Analysis of xx-top500-365-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .1..7.......8..5...........6......123.45..................12.7.5.....3..4....9... initial

Autosolve

position: .15.7....7..82.591..81.5..765.....123245.17.918.2...538..412975591...3244723591.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B2: 3,6 => CTR => B2: 4
* DIS # F2: 4 => CTR => F2: 3,6
* DIS # F2: 3,4 => CTR => F2: 6
* PRF # F2: 6 => SOL
* PRF # E3: 3,4 => SOL
* DIS # E3: 9 => CTR => E3: 3,4
* DIS # F4: 3,4 => CTR => F4: 8
* PRF # F4: 8 => SOL
* PRF # G1: 6,8 => SOL
* DIS # G1: 2 => CTR => G1: 6,8
* DIS # G1: 2,6 => CTR => G1: 8
* PRF # G1: 8 => SOL
* DIS # B3: 3,4 => CTR => B3: 6
* PRF # B3: 6 => SOL
* PRF # E3: 3,4 => SOL
* DIS # E3: 9 => CTR => E3: 3,4
* DIS # F4: 3,4 => CTR => F4: 8
* PRF # F4: 8 => SOL
* PRF # E3: 3,4 => SOL
* DIS # E3: 9 => CTR => E3: 3,4
* DIS # E3: 3 => CTR => E3: 4,9
* DIS # F4: 3 => CTR => F4: 4,8
* PRF # F6: 4,6 => SOL
* DIS # F6: 7 => CTR => F6: 4,6
* DIS # B2: 3,6 => CTR => B2: 4
* PRF # F8: 6,7 => SOL
* DIS # F8: 8 => CTR => F8: 6,7
* DIS # F8: 6,8 => CTR => F8: 7
* PRF # F8: 7 => SOL
* CNT  29 HDP CHAINS /  36 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: 3,6 => CTR => B2: 4
* PRF B2: 4 # E3: 3,4 => SOL
* STA B2: 4 + E3: 3,4
* CNT   2 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

.1..7.......8..5...........6......123.45..................12.7.5.....3..4....9... initial
.15.7....7..82.591..81.5..765.....123245.17.918.2...538..412975591...3244723591.. autosolve
215973846743826591968145237659738412324561789187294653836412975591687324472359168 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (24)
A1: 2,9
C2: 3,6
A3: 2,9
D1: 6,9
F1: 3,4
H1: 3,4
I1: 6,8
G3: 2,6
H3: 3,4
C4: 7,9
C6: 7,9
D4: 7,9
E4: 3,4
E5: 6,8
E6: 4,9
G4: 4,8
H5: 6,8
G6: 4,6
B7: 3,6
C7: 3,6
D8: 6,7
E8: 6,8
H9: 6,8
I9: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,A3: 2.. / A1 = 2  =>  0 pairs (*) / A3 = 2  =>  0 pairs (X)
G1,G3: 2.. / G1 = 2  =>  0 pairs (X) / G3 = 2  =>  0 pairs (_)
A1,G1: 2.. / A1 = 2  =>  0 pairs (*) / G1 = 2  =>  0 pairs (X)
A3,G3: 2.. / A3 = 2  =>  0 pairs (X) / G3 = 2  =>  0 pairs (_)
H1,H3: 3.. / H1 = 3  => 26 pairs (_) / H3 = 3  => 24 pairs (_)
E4,F4: 3.. / E4 = 3  => 25 pairs (_) / F4 = 3  =>  0 pairs (X)
B7,C7: 3.. / B7 = 3  => 24 pairs (_) / C7 = 3  =>  0 pairs (X)
F1,H1: 3.. / F1 = 3  => 24 pairs (_) / H1 = 3  => 26 pairs (_)
C2,C7: 3.. / C2 = 3  => 24 pairs (_) / C7 = 3  =>  0 pairs (X)
E3,E4: 3.. / E3 = 3  =>  0 pairs (X) / E4 = 3  => 25 pairs (_)
B2,B3: 4.. / B2 = 4  => 26 pairs (_) / B3 = 4  =>  0 pairs (X)
H1,H3: 4.. / H1 = 4  => 24 pairs (_) / H3 = 4  => 26 pairs (_)
G4,G6: 4.. / G4 = 4  =>  0 pairs (*) / G6 = 4  =>  0 pairs (X)
F1,H1: 4.. / F1 = 4  => 26 pairs (_) / H1 = 4  => 24 pairs (_)
B2,F2: 4.. / B2 = 4  => 26 pairs (_) / F2 = 4  =>  0 pairs (X)
D1,F2: 6.. / D1 = 6  =>  0 pairs (X) / F2 = 6  =>  0 pairs (_)
E5,F6: 6.. / E5 = 6  =>  0 pairs (*) / F6 = 6  =>  0 pairs (X)
H5,G6: 6.. / H5 = 6  =>  0 pairs (X) / G6 = 6  =>  0 pairs (_)
B7,C7: 6.. / B7 = 6  =>  0 pairs (X) / C7 = 6  => 24 pairs (_)
H9,I9: 6.. / H9 = 6  =>  0 pairs (*) / I9 = 6  =>  0 pairs (X)
B3,G3: 6.. / B3 = 6  =>  0 pairs (*) / G3 = 6  =>  0 pairs (X)
E5,H5: 6.. / E5 = 6  =>  0 pairs (*) / H5 = 6  =>  0 pairs (X)
F6,G6: 6.. / F6 = 6  =>  0 pairs (X) / G6 = 6  =>  0 pairs (_)
C2,C7: 6.. / C2 = 6  =>  0 pairs (X) / C7 = 6  => 24 pairs (_)
D1,D8: 6.. / D1 = 6  =>  0 pairs (X) / D8 = 6  =>  0 pairs (_)
E5,E8: 6.. / E5 = 6  =>  0 pairs (*) / E8 = 6  =>  0 pairs (X)
H5,H9: 6.. / H5 = 6  =>  0 pairs (X) / H9 = 6  =>  0 pairs (_)
I1,I9: 6.. / I1 = 6  =>  0 pairs (*) / I9 = 6  =>  0 pairs (X)
C4,C6: 7.. / C4 = 7  =>  0 pairs (X) / C6 = 7  =>  0 pairs (_)
D4,F6: 7.. / D4 = 7  =>  0 pairs (*) / F6 = 7  =>  0 pairs (X)
D8,F8: 7.. / D8 = 7  =>  0 pairs (X) / F8 = 7  =>  0 pairs (_)
C4,D4: 7.. / C4 = 7  =>  0 pairs (X) / D4 = 7  =>  0 pairs (_)
C6,F6: 7.. / C6 = 7  =>  0 pairs (*) / F6 = 7  =>  0 pairs (X)
D4,D8: 7.. / D4 = 7  =>  0 pairs (*) / D8 = 7  =>  0 pairs (X)
F6,F8: 7.. / F6 = 7  =>  0 pairs (X) / F8 = 7  =>  0 pairs (_)
G1,I1: 8.. / G1 = 8  =>  0 pairs (*) / I1 = 8  =>  0 pairs (X)
F4,E5: 8.. / F4 = 8  =>  0 pairs (*) / E5 = 8  =>  0 pairs (X)
G4,H5: 8.. / G4 = 8  =>  0 pairs (X) / H5 = 8  =>  0 pairs (_)
E8,F8: 8.. / E8 = 8  =>  0 pairs (*) / F8 = 8  =>  0 pairs (X)
H9,I9: 8.. / H9 = 8  =>  0 pairs (X) / I9 = 8  =>  0 pairs (_)
F4,G4: 8.. / F4 = 8  =>  0 pairs (*) / G4 = 8  =>  0 pairs (X)
E5,H5: 8.. / E5 = 8  =>  0 pairs (X) / H5 = 8  =>  0 pairs (_)
E5,E8: 8.. / E5 = 8  =>  0 pairs (X) / E8 = 8  =>  0 pairs (_)
F4,F8: 8.. / F4 = 8  =>  0 pairs (*) / F8 = 8  =>  0 pairs (X)
G1,G4: 8.. / G1 = 8  =>  0 pairs (*) / G4 = 8  =>  0 pairs (X)
H5,H9: 8.. / H5 = 8  =>  0 pairs (*) / H9 = 8  =>  0 pairs (X)
I1,I9: 8.. / I1 = 8  =>  0 pairs (X) / I9 = 8  =>  0 pairs (_)
A1,A3: 9.. / A1 = 9  =>  0 pairs (X) / A3 = 9  =>  0 pairs (_)
D1,E3: 9.. / D1 = 9  =>  0 pairs (*) / E3 = 9  =>  0 pairs (X)
C4,C6: 9.. / C4 = 9  =>  0 pairs (*) / C6 = 9  =>  0 pairs (X)
D4,E6: 9.. / D4 = 9  =>  0 pairs (X) / E6 = 9  =>  0 pairs (_)
A1,D1: 9.. / A1 = 9  =>  0 pairs (X) / D1 = 9  =>  0 pairs (_)
A3,E3: 9.. / A3 = 9  =>  0 pairs (*) / E3 = 9  =>  0 pairs (X)
C4,D4: 9.. / C4 = 9  =>  0 pairs (*) / D4 = 9  =>  0 pairs (X)
C6,E6: 9.. / C6 = 9  =>  0 pairs (X) / E6 = 9  =>  0 pairs (_)
D1,D4: 9.. / D1 = 9  =>  0 pairs (*) / D4 = 9  =>  0 pairs (X)
E3,E6: 9.. / E3 = 9  =>  0 pairs (X) / E6 = 9  =>  0 pairs (_)
* DURATION: 0:02:13.540256  START: 15:17:27.943563  END: 15:19:41.483819 2017-05-04
* CP COUNT: (57)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B7,C2,C4,C6,C7,D1,D4,D8,E4,E5,E6,E8,F1,G3,G4,G6,H1,H3,H5,H9,I1,I9)
* .15.7....7..82.591..81.5..765.....123245.17.918.2...538..412975591...3244723591..
* PAIR C2: 3,6 BLK 1
B2: 3,6,4                                # reduction candidate for 3,6
B2: 3,6 => CTR
* .15.7....7..824591.481.563765..384123245.17.918.2...538..412975591...3244723591..
B2: 4                                    # 26 pairs
B3: 3,6,4                                # reduction candidate for 3,6
B3: 3,6                                  # 26 pairs
* PAIR C2: 3,6 ROW 2
F2: 3,6,4                                # reduction candidate for 3,6
F2: 4 => CTR
* .1567...87..824591.4819563765.93..123245.17.918.2...538..412975591...3244723591..
F2: 3,6                                  # 26 pairs
* PAIR F1: 3,4 BLK 2
F2: 3,4,6                                # reduction candidate for 3,4
F2: 3,4 => CTR
* .1567...87..82.591..81956.765.93..123245.17.918.2...538..412975591...3244723591..
F2: 6 => SOLVED
* 215973846743826591968145237659738412324561789187294653836412975591687324472359168
E3: 3,4,9                                # reduction candidate for 3,4
E3: 3,4 => SOLVED
* 215973846743826591968145237659738412324561789187294653836412975591687324472359168
E3: 9 => CTR
* .15.7....7..82.591..8195..765.93..123245.17.91892476538..4129755917..324472359168
* PAIR F1: 3,4 COL F
F4: 3,4,8                                # reduction candidate for 3,4
F4: 3,4 => CTR
* .15.7....7..82.591..81.5..765....81232458176918.2.64538..412975591.6.3244723591..
F4: 8 => SOLVED
* 215973846743826591968145237659738412324561789187294653836412975591687324472359168
* PAIR I1: 6,8 BLK 3
G1: 6,8,2                                # reduction candidate for 6,8
G1: 6,8 => SOLVED
* 215973846743826591968145237659738412324561789187294653836412975591687324472359168
G1: 2 => CTR
* .15.7.2.87..82.5912.81956.765.93..123245.17.918.2...538..412975591...3244723591..
* PAIR G3: 2,6 BLK 3
G1: 2,6,8                                # reduction candidate for 2,6
G1: 2,6 => CTR
* .15.7...87..82.591..81.5..765....81232458176918.2.64538..412975591.6.3244723591..
G1: 8 => SOLVED
* 215973846743826591968145237659738412324561789187294653836412975591687324472359168
* PAIR H3: 3,4 ROW 3
B3: 3,4,6                                # reduction candidate for 3,4
B3: 3,4 => CTR
* .15.7....7..82.591..81.56.765.....123245.176918.2.64538..412975591.6.3244723591..
B3: 6 => SOLVED
* 215973846743826591968145237659738412324561789187294653836412975591687324472359168
E3: 3,4,9                                # reduction candidate for 3,4
E3: 3,4 => SOLVED
* 215973846743826591968145237659738412324561789187294653836412975591687324472359168
E3: 9 => CTR
* .15.7....7..82.591..8195..765.93..123245.17.91892476538..4129755917..324472359168
* PAIR E4: 3,4 BLK 5
F4: 3,4,8                                # reduction candidate for 3,4
F4: 3,4 => CTR
* .15.7....7..82.591..81.5..765....81232458176918.2.64538..412975591.6.3244723591..
F4: 8 => SOLVED
* 215973846743826591968145237659738412324561789187294653836412975591687324472359168
* PAIR E4: 3,4 COL E
E3: 3,4,9                                # reduction candidate for 3,4
E3: 3,4 => SOLVED
* 215973846743826591968145237659738412324561789187294653836412975591687324472359168
E3: 9 => CTR
* .15.7....7..82.591..8195..765.93..123245.17.91892476538..4129755917..324472359168
* PAIR E6: 4,9 COL E
E3: 4,9,3                                # reduction candidate for 4,9
E3: 3 => CTR
* .1597....7..82659196813524765974..123245.17.918.2...538..412975591...3244723591..
E3: 4,9                                  # 25 pairs
* PAIR G4: 4,8 ROW 4
F4: 4,8,3                                # reduction candidate for 4,8
F4: 3 => CTR
* .15.7....7..82.591..81.5..765...381232458176918.2.64538..412975591.6.3244723591..
F4: 4,8                                  # 25 pairs
* PAIR G6: 4,6 ROW 6
F6: 4,6,7                                # reduction candidate for 4,6
F6: 4,6 => SOLVED
* 215973846743826591968145237659738412324561789187294653836412975591687324472359168
F6: 7 => CTR
* .1567....7..82.591..81.5..765.....1232456178918.2.76538..412975591786324472359168
* PAIR B7: 3,6 COL B
B2: 3,6,4                                # reduction candidate for 3,6
B2: 3,6 => CTR
* .15.7....7..824591.481.563765..384123245.17.918.2...538..412975591...3244723591..
B2: 4                                    # 26 pairs
B3: 3,6,4                                # reduction candidate for 3,6
B3: 3,6                                  # 26 pairs
* PAIR D8: 6,7 BLK 8
F8: 6,7,8                                # reduction candidate for 6,7
F8: 6,7 => SOLVED
* 215973846743826591968145237659738412324561789187294653836412975591687324472359168
F8: 8 => CTR
* .15.7....7..82.591..81.5..765.....123245.17.918.2.76538..412975591768324472359168
* PAIR E8: 6,8 BLK 8
F8: 6,8,7                                # reduction candidate for 6,8
F8: 6,8 => CTR
* .1567....7..82.591..81.5..765.....123245.17.918.2.76538..4129755917..324472359168
F8: 7 => SOLVED
* 215973846743826591968145237659738412324561789187294653836412975591687324472359168
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-365-base-pr-000.dot
* REASONING
* DIS # B2: 3,6 => CTR => B2: 4
* DIS # F2: 4 => CTR => F2: 3,6
* DIS # F2: 3,4 => CTR => F2: 6
* PRF # F2: 6 => SOL
* PRF # E3: 3,4 => SOL
* DIS # E3: 9 => CTR => E3: 3,4
* DIS # F4: 3,4 => CTR => F4: 8
* PRF # F4: 8 => SOL
* PRF # G1: 6,8 => SOL
* DIS # G1: 2 => CTR => G1: 6,8
* DIS # G1: 2,6 => CTR => G1: 8
* PRF # G1: 8 => SOL
* DIS # B3: 3,4 => CTR => B3: 6
* PRF # B3: 6 => SOL
* PRF # E3: 3,4 => SOL
* DIS # E3: 9 => CTR => E3: 3,4
* DIS # F4: 3,4 => CTR => F4: 8
* PRF # F4: 8 => SOL
* PRF # E3: 3,4 => SOL
* DIS # E3: 9 => CTR => E3: 3,4
* DIS # E3: 3 => CTR => E3: 4,9
* DIS # F4: 3 => CTR => F4: 4,8
* PRF # F6: 4,6 => SOL
* DIS # F6: 7 => CTR => F6: 4,6
* DIS # B2: 3,6 => CTR => B2: 4
* PRF # F8: 6,7 => SOL
* DIS # F8: 8 => CTR => F8: 6,7
* DIS # F8: 6,8 => CTR => F8: 7
* PRF # F8: 7 => SOL
* CNT  29 HDP CHAINS /  36 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B7,C2,C4,C6,C7,D1,D4,D8,E4,E5,E6,E8,F1,G3,G4,G6,H1,H3,H5,H9,I1,I9)
* .15.7....7..82.591..81.5..765.....123245.17.918.2...538..412975591...3244723591..
* PAIR C2: 3,6 BLK 1
B2: 3,6,4                                # reduction candidate for 3,6
B2: 3,6 => CTR
* .15.7....7..824591.481.563765..384123245.17.918.2...538..412975591...3244723591..
* RESTART
* PAIR F1: 3,4 BLK 2
E3: 3,4,9                                # reduction candidate for 3,4
E3: 3,4 => SOLVED
* 215973846743826591968145237659738412324561789187294653836412975591687324472359168
* DURATION: 0:00:04.113645  START: 15:20:34.792755  END: 15:20:38.906400 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-365-base-pr-001.dot
* REASONING
* DIS # B2: 3,6 => CTR => B2: 4
* PRF B2: 4 # E3: 3,4 => SOL
* STA B2: 4 + E3: 3,4
* CNT   2 HDP CHAINS /   2 HYP OPENED

Header Info

Top 500 Minimum 17 365

solution: 215973846743826591968145237659738412324561789187294653836412975591687324472359168
info: 4984     FNBTHWY  S8.f     15372

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

Solution

position: 215973846743826591968145237659738412324561789187294653836412975591687324472359168 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: 3,6 => CTR => B2: 4
* INC # B2: 4 => UNS
* INC # B3: 3,6 => UNS
* INC # F2: 3,6 => UNS
* DIS # F2: 4 => CTR => F2: 3,6
* DIS # F2: 3,4 => CTR => F2: 6
* PRF # F2: 6 => SOL
* PRF # E3: 3,4 => SOL
* DIS # E3: 9 => CTR => E3: 3,4
* DIS # F4: 3,4 => CTR => F4: 8
* PRF # F4: 8 => SOL
* PRF # G1: 6,8 => SOL
* DIS # G1: 2 => CTR => G1: 6,8
* DIS # G1: 2,6 => CTR => G1: 8
* PRF # G1: 8 => SOL
* DIS # B3: 3,4 => CTR => B3: 6
* PRF # B3: 6 => SOL
* PRF # E3: 3,4 => SOL
* DIS # E3: 9 => CTR => E3: 3,4
* DIS # F4: 3,4 => CTR => F4: 8
* PRF # F4: 8 => SOL
* PRF # E3: 3,4 => SOL
* DIS # E3: 9 => CTR => E3: 3,4
* INC # E3: 4,9 => UNS
* DIS # E3: 3 => CTR => E3: 4,9
* INC # F4: 4,8 => UNS
* DIS # F4: 3 => CTR => F4: 4,8
* PRF # F6: 4,6 => SOL
* DIS # F6: 7 => CTR => F6: 4,6
* DIS # B2: 3,6 => CTR => B2: 4
* INC # B2: 4 => UNS
* INC # B3: 3,6 => UNS
* PRF # F8: 6,7 => SOL
* DIS # F8: 8 => CTR => F8: 6,7
* DIS # F8: 6,8 => CTR => F8: 7
* PRF # F8: 7 => SOL
* CNT  36 HDP CHAINS /  36 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B2: 3,6 => CTR => B2: 4
* PRF B2: 4 # E3: 3,4 => SOL
* STA B2: 4 + E3: 3,4
* CNT   2 HDP CHAINS /   2 HYP OPENED