Analysis of xx-top500-376-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 5....64.....3................2.4.8...3.25.....9.......7....4...1......2........39 initial

Autosolve

position: 52..964.39..3.52..3..4.29..6.2.4389.83.259.4.49....3.27.3924...1.9.3..242......39 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # C6: 1,7 => SOL
* PRF # I4: 1,7 => SOL
* DIS # I5: 7 => CTR => I5: 1,6
* DIS # F9: 7,8 => CTR => F9: 1
* DIS # F6: 1 => CTR => F6: 7,8
* CNT   5 HDP CHAINS /  32 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 # C6: 1,7 => SOL
* STA C6: 1,7
* CNT   1 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

5....64.....3................2.4.8...3.25.....9.......7....4...1......2........39 initial
52..964.39..3.52..3..4.29..6.2.4389.83.259.4.49....3.27.3924...1.9.3..242......39 autosolve
528796413974315268316482975652143897837259146491678352763924581189537624245861739 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
C5: 1,7
D4: 1,7
G5: 1,6
B7: 5,6
F8: 7,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F6,F9: 1.. / F6 = 1  =>  0 pairs (X) / F9 = 1  =>  6 pairs (_)
G5,G7: 1.. / G5 = 1  => 11 pairs (_) / G7 = 1  => 11 pairs (_)
B2,C2: 4.. / B2 = 4  =>  8 pairs (_) / C2 = 4  =>  5 pairs (_)
B9,C9: 4.. / B9 = 4  =>  5 pairs (_) / C9 = 4  =>  8 pairs (_)
B2,B9: 4.. / B2 = 4  =>  8 pairs (_) / B9 = 4  =>  5 pairs (_)
C2,C9: 4.. / C2 = 4  =>  5 pairs (_) / C9 = 4  =>  8 pairs (_)
H3,I3: 5.. / H3 = 5  =>  7 pairs (_) / I3 = 5  =>  0 pairs (*)
B4,C6: 5.. / B4 = 5  =>  0 pairs (*) / C6 = 5  =>  0 pairs (X)
I4,H6: 5.. / I4 = 5  =>  7 pairs (_) / H6 = 5  =>  0 pairs (*)
D8,D9: 5.. / D8 = 5  =>  8 pairs (_) / D9 = 5  =>  8 pairs (_)
B4,I4: 5.. / B4 = 5  =>  0 pairs (*) / I4 = 5  =>  0 pairs (X)
C6,H6: 5.. / C6 = 5  =>  7 pairs (_) / H6 = 5  =>  0 pairs (*)
B7,G7: 5.. / B7 = 5  => 10 pairs (_) / G7 = 5  => 12 pairs (_)
C6,C9: 5.. / C6 = 5  =>  7 pairs (_) / C9 = 5  =>  0 pairs (*)
H3,H6: 5.. / H3 = 5  =>  7 pairs (_) / H6 = 5  =>  0 pairs (*)
I3,I4: 5.. / I3 = 5  =>  0 pairs (*) / I4 = 5  =>  0 pairs (X)
D6,E6: 6.. / D6 = 6  =>  6 pairs (_) / E6 = 6  =>  7 pairs (_)
G5,I5: 6.. / G5 = 6  => 11 pairs (_) / I5 = 6  => 11 pairs (_)
E6,E9: 6.. / E6 = 6  =>  7 pairs (_) / E9 = 6  =>  6 pairs (_)
G8,G9: 7.. / G8 = 7  => 15 pairs (_) / G9 = 7  =>  7 pairs (_)
C5,I5: 7.. / C5 = 7  => 10 pairs (_) / I5 = 7  =>  0 pairs (X)
H7,I7: 8.. / H7 = 8  =>  7 pairs (_) / I7 = 8  =>  6 pairs (_)
* DURATION: 0:00:37.876072  START: 15:44:40.360078  END: 15:45:18.236150 2017-05-04
* CP COUNT: (22)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,C5,D4,F8,G5)
* 52..964.39..3.52..3..4.29..6.2.4389.83.259.4.49....3.27.3924...1.9.3..242......39
* PAIR C5: 1,7 BLK 4
B4: 1,7,5                                # reduction candidate for 1,7
B4: 1,7                                  #  7 pairs
C6: 1,7,5                                # reduction candidate for 1,7
C6: 1,7 => SOLVED
* 528796413974315268316482975652143897837259146491678352763924581189537624245861739
C6: 5                                    #  7 pairs
* PAIR C5: 1,7 ROW 5
I5: 1,7,6                                # reduction candidate for 1,7
I5: 6                                    # 11 pairs
I5: 1,7                                  # 11 pairs
* PAIR C5: 1,7 COL C
C1: 1,7,8                                # reduction candidate for 1,7
C1: 1,7                                  #  9 pairs
C2: 1,7,4,6,8                            # reduction candidate for 1,7
C2: 1,7                                  # 14 pairs
C3: 1,7,6,8                              # reduction candidate for 1,7
C3: 1,7                                  # 15 pairs
* PAIR D4: 1,7 BLK 5
D6: 1,7,6,8                              # reduction candidate for 1,7
D6: 1,7                                  # 18 pairs
E6: 1,7,6,8                              # reduction candidate for 1,7
E6: 1,7                                  #  9 pairs
F6: 1,7,8                                # reduction candidate for 1,7
F6: 1,7                                  #  8 pairs
* PAIR D4: 1,7 ROW 4
B4: 1,7,5                                # reduction candidate for 1,7
B4: 1,7                                  #  7 pairs
I4: 1,7,5                                # reduction candidate for 1,7
I4: 1,7 => SOLVED
* 528796413974315268316482975652143897837259146491678352763924581189537624245861739
I4: 5                                    #  7 pairs
* PAIR D4: 1,7 COL D
D1: 1,7,8                                # reduction candidate for 1,7
D1: 1,7                                  #  7 pairs
D9: 1,7,5,6,8                            # reduction candidate for 1,7
D9: 1,7                                  # 20 pairs
* PAIR G5: 1,6 BLK 6
I5: 1,6,7                                # reduction candidate for 1,6
I5: 7 => CTR
* 52..964.39..3.52..3..4.29..672143895831259647495...3127539241..1.9.3..242....1.39
I5: 1,6                                  # 10 pairs
* PAIR G5: 1,6 COL G
G7: 1,6,5                                # reduction candidate for 1,6
G7: 5                                    # 12 pairs
G7: 1,6                                  # 10 pairs
* PAIR B7: 5,6 BLK 7
B8: 5,6,8                                # reduction candidate for 5,6
B8: 5,6                                  # 11 pairs
B9: 5,6,4,8                              # reduction candidate for 5,6
B9: 5,6                                  # 12 pairs
C9: 5,6,4,8                              # reduction candidate for 5,6
C9: 5,6                                  #  9 pairs
* PAIR B7: 5,6 ROW 7
G7: 5,6,1                                # reduction candidate for 5,6
G7: 5,6                                  # 11 pairs
G7: 1                                    # 11 pairs
* PAIR F8: 7,8 BLK 8
D8: 7,8,5,6                              # reduction candidate for 7,8
D8: 7,8                                  # 13 pairs
D9: 7,8,1,5,6                            # reduction candidate for 7,8
D9: 7,8                                  # 10 pairs
E9: 7,8,1,6                              # reduction candidate for 7,8
E9: 7,8                                  # 10 pairs
F9: 7,8,1                                # reduction candidate for 7,8
F9: 7,8 => CTR
* 52..964739.43.52..3.64.29.5652743891831259647497..13527.3924...1.9.3..242.5....39
F9: 1                                    #  6 pairs
* PAIR F8: 7,8 COL F
F6: 7,8,1                                # reduction candidate for 7,8
F6: 1 => CTR
* 52..964739.43.52..3.64.29.5652743891831259647497..13527.3924...1.9.3..242.5....39
F6: 7,8                                  #  6 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-376-base-pr-000.dot
* REASONING
* PRF # C6: 1,7 => SOL
* PRF # I4: 1,7 => SOL
* DIS # I5: 7 => CTR => I5: 1,6
* DIS # F9: 7,8 => CTR => F9: 1
* DIS # F6: 1 => CTR => F6: 7,8
* CNT   5 HDP CHAINS /  32 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,C5,D4,F8,G5)
* 52..964.39..3.52..3..4.29..6.2.4389.83.259.4.49....3.27.3924...1.9.3..242......39
* PAIR C5: 1,7 BLK 4
B4: 1,7,5                                # reduction candidate for 1,7
B4: 1,7                                  #  7 pairs
C6: 1,7,5                                # reduction candidate for 1,7
C6: 1,7 => SOLVED
* 528796413974315268316482975652143897837259146491678352763924581189537624245861739
* DURATION: 0:00:03.214843  START: 15:45:49.206105  END: 15:45:52.420948 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-376-base-pr-001.dot
* REASONING
* PRF # C6: 1,7 => SOL
* STA C6: 1,7
* CNT   1 HDP CHAINS /   2 HYP OPENED

Header Info

Top 500 Minimum 17 376

solution: 528796413974315268316482975652143897837259146491678352763924581189537624245861739
info: 17695    FNBXK    S8.f     41972

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

Solution

position: 528796413974315268316482975652143897837259146491678352763924581189537624245861739 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 # B4: 1,7 => UNS
* PRF # C6: 1,7 => SOL
* INC # C6: 5 => UNS
* INC # I5: 1,7 => UNS
* INC # I5: 6 => UNS
* INC # C1: 1,7 => UNS
* INC # C2: 1,7 => UNS
* INC # C3: 1,7 => UNS
* INC # D6: 1,7 => UNS
* INC # E6: 1,7 => UNS
* INC # F6: 1,7 => UNS
* INC # B4: 1,7 => UNS
* PRF # I4: 1,7 => SOL
* INC # I4: 5 => UNS
* INC # D1: 1,7 => UNS
* INC # D9: 1,7 => UNS
* INC # I5: 1,6 => UNS
* DIS # I5: 7 => CTR => I5: 1,6
* INC # G7: 1,6 => UNS
* INC # G7: 5 => UNS
* INC # B8: 5,6 => UNS
* INC # B9: 5,6 => UNS
* INC # C9: 5,6 => UNS
* INC # G7: 5,6 => UNS
* INC # G7: 1 => UNS
* INC # D8: 7,8 => UNS
* INC # D9: 7,8 => UNS
* INC # E9: 7,8 => UNS
* DIS # F9: 7,8 => CTR => F9: 1
* INC # F9: 1 => UNS
* INC # F6: 7,8 => UNS
* DIS # F6: 1 => CTR => F6: 7,8
* CNT  32 HDP CHAINS /  32 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B4: 1,7 => UNS
* PRF # C6: 1,7 => SOL
* STA C6: 1,7
* CNT   2 HDP CHAINS /   2 HYP OPENED