Analysis of xx-top500-186-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...4.5...7.....3........1..3..7.........8..6.....3...5.65..8......2..7...4....... initial

Autosolve

position: ...4.56.77.486.35.5.63.714.35.7468..47.58..636...3.475.65.78.34...2547.6.476.35.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # E1: 2 => SOL
* DIS # B2: 2 => CTR => B2: 1,9
* PRF # E1: 2,9 => SOL
* PRF # B2: 2,9 => SOL
* DIS # I4: 2,9 => CTR => I4: 1
* DIS # C5: 2,9 => CTR => C5: 1
* DIS # I4: 2,9 => CTR => I4: 1
* DIS # I4: 2,9 => CTR => I4: 1
* DIS # C5: 2,9 => CTR => C5: 1
* DIS # A7: 2 => CTR => A7: 1,9
* DIS # A9: 1,9 => CTR => A9: 2,8
* PRF # E1: 2 => SOL
* PRF # A7: 1 => SOL
* CNT  13 HDP CHAINS /  48 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # E1: 2 => SOL
* STA E1: 2
* CNT   1 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

...4.5...7.....3........1..3..7.........8..6.....3...5.65..8......2..7...4....... initial
...4.56.77.486.35.5.63.714.35.7468..47.58..636...3.475.65.78.34...2547.6.476.35.. autosolve
813425697794861352526397148359746821471582963682139475165978234938254716247613589 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
F2: 1,9
E3: 2,9
I2: 2,9
C4: 2,9
D6: 1,9
G5: 2,9
D7: 1,9
E9: 1,9
G7: 2,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E1,F2: 1.. / E1 = 1  => 16 pairs (_) / F2 = 1  =>  0 pairs (*)
H4,I4: 1.. / H4 = 1  =>  0 pairs (X) / I4 = 1  => 10 pairs (_)
D7,E9: 1.. / D7 = 1  => 16 pairs (_) / E9 = 1  =>  0 pairs (*)
B2,F2: 1.. / B2 = 1  => 16 pairs (_) / F2 = 1  =>  0 pairs (*)
C5,F5: 1.. / C5 = 1  => 10 pairs (_) / F5 = 1  =>  0 pairs (X)
A7,D7: 1.. / A7 = 1  =>  0 pairs (*) / D7 = 1  =>  0 pairs (X)
D6,D7: 1.. / D6 = 1  =>  0 pairs (*) / D7 = 1  =>  0 pairs (X)
E1,E9: 1.. / E1 = 1  => 16 pairs (_) / E9 = 1  =>  0 pairs (*)
I4,I9: 1.. / I4 = 1  => 10 pairs (_) / I9 = 1  =>  0 pairs (X)
E1,E3: 2.. / E1 = 2  =>  0 pairs (*) / E3 = 2  =>  0 pairs (X)
F5,F6: 2.. / F5 = 2  => 14 pairs (_) / F6 = 2  => 10 pairs (_)
A7,A9: 2.. / A7 = 2  =>  0 pairs (X) / A9 = 2  => 12 pairs (_)
B2,I2: 2.. / B2 = 2  =>  0 pairs (X) / I2 = 2  => 12 pairs (_)
A7,G7: 2.. / A7 = 2  =>  0 pairs (X) / G7 = 2  => 12 pairs (_)
G5,G7: 2.. / G5 = 2  =>  0 pairs (X) / G7 = 2  => 12 pairs (_)
B1,C1: 3.. / B1 = 3  =>  9 pairs (_) / C1 = 3  =>  9 pairs (_)
B8,C8: 3.. / B8 = 3  =>  9 pairs (_) / C8 = 3  =>  9 pairs (_)
B1,B8: 3.. / B1 = 3  =>  9 pairs (_) / B8 = 3  =>  9 pairs (_)
C1,C8: 3.. / C1 = 3  =>  9 pairs (_) / C8 = 3  =>  9 pairs (_)
H1,I3: 8.. / H1 = 8  => 13 pairs (_) / I3 = 8  => 11 pairs (_)
B6,C6: 8.. / B6 = 8  => 13 pairs (_) / C6 = 8  =>  9 pairs (_)
B3,I3: 8.. / B3 = 8  => 13 pairs (_) / I3 = 8  => 11 pairs (_)
I3,I9: 8.. / I3 = 8  => 11 pairs (_) / I9 = 8  => 13 pairs (_)
D7,E9: 9.. / D7 = 9  =>  0 pairs (*) / E9 = 9  =>  0 pairs (X)
D6,D7: 9.. / D6 = 9  => 16 pairs (_) / D7 = 9  =>  0 pairs (*)
G5,G7: 9.. / G5 = 9  => 12 pairs (_) / G7 = 9  =>  0 pairs (X)
* DURATION: 0:00:43.046360  START: 09:02:41.825250  END: 09:03:24.871610 2017-05-04
* CP COUNT: (26)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C4,D6,D7,E3,E9,F2,G5,G7,I2)
* ...4.56.77.486.35.5.63.714.35.7468..47.58..636...3.475.65.78.34...2547.6.476.35..
* PAIR F2: 1,9 BLK 2
E1: 1,9,2                                # reduction candidate for 1,9
E1: 2 => SOLVED
* 813425697794861352526397148359746821471582963682139475165978234938254716247613589
E1: 1,9                                  # 11 pairs
* PAIR F2: 1,9 ROW 2
B2: 1,9,2                                # reduction candidate for 1,9
B2: 2 => CTR
* .134.56877248613595863971423597468..47158..636..13.475165978234...254716247613598
B2: 1,9                                  # 12 pairs
* PAIR F2: 1,9 COL F
F5: 1,9,2                                # reduction candidate for 1,9
F5: 1,9                                  # 10 pairs
F6: 1,9,2                                # reduction candidate for 1,9
F6: 1,9                                  # 14 pairs
* PAIR E3: 2,9 BLK 2
E1: 2,9,1                                # reduction candidate for 2,9
E1: 2,9 => SOLVED
* 813425697794861352526397148359746821471582963682139475165978234938254716247613589
E1: 1                                    # 16 pairs
* PAIR E3: 2,9 ROW 3
B3: 2,9,8                                # reduction candidate for 2,9
B3: 2,9                                  # 11 pairs
I3: 2,9,8                                # reduction candidate for 2,9
I3: 2,9                                  # 13 pairs
* PAIR I2: 2,9 BLK 3
H1: 2,9,8                                # reduction candidate for 2,9
H1: 2,9                                  # 11 pairs
I3: 2,9,8                                # reduction candidate for 2,9
I3: 2,9                                  # 13 pairs
* PAIR I2: 2,9 ROW 2
B2: 2,9,1                                # reduction candidate for 2,9
B2: 2,9 => SOLVED
* 813425697794861352526397148359746821471582963682139475165978234938254716247613589
B2: 1                                    # 16 pairs
* PAIR I2: 2,9 COL I
I4: 2,9,1                                # reduction candidate for 2,9
I4: 2,9 => CTR
* ...4156.77148693525.632714835274681947958126368193247526517893419.2547.6.476.35.1
I4: 1                                    # 10 pairs
I9: 2,9,1,8                              # reduction candidate for 2,9
I9: 2,9                                  # 16 pairs
* PAIR C4: 2,9 BLK 4
C5: 2,9,1                                # reduction candidate for 2,9
C5: 2,9 => CTR
* .234156.771486935259632714835.7468.9479581263681932475265178934938254716.476935..
C5: 1                                    # 10 pairs
B6: 2,9,1,8                              # reduction candidate for 2,9
B6: 2,9                                  # 12 pairs
C6: 2,9,1,8                              # reduction candidate for 2,9
C6: 2,9                                  # 15 pairs
* PAIR C4: 2,9 ROW 4
H4: 2,9,1                                # reduction candidate for 2,9
H4: 2,9                                  # 10 pairs
I4: 2,9,1                                # reduction candidate for 2,9
I4: 2,9 => CTR
* ...4156.77148693525.632714835274681947958126368193247526517893419.2547.6.476.35.1
I4: 1                                    # 10 pairs
* PAIR C4: 2,9 COL C
C1: 2,9,1,3,8                            # reduction candidate for 2,9
C1: 2,9                                  # 12 pairs
C1: 1,3,8                                #  9 pairs
* PAIR D6: 1,9 BLK 5
F5: 1,9,2                                # reduction candidate for 1,9
F5: 1,9                                  # 10 pairs
F6: 1,9,2                                # reduction candidate for 1,9
F6: 1,9                                  # 14 pairs
* PAIR D6: 1,9 ROW 6
B6: 1,9,2,8                              # reduction candidate for 1,9
B6: 1,9                                  # 11 pairs
C6: 1,9,2,8                              # reduction candidate for 1,9
C6: 1,9                                  # 15 pairs
* PAIR G5: 2,9 BLK 6
H4: 2,9,1                                # reduction candidate for 2,9
H4: 2,9                                  # 10 pairs
I4: 2,9,1                                # reduction candidate for 2,9
I4: 2,9 => CTR
* ...4156.77148693525.632714835274681947958126368193247526517893419.2547.6.476.35.1
I4: 1                                    # 10 pairs
* PAIR G5: 2,9 ROW 5
C5: 2,9,1                                # reduction candidate for 2,9
C5: 2,9 => CTR
* .234156.771486935259632714835.7468.9479581263681932475265178934938254716.476935..
C5: 1                                    # 10 pairs
F5: 2,9,1                                # reduction candidate for 2,9
F5: 2,9                                  # 10 pairs
* PAIR D7: 1,9 ROW 7
A7: 1,9,2                                # reduction candidate for 1,9
A7: 2 => CTR
* .234156.77148693525.632714.3527468..479581263681932475265178934.38254716147693528
A7: 1,9                                  # 12 pairs
* PAIR E9: 1,9 ROW 9
A9: 1,9,2,8                              # reduction candidate for 1,9
A9: 1,9 => CTR
* .2341568771486935258632714.35.7468..4795812636.1932475265178934...2547.6147693528
A9: 2,8                                  # 10 pairs
H9: 1,9,2,8                              # reduction candidate for 1,9
H9: 1,9                                  # 14 pairs
I9: 1,9,2,8                              # reduction candidate for 1,9
I9: 1,9                                  # 14 pairs
* PAIR E9: 1,9 COL E
E1: 1,9,2                                # reduction candidate for 1,9
E1: 2 => SOLVED
* 813425697794861352526397148359746821471582963682139475165978234938254716247613589
E1: 1,9                                  # 11 pairs
* PAIR G7: 2,9 BLK 9
H9: 2,9,1,8                              # reduction candidate for 2,9
H9: 2,9                                  # 13 pairs
I9: 2,9,1,8                              # reduction candidate for 2,9
I9: 2,9                                  # 16 pairs
* PAIR G7: 2,9 ROW 7
A7: 2,9,1                                # reduction candidate for 2,9
A7: 1 => SOLVED
* 813425697794861352526397148359746821471582963682139475165978234938254716247613589
A7: 2,9                                  # 16 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-186-base-pr-000.dot
* REASONING
* PRF # E1: 2 => SOL
* DIS # B2: 2 => CTR => B2: 1,9
* PRF # E1: 2,9 => SOL
* PRF # B2: 2,9 => SOL
* DIS # I4: 2,9 => CTR => I4: 1
* DIS # C5: 2,9 => CTR => C5: 1
* DIS # I4: 2,9 => CTR => I4: 1
* DIS # I4: 2,9 => CTR => I4: 1
* DIS # C5: 2,9 => CTR => C5: 1
* DIS # A7: 2 => CTR => A7: 1,9
* DIS # A9: 1,9 => CTR => A9: 2,8
* PRF # E1: 2 => SOL
* PRF # A7: 1 => SOL
* CNT  13 HDP CHAINS /  48 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C4,D6,D7,E3,E9,F2,G5,G7,I2)
* ...4.56.77.486.35.5.63.714.35.7468..47.58..636...3.475.65.78.34...2547.6.476.35..
* PAIR F2: 1,9 BLK 2
E1: 1,9,2                                # reduction candidate for 1,9
E1: 2 => SOLVED
* 813425697794861352526397148359746821471582963682139475165978234938254716247613589
* DURATION: 0:00:02.765281  START: 09:04:08.569984  END: 09:04:11.335265 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-186-base-pr-001.dot
* REASONING
* PRF # E1: 2 => SOL
* STA E1: 2
* CNT   1 HDP CHAINS /   2 HYP OPENED

Header Info

Top 500 Minimum 17 186

solution: 813425697794861352526397148359746821471582963682139475165978234938254716247613589
info: 1835     FNBTWXY  S8.f     9305

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

Solution

position: 813425697794861352526397148359746821471582963682139475165978234938254716247613589 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 # E1: 1,9 => UNS
* PRF # E1: 2 => SOL
* INC # B2: 1,9 => UNS
* DIS # B2: 2 => CTR => B2: 1,9
* INC # F5: 1,9 => UNS
* INC # F6: 1,9 => UNS
* PRF # E1: 2,9 => SOL
* INC # E1: 1 => UNS
* INC # B3: 2,9 => UNS
* INC # I3: 2,9 => UNS
* INC # H1: 2,9 => UNS
* INC # I3: 2,9 => UNS
* PRF # B2: 2,9 => SOL
* INC # B2: 1 => UNS
* DIS # I4: 2,9 => CTR => I4: 1
* INC # I4: 1 => UNS
* INC # I9: 2,9 => UNS
* DIS # C5: 2,9 => CTR => C5: 1
* INC # C5: 1 => UNS
* INC # B6: 2,9 => UNS
* INC # C6: 2,9 => UNS
* INC # H4: 2,9 => UNS
* DIS # I4: 2,9 => CTR => I4: 1
* INC # I4: 1 => UNS
* INC # C1: 2,9 => UNS
* INC # C1: 1,3,8 => UNS
* INC # F5: 1,9 => UNS
* INC # F6: 1,9 => UNS
* INC # B6: 1,9 => UNS
* INC # C6: 1,9 => UNS
* INC # H4: 2,9 => UNS
* DIS # I4: 2,9 => CTR => I4: 1
* INC # I4: 1 => UNS
* DIS # C5: 2,9 => CTR => C5: 1
* INC # C5: 1 => UNS
* INC # F5: 2,9 => UNS
* INC # A7: 1,9 => UNS
* DIS # A7: 2 => CTR => A7: 1,9
* DIS # A9: 1,9 => CTR => A9: 2,8
* INC # A9: 2,8 => UNS
* INC # H9: 1,9 => UNS
* INC # I9: 1,9 => UNS
* INC # E1: 1,9 => UNS
* PRF # E1: 2 => SOL
* INC # H9: 2,9 => UNS
* INC # I9: 2,9 => UNS
* INC # A7: 2,9 => UNS
* PRF # A7: 1 => SOL
* CNT  48 HDP CHAINS /  48 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E1: 1,9 => UNS
* PRF # E1: 2 => SOL
* STA E1: 2
* CNT   2 HDP CHAINS /   2 HYP OPENED