Analysis of xx-top500-318-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ..2.9.3..8.1......5.........9..6..4........18........5.7....2..3..5........1..... initial

Autosolve

position: 7.2.9.3..8.1......5.9.......9..6.74........18........5.7....2..3..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: 8
* PRF # D1: 8 => SOL
* DIS # F1: 4,6 => CTR => F1: 1,5,8
* PRF # I1: 4,6 => SOL
* DIS # I1: 1 => CTR => I1: 4,6
* DIS # F2: 4,5 => CTR => F2: 2,3,6,7
* DIS # G9: 8 => CTR => G9: 4,5
* DIS # A6: 1,2 => CTR => A6: 4,6
* PRF # B6: 1,2 => SOL
* DIS # B6: 8 => CTR => B6: 1,2
* DIS # F4: 1,2 => CTR => F4: 3,5,8
* PRF # F4: 3,5,8 => SOL
* PRF # F5: 2,5 => SOL
* PRF # B9: 8 => SOL
* PRF # D4: 2,3 => SOL
* DIS # D4: 8 => CTR => D4: 2,3
* DIS # F4: 2,3 => CTR => F4: 1,5,8
* DIS # E6: 2,3 => CTR => E6: 1,4,7,8
* CNT  18 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:

* DIS # D1: 4,6 => CTR => D1: 8
* PRF D1: 8 => SOL
* STA D1: 8
* CNT   2 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

..2.9.3..8.1......5.........9..6..4........18........5.7....2..3..5........1..... initial
7.2.9.3..8.1......5.9.......9..6.74........18........5.7....2..3..5........1..... autosolve
742891356831657429569234187198365742653742918427918635975483261316529874284176593 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
B1: 4,6
G2: 4,5
A4: 1,2
B5: 2,5
I4: 2,3
G5: 6,9
G6: 6,9
H6: 2,3

--------------------------------------------------
* 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  =>  0 pairs (*) / H6 = 2  =>  0 pairs (X)
B2,B3: 3.. / B2 = 3  =>  9 pairs (_) / B3 = 3  =>  9 pairs (_)
I4,H6: 3.. / I4 = 3  => 15 pairs (_) / H6 = 3  =>  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)
E2,E5: 5.. / E2 = 5  =>  0 pairs (*) / E5 = 5  =>  0 pairs (X)
G2,G9: 5.. / G2 = 5  =>  0 pairs (X) / G9 = 5  =>  0 pairs (_)
G5,G6: 6.. / G5 = 6  =>  7 pairs (_) / G6 = 6  =>  6 pairs (_)
C5,C6: 7.. / C5 = 7  =>  9 pairs (_) / C6 = 7  =>  8 pairs (_)
H2,I2: 9.. / H2 = 9  =>  8 pairs (_) / I2 = 9  =>  8 pairs (_)
G5,G6: 9.. / G5 = 9  =>  6 pairs (_) / G6 = 9  =>  7 pairs (_)
A7,A9: 9.. / A7 = 9  =>  0 pairs (*) / A9 = 9  =>  0 pairs (X)
* DURATION: 0:00:32.339160  START: 13:50:34.292640  END: 13:51:06.631800 2017-05-04
* CP COUNT: (21)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B1,B5,G2,G5,G6,H6,I4)
* 7.2.9.3..8.1......5.9.......9..6.74........18........5.7....2..3..5........1.....
* PAIR B1: 4,6 BLK 1
B2: 4,6,3                                # reduction candidate for 4,6
B2: 4,6                                  #  9 pairs
B3: 4,6,3                                # reduction candidate for 4,6
B3: 4,6                                  #  9 pairs
* PAIR B1: 4,6 ROW 1
D1: 4,6,8                                # reduction candidate for 4,6
D1: 4,6 => CTR
* 7.2.9.3.18.1......5.9......29..61743.5.....18.1.....2517....2..3..5..1..9..1.....
D1: 8 => SOLVED
* 742891356831657429569234187198365742653742918427918635975483261316529874284176593
F1: 4,6,1,5,8                            # reduction candidate for 4,6
F1: 4,6 => CTR
* 7.2.9.3518.1...4..5.9...8...9..6.74........18........5175...2..3..5..1..9..1..5..
F1: 1,5,8                                #  8 pairs
I1: 4,6,1                                # reduction candidate for 4,6
I1: 4,6 => SOLVED
* 742891356831657429569234187198365742653742918427918635975483261316529874284176593
I1: 1 => CTR
* 7.2.9.3.18.1......5.9......29..61743.5.....18.1.....2517....2..3..5..1..9..1.....
* PAIR G2: 4,5 ROW 2
E2: 4,5,2,3,7                            # reduction candidate for 4,5
E2: 4,5                                  # 10 pairs
F2: 4,5,2,3,6,7                          # reduction candidate for 4,5
F2: 4,5 => CTR
* 7.2.953.18.1..45..5.9......195.6.74..2..5..18........5.7....25.3..5.....25.1.....
F2: 2,3,6,7                              #  8 pairs
* PAIR G2: 4,5 COL G
G9: 4,5,8                                # reduction candidate for 4,5
G9: 8 => CTR
* 7.2.953.18.1...5..5.9...4...95.6.74..2..5..18........517....2..3..5......5.1..8..
G9: 4,5                                  # 11 pairs
* PAIR A4: 1,2 BLK 4
A6: 1,2,4,6                              # reduction candidate for 1,2
A6: 1,2 => CTR
* 7.2.9135.8.1.5.4..5.9...18.193865742.5.....1828..1..35.75...2.131.5..8.4.281..5.3
A6: 4,6                                  #  9 pairs
B6: 1,2,8                                # reduction candidate for 1,2
B6: 1,2 => SOLVED
* 742891356831657429569234187198365742653742918427918635975483261316529874284176593
B6: 8 => CTR
* 7.28913568.1...4..5.9...18.193.6.74........18.8..1...5.75...2.131.5..8...281..5..
* PAIR A4: 1,2 ROW 4
F4: 1,2,3,5,8                            # reduction candidate for 1,2
F4: 1,2 => CTR
* 7.2.953818.1...5..5.9...4..19586.743.2.....18.......25.7....25.3..5.....25.1...3.
F4: 3,5,8 => SOLVED
* 742891356831657429569234187198365742653742918427918635975483261316529874284176593
* PAIR B5: 2,5 ROW 5
E5: 2,5,3,4,7                            # reduction candidate for 2,5
E5: 2,5                                  # 10 pairs
F5: 2,5,3,4,7,9                          # reduction candidate for 2,5
F5: 2,5 => SOLVED
* 742891356831657429569234187198365742653742918427918635975483261316529874284176593
F5: 3,4,7,9                              #  8 pairs
* PAIR B5: 2,5 COL B
B9: 2,5,8                                # reduction candidate for 2,5
B9: 8 => SOLVED
* 742891356831657429569234187198365742653742918427918635975483261316529874284176593
B9: 2,5                                  # 11 pairs
* PAIR I4: 2,3 ROW 4
D4: 2,3,8                                # reduction candidate for 2,3
D4: 2,3 => SOLVED
* 742891356831657429569234187198365742653742918427918635975483261316529874284176593
D4: 8 => CTR
* 7.2.9.3.18.1......5.9......29.861743.5.....18........517....2..3..5..1..9..1.....
F4: 2,3,1,5,8                            # reduction candidate for 2,3
F4: 2,3 => CTR
* 7.2.9.3..8.1......5.9......19586.74..2.....18.8......5.7....25131.5.....25.1.....
F4: 1,5,8                                #  8 pairs
* PAIR H6: 2,3 ROW 6
D6: 2,3,4,7,8,9                          # reduction candidate for 2,3
D6: 2,3                                  # 10 pairs
E6: 2,3,1,4,7,8                          # reduction candidate for 2,3
E6: 2,3 => CTR
* 7.2.9.3.18.1......5.9.1....29..61743.5.....18.1.....2517....2..3..5..1..9..1.....
E6: 1,4,7,8                              #  8 pairs
F6: 2,3,1,4,7,8,9                        # reduction candidate for 2,3
F6: 2,3                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-318-base-pr-000.dot
* REASONING
* DIS # D1: 4,6 => CTR => D1: 8
* PRF # D1: 8 => SOL
* DIS # F1: 4,6 => CTR => F1: 1,5,8
* PRF # I1: 4,6 => SOL
* DIS # I1: 1 => CTR => I1: 4,6
* DIS # F2: 4,5 => CTR => F2: 2,3,6,7
* DIS # G9: 8 => CTR => G9: 4,5
* DIS # A6: 1,2 => CTR => A6: 4,6
* PRF # B6: 1,2 => SOL
* DIS # B6: 8 => CTR => B6: 1,2
* DIS # F4: 1,2 => CTR => F4: 3,5,8
* PRF # F4: 3,5,8 => SOL
* PRF # F5: 2,5 => SOL
* PRF # B9: 8 => SOL
* PRF # D4: 2,3 => SOL
* DIS # D4: 8 => CTR => D4: 2,3
* DIS # F4: 2,3 => CTR => F4: 1,5,8
* DIS # E6: 2,3 => CTR => E6: 1,4,7,8
* CNT  18 HDP CHAINS /  32 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B1,B5,G2,G5,G6,H6,I4)
* 7.2.9.3..8.1......5.9.......9..6.74........18........5.7....2..3..5........1.....
* PAIR B1: 4,6 BLK 1
B2: 4,6,3                                # reduction candidate for 4,6
B2: 4,6                                  #  9 pairs
B3: 4,6,3                                # reduction candidate for 4,6
B3: 4,6                                  #  9 pairs
* PAIR B1: 4,6 ROW 1
D1: 4,6,8                                # reduction candidate for 4,6
D1: 4,6 => CTR
* 7.2.9.3.18.1......5.9......29..61743.5.....18.1.....2517....2..3..5..1..9..1.....
D1: 8 => SOLVED
* 742891356831657429569234187198365742653742918427918635975483261316529874284176593
* DURATION: 0:00:02.951496  START: 13:51:32.455573  END: 13:51:35.407069 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-318-base-pr-001.dot
* REASONING
* DIS # D1: 4,6 => CTR => D1: 8
* PRF D1: 8 => SOL
* STA D1: 8
* CNT   2 HDP CHAINS /   3 HYP OPENED

Header Info

Top 500 Minimum 17 318

solution: 742891356831657429569234187198365742653742918427918635975483261316529874284176593
info: 2914     FNBTHWY  S8.f     13276

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

Solution

position: 742891356831657429569234187198365742653742918427918635975483261316529874284176593 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: 8
* PRF # D1: 8 => SOL
* DIS # F1: 4,6 => CTR => F1: 1,5,8
* INC # F1: 1,5,8 => UNS
* PRF # I1: 4,6 => SOL
* DIS # I1: 1 => CTR => I1: 4,6
* INC # E2: 4,5 => UNS
* DIS # F2: 4,5 => CTR => F2: 2,3,6,7
* INC # F2: 2,3,6,7 => UNS
* INC # G9: 4,5 => UNS
* DIS # G9: 8 => CTR => G9: 4,5
* DIS # A6: 1,2 => CTR => A6: 4,6
* INC # A6: 4,6 => UNS
* PRF # B6: 1,2 => SOL
* DIS # B6: 8 => CTR => B6: 1,2
* DIS # F4: 1,2 => CTR => F4: 3,5,8
* PRF # F4: 3,5,8 => SOL
* INC # E5: 2,5 => UNS
* PRF # F5: 2,5 => SOL
* INC # F5: 3,4,7,9 => UNS
* INC # B9: 2,5 => UNS
* PRF # B9: 8 => SOL
* PRF # D4: 2,3 => SOL
* DIS # D4: 8 => CTR => D4: 2,3
* DIS # F4: 2,3 => CTR => F4: 1,5,8
* INC # F4: 1,5,8 => 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
* CNT  32 HDP CHAINS /  32 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: 8
* PRF D1: 8 => SOL
* STA D1: 8
* CNT   4 HDP CHAINS /   3 HYP OPENED