Analysis of xx-top500-236-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 5.2..........5..8.....13...6..74..........3.18...........6...5....2..4...1....... initial

Autosolve

position: 5.2.679131.3.5268..6..132.5631749528...5283618251367..3..6.4152.5628143.2143.58.6 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D3: 9 => CTR => D3: 4,8
* PRF # B2: 4,9 => SOL
* DIS # B2: 7 => CTR => B2: 4,9
* DIS # B2: 9 => CTR => B2: 4,7
* PRF # A3: 9 => SOL
* DIS # A5: 7,9 => CTR => A5: 4
* DIS # A5: 7,9 => CTR => A5: 4
* CNT   7 HDP CHAINS /  22 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 # D3: 9 => CTR => D3: 4,8
* PRF D3: 4,8 # A3: 9 => SOL
* STA D3: 4,8 + A3: 9
* CNT   2 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

5.2..........5..8.....13...6..74..........3.18...........6...5....2..4...1....... initial
5.2.679131.3.5268..6..132.5631749528...5283618251367..3..6.4152.5628143.2143.58.6 autosolve
582467913143952687967813245631749528479528361825136794398674152756281439214395876 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
B1: 4,8
D1: 4,8
D2: 4,9
I2: 4,7
H3: 4,7
C5: 7,9
H6: 4,9
I6: 4,9
A8: 7,9
E7: 7,9
E9: 7,9
I8: 7,9
H9: 7,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I2,H3: 4.. / I2 = 4  =>  0 pairs (X) / H3 = 4  =>  0 pairs (_)
A5,B5: 4.. / A5 = 4  => 15 pairs (_) / B5 = 4  =>  0 pairs (X)
H6,I6: 4.. / H6 = 4  =>  0 pairs (X) / I6 = 4  =>  0 pairs (_)
B1,D1: 4.. / B1 = 4  => 16 pairs (_) / D1 = 4  => 13 pairs (_)
A3,A5: 4.. / A3 = 4  =>  0 pairs (X) / A5 = 4  => 15 pairs (_)
H3,H6: 4.. / H3 = 4  =>  0 pairs (*) / H6 = 4  =>  0 pairs (X)
I2,I6: 4.. / I2 = 4  =>  0 pairs (X) / I6 = 4  =>  0 pairs (_)
I2,H3: 7.. / I2 = 7  =>  0 pairs (*) / H3 = 7  =>  0 pairs (X)
E7,E9: 7.. / E7 = 7  =>  0 pairs (*) / E9 = 7  =>  0 pairs (X)
I8,H9: 7.. / I8 = 7  =>  0 pairs (X) / H9 = 7  =>  0 pairs (_)
B2,I2: 7.. / B2 = 7  =>  0 pairs (X) / I2 = 7  =>  0 pairs (_)
A8,I8: 7.. / A8 = 7  =>  0 pairs (*) / I8 = 7  =>  0 pairs (X)
E9,H9: 7.. / E9 = 7  =>  0 pairs (X) / H9 = 7  =>  0 pairs (_)
H3,H9: 7.. / H3 = 7  =>  0 pairs (X) / H9 = 7  =>  0 pairs (_)
I2,I8: 7.. / I2 = 7  =>  0 pairs (*) / I8 = 7  =>  0 pairs (X)
B1,C3: 8.. / B1 = 8  => 13 pairs (_) / C3 = 8  => 16 pairs (_)
D1,D3: 8.. / D1 = 8  => 16 pairs (_) / D3 = 8  => 13 pairs (_)
B7,C7: 8.. / B7 = 8  => 16 pairs (_) / C7 = 8  => 13 pairs (_)
B1,D1: 8.. / B1 = 8  => 13 pairs (_) / D1 = 8  => 16 pairs (_)
C3,D3: 8.. / C3 = 8  => 16 pairs (_) / D3 = 8  => 13 pairs (_)
B1,B7: 8.. / B1 = 8  => 13 pairs (_) / B7 = 8  => 16 pairs (_)
C3,C7: 8.. / C3 = 8  => 16 pairs (_) / C7 = 8  => 13 pairs (_)
D2,D3: 9.. / D2 = 9  => 14 pairs (_) / D3 = 9  =>  0 pairs (X)
H6,I6: 9.. / H6 = 9  =>  0 pairs (*) / I6 = 9  =>  0 pairs (X)
E7,E9: 9.. / E7 = 9  =>  0 pairs (X) / E9 = 9  =>  0 pairs (_)
I8,H9: 9.. / I8 = 9  =>  0 pairs (*) / H9 = 9  =>  0 pairs (X)
B2,D2: 9.. / B2 = 9  =>  0 pairs (X) / D2 = 9  => 14 pairs (_)
A8,I8: 9.. / A8 = 9  =>  0 pairs (X) / I8 = 9  =>  0 pairs (_)
E9,H9: 9.. / E9 = 9  =>  0 pairs (*) / H9 = 9  =>  0 pairs (X)
H6,H9: 9.. / H6 = 9  =>  0 pairs (*) / H9 = 9  =>  0 pairs (X)
I6,I8: 9.. / I6 = 9  =>  0 pairs (X) / I8 = 9  =>  0 pairs (_)
* DURATION: 0:00:55.533261  START: 10:53:38.351019  END: 10:54:33.884280 2017-05-04
* CP COUNT: (31)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B1,C5,D1,D2,E7,E9,H3,H6,H9,I2,I6,I8)
* 5.2.679131.3.5268..6..132.5631749528...5283618251367..3..6.4152.5628143.2143.58.6
* PAIR D1: 4,8 BLK 2
D3: 4,8,9                                # reduction candidate for 4,8
D3: 9 => CTR
* 5.28679131.3452687.689132456317495284..52836182513679438.6.4152.5628143.2143.58.6
D3: 4,8                                  # 14 pairs
* PAIR D2: 4,9 BLK 2
D3: 4,9,8                                # reduction candidate for 4,9
D3: 4,9                                  # 16 pairs
D3: 8                                    # 13 pairs
* PAIR D2: 4,9 ROW 2
B2: 4,9,7                                # reduction candidate for 4,9
B2: 4,9 => SOLVED
* 582467913143952687967813245631749528479528361825136794398674152756281439214395876
B2: 7 => CTR
* 5.2.679131739526844698132756317495287..5283618251367493..6.4152956281437214375896
* PAIR I2: 4,7 ROW 2
B2: 4,7,9                                # reduction candidate for 4,7
B2: 9 => CTR
* 5.2.67913193452687.6.91324563174952847952836182513679438.6.4152.5628143.2143.58.6
B2: 4,7                                  # 14 pairs
* PAIR H3: 4,7 ROW 3
A3: 4,7,9                                # reduction candidate for 4,7
A3: 9 => SOLVED
* 582467913143952687967813245631749528479528361825136794398674152756281439214395876
A3: 4,7                                  # 16 pairs
* PAIR C5: 7,9 BLK 4
A5: 7,9,4                                # reduction candidate for 7,9
A5: 7,9 => CTR
* 5.2.679131.3.5268.46..13275631749528.4.5283618251367493..6.4152956281437214375896
A5: 4                                    # 15 pairs
B5: 7,9,4                                # reduction candidate for 7,9
B5: 7,9                                  # 15 pairs
* PAIR C5: 7,9 COL C
C3: 7,9,8                                # reduction candidate for 7,9
C3: 7,9                                  # 13 pairs
C7: 7,9,8                                # reduction candidate for 7,9
C7: 7,9                                  # 16 pairs
* PAIR A8: 7,9 BLK 7
B7: 7,9,8                                # reduction candidate for 7,9
B7: 7,9                                  # 13 pairs
C7: 7,9,8                                # reduction candidate for 7,9
C7: 7,9                                  # 16 pairs
* PAIR A8: 7,9 COL A
A3: 7,9,4                                # reduction candidate for 7,9
A3: 7,9                                  # 15 pairs
A5: 7,9,4                                # reduction candidate for 7,9
A5: 7,9 => CTR
* 5.2.679131.3.5268.46..13275631749528.4.5283618251367493..6.4152956281437214375896
A5: 4                                    # 15 pairs
* PAIR E7: 7,9 ROW 7
B7: 7,9,8                                # reduction candidate for 7,9
B7: 7,9                                  # 13 pairs
C7: 7,9,8                                # reduction candidate for 7,9
C7: 7,9                                  # 16 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-236-base-pr-000.dot
* REASONING
* DIS # D3: 9 => CTR => D3: 4,8
* PRF # B2: 4,9 => SOL
* DIS # B2: 7 => CTR => B2: 4,9
* DIS # B2: 9 => CTR => B2: 4,7
* PRF # A3: 9 => SOL
* DIS # A5: 7,9 => CTR => A5: 4
* DIS # A5: 7,9 => CTR => A5: 4
* CNT   7 HDP CHAINS /  22 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B1,C5,D1,D2,E7,E9,H3,H6,H9,I2,I6,I8)
* 5.2.679131.3.5268..6..132.5631749528...5283618251367..3..6.4152.5628143.2143.58.6
* PAIR D1: 4,8 BLK 2
D3: 4,8,9                                # reduction candidate for 4,8
D3: 9 => CTR
* 5.28679131.3452687.689132456317495284..52836182513679438.6.4152.5628143.2143.58.6
* PAIR H3: 4,7 ROW 3
A3: 4,7,9                                # reduction candidate for 4,7
A3: 9 => SOLVED
* 582467913143952687967813245631749528479528361825136794398674152756281439214395876
* DURATION: 0:00:04.999962  START: 10:54:56.819543  END: 10:55:01.819505 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-236-base-pr-001.dot
* REASONING
* DIS # D3: 9 => CTR => D3: 4,8
* PRF D3: 4,8 # A3: 9 => SOL
* STA D3: 4,8 + A3: 9
* CNT   2 HDP CHAINS /   4 HYP OPENED

Header Info

Top 500 Minimum 17 236

solution: 582467913143952687967813245631749528479528361825136794398674152756281439214395876
info: 2068     FNWXY    S8.f     46765

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

Solution

position: 582467913143952687967813245631749528479528361825136794398674152756281439214395876 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 # D3: 4,8 => UNS
* DIS # D3: 9 => CTR => D3: 4,8
* INC # D3: 4,9 => UNS
* INC # D3: 8 => UNS
* PRF # B2: 4,9 => SOL
* DIS # B2: 7 => CTR => B2: 4,9
* INC # B2: 4,7 => UNS
* DIS # B2: 9 => CTR => B2: 4,7
* INC # A3: 4,7 => UNS
* PRF # A3: 9 => SOL
* DIS # A5: 7,9 => CTR => A5: 4
* INC # A5: 4 => UNS
* INC # B5: 7,9 => UNS
* INC # C3: 7,9 => UNS
* INC # C7: 7,9 => UNS
* INC # B7: 7,9 => UNS
* INC # C7: 7,9 => UNS
* INC # A3: 7,9 => UNS
* DIS # A5: 7,9 => CTR => A5: 4
* INC # A5: 4 => UNS
* INC # B7: 7,9 => UNS
* INC # C7: 7,9 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D3: 4,8 => UNS
* DIS # D3: 9 => CTR => D3: 4,8
* INC D3: 4,8 # A3: 4,7 => UNS
* PRF D3: 4,8 # A3: 9 => SOL
* STA D3: 4,8 + A3: 9
* CNT   4 HDP CHAINS /   4 HYP OPENED