14.8.7
I4: 1,8                                  #  9 pairs
* PAIR B4: 1,8 COL B
B8: 1,8,4,6                              # reduction candidate for 1,8
B8: 4,6 => CTR
* .5.6...7..38...............4..9...2....431......528.........1.39..78.......14.8.7
B8: 1,8                                  #  9 pairs
* PAIR G4: 3,5 ROW 4
C4: 3,5,1                                # reduction candidate for 3,5
C4: 1 => CTR
* .5.6.3.7..38.............3.4819..325...431.8....528...8..2..1.39.378........4.8.7
C4: 3,5                                  #  9 pairs
* PAIR G4: 3,5 COL G
G3: 3,5,2,4,6,9                          # reduction candidate for 3,5
G3: 3,5 => CTR
* .5.6.3.7..38............53.4..9..32....431.8.3..528...8..2..1.39.371.......34.8.7
G3: 2,4,6,9                              #  7 pairs
* PAIR D7: 2,8 ROW 7
A7: 2,8,5,6,7                            # reduction candidate for 2,8
A7: 2,8                                  #  8 pairs
B7: 2,8,4,6,7                            # reduction candidate for 2,8
B7: 2,8 => CTR
* .5.68..7..38....1..4.31..8.4139..5288.5431.69.9.52843152.8..1.398.7.....3...4.8.7
B7: 4,6,7                                #  7 pairs
* PAIR D7: 2,8 COL D
D3: 2,8,1,3                              # reduction candidate for 2,8
D3: 2,8 => CTR
* .5.6...7..381............3.4..9..32....431.8.3..528.1.8..2..1.39.371.......34.8.7
D3: 1,3 => SOLVED
* 159684372738295614246317985413976528825431769697528431574862193981753246362149857
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-480-base-pr-000.dot
* REASONING
* DIS # A2: 1,2 => CTR => A2: 6,7
* PRF # I1: 1,2 => SOL
* DIS # A9: 1,2 => CTR => A9: 3,5,6
* DIS # D3: 1,2 => CTR => D3: 3,8
* DIS # A2: 1,2 => CTR => A2: 6,7
* DIS # I2: 1,2 => CTR => I2: 4,5,6,9
* PRF # D9: 1,2 => SOL
* DIS # D9: 3 => CTR => D9: 1,2
* DIS # I4: 5 => CTR => I4: 1,8
* DIS # B8: 4,6 => CTR => B8: 1,8
* DIS # C4: 1 => CTR => C4: 3,5
* DIS # G3: 3,5 => CTR => G3: 2,4,6,9
* DIS # B7: 2,8 => CTR => B7: 4,6,7
* DIS # D3: 2,8 => CTR => D3: 1,3
* PRF # D3: 1,3 => SOL
* CNT  15 HDP CHAINS /  31 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B4,D2,D7,E4,F4,G4)
* .5.6...7..38...............4..9...2....431......528.........1.39..7.........4.8.7
* PAIR A1: 1,2 BLK 1
C1: 1,2,4,9                              # reduction candidate for 1,2
C1: 1,2                                  # 14 pairs
A2: 1,2,6,7                              # reduction candidate for 1,2
A2: 1,2 => CTR
* .5.6...7..38...............4..9...2....431.8....528...8..2..1.39..78.......14.8.7
A3: 1,2,6,7                              # reduction candidate for 1,2
A3: 1,2                                  # 10 pairs
B3: 1,2,4,6,7,9                          # reduction candidate for 1,2
B3: 1,2                                  # 13 pairs
C3: 1,2,4,6,7,9                          # reduction candidate for 1,2
C3: 1,2                                  # 13 pairs
* PAIR A1: 1,2 ROW 1
I1: 1,2,4,8,9                            # reduction candidate for 1,2
I1: 1,2 => SOLVED
* 159684372738295614246317985413976528825431769697528431574862193981753246362149857
* DURATION: 0:00:05.894230  START: 19:05:03.796821  END: 19:05:09.691051 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-480-base-pr-001.dot
* REASONING
* DIS # A2: 1,2 => CTR => A2: 6,7
* PRF A2: 6,7 # I1: 1,2 => SOL
* STA A2: 6,7 + I1: 1,2
* CNT   2 HDP CHAINS /   6 HYP OPENED

Header Info

Top 500 Minimum 17 480

solution: 159684372738295614246317985413976528825431769697528431574862193981753246362149857
info: 95780    FNBHWYK  S8.f     20311

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

Solution

position: 159684372738295614246317985413976528825431769697528431574862193981753246362149857 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 # C1: 1,2 => UNS
* DIS # A2: 1,2 => CTR => A2: 6,7
* INC # A2: 6,7 => UNS
* INC # A3: 1,2 => UNS
* INC # B3: 1,2 => UNS
* INC # C3: 1,2 => UNS
* PRF # I1: 1,2 => SOL
* INC # I1: 4,8,9 => UNS
* DIS # A9: 1,2 => CTR => A9: 3,5,6
* INC # A9: 3,5,6 => UNS
* DIS # D3: 1,2 => CTR => D3: 3,8
* INC # D3: 3,8 => UNS
* DIS # A2: 1,2 => CTR => A2: 6,7
* INC # A2: 6,7 => UNS
* DIS # I2: 1,2 => CTR => I2: 4,5,6,9
* INC # I2: 4,5,6,9 => UNS
* PRF # D9: 1,2 => SOL
* DIS # D9: 3 => CTR => D9: 1,2
* INC # I4: 1,8 => UNS
* DIS # I4: 5 => CTR => I4: 1,8
* INC # B8: 1,8 => UNS
* DIS # B8: 4,6 => CTR => B8: 1,8
* INC # C4: 3,5 => UNS
* DIS # C4: 1 => CTR => C4: 3,5
* DIS # G3: 3,5 => CTR => G3: 2,4,6,9
* INC # G3: 2,4,6,9 => UNS
* INC # A7: 2,8 => UNS
* DIS # B7: 2,8 => CTR => B7: 4,6,7
* INC # B7: 4,6,7 => UNS
* DIS # D3: 2,8 => CTR => D3: 1,3
* PRF # D3: 1,3 => SOL
* CNT  31 HDP CHAINS /  31 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 1,2 => UNS
* DIS # A2: 1,2 => CTR => A2: 6,7
* INC A2: 6,7 # A3: 1,2 => UNS
* INC A2: 6,7 # B3: 1,2 => UNS
* INC A2: 6,7 # C3: 1,2 => UNS
* PRF A2: 6,7 # I1: 1,2 => SOL
* STA A2: 6,7 + I1: 1,2
* CNT   6 HDP CHAINS /   6 HYP OPENED