Analysis of xx-top500-431-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 9.......4...3..6.............75.4.........71.....2..9....6..8..49.......2...1.... initial

Autosolve

position: 9.......4...3..6...........1275943..5498..712....2.495...6..8..49.......2...1.... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # F2: 7,8 => CTR => F2: 1,2,5,9
* DIS # D1: 1,7 => CTR => D1: 2
* DIS # F2: 1,7 => CTR => F2: 2,5,8,9
* DIS # E7: 3,7 => CTR => E7: 4,5
* DIS # F7: 3,7 => CTR => F7: 2,5,9
* DIS # I7: 3,7 => CTR => I7: 1,9
* DIS # F8: 2,7 => CTR => F8: 3,5,8
* DIS # D1: 1 => CTR => D1: 2,7
* DIS # F9: 5,9 => CTR => F9: 3,7,8
* DIS # G3: 1,2 => CTR => G3: 5,9
* CNT  10 HDP CHAINS /  37 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 # F2: 7,8 => CTR => F2: 1,2,5,9
* DIS F2: 1,2,5,9 # D1: 1,7 => CTR => D1: 2
* DIS F2: 1,2,5,9 + D1: 2 # I7: 3,7 => CTR => I7: 1,9
* DIS F2: 1,2,5,9 + D1: 2 + I7: 1,9 # F9: 5,9 => CTR => F9: 3,8
* DIS F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 # G3: 1,2 => CTR => G3: 5,9
* PRF F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 + G3: 5,9 # B1: 7,8 => SOL
* STA F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 + G3: 5,9 + B1: 7,8
* CNT   6 HDP CHAINS /  34 HYP OPENED

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

Details

Positions

9.......4...3..6.............75.4.........71.....2..9....6..8..49.......2...1.... initial
9.......4...3..6...........1275943..5498..712....2.495...6..8..49.......2...1.... autosolve
985276134714359628632481957127594386549863712863127495351642879498735261276918543 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (12)
A2: 7,8
D3: 4,9
E5: 3,6
F5: 3,6
D6: 1,7
F6: 1,7
H4: 6,8
I4: 6,8
A7: 3,7
D8: 2,7
D9: 4,9
G9: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D6,F6: 1.. / D6 = 1  => 11 pairs (_) / F6 = 1  =>  0 pairs (X)
D1,D6: 1.. / D1 = 1  =>  0 pairs (X) / D6 = 1  => 11 pairs (_)
F7,H7: 2.. / F7 = 2  => 12 pairs (_) / H7 = 2  =>  0 pairs (X)
D1,D8: 2.. / D1 = 2  => 12 pairs (_) / D8 = 2  =>  0 pairs (X)
E5,F5: 3.. / E5 = 3  => 10 pairs (_) / F5 = 3  => 10 pairs (_)
C2,C3: 4.. / C2 = 4  => 12 pairs (_) / C3 = 4  =>  0 pairs (X)
E7,D9: 4.. / E7 = 4  => 12 pairs (_) / D9 = 4  =>  0 pairs (X)
H7,H9: 4.. / H7 = 4  =>  0 pairs (X) / H9 = 4  => 12 pairs (_)
C2,E2: 4.. / C2 = 4  => 12 pairs (_) / E2 = 4  =>  0 pairs (X)
E7,H7: 4.. / E7 = 4  => 12 pairs (_) / H7 = 4  =>  0 pairs (X)
D9,H9: 4.. / D9 = 4  =>  0 pairs (X) / H9 = 4  => 12 pairs (_)
D3,D9: 4.. / D3 = 4  => 12 pairs (_) / D9 = 4  =>  0 pairs (X)
E5,F5: 6.. / E5 = 6  => 10 pairs (_) / F5 = 6  => 10 pairs (_)
H4,I4: 6.. / H4 = 6  => 10 pairs (_) / I4 = 6  => 10 pairs (_)
A3,A6: 6.. / A3 = 6  => 13 pairs (_) / A6 = 6  => 14 pairs (_)
D6,F6: 7.. / D6 = 7  =>  0 pairs (X) / F6 = 7  => 11 pairs (_)
H4,I4: 8.. / H4 = 8  => 10 pairs (_) / I4 = 8  => 10 pairs (_)
F2,I2: 9.. / F2 = 9  => 12 pairs (_) / I2 = 9  =>  0 pairs (X)
F7,I7: 9.. / F7 = 9  =>  0 pairs (X) / I7 = 9  => 12 pairs (_)
D3,D9: 9.. / D3 = 9  =>  0 pairs (X) / D9 = 9  => 12 pairs (_)
G3,G9: 9.. / G3 = 9  => 12 pairs (_) / G9 = 9  =>  0 pairs (X)
* DURATION: 0:00:26.529006  START: 17:30:11.925906  END: 17:30:38.454912 2017-05-04
* CP COUNT: (21)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,D3,D6,D8,D9,E5,F5,F6,G9,H4,I4)
* 9.......4...3..6...........1275943..5498..712....2.495...6..8..49.......2...1....
* PAIR A2: 7,8 BLK 1
B1: 7,8,1,3,5,6                          # reduction candidate for 7,8
B1: 7,8                                  # 15 pairs
B2: 7,8,1,5                              # reduction candidate for 7,8
B2: 7,8                                  # 17 pairs
A3: 7,8,3,6                              # reduction candidate for 7,8
A3: 7,8                                  # 16 pairs
B3: 7,8,1,3,5,6                          # reduction candidate for 7,8
B3: 7,8                                  # 15 pairs
* PAIR A2: 7,8 ROW 2
E2: 7,8,4,5                              # reduction candidate for 7,8
E2: 7,8                                  # 16 pairs
F2: 7,8,1,2,5,9                          # reduction candidate for 7,8
F2: 7,8 => CTR
* 9.......4...3..6.9.........1275943..5498..712....2.495...6.982.49.......2..41.9..
F2: 1,2,5,9                              # 12 pairs
H2: 7,8,2,5                              # reduction candidate for 7,8
H2: 7,8                                  # 16 pairs
I2: 7,8,1,9                              # reduction candidate for 7,8
I2: 7,8                                  # 12 pairs
* PAIR D6: 1,7 COL D
D1: 1,7,2                                # reduction candidate for 1,7
D1: 1,7 => CTR
* 9.......4..43.26.9...4.9...1275943..5498..712....2.495...64.82.49.2..1..2..91.54.
D1: 2                                    # 12 pairs
* PAIR F6: 1,7 COL F
F1: 1,7,2,5,6,8                          # reduction candidate for 1,7
F1: 1,7                                  # 14 pairs
F2: 1,7,2,5,8,9                          # reduction candidate for 1,7
F2: 1,7 => CTR
* 9.......4...3..6.9.........1275943..5498..712....2.495...6.982.49.......2..41.9..
F2: 2,5,8,9                              # 12 pairs
F3: 1,7,2,5,6,8,9                        # reduction candidate for 1,7
F3: 1,7                                  # 13 pairs
* PAIR A7: 3,7 BLK 7
B7: 3,7,1,5                              # reduction candidate for 3,7
B7: 3,7                                  # 16 pairs
B9: 3,7,5,6,8                            # reduction candidate for 3,7
B9: 3,7                                  # 19 pairs
* PAIR A7: 3,7 ROW 7
E7: 3,7,4,5                              # reduction candidate for 3,7
E7: 3,7 => CTR
* 9.......4...3..6.....9.....1275943..5498..712....2.495...6.284949.7.....2..4195..
E7: 4,5                                  # 13 pairs
F7: 3,7,2,5,9                            # reduction candidate for 3,7
F7: 3,7 => CTR
* 9.......4...3.96.....4..9..1275943..5498..712....2.495...64.82949....1..2..91.54.
F7: 2,5,9                                # 12 pairs
H7: 3,7,2,4,5                            # reduction candidate for 3,7
H7: 3,7                                  # 12 pairs
I7: 3,7,1,9                              # reduction candidate for 3,7
I7: 3,7 => CTR
* 9.......4...3..6...........1275943..5498..712....2.495...6.982.49.......2..41....
I7: 1,9                                  # 13 pairs
* PAIR A7: 3,7 COL A
A3: 3,7,6,8                              # reduction candidate for 3,7
A3: 3,7                                  # 14 pairs
A3: 6,8                                  # 13 pairs
* PAIR D8: 2,7 BLK 8
F7: 2,7,3,5,9                            # reduction candidate for 2,7
F7: 2,7                                  # 12 pairs
F8: 2,7,3,5,8                            # reduction candidate for 2,7
F8: 2,7 => CTR
* 9.......4..43.26.9...4.9...1275943..5498..712....2.495...64.82.49.2.71..2..91.54.
F8: 3,5,8                                # 12 pairs
* PAIR D8: 2,7 ROW 8
H8: 2,7,3,5,6                            # reduction candidate for 2,7
H8: 2,7                                  # 14 pairs
H8: 3,5,6                                # 12 pairs
* PAIR D8: 2,7 COL D
D1: 2,7,1                                # reduction candidate for 2,7
D1: 1 => CTR
* 9..1..2.4..43.26.9..24.91..1275943..5498..712...721495...64.82.49.2.....2..91.54.
D1: 2,7                                  # 11 pairs
* PAIR G9: 5,9 ROW 9
F9: 5,9,3,7,8                            # reduction candidate for 5,9
F9: 5,9 => CTR
* 9.......4...3..6.....9.....1275943..5498..712....2.495...6..84.49.......2..41.9..
F9: 3,7,8                                # 12 pairs
* PAIR G9: 5,9 COL G
G3: 5,9,1,2                              # reduction candidate for 5,9
G3: 1,2 => CTR
* 9.......4...3..6.....9.....1275943..5498..712....2.495...6.982.49.......2..41.9..
G3: 5,9                                  # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-431-base-pr-000.dot
* REASONING
* DIS # F2: 7,8 => CTR => F2: 1,2,5,9
* DIS # D1: 1,7 => CTR => D1: 2
* DIS # F2: 1,7 => CTR => F2: 2,5,8,9
* DIS # E7: 3,7 => CTR => E7: 4,5
* DIS # F7: 3,7 => CTR => F7: 2,5,9
* DIS # I7: 3,7 => CTR => I7: 1,9
* DIS # F8: 2,7 => CTR => F8: 3,5,8
* DIS # D1: 1 => CTR => D1: 2,7
* DIS # F9: 5,9 => CTR => F9: 3,7,8
* DIS # G3: 1,2 => CTR => G3: 5,9
* CNT  10 HDP CHAINS /  37 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,D3,D6,D8,D9,E5,F5,F6,G9,H4,I4)
* 9.......4...3..6...........1275943..5498..712....2.495...6..8..49.......2...1....
* PAIR A2: 7,8 BLK 1
B1: 7,8,1,3,5,6                          # reduction candidate for 7,8
B1: 7,8                                  # 15 pairs
B2: 7,8,1,5                              # reduction candidate for 7,8
B2: 7,8                                  # 17 pairs
A3: 7,8,3,6                              # reduction candidate for 7,8
A3: 7,8                                  # 16 pairs
B3: 7,8,1,3,5,6                          # reduction candidate for 7,8
B3: 7,8                                  # 15 pairs
* PAIR A2: 7,8 ROW 2
E2: 7,8,4,5                              # reduction candidate for 7,8
E2: 7,8                                  # 16 pairs
F2: 7,8,1,2,5,9                          # reduction candidate for 7,8
F2: 7,8 => CTR
* 9.......4...3..6.9.........1275943..5498..712....2.495...6.982.49.......2..41.9..
H2: 7,8,2,5                              # reduction candidate for 7,8
H2: 7,8                                  # 16 pairs
I2: 7,8,1,9                              # reduction candidate for 7,8
I2: 7,8                                  # 12 pairs
* PAIR RESTART
* PAIR A2: 7,8 BLK 1
B1: 7,8,1,3,5,6                          # reduction candidate for 7,8
B1: 7,8                                  # 15 pairs
B2: 7,8,1,5                              # reduction candidate for 7,8
B2: 7,8                                  # 17 pairs
A3: 7,8,3,6                              # reduction candidate for 7,8
A3: 7,8                                  # 16 pairs
B3: 7,8,1,3,5,6                          # reduction candidate for 7,8
B3: 7,8                                  # 15 pairs
* PAIR A2: 7,8 ROW 2
E2: 7,8,4,5                              # reduction candidate for 7,8
E2: 7,8                                  # 16 pairs
H2: 7,8,2,5                              # reduction candidate for 7,8
H2: 7,8                                  # 16 pairs
I2: 7,8,1,9                              # reduction candidate for 7,8
I2: 7,8                                  # 12 pairs
* PAIR D6: 1,7 COL D
D1: 1,7,2                                # reduction candidate for 1,7
D1: 1,7 => CTR
* 9.......4..43.26.9...4.9...1275943..5498..712....2.495...64.82.49.2..1..2..91.54.
* PAIR RESTART
* PAIR A7: 3,7 BLK 7
B7: 3,7,1,5                              # reduction candidate for 3,7
B7: 3,7                                  # 16 pairs
B9: 3,7,5,6,8                            # reduction candidate for 3,7
B9: 3,7                                  # 22 pairs
* PAIR A7: 3,7 ROW 7
H7: 3,7,2,4,5                            # reduction candidate for 3,7
H7: 3,7                                  # 12 pairs
I7: 3,7,1,9                              # reduction candidate for 3,7
I7: 3,7 => CTR
* 9..2....4...3..6...........1275943..5498..712...127495...6.982.49.7.2...2..41....
* RESTART
* PAIR A7: 3,7 ROW 7
H7: 3,7,2,4,5                            # reduction candidate for 3,7
H7: 2,4,5                                # 13 pairs
H7: 3,7                                  # 12 pairs
* PAIR A7: 3,7 COL A
A3: 3,7,6,8                              # reduction candidate for 3,7
A3: 3,7                                  # 15 pairs
A3: 6,8                                  # 14 pairs
* PAIR RESTART
* PAIR A7: 3,7 BLK 7
B7: 3,7,1,5                              # reduction candidate for 3,7
B7: 3,7                                  # 16 pairs
B9: 3,7,5,6,8                            # reduction candidate for 3,7
B9: 3,7                                  # 17 pairs
* PAIR A7: 3,7 ROW 7
H7: 3,7,2,4,5                            # reduction candidate for 3,7
H7: 2,4,5                                # 13 pairs
H7: 3,7                                  # 12 pairs
* PAIR A7: 3,7 COL A
A3: 3,7,6,8                              # reduction candidate for 3,7
A3: 3,7                                  # 15 pairs
A3: 6,8                                  # 14 pairs
* PAIR G9: 5,9 ROW 9
F9: 5,9,3,8                              # reduction candidate for 5,9
F9: 5,9 => CTR
* 9..2....4...3..6.....9.....1275943..5498..712...127495...6..84.49.7.....2..41.9..
* PAIR G9: 5,9 COL G
G3: 5,9,1,2                              # reduction candidate for 5,9
G3: 1,2 => CTR
* 9..2....4...3..6.....9.....1275943..5498..712...127495...6.98214917.25..2..41.9..
* PAIR RESTART

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,A7,E5,E8,F1,F5,F9,H4,H7,H8,I2,I4)
* 9.52..1.4.1435962...24.195.1275943..5498..712...127495.516428.949.7.52.12..91.54.
* PAIR A2: 7,8 BLK 1
B1: 7,8,3,6                              # reduction candidate for 7,8
B1: 7,8 => SOLVED
* 985276134714359628632481957127594386549863712863127495351642879498735261276918543
* DURATION: 0:00:29.816593  START: 17:31:02.717430  END: 17:31:32.534023 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-431-base-pr-001.dot
* REASONING
* DIS # F2: 7,8 => CTR => F2: 1,2,5,9
* DIS F2: 1,2,5,9 # D1: 1,7 => CTR => D1: 2
* DIS F2: 1,2,5,9 + D1: 2 # I7: 3,7 => CTR => I7: 1,9
* DIS F2: 1,2,5,9 + D1: 2 + I7: 1,9 # F9: 5,9 => CTR => F9: 3,8
* DIS F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 # G3: 1,2 => CTR => G3: 5,9
* PRF F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 + G3: 5,9 # B1: 7,8 => SOL
* STA F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 + G3: 5,9 + B1: 7,8
* CNT   6 HDP CHAINS /  34 HYP OPENED

Header Info

Top 500 Minimum 17 431

solution: 985276134714359628632481957127594386549863712863127495351642879498735261276918543
info: 95188    FNBHWXYK S8.f     41318

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

Solution

position: 985276134714359628632481957127594386549863712863127495351642879498735261276918543 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 # B1: 7,8 => UNS
* INC # B2: 7,8 => UNS
* INC # A3: 7,8 => UNS
* INC # B3: 7,8 => UNS
* INC # E2: 7,8 => UNS
* DIS # F2: 7,8 => CTR => F2: 1,2,5,9
* INC # F2: 1,2,5,9 => UNS
* INC # H2: 7,8 => UNS
* INC # I2: 7,8 => UNS
* DIS # D1: 1,7 => CTR => D1: 2
* INC # D1: 2 => UNS
* INC # F1: 1,7 => UNS
* DIS # F2: 1,7 => CTR => F2: 2,5,8,9
* INC # F2: 2,5,8,9 => UNS
* INC # F3: 1,7 => UNS
* INC # B7: 3,7 => UNS
* INC # B9: 3,7 => UNS
* DIS # E7: 3,7 => CTR => E7: 4,5
* INC # E7: 4,5 => UNS
* DIS # F7: 3,7 => CTR => F7: 2,5,9
* INC # F7: 2,5,9 => UNS
* INC # H7: 3,7 => UNS
* DIS # I7: 3,7 => CTR => I7: 1,9
* INC # I7: 1,9 => UNS
* INC # A3: 3,7 => UNS
* INC # A3: 6,8 => UNS
* INC # F7: 2,7 => UNS
* DIS # F8: 2,7 => CTR => F8: 3,5,8
* INC # F8: 3,5,8 => UNS
* INC # H8: 2,7 => UNS
* INC # H8: 3,5,6 => UNS
* INC # D1: 2,7 => UNS
* DIS # D1: 1 => CTR => D1: 2,7
* DIS # F9: 5,9 => CTR => F9: 3,7,8
* INC # F9: 3,7,8 => UNS
* INC # G3: 5,9 => UNS
* DIS # G3: 1,2 => CTR => G3: 5,9
* CNT  37 HDP CHAINS /  37 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 7,8 => UNS
* INC # B2: 7,8 => UNS
* INC # A3: 7,8 => UNS
* INC # B3: 7,8 => UNS
* INC # E2: 7,8 => UNS
* DIS # F2: 7,8 => CTR => F2: 1,2,5,9
* INC F2: 1,2,5,9 # H2: 7,8 => UNS
* INC F2: 1,2,5,9 # I2: 7,8 => UNS
* INC F2: 1,2,5,9 # B1: 7,8 => UNS
* INC F2: 1,2,5,9 # B2: 7,8 => UNS
* INC F2: 1,2,5,9 # A3: 7,8 => UNS
* INC F2: 1,2,5,9 # B3: 7,8 => UNS
* INC F2: 1,2,5,9 # E2: 7,8 => UNS
* INC F2: 1,2,5,9 # H2: 7,8 => UNS
* INC F2: 1,2,5,9 # I2: 7,8 => UNS
* DIS F2: 1,2,5,9 # D1: 1,7 => CTR => D1: 2
* INC F2: 1,2,5,9 + D1: 2 # B7: 3,7 => UNS
* INC F2: 1,2,5,9 + D1: 2 # B9: 3,7 => UNS
* INC F2: 1,2,5,9 + D1: 2 # H7: 3,7 => UNS
* DIS F2: 1,2,5,9 + D1: 2 # I7: 3,7 => CTR => I7: 1,9
* INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # H7: 3,7 => UNS
* INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # H7: 2,4,5 => UNS
* INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # A3: 3,7 => UNS
* INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # A3: 6,8 => UNS
* INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # B7: 3,7 => UNS
* INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # B9: 3,7 => UNS
* INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # H7: 3,7 => UNS
* INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # H7: 2,4,5 => UNS
* INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # A3: 3,7 => UNS
* INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 # A3: 6,8 => UNS
* DIS F2: 1,2,5,9 + D1: 2 + I7: 1,9 # F9: 5,9 => CTR => F9: 3,8
* INC F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 # G3: 5,9 => UNS
* DIS F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 # G3: 1,2 => CTR => G3: 5,9
* PRF F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 + G3: 5,9 # B1: 7,8 => SOL
* STA F2: 1,2,5,9 + D1: 2 + I7: 1,9 + F9: 3,8 + G3: 5,9 + B1: 7,8
* CNT  34 HDP CHAINS /  34 HYP OPENED