Analysis of xx-top500-336-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...35....4......1.....9....8..6.1.........9.7......3....3...5.4.9.7............2. initial

Autosolve

position: 91.35..72435..7.19..719..538796312453415..9675..4793817.3.1.594.9.7.513.15.9.372. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # B3: 6,8 => SOL
* DIS # B3: 2 => CTR => B3: 6,8
* DIS # C8: 6,8 => CTR => C8: 2,4
* PRF # C9: 6,8 => SOL
* DIS # B3: 2,6 => CTR => B3: 8
* PRF # B3: 8 => SOL
* DIS # E2: 2,8 => CTR => E2: 6
* PRF # E2: 6 => SOL
* PRF # E2: 6,8 => SOL
* DIS # E2: 2 => CTR => E2: 6,8
* DIS # B3: 2,6 => CTR => B3: 8
* PRF # B3: 8 => SOL
* PRF # B7: 2,6 => SOL
* DIS # B7: 8 => CTR => B7: 2,6
* DIS # C8: 2,6 => CTR => C8: 4,8
* PRF # C8: 4,8 => SOL
* DIS # E2: 2,8 => CTR => E2: 6
* PRF # E2: 6 => SOL
* PRF # E8: 2,8 => SOL
* DIS # F7: 2,8 => CTR => F7: 6
* PRF # F7: 6 => SOL
* PRF # B7: 2,6 => SOL
* DIS # B7: 8 => CTR => B7: 2,6
* DIS # C8: 2,6 => CTR => C8: 4,8
* PRF # C8: 4,8 => SOL
* PRF # E8: 2,6 => SOL
* DIS # F7: 2,8 => CTR => F7: 6
* PRF # F7: 6 => SOL
* PRF # E8: 2,8 => SOL
* PRF # B7: 2,8 => SOL
* DIS # B7: 6 => CTR => B7: 2,8
* DIS # C8: 6,8 => CTR => C8: 2,4
* DIS # E8: 6,8 => CTR => E8: 2,4
* PRF # C9: 6,8 => SOL
* CNT  34 HDP CHAINS /  47 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 # B3: 6,8 => SOL
* STA B3: 6,8
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

...35....4......1.....9....8..6.1.........9.7......3....3...5.4.9.7............2. initial
91.35..72435..7.19..719..538796312453415..9675..4793817.3.1.594.9.7.513.15.9.372. autosolve
916358472435267819287194653879631245341582967562479381723816594694725138158943726 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (12)
C1: 6,8
A3: 2,6
D2: 2,8
G2: 6,8
B6: 2,6
C6: 2,6
E5: 2,8
F5: 2,8
A8: 2,6
D7: 2,8
I8: 6,8
I9: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A3,B3: 2.. / A3 = 2  =>  0 pairs (*) / B3 = 2  =>  0 pairs (X)
D2,E2: 2.. / D2 = 2  =>  0 pairs (*) / E2 = 2  =>  0 pairs (X)
B6,C6: 2.. / B6 = 2  =>  0 pairs (X) / C6 = 2  =>  0 pairs (_)
E5,F5: 2.. / E5 = 2  =>  0 pairs (X) / F5 = 2  =>  0 pairs (_)
A3,A8: 2.. / A3 = 2  =>  0 pairs (*) / A8 = 2  =>  0 pairs (X)
C6,C8: 2.. / C6 = 2  =>  0 pairs (*) / C8 = 2  =>  0 pairs (X)
D2,D7: 2.. / D2 = 2  =>  0 pairs (*) / D7 = 2  =>  0 pairs (X)
F5,F7: 2.. / F5 = 2  =>  0 pairs (*) / F7 = 2  =>  0 pairs (X)
F1,F3: 4.. / F1 = 4  => 14 pairs (_) / F3 = 4  => 14 pairs (_)
G1,G3: 4.. / G1 = 4  => 14 pairs (_) / G3 = 4  => 14 pairs (_)
C8,C9: 4.. / C8 = 4  =>  0 pairs (*) / C9 = 4  =>  0 pairs (X)
E8,E9: 4.. / E8 = 4  => 14 pairs (_) / E9 = 4  =>  0 pairs (*)
F1,G1: 4.. / F1 = 4  => 14 pairs (_) / G1 = 4  => 14 pairs (_)
F3,G3: 4.. / F3 = 4  => 14 pairs (_) / G3 = 4  => 14 pairs (_)
C8,E8: 4.. / C8 = 4  =>  0 pairs (*) / E8 = 4  =>  0 pairs (X)
C9,E9: 4.. / C9 = 4  => 14 pairs (_) / E9 = 4  =>  0 pairs (*)
B6,C6: 6.. / B6 = 6  =>  0 pairs (*) / C6 = 6  =>  0 pairs (X)
I8,I9: 6.. / I8 = 6  =>  0 pairs (X) / I9 = 6  => 12 pairs (_)
E2,G2: 6.. / E2 = 6  =>  0 pairs (*) / G2 = 6  =>  0 pairs (X)
B7,F7: 6.. / B7 = 6  =>  0 pairs (X) / F7 = 6  =>  0 pairs (_)
A3,A8: 6.. / A3 = 6  =>  0 pairs (X) / A8 = 6  =>  0 pairs (_)
C1,B3: 8.. / C1 = 8  =>  0 pairs (X) / B3 = 8  =>  0 pairs (_)
E5,F5: 8.. / E5 = 8  =>  0 pairs (*) / F5 = 8  =>  0 pairs (X)
I8,I9: 8.. / I8 = 8  => 12 pairs (_) / I9 = 8  =>  0 pairs (X)
B3,B7: 8.. / B3 = 8  =>  0 pairs (*) / B7 = 8  =>  0 pairs (X)
D2,D7: 8.. / D2 = 8  =>  0 pairs (X) / D7 = 8  =>  0 pairs (_)
* DURATION: 0:00:49.175705  START: 14:14:38.526411  END: 14:15:27.702116 2017-05-04
* CP COUNT: (26)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B6,C1,C6,D2,D7,E5,F5,G2,I8,I9)
* 91.35..72435..7.19..719..538796312453415..9675..4793817.3.1.594.9.7.513.15.9.372.
* PAIR C1: 6,8 BLK 1
B3: 6,8,2                                # reduction candidate for 6,8
B3: 6,8 => SOLVED
* 916358472435267819287194653879631245341582967562479381723816594694725138158943726
B3: 2 => CTR
* 91835..72435..7.1962719..538796312453415..96756247938178321659429.7.513.15.9.372.
* PAIR C1: 6,8 ROW 1
F1: 6,8,4                                # reduction candidate for 6,8
F1: 6,8                                  # 14 pairs
G1: 6,8,4                                # reduction candidate for 6,8
G1: 6,8                                  # 14 pairs
* PAIR C1: 6,8 COL C
C8: 6,8,2,4                              # reduction candidate for 6,8
C8: 6,8 => CTR
* 91.35..72435..7.19..719..538796312453415..9675624793817.3.16594296745138154983726
C8: 2,4                                  # 13 pairs
C9: 6,8,4                                # reduction candidate for 6,8
C9: 6,8 => SOLVED
* 916358472435267819287194653879631245341582967562479381723816594694725138158943726
C9: 4                                    # 14 pairs
* PAIR A3: 2,6 BLK 1
B3: 2,6,8                                # reduction candidate for 2,6
B3: 2,6 => CTR
* 91835..72435..7.19..719..538796312453415..9675..479381783216594.9.7.513.15.9.372.
B3: 8 => SOLVED
* 916358472435267819287194653879631245341582967562479381723816594694725138158943726
* PAIR D2: 2,8 BLK 2
E2: 2,8,6                                # reduction candidate for 2,8
E2: 2,8 => CTR
* 91.35..72435..7619..719..538796312453415..9675..479381763.1.59429.7.513.15.9.372.
E2: 6 => SOLVED
* 916358472435267819287194653879631245341582967562479381723816594694725138158943726
* PAIR G2: 6,8 BLK 3
G1: 6,8,4                                # reduction candidate for 6,8
G1: 6,8                                  # 14 pairs
G3: 6,8,4                                # reduction candidate for 6,8
G3: 6,8                                  # 14 pairs
* PAIR G2: 6,8 ROW 2
E2: 6,8,2                                # reduction candidate for 6,8
E2: 6,8 => SOLVED
* 916358472435267819287194653879631245341582967562479381723816594694725138158943726
E2: 2 => CTR
* 91.35..72435827619.8719.4538796312453415829675264793817.3218594.9.7.513.15.9.372.
* PAIR B6: 2,6 COL B
B3: 2,6,8                                # reduction candidate for 2,6
B3: 2,6 => CTR
* 91835..72435..7.19..719..538796312453415..9675..479381783216594.9.7.513.15.9.372.
B3: 8 => SOLVED
* 916358472435267819287194653879631245341582967562479381723816594694725138158943726
B7: 2,6,8                                # reduction candidate for 2,6
B7: 2,6 => SOLVED
* 916358472435267819287194653879631245341582967562479381723816594694725138158943726
B7: 8 => CTR
* 91.35..72435..7.19..719..538796312453415..9675..479381783216594.9.7.513.15.9.372.
* PAIR C6: 2,6 COL C
C8: 2,6,4,8                              # reduction candidate for 2,6
C8: 2,6 => CTR
* 91835..724358.7.19..719..538796312453415..9675..4793817.3.1.594.9.745138154983726
C8: 4,8 => SOLVED
* 916358472435267819287194653879631245341582967562479381723816594694725138158943726
* PAIR E5: 2,8 COL E
E2: 2,8,6                                # reduction candidate for 2,8
E2: 2,8 => CTR
* 91.35..72435..7619..719..538796312453415..9675..479381763.1.59429.7.513.15.9.372.
E2: 6 => SOLVED
* 916358472435267819287194653879631245341582967562479381723816594694725138158943726
E8: 2,8,4,6                              # reduction candidate for 2,8
E8: 2,8 => SOLVED
* 916358472435267819287194653879631245341582967562479381723816594694725138158943726
E8: 4,6                                  # 14 pairs
* PAIR F5: 2,8 COL F
F7: 2,8,6                                # reduction candidate for 2,8
F7: 2,8 => CTR
* 91.35..72435..7.19..719..538796312453415..9675..479381763.1.59429.7.513.15.9.372.
F7: 6 => SOLVED
* 916358472435267819287194653879631245341582967562479381723816594694725138158943726
* PAIR A8: 2,6 BLK 7
B7: 2,6,8                                # reduction candidate for 2,6
B7: 2,6 => SOLVED
* 916358472435267819287194653879631245341582967562479381723816594694725138158943726
B7: 8 => CTR
* 91.35..72435..7.19..719..538796312453415..9675..479381783216594.9.7.513.15.9.372.
C8: 2,6,4,8                              # reduction candidate for 2,6
C8: 2,6 => CTR
* 91835..724358.7.19..719..538796312453415..9675..4793817.3.1.594.9.745138154983726
C8: 4,8 => SOLVED
* 916358472435267819287194653879631245341582967562479381723816594694725138158943726
* PAIR A8: 2,6 ROW 8
E8: 2,6,4,8                              # reduction candidate for 2,6
E8: 2,6 => SOLVED
* 916358472435267819287194653879631245341582967562479381723816594694725138158943726
E8: 4,8                                  # 14 pairs
* PAIR D7: 2,8 BLK 8
F7: 2,8,6                                # reduction candidate for 2,8
F7: 2,8 => CTR
* 91.35..72435..7.19..719..538796312453415..9675..479381763.1.59429.7.513.15.9.372.
F7: 6 => SOLVED
* 916358472435267819287194653879631245341582967562479381723816594694725138158943726
E8: 2,8,4,6                              # reduction candidate for 2,8
E8: 2,8 => SOLVED
* 916358472435267819287194653879631245341582967562479381723816594694725138158943726
E8: 4,6                                  # 14 pairs
* PAIR D7: 2,8 ROW 7
B7: 2,8,6                                # reduction candidate for 2,8
B7: 2,8 => SOLVED
* 916358472435267819287194653879631245341582967562479381723816594694725138158943726
B7: 6 => CTR
* 91.35..72435..7.19.8719..538796312453415..9675264793817.3.1.594.9.7.513.15.9.372.
* PAIR I8: 6,8 ROW 8
C8: 6,8,2,4                              # reduction candidate for 6,8
C8: 6,8 => CTR
* 91.35..72435..7.19..719..538796312453415..9675624793817.3.16594296745138154983726
C8: 2,4                                  # 13 pairs
E8: 6,8,2,4                              # reduction candidate for 6,8
E8: 6,8 => CTR
* 91.35..72435..7.1962719..538796312453415..96756247938178321659429478513.15.94372.
E8: 2,4                                  # 13 pairs
* PAIR I9: 6,8 ROW 9
C9: 6,8,4                                # reduction candidate for 6,8
C9: 6,8 => SOLVED
* 916358472435267819287194653879631245341582967562479381723816594694725138158943726
C9: 4                                    # 14 pairs
E9: 6,8,4                                # reduction candidate for 6,8
E9: 6,8                                  # 14 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-336-base-pr-000.dot
* REASONING
* PRF # B3: 6,8 => SOL
* DIS # B3: 2 => CTR => B3: 6,8
* DIS # C8: 6,8 => CTR => C8: 2,4
* PRF # C9: 6,8 => SOL
* DIS # B3: 2,6 => CTR => B3: 8
* PRF # B3: 8 => SOL
* DIS # E2: 2,8 => CTR => E2: 6
* PRF # E2: 6 => SOL
* PRF # E2: 6,8 => SOL
* DIS # E2: 2 => CTR => E2: 6,8
* DIS # B3: 2,6 => CTR => B3: 8
* PRF # B3: 8 => SOL
* PRF # B7: 2,6 => SOL
* DIS # B7: 8 => CTR => B7: 2,6
* DIS # C8: 2,6 => CTR => C8: 4,8
* PRF # C8: 4,8 => SOL
* DIS # E2: 2,8 => CTR => E2: 6
* PRF # E2: 6 => SOL
* PRF # E8: 2,8 => SOL
* DIS # F7: 2,8 => CTR => F7: 6
* PRF # F7: 6 => SOL
* PRF # B7: 2,6 => SOL
* DIS # B7: 8 => CTR => B7: 2,6
* DIS # C8: 2,6 => CTR => C8: 4,8
* PRF # C8: 4,8 => SOL
* PRF # E8: 2,6 => SOL
* DIS # F7: 2,8 => CTR => F7: 6
* PRF # F7: 6 => SOL
* PRF # E8: 2,8 => SOL
* PRF # B7: 2,8 => SOL
* DIS # B7: 6 => CTR => B7: 2,8
* DIS # C8: 6,8 => CTR => C8: 2,4
* DIS # E8: 6,8 => CTR => E8: 2,4
* PRF # C9: 6,8 => SOL
* CNT  34 HDP CHAINS /  47 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B6,C1,C6,D2,D7,E5,F5,G2,I8,I9)
* 91.35..72435..7.19..719..538796312453415..9675..4793817.3.1.594.9.7.513.15.9.372.
* PAIR C1: 6,8 BLK 1
B3: 6,8,2                                # reduction candidate for 6,8
B3: 6,8 => SOLVED
* 916358472435267819287194653879631245341582967562479381723816594694725138158943726
* DURATION: 0:00:02.077595  START: 14:16:25.588286  END: 14:16:27.665881 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-336-base-pr-001.dot
* REASONING
* PRF # B3: 6,8 => SOL
* STA B3: 6,8
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 336

solution: 916358472435267819287194653879631245341582967562479381723816594694725138158943726
info: 3103     FNBWXY   S8.f     8757

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

Solution

position: 916358472435267819287194653879631245341582967562479381723816594694725138158943726 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:

* PRF # B3: 6,8 => SOL
* DIS # B3: 2 => CTR => B3: 6,8
* INC # F1: 6,8 => UNS
* INC # G1: 6,8 => UNS
* DIS # C8: 6,8 => CTR => C8: 2,4
* INC # C8: 2,4 => UNS
* PRF # C9: 6,8 => SOL
* INC # C9: 4 => UNS
* DIS # B3: 2,6 => CTR => B3: 8
* PRF # B3: 8 => SOL
* DIS # E2: 2,8 => CTR => E2: 6
* PRF # E2: 6 => SOL
* INC # G1: 6,8 => UNS
* INC # G3: 6,8 => UNS
* PRF # E2: 6,8 => SOL
* DIS # E2: 2 => CTR => E2: 6,8
* DIS # B3: 2,6 => CTR => B3: 8
* PRF # B3: 8 => SOL
* PRF # B7: 2,6 => SOL
* DIS # B7: 8 => CTR => B7: 2,6
* DIS # C8: 2,6 => CTR => C8: 4,8
* PRF # C8: 4,8 => SOL
* DIS # E2: 2,8 => CTR => E2: 6
* PRF # E2: 6 => SOL
* PRF # E8: 2,8 => SOL
* INC # E8: 4,6 => UNS
* DIS # F7: 2,8 => CTR => F7: 6
* PRF # F7: 6 => SOL
* PRF # B7: 2,6 => SOL
* DIS # B7: 8 => CTR => B7: 2,6
* DIS # C8: 2,6 => CTR => C8: 4,8
* PRF # C8: 4,8 => SOL
* PRF # E8: 2,6 => SOL
* INC # E8: 4,8 => UNS
* DIS # F7: 2,8 => CTR => F7: 6
* PRF # F7: 6 => SOL
* PRF # E8: 2,8 => SOL
* INC # E8: 4,6 => UNS
* PRF # B7: 2,8 => SOL
* DIS # B7: 6 => CTR => B7: 2,8
* DIS # C8: 6,8 => CTR => C8: 2,4
* INC # C8: 2,4 => UNS
* DIS # E8: 6,8 => CTR => E8: 2,4
* INC # E8: 2,4 => UNS
* PRF # C9: 6,8 => SOL
* INC # C9: 4 => UNS
* INC # E9: 6,8 => UNS
* CNT  47 HDP CHAINS /  47 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # B3: 6,8 => SOL
* STA B3: 6,8
* CNT   1 HDP CHAINS /   1 HYP OPENED