Analysis of xx-top500-334-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ..2.9.3..5.1......7.........9..6..4........17........5.8....2..4..5........1..... initial

Autosolve

position: 8.2.9.3..5.1......7.9.......9..6.84........17........5.8....2..4..5........1..... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D1: 4,6 => CTR => D1: 7
* PRF # D1: 7 => SOL
* DIS # F1: 4,6 => CTR => F1: 1,5,7
* PRF # I1: 4,6 => SOL
* DIS # I1: 1 => CTR => I1: 4,6
* DIS # G9: 4,7 => CTR => G9: 5
* PRF # G9: 5 => SOL
* PRF # F5: 2,5 => SOL
* PRF # B9: 7 => SOL
* PRF # E5: 4,8 => SOL
* DIS # E6: 4,8 => CTR => E6: 1,2,3,7
* DIS # A4: 2,3 => CTR => A4: 1
* PRF # A4: 1 => SOL
* PRF # D4: 2,3 => SOL
* DIS # D4: 7 => CTR => D4: 2,3
* DIS # F4: 2,3 => CTR => F4: 1,5,7
* DIS # E6: 2,3 => CTR => E6: 1,4,7,8
* DIS # B8: 2 => CTR => B8: 1,7
* CNT  18 HDP CHAINS /  39 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 # D1: 4,6 => CTR => D1: 7
* PRF D1: 7 => SOL
* STA D1: 7
* CNT   2 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

..2.9.3..5.1......7.........9..6..4........17........5.8....2..4..5........1..... initial
8.2.9.3..5.1......7.9.......9..6.84........17........5.8....2..4..5........1..... autosolve
842791356561238479739654128197365842358942617624817935985473261416529783273186594 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
B1: 4,6
G2: 4,7
B5: 2,5
C5: 4,8
C6: 4,8
I4: 2,3
G5: 6,9
G6: 6,9
H6: 2,3
G8: 1,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A7,B8: 1.. / A7 = 1  =>  0 pairs (X) / B8 = 1  =>  0 pairs (_)
F1,I1: 1.. / F1 = 1  =>  0 pairs (*) / I1 = 1  =>  0 pairs (X)
A4,F4: 1.. / A4 = 1  =>  0 pairs (*) / F4 = 1  =>  0 pairs (X)
A7,I7: 1.. / A7 = 1  =>  0 pairs (X) / I7 = 1  =>  0 pairs (_)
B6,B8: 1.. / B6 = 1  =>  0 pairs (X) / B8 = 1  =>  0 pairs (_)
E3,E6: 1.. / E3 = 1  =>  0 pairs (X) / E6 = 1  =>  0 pairs (_)
G3,G8: 1.. / G3 = 1  =>  0 pairs (*) / G8 = 1  =>  0 pairs (X)
I4,H6: 2.. / I4 = 2  => 10 pairs (_) / H6 = 2  => 16 pairs (_)
B2,B3: 3.. / B2 = 3  => 11 pairs (_) / B3 = 3  => 11 pairs (_)
I4,H6: 3.. / I4 = 3  => 16 pairs (_) / H6 = 3  => 10 pairs (_)
C5,C6: 4.. / C5 = 4  =>  8 pairs (_) / C6 = 4  =>  8 pairs (_)
C4,B5: 5.. / C4 = 5  =>  0 pairs (X) / B5 = 5  =>  0 pairs (_)
F1,H1: 5.. / F1 = 5  =>  0 pairs (X) / H1 = 5  =>  0 pairs (_)
C4,F4: 5.. / C4 = 5  =>  0 pairs (X) / F4 = 5  =>  0 pairs (_)
C7,H7: 5.. / C7 = 5  =>  0 pairs (*) / H7 = 5  =>  0 pairs (X)
B5,B9: 5.. / B5 = 5  =>  0 pairs (*) / B9 = 5  =>  0 pairs (X)
E3,E5: 5.. / E3 = 5  =>  0 pairs (*) / E5 = 5  =>  0 pairs (X)
G3,G9: 5.. / G3 = 5  =>  0 pairs (X) / G9 = 5  =>  0 pairs (_)
A5,A6: 6.. / A5 = 6  =>  9 pairs (_) / A6 = 6  =>  9 pairs (_)
G5,G6: 6.. / G5 = 6  =>  9 pairs (_) / G6 = 6  =>  9 pairs (_)
A5,G5: 6.. / A5 = 6  =>  9 pairs (_) / G5 = 6  =>  9 pairs (_)
A6,G6: 6.. / A6 = 6  =>  9 pairs (_) / G6 = 6  =>  9 pairs (_)
C4,B6: 7.. / C4 = 7  =>  0 pairs (*) / B6 = 7  =>  0 pairs (X)
C5,C6: 8.. / C5 = 8  =>  8 pairs (_) / C6 = 8  =>  8 pairs (_)
H2,I2: 9.. / H2 = 9  => 10 pairs (_) / I2 = 9  => 10 pairs (_)
G5,G6: 9.. / G5 = 9  =>  9 pairs (_) / G6 = 9  =>  9 pairs (_)
A7,A9: 9.. / A7 = 9  =>  0 pairs (*) / A9 = 9  =>  0 pairs (X)
* DURATION: 0:00:41.782652  START: 14:10:59.522137  END: 14:11:41.304789 2017-05-04
* CP COUNT: (27)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B5,C5,C6,G2,G5,G6,G8,H6,I4)
* 8.2.9.3..5.1......7.9.......9..6.84........17........5.8....2..4..5........1.....
* PAIR B1: 4,6 BLK 1
B2: 4,6,3                                # reduction candidate for 4,6
B2: 4,6                                  # 11 pairs
B3: 4,6,3                                # reduction candidate for 4,6
B3: 4,6                                  # 11 pairs
* PAIR B1: 4,6 ROW 1
D1: 4,6,7                                # reduction candidate for 4,6
D1: 4,6 => CTR
* 8.2.9.3.15.1......7.9.......9..6184........17.1......518....2..4..5..1..9..1.....
D1: 7 => SOLVED
* 842791356561238479739654128197365842358942617624817935985473261416529783273186594
F1: 4,6,1,5,7                            # reduction candidate for 4,6
F1: 4,6 => CTR
* 8.2.9.3515.1......7.9...4...9..6.84........17........5185...2..4..5..1..9..1..5..
F1: 1,5,7                                # 10 pairs
I1: 4,6,1                                # reduction candidate for 4,6
I1: 4,6 => SOLVED
* 842791356561238479739654128197365842358942617624817935985473261416529783273186594
I1: 1 => CTR
* 8.2.9.3.15.1......7.9.......9..6184........17.1......518....2..4..5..1..9..1.....
* PAIR G2: 4,7 ROW 2
D2: 4,7,2,3,6,8                          # reduction candidate for 4,7
D2: 4,7                                  # 12 pairs
E2: 4,7,2,3,8                            # reduction candidate for 4,7
E2: 4,7                                  # 12 pairs
F2: 4,7,2,3,6,8                          # reduction candidate for 4,7
F2: 4,7                                  # 12 pairs
* PAIR G2: 4,7 COL G
G9: 4,7,5                                # reduction candidate for 4,7
G9: 4,7 => CTR
* 8.2.953.15.1......7.9...5...95.6.84..2..5..17........5.8....2..4..5..1...5.1.....
G9: 5 => SOLVED
* 842791356561238479739654128197365842358942617624817935985473261416529783273186594
* PAIR B5: 2,5 ROW 5
E5: 2,5,3,4,8                            # reduction candidate for 2,5
E5: 2,5                                  # 12 pairs
F5: 2,5,3,4,8,9                          # reduction candidate for 2,5
F5: 2,5 => SOLVED
* 842791356561238479739654128197365842358942617624817935985473261416529783273186594
F5: 3,4,8,9                              # 10 pairs
* PAIR B5: 2,5 COL B
B9: 2,5,7                                # reduction candidate for 2,5
B9: 7 => SOLVED
* 842791356561238479739654128197365842358942617624817935985473261416529783273186594
B9: 2,5                                  # 14 pairs
* PAIR C5: 4,8 ROW 5
D5: 4,8,2,3,9                            # reduction candidate for 4,8
D5: 4,8                                  # 11 pairs
E5: 4,8,2,3,5                            # reduction candidate for 4,8
E5: 4,8 => SOLVED
* 842791356561238479739654128197365842358942617624817935985473261416529783273186594
E5: 2,3,5                                # 10 pairs
F5: 4,8,2,3,5,9                          # reduction candidate for 4,8
F5: 4,8                                  # 11 pairs
* PAIR C6: 4,8 ROW 6
D6: 4,8,2,3,7,9                          # reduction candidate for 4,8
D6: 4,8                                  # 11 pairs
E6: 4,8,1,2,3,7                          # reduction candidate for 4,8
E6: 4,8 => CTR
* 8.2.9.3.15.1......7.9.1.5...95.6.84..2..5..17........5.8....2..4..5..1...5.1.....
E6: 1,2,3,7                              # 10 pairs
F6: 4,8,1,2,3,7,9                        # reduction candidate for 4,8
F6: 4,8                                  # 11 pairs
* PAIR I4: 2,3 ROW 4
A4: 2,3,1                                # reduction candidate for 2,3
A4: 2,3 => CTR
* 8.2.9.3.15.1......7.9.1.....9576184..2..5..17.7......518....2..4..5........1.....
A4: 1 => SOLVED
* 842791356561238479739654128197365842358942617624817935985473261416529783273186594
D4: 2,3,7                                # reduction candidate for 2,3
D4: 2,3 => SOLVED
* 842791356561238479739654128197365842358942617624817935985473261416529783273186594
D4: 7 => CTR
* 8.2.913..5.1...4..7.9...1...9.76.84........17.7..1...5.8....2.141.5..7.....1..5.4
F4: 2,3,1,5,7                            # reduction candidate for 2,3
F4: 2,3 => CTR
* 8.2.9.3..5.1......7.9......19576.84..2.....17.7......5.8....25141.5..7.....1.....
F4: 1,5,7                                # 10 pairs
* PAIR H6: 2,3 ROW 6
A6: 2,3,1,6                              # reduction candidate for 2,3
A6: 2,3                                  # 11 pairs
D6: 2,3,4,7,8,9                          # reduction candidate for 2,3
D6: 2,3                                  # 13 pairs
E6: 2,3,1,4,7,8                          # reduction candidate for 2,3
E6: 2,3 => CTR
* 8.2.9.3.15.1......7.9.1.5...95.6.84..2..5..17........5.8....2..4..5..1...5.1.....
E6: 1,4,7,8                              # 10 pairs
F6: 2,3,1,4,7,8,9                        # reduction candidate for 2,3
F6: 2,3                                  # 13 pairs
* PAIR G8: 1,7 ROW 8
B8: 1,7,2                                # reduction candidate for 1,7
B8: 2 => CTR
* 8.2.9.3..5.1......7.9.1.....97.6.84........17.1......518....2..42.5.....97.1.....
B8: 1,7                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-334-base-pr-000.dot
* REASONING
* DIS # D1: 4,6 => CTR => D1: 7
* PRF # D1: 7 => SOL
* DIS # F1: 4,6 => CTR => F1: 1,5,7
* PRF # I1: 4,6 => SOL
* DIS # I1: 1 => CTR => I1: 4,6
* DIS # G9: 4,7 => CTR => G9: 5
* PRF # G9: 5 => SOL
* PRF # F5: 2,5 => SOL
* PRF # B9: 7 => SOL
* PRF # E5: 4,8 => SOL
* DIS # E6: 4,8 => CTR => E6: 1,2,3,7
* DIS # A4: 2,3 => CTR => A4: 1
* PRF # A4: 1 => SOL
* PRF # D4: 2,3 => SOL
* DIS # D4: 7 => CTR => D4: 2,3
* DIS # F4: 2,3 => CTR => F4: 1,5,7
* DIS # E6: 2,3 => CTR => E6: 1,4,7,8
* DIS # B8: 2 => CTR => B8: 1,7
* CNT  18 HDP CHAINS /  39 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B5,C5,C6,G2,G5,G6,G8,H6,I4)
* 8.2.9.3..5.1......7.9.......9..6.84........17........5.8....2..4..5........1.....
* PAIR B1: 4,6 BLK 1
B2: 4,6,3                                # reduction candidate for 4,6
B2: 4,6                                  # 11 pairs
B3: 4,6,3                                # reduction candidate for 4,6
B3: 4,6                                  # 11 pairs
* PAIR B1: 4,6 ROW 1
D1: 4,6,7                                # reduction candidate for 4,6
D1: 4,6 => CTR
* 8.2.9.3.15.1......7.9.......9..6184........17.1......518....2..4..5..1..9..1.....
D1: 7 => SOLVED
* 842791356561238479739654128197365842358942617624817935985473261416529783273186594
* DURATION: 0:00:03.096351  START: 14:12:14.424866  END: 14:12:17.521217 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-334-base-pr-001.dot
* REASONING
* DIS # D1: 4,6 => CTR => D1: 7
* PRF D1: 7 => SOL
* STA D1: 7
* CNT   2 HDP CHAINS /   3 HYP OPENED

Header Info

Top 500 Minimum 17 334

solution: 842791356561238479739654128197365842358942617624817935985473261416529783273186594
info: 3045     FNBTHWY  S8.f     13275

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

Solution

position: 842791356561238479739654128197365842358942617624817935985473261416529783273186594 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 # B2: 4,6 => UNS
* INC # B3: 4,6 => UNS
* DIS # D1: 4,6 => CTR => D1: 7
* PRF # D1: 7 => SOL
* DIS # F1: 4,6 => CTR => F1: 1,5,7
* INC # F1: 1,5,7 => UNS
* PRF # I1: 4,6 => SOL
* DIS # I1: 1 => CTR => I1: 4,6
* INC # D2: 4,7 => UNS
* INC # E2: 4,7 => UNS
* INC # F2: 4,7 => UNS
* DIS # G9: 4,7 => CTR => G9: 5
* PRF # G9: 5 => SOL
* INC # E5: 2,5 => UNS
* PRF # F5: 2,5 => SOL
* INC # F5: 3,4,8,9 => UNS
* INC # B9: 2,5 => UNS
* PRF # B9: 7 => SOL
* INC # D5: 4,8 => UNS
* PRF # E5: 4,8 => SOL
* INC # E5: 2,3,5 => UNS
* INC # F5: 4,8 => UNS
* INC # D6: 4,8 => UNS
* DIS # E6: 4,8 => CTR => E6: 1,2,3,7
* INC # E6: 1,2,3,7 => UNS
* INC # F6: 4,8 => UNS
* DIS # A4: 2,3 => CTR => A4: 1
* PRF # A4: 1 => SOL
* PRF # D4: 2,3 => SOL
* DIS # D4: 7 => CTR => D4: 2,3
* DIS # F4: 2,3 => CTR => F4: 1,5,7
* INC # F4: 1,5,7 => UNS
* INC # A6: 2,3 => UNS
* INC # D6: 2,3 => UNS
* DIS # E6: 2,3 => CTR => E6: 1,4,7,8
* INC # E6: 1,4,7,8 => UNS
* INC # F6: 2,3 => UNS
* INC # B8: 1,7 => UNS
* DIS # B8: 2 => CTR => B8: 1,7
* CNT  39 HDP CHAINS /  39 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 4,6 => UNS
* INC # B3: 4,6 => UNS
* DIS # D1: 4,6 => CTR => D1: 7
* PRF D1: 7 => SOL
* STA D1: 7
* CNT   4 HDP CHAINS /   3 HYP OPENED