Analysis of xx-top500-029-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .4....86.....91...7........3.......1.2.4........5.....1.9.2..........54.2........ initial

Autosolve

position: 5412..869.32.9175479..45..33.59..4.192.41...541.5.....159724....731.95422.435...7 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # F4: 6,8 => SOL
* PRF # F4: 6,8 => SOL
* CNT   2 HDP CHAINS /  26 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 # F4: 6,8 => SOL
* STA F4: 6,8
* CNT   1 HDP CHAINS /  10 HYP OPENED

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

Details

Positions

.4....86.....91...7........3.......1.2.4........5.....1.9.2..........54.2........ initial
5412..869.32.9175479..45..33.59..4.192.41...541.5.....159724....731.95422.435...7 autosolve
541237869832691754796845213365978421928413675417562938159724386673189542284356197 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (21)
A2: 6,8
C3: 6,8
E1: 3,7
F1: 3,7
D2: 6,8
D3: 6,8
G3: 1,2
H3: 1,2
B4: 6,8
G5: 3,6
G6: 2,9
I6: 6,8
A8: 6,8
B9: 6,8
E8: 6,8
F9: 6,8
G7: 3,6
H7: 3,8
I7: 6,8
G9: 1,9
H9: 1,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G3,H3: 1.. / G3 = 1  => 17 pairs (_) / H3 = 1  => 16 pairs (_)
G9,H9: 1.. / G9 = 1  => 16 pairs (_) / H9 = 1  => 17 pairs (_)
G3,G9: 1.. / G3 = 1  => 17 pairs (_) / G9 = 1  => 16 pairs (_)
H3,H9: 1.. / H3 = 1  => 16 pairs (_) / H9 = 1  => 17 pairs (_)
G3,H3: 2.. / G3 = 2  => 16 pairs (_) / H3 = 2  => 17 pairs (_)
F4,F6: 2.. / F4 = 2  => 23 pairs (_) / F6 = 2  => 16 pairs (_)
F4,H4: 2.. / F4 = 2  => 23 pairs (_) / H4 = 2  => 16 pairs (_)
G3,G6: 2.. / G3 = 2  => 16 pairs (_) / G6 = 2  => 17 pairs (_)
E1,F1: 3.. / E1 = 3  => 20 pairs (_) / F1 = 3  => 22 pairs (_)
G7,H7: 3.. / G7 = 3  => 20 pairs (_) / H7 = 3  => 18 pairs (_)
E1,E6: 3.. / E1 = 3  => 20 pairs (_) / E6 = 3  => 22 pairs (_)
G5,G7: 3.. / G5 = 3  => 18 pairs (_) / G7 = 3  => 20 pairs (_)
A2,C3: 6.. / A2 = 6  =>  0 pairs (X) / C3 = 6  =>  0 pairs (_)
D2,D3: 6.. / D2 = 6  =>  0 pairs (*) / D3 = 6  =>  0 pairs (X)
G5,I6: 6.. / G5 = 6  => 20 pairs (_) / I6 = 6  => 18 pairs (_)
A8,B9: 6.. / A8 = 6  =>  0 pairs (*) / B9 = 6  =>  0 pairs (X)
E8,F9: 6.. / E8 = 6  =>  0 pairs (X) / F9 = 6  =>  0 pairs (_)
G7,I7: 6.. / G7 = 6  => 18 pairs (_) / I7 = 6  => 20 pairs (_)
A2,D2: 6.. / A2 = 6  =>  0 pairs (X) / D2 = 6  =>  0 pairs (_)
C3,D3: 6.. / C3 = 6  =>  0 pairs (*) / D3 = 6  =>  0 pairs (X)
A8,E8: 6.. / A8 = 6  =>  0 pairs (*) / E8 = 6  =>  0 pairs (X)
B9,F9: 6.. / B9 = 6  =>  0 pairs (X) / F9 = 6  =>  0 pairs (_)
A2,A8: 6.. / A2 = 6  =>  0 pairs (X) / A8 = 6  =>  0 pairs (_)
B4,B9: 6.. / B4 = 6  =>  0 pairs (*) / B9 = 6  =>  0 pairs (X)
G5,G7: 6.. / G5 = 6  => 20 pairs (_) / G7 = 6  => 18 pairs (_)
I6,I7: 6.. / I6 = 6  => 18 pairs (_) / I7 = 6  => 20 pairs (_)
E1,F1: 7.. / E1 = 7  => 22 pairs (_) / F1 = 7  => 20 pairs (_)
C5,C6: 7.. / C5 = 7  => 28 pairs (_) / C6 = 7  => 22 pairs (_)
A2,C3: 8.. / A2 = 8  =>  0 pairs (*) / C3 = 8  =>  0 pairs (X)
D2,D3: 8.. / D2 = 8  =>  0 pairs (X) / D3 = 8  =>  0 pairs (_)
A8,B9: 8.. / A8 = 8  =>  0 pairs (X) / B9 = 8  =>  0 pairs (_)
E8,F9: 8.. / E8 = 8  =>  0 pairs (*) / F9 = 8  =>  0 pairs (X)
H7,I7: 8.. / H7 = 8  => 20 pairs (_) / I7 = 8  => 18 pairs (_)
A2,D2: 8.. / A2 = 8  =>  0 pairs (*) / D2 = 8  =>  0 pairs (X)
C3,D3: 8.. / C3 = 8  =>  0 pairs (X) / D3 = 8  =>  0 pairs (_)
A8,E8: 8.. / A8 = 8  =>  0 pairs (X) / E8 = 8  =>  0 pairs (_)
B9,F9: 8.. / B9 = 8  =>  0 pairs (*) / F9 = 8  =>  0 pairs (X)
A2,A8: 8.. / A2 = 8  =>  0 pairs (*) / A8 = 8  =>  0 pairs (X)
B4,B9: 8.. / B4 = 8  =>  0 pairs (X) / B9 = 8  =>  0 pairs (_)
I6,I7: 8.. / I6 = 8  => 20 pairs (_) / I7 = 8  => 18 pairs (_)
G6,H6: 9.. / G6 = 9  => 16 pairs (_) / H6 = 9  => 17 pairs (_)
G9,H9: 9.. / G9 = 9  => 17 pairs (_) / H9 = 9  => 16 pairs (_)
G6,G9: 9.. / G6 = 9  => 16 pairs (_) / G9 = 9  => 17 pairs (_)
H6,H9: 9.. / H6 = 9  => 17 pairs (_) / H9 = 9  => 16 pairs (_)
* DURATION: 0:01:25.683872  START: 03:37:11.706195  END: 03:38:37.390067 2017-05-04
* CP COUNT: (44)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B4,B9,C3,D2,D3,E1,E8,F1,F9,G3,G5,G6,G7,G9,H3,H7,H9,I6,I7)
* 5412..869.32.9175479..45..33.59..4.192.41...541.5.....159724....731.95422.435...7
* PAIR C3: 6,8 COL C
C5: 6,8,7                                # reduction candidate for 6,8
C5: 6,8                                  # 22 pairs
C6: 6,8,7                                # reduction candidate for 6,8
C6: 6,8                                  # 28 pairs
* PAIR E1: 3,7 COL E
E6: 3,7,6,8                              # reduction candidate for 3,7
E6: 3,7                                  # 25 pairs
E6: 6,8                                  # 23 pairs
* PAIR F1: 3,7 COL F
F5: 3,7,6,8                              # reduction candidate for 3,7
F5: 3,7                                  # 22 pairs
F6: 3,7,2,6,8                            # reduction candidate for 3,7
F6: 3,7                                  # 25 pairs
* PAIR B4: 6,8 BLK 4
C5: 6,8,7                                # reduction candidate for 6,8
C5: 6,8                                  # 22 pairs
C6: 6,8,7                                # reduction candidate for 6,8
C6: 6,8                                  # 28 pairs
* PAIR B4: 6,8 ROW 4
E4: 6,8,7                                # reduction candidate for 6,8
E4: 6,8                                  # 25 pairs
F4: 6,8,2,7                              # reduction candidate for 6,8
F4: 6,8 => SOLVED
* 541237869832691754796845213365978421928413675417562938159724386673189542284356197
F4: 2,7                                  # 22 pairs
* PAIR G5: 3,6 ROW 5
F5: 3,6,7,8                              # reduction candidate for 3,6
F5: 3,6                                  # 24 pairs
F5: 7,8                                  # 22 pairs
* PAIR G6: 2,9 BLK 6
H6: 2,9,3,7,8                            # reduction candidate for 2,9
H6: 2,9                                  # 23 pairs
H6: 3,7,8                                # 16 pairs
* PAIR I6: 6,8 ROW 6
C6: 6,8,7                                # reduction candidate for 6,8
C6: 6,8                                  # 28 pairs
E6: 6,8,3,7                              # reduction candidate for 6,8
E6: 6,8                                  # 23 pairs
F6: 6,8,2,3,7                            # reduction candidate for 6,8
F6: 6,8                                  # 24 pairs
* PAIR E8: 6,8 COL E
E4: 6,8,7                                # reduction candidate for 6,8
E4: 6,8                                  # 25 pairs
E6: 6,8,3,7                              # reduction candidate for 6,8
E6: 6,8                                  # 23 pairs
* PAIR F9: 6,8 COL F
F4: 6,8,2,7                              # reduction candidate for 6,8
F4: 6,8 => SOLVED
* 541237869832691754796845213365978421928413675417562938159724386673189542284356197
F4: 2,7                                  # 22 pairs
F5: 6,8,3,7                              # reduction candidate for 6,8
F5: 6,8                                  # 23 pairs
F6: 6,8,2,3,7                            # reduction candidate for 6,8
F6: 6,8                                  # 24 pairs
* PAIR H7: 3,8 COL H
H5: 3,8,7                                # reduction candidate for 3,8
H5: 3,8                                  # 23 pairs
H6: 3,8,2,7,9                            # reduction candidate for 3,8
H6: 3,8                                  # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-029-base-pr-000.dot
* REASONING
* PRF # F4: 6,8 => SOL
* PRF # F4: 6,8 => SOL
* CNT   2 HDP CHAINS /  26 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B4,B9,C3,D2,D3,E1,E8,F1,F9,G3,G5,G6,G7,G9,H3,H7,H9,I6,I7)
* 5412..869.32.9175479..45..33.59..4.192.41...541.5.....159724....731.95422.435...7
* PAIR C3: 6,8 COL C
C5: 6,8,7                                # reduction candidate for 6,8
C5: 6,8                                  # 22 pairs
C6: 6,8,7                                # reduction candidate for 6,8
C6: 6,8                                  # 28 pairs
* PAIR E1: 3,7 COL E
E6: 3,7,6,8                              # reduction candidate for 3,7
E6: 3,7                                  # 25 pairs
E6: 6,8                                  # 23 pairs
* PAIR F1: 3,7 COL F
F5: 3,7,6,8                              # reduction candidate for 3,7
F5: 3,7                                  # 22 pairs
F6: 3,7,2,6,8                            # reduction candidate for 3,7
F6: 3,7                                  # 25 pairs
* PAIR B4: 6,8 BLK 4
C5: 6,8,7                                # reduction candidate for 6,8
C5: 6,8                                  # 22 pairs
C6: 6,8,7                                # reduction candidate for 6,8
C6: 6,8                                  # 28 pairs
* PAIR B4: 6,8 ROW 4
E4: 6,8,7                                # reduction candidate for 6,8
E4: 6,8                                  # 25 pairs
F4: 6,8,2,7                              # reduction candidate for 6,8
F4: 6,8 => SOLVED
* 541237869832691754796845213365978421928413675417562938159724386673189542284356197
* DURATION: 0:00:11.453430  START: 03:39:06.320547  END: 03:39:17.773977 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-029-base-pr-001.dot
* REASONING
* PRF # F4: 6,8 => SOL
* STA F4: 6,8
* CNT   1 HDP CHAINS /  10 HYP OPENED

Header Info

Top 500 Minimum 17 029

solution: 541237869832691754796845213365978421928413675417562938159724386673189542284356197
info: 1326     FNBTWX   S8.f     18776

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

Solution

position: 541237869832691754796845213365978421928413675417562938159724386673189542284356197 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 # C5: 6,8 => UNS
* INC # C6: 6,8 => UNS
* INC # E6: 3,7 => UNS
* INC # E6: 6,8 => UNS
* INC # F5: 3,7 => UNS
* INC # F6: 3,7 => UNS
* INC # C5: 6,8 => UNS
* INC # C6: 6,8 => UNS
* INC # E4: 6,8 => UNS
* PRF # F4: 6,8 => SOL
* INC # F4: 2,7 => UNS
* INC # F5: 3,6 => UNS
* INC # F5: 7,8 => UNS
* INC # H6: 2,9 => UNS
* INC # H6: 3,7,8 => UNS
* INC # C6: 6,8 => UNS
* INC # E6: 6,8 => UNS
* INC # F6: 6,8 => UNS
* INC # E4: 6,8 => UNS
* INC # E6: 6,8 => UNS
* PRF # F4: 6,8 => SOL
* INC # F4: 2,7 => UNS
* INC # F5: 6,8 => UNS
* INC # F6: 6,8 => UNS
* INC # H5: 3,8 => UNS
* INC # H6: 3,8 => UNS
* CNT  26 HDP CHAINS /  26 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C5: 6,8 => UNS
* INC # C6: 6,8 => UNS
* INC # E6: 3,7 => UNS
* INC # E6: 6,8 => UNS
* INC # F5: 3,7 => UNS
* INC # F6: 3,7 => UNS
* INC # C5: 6,8 => UNS
* INC # C6: 6,8 => UNS
* INC # E4: 6,8 => UNS
* PRF # F4: 6,8 => SOL
* STA F4: 6,8
* CNT  10 HDP CHAINS /  10 HYP OPENED