Analysis of xx-top500-044-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 1.....73....5.6........9.......1...3.......564.........6.2.........8.4..59....... initial

Autosolve

position: 156...739...5.6......1.9...6...1..43.......564.........6.2.........8.4..59....... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # F1: 2 => CTR => F1: 4,8
* DIS # E5: 2,4 => CTR => E5: 9
* PRF # E5: 9 => SOL
* DIS # A2: 3,7 => CTR => A2: 2,8,9
* DIS # B3: 3,7 => CTR => B3: 2,4,8
* DIS # D6: 3,8 => CTR => D6: 6,9
* DIS # D9: 4,6 => CTR => D9: 3,7
* PRF # F7: 3,5 => SOL
* DIS # D9: 3,6 => CTR => D9: 4,7
* CNT   9 HDP CHAINS /  24 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 # F1: 2 => CTR => F1: 4,8
* DIS F1: 4,8 # A2: 3,7 => CTR => A2: 2,8,9
* DIS F1: 4,8 + A2: 2,8,9 # B3: 3,7 => CTR => B3: 2,4,8
* DIS F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 # D6: 3,8 => CTR => D6: 6,9
* PRF F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 + D6: 6,9 # F7: 3,5 => SOL
* STA F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 + D6: 6,9 + F7: 3,5
* CNT   5 HDP CHAINS /  17 HYP OPENED

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

Details

Positions

1.....73....5.6........9.......1...3.......564.........6.2.........8.4..59....... initial
156...739...5.6......1.9...6...1..43.......564.........6.2.........8.4..59....... autosolve
156428739972536814348179625625817943781394256439652178867243591213985467594761382 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
D1: 4,8
E1: 2,4
E2: 3,7
E3: 3,7
G3: 5,6
D8: 6,9
E9: 4,6
G7: 3,5
H8: 6,9
G9: 3,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E1,F1: 2.. / E1 = 2  => 11 pairs (_) / F1 = 2  =>  0 pairs (X)
E2,E3: 3.. / E2 = 3  =>  8 pairs (_) / E3 = 3  =>  8 pairs (_)
G7,G9: 3.. / G7 = 3  =>  0 pairs (X) / G9 = 3  =>  0 pairs (_)
B2,B3: 4.. / B2 = 4  =>  0 pairs (X) / B3 = 4  => 10 pairs (_)
I2,I3: 4.. / I2 = 4  => 10 pairs (_) / I3 = 4  =>  0 pairs (X)
C7,C9: 4.. / C7 = 4  => 11 pairs (_) / C9 = 4  =>  0 pairs (*)
B2,I2: 4.. / B2 = 4  =>  0 pairs (X) / I2 = 4  => 10 pairs (_)
B3,I3: 4.. / B3 = 4  => 10 pairs (_) / I3 = 4  =>  0 pairs (X)
G3,I3: 5.. / G3 = 5  =>  0 pairs (X) / I3 = 5  =>  0 pairs (_)
C4,C6: 5.. / C4 = 5  => 10 pairs (_) / C6 = 5  =>  0 pairs (X)
C4,F4: 5.. / C4 = 5  => 10 pairs (_) / F4 = 5  =>  0 pairs (X)
F8,I8: 5.. / F8 = 5  =>  0 pairs (*) / I8 = 5  =>  0 pairs (X)
E6,E7: 5.. / E6 = 5  =>  0 pairs (*) / E7 = 5  =>  0 pairs (X)
G3,G7: 5.. / G3 = 5  =>  0 pairs (X) / G7 = 5  =>  0 pairs (_)
G3,H3: 6.. / G3 = 6  =>  0 pairs (*) / H3 = 6  =>  0 pairs (X)
D6,E6: 6.. / D6 = 6  =>  0 pairs (*) / E6 = 6  =>  0 pairs (X)
D8,H8: 6.. / D8 = 6  =>  0 pairs (X) / H8 = 6  =>  0 pairs (_)
E6,E9: 6.. / E6 = 6  =>  0 pairs (X) / E9 = 6  =>  0 pairs (_)
G3,G9: 6.. / G3 = 6  =>  0 pairs (*) / G9 = 6  =>  0 pairs (X)
E2,E3: 7.. / E2 = 7  =>  8 pairs (_) / E3 = 7  =>  8 pairs (_)
H6,I6: 7.. / H6 = 7  => 10 pairs (_) / I6 = 7  => 10 pairs (_)
D1,F1: 8.. / D1 = 8  => 11 pairs (_) / F1 = 8  =>  9 pairs (_)
A2,C2: 9.. / A2 = 9  => 10 pairs (_) / C2 = 9  =>  0 pairs (X)
E7,D8: 9.. / E7 = 9  =>  0 pairs (X) / D8 = 9  =>  0 pairs (_)
H7,H8: 9.. / H7 = 9  =>  0 pairs (*) / H8 = 9  =>  0 pairs (X)
E7,H7: 9.. / E7 = 9  =>  0 pairs (X) / H7 = 9  =>  0 pairs (_)
D8,H8: 9.. / D8 = 9  =>  0 pairs (*) / H8 = 9  =>  0 pairs (X)
A2,A5: 9.. / A2 = 9  => 10 pairs (_) / A5 = 9  =>  0 pairs (X)
* DURATION: 0:00:45.864038  START: 04:10:07.856323  END: 04:10:53.720361 2017-05-04
* CP COUNT: (28)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,D8,E1,E2,E3,E9,G3,G7,G9,H8)
* 156...739...5.6......1.9...6...1..43.......564.........6.2.........8.4..59.......
* PAIR D1: 4,8 BLK 2
F1: 4,8,2                                # reduction candidate for 4,8
F1: 2 => CTR
* 156842739...5.6......1.96.56...1..43.......564..6......6.2..5.....98.4..59..6.3..
F1: 4,8                                  # 11 pairs
* PAIR D1: 4,8 COL D
D5: 4,8,3,7,9                            # reduction candidate for 4,8
D5: 4,8                                  # 12 pairs
D5: 3,7,9                                # 10 pairs
* PAIR E1: 2,4 BLK 2
F1: 2,4,8                                # reduction candidate for 2,4
F1: 2,4                                  # 11 pairs
F1: 8                                    #  9 pairs
* PAIR E1: 2,4 COL E
E5: 2,4,9                                # reduction candidate for 2,4
E5: 2,4 => CTR
* 156...739...5.6......1.9...6...1..43.......564..6......6.2........98.46.59..6.3..
E5: 9 => SOLVED
* 156428739972536814348179625625817943781394256439652178867243591213985467594761382
* PAIR E2: 3,7 ROW 2
A2: 3,7,2,8,9                            # reduction candidate for 3,7
A2: 3,7 => CTR
* 156...739..95.6......1.9...6...1..439......564..6......6.2........98.46.59..6.3..
A2: 2,8,9                                # 10 pairs
B2: 3,7,2,4,8                            # reduction candidate for 3,7
B2: 3,7                                  # 11 pairs
C2: 3,7,2,8,9                            # reduction candidate for 3,7
C2: 3,7                                  # 11 pairs
* PAIR E3: 3,7 ROW 3
A3: 3,7,2,8                              # reduction candidate for 3,7
A3: 3,7                                  # 12 pairs
B3: 3,7,2,4,8                            # reduction candidate for 3,7
B3: 3,7 => CTR
* 156.2.739.4.5.6......1.95646...1..43....9..564...6.....6425.3.....68.49559..4.6..
B3: 2,4,8                                # 10 pairs
C3: 3,7,2,8                              # reduction candidate for 3,7
C3: 3,7                                  # 12 pairs
* PAIR D8: 6,9 COL D
D6: 6,9,3,8                              # reduction candidate for 6,9
D6: 3,8 => CTR
* 156...739...5.6......1.9...6...1..43.......564...6.....6.25.39....98.46.59.......
D6: 6,9                                  # 12 pairs
* PAIR E9: 4,6 BLK 8
D9: 4,6,3,7                              # reduction candidate for 4,6
D9: 4,6 => CTR
* 156...739...5.6......1.96.56...1..43.......564.........6425.3......8.4..59.......
D9: 3,7                                  # 11 pairs
* PAIR G7: 3,5 ROW 7
F7: 3,5,1,4,7                            # reduction candidate for 3,5
F7: 3,5 => SOLVED
* 156428739972536814348179625625817943781394256439652178867243591213985467594761382
F7: 1,4,7                                # 10 pairs
* PAIR G9: 3,6 ROW 9
D9: 3,6,4,7                              # reduction candidate for 3,6
D9: 3,6 => CTR
* 156...739...5.6......1.9...6...1..43.......564...6.....6.25.39....98.46.59.......
D9: 4,7                                  # 11 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-044-base-pr-000.dot
* REASONING
* DIS # F1: 2 => CTR => F1: 4,8
* DIS # E5: 2,4 => CTR => E5: 9
* PRF # E5: 9 => SOL
* DIS # A2: 3,7 => CTR => A2: 2,8,9
* DIS # B3: 3,7 => CTR => B3: 2,4,8
* DIS # D6: 3,8 => CTR => D6: 6,9
* DIS # D9: 4,6 => CTR => D9: 3,7
* PRF # F7: 3,5 => SOL
* DIS # D9: 3,6 => CTR => D9: 4,7
* CNT   9 HDP CHAINS /  24 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,D8,E1,E2,E3,E9,G3,G7,G9,H8)
* 156...739...5.6......1.9...6...1..43.......564.........6.2.........8.4..59.......
* PAIR D1: 4,8 BLK 2
F1: 4,8,2                                # reduction candidate for 4,8
F1: 2 => CTR
* 156842739...5.6......1.96.56...1..43.......564..6......6.2..5.....98.4..59..6.3..
* PAIR D1: 4,8 COL D
D5: 4,8,3,7,9                            # reduction candidate for 4,8
D5: 4,8                                  # 13 pairs
D5: 3,7,9                                # 11 pairs
* PAIR E2: 3,7 ROW 2
A2: 3,7,2,8,9                            # reduction candidate for 3,7
A2: 3,7 => CTR
* 156.2.739..95.6......1.96.56...1..439...4..564..6......6.2..5.....98.4..59..6.3..
B2: 3,7,2,4,8                            # reduction candidate for 3,7
B2: 3,7                                  # 12 pairs
C2: 3,7,2,8,9                            # reduction candidate for 3,7
C2: 3,7                                  # 12 pairs
* PAIR RESTART
* PAIR E2: 3,7 ROW 2
B2: 3,7,2,4,8                            # reduction candidate for 3,7
B2: 3,7                                  # 12 pairs
C2: 3,7,2,8,9                            # reduction candidate for 3,7
C2: 3,7                                  # 12 pairs
* PAIR E3: 3,7 ROW 3
A3: 3,7,2,8                              # reduction candidate for 3,7
A3: 3,7                                  # 13 pairs
B3: 3,7,2,4,8                            # reduction candidate for 3,7
B3: 3,7 => CTR
* 156.2.739.4.5.6......1.95646...1..43....9..564...6.....6425.3.....68.49559..4.6..
C3: 3,7,2,8                              # reduction candidate for 3,7
C3: 3,7                                  # 13 pairs
* PAIR RESTART
* PAIR E3: 3,7 ROW 3
A3: 3,7,2,8                              # reduction candidate for 3,7
A3: 3,7                                  # 13 pairs
C3: 3,7,2,8                              # reduction candidate for 3,7
C3: 3,7                                  # 13 pairs
* PAIR D8: 6,9 COL D
D6: 6,9,3,8                              # reduction candidate for 6,9
D6: 3,8 => CTR
* 156.2.739...5.6......1.9...6...1..43.......564...6.....6.25.39....98.46.59.......
* PAIR RESTART
* PAIR G7: 3,5 ROW 7
F7: 3,5,1,4,7                            # reduction candidate for 3,5
F7: 3,5 => SOLVED
* 156428739972536814348179625625817943781394256439652178867243591213985467594761382
* DURATION: 0:00:15.855536  START: 04:11:13.695201  END: 04:11:29.550737 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-044-base-pr-001.dot
* REASONING
* DIS # F1: 2 => CTR => F1: 4,8
* DIS F1: 4,8 # A2: 3,7 => CTR => A2: 2,8,9
* DIS F1: 4,8 + A2: 2,8,9 # B3: 3,7 => CTR => B3: 2,4,8
* DIS F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 # D6: 3,8 => CTR => D6: 6,9
* PRF F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 + D6: 6,9 # F7: 3,5 => SOL
* STA F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 + D6: 6,9 + F7: 3,5
* CNT   5 HDP CHAINS /  17 HYP OPENED

Header Info

Top 500 Minimum 17 044

solution: 156428739972536814348179625625817943781394256439652178867243591213985467594761382
info: 1375     FNBHY    S8.f     25103

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

Solution

position: 156428739972536814348179625625817943781394256439652178867243591213985467594761382 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: 4,8 => UNS
* DIS # F1: 2 => CTR => F1: 4,8
* INC # D5: 4,8 => UNS
* INC # D5: 3,7,9 => UNS
* INC # F1: 2,4 => UNS
* INC # F1: 8 => UNS
* DIS # E5: 2,4 => CTR => E5: 9
* PRF # E5: 9 => SOL
* DIS # A2: 3,7 => CTR => A2: 2,8,9
* INC # A2: 2,8,9 => UNS
* INC # B2: 3,7 => UNS
* INC # C2: 3,7 => UNS
* INC # A3: 3,7 => UNS
* DIS # B3: 3,7 => CTR => B3: 2,4,8
* INC # B3: 2,4,8 => UNS
* INC # C3: 3,7 => UNS
* INC # D6: 6,9 => UNS
* DIS # D6: 3,8 => CTR => D6: 6,9
* DIS # D9: 4,6 => CTR => D9: 3,7
* INC # D9: 3,7 => UNS
* PRF # F7: 3,5 => SOL
* INC # F7: 1,4,7 => UNS
* DIS # D9: 3,6 => CTR => D9: 4,7
* INC # D9: 4,7 => UNS
* CNT  24 HDP CHAINS /  24 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F1: 4,8 => UNS
* DIS # F1: 2 => CTR => F1: 4,8
* INC F1: 4,8 # D5: 4,8 => UNS
* INC F1: 4,8 # D5: 3,7,9 => UNS
* DIS F1: 4,8 # A2: 3,7 => CTR => A2: 2,8,9
* INC F1: 4,8 + A2: 2,8,9 # B2: 3,7 => UNS
* INC F1: 4,8 + A2: 2,8,9 # C2: 3,7 => UNS
* INC F1: 4,8 + A2: 2,8,9 # B2: 3,7 => UNS
* INC F1: 4,8 + A2: 2,8,9 # C2: 3,7 => UNS
* INC F1: 4,8 + A2: 2,8,9 # A3: 3,7 => UNS
* DIS F1: 4,8 + A2: 2,8,9 # B3: 3,7 => CTR => B3: 2,4,8
* INC F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 # C3: 3,7 => UNS
* INC F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 # A3: 3,7 => UNS
* INC F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 # C3: 3,7 => UNS
* INC F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 # D6: 6,9 => UNS
* DIS F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 # D6: 3,8 => CTR => D6: 6,9
* PRF F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 + D6: 6,9 # F7: 3,5 => SOL
* STA F1: 4,8 + A2: 2,8,9 + B3: 2,4,8 + D6: 6,9 + F7: 3,5
* CNT  17 HDP CHAINS /  17 HYP OPENED