Analysis of xx-top500-313-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 2.......6...7..3.......1...5...2..4..7.3..8............376.........4..25......... initial

Autosolve

position: 2..4.5.76.547.63.27..2.15.45...27.43.7236485.34.51.267.376524..6...43725425.7.63. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # E3: 8,9 => SOL
* PRF # A2: 8,9 => SOL
* DIS # A2: 1 => CTR => A2: 8,9
* DIS # H2: 8,9 => CTR => H2: 1
* PRF # H2: 1 => SOL
* DIS # H2: 8 => CTR => H2: 1,9
* DIS # C1: 1,9 => CTR => C1: 3,8
* DIS # H2: 8,9 => CTR => H2: 1
* PRF # H2: 1 => SOL
* PRF # E3: 8,9 => SOL
* DIS # B4: 1,9 => CTR => B4: 6,8
* DIS # C4: 1,9 => CTR => C4: 6,8
* PRF # A2: 1,9 => SOL
* DIS # A2: 8 => CTR => A2: 1,9
* DIS # A7: 1,9 => CTR => A7: 8
* PRF # A7: 8 => SOL
* PRF # B4: 8,9 => SOL
* DIS # C4: 8,9 => CTR => C4: 1,6
* PRF # C1: 8,9 => SOL
* PRF # B4: 8,9 => SOL
* DIS # C4: 8,9 => CTR => C4: 1,6
* DIS # D9: 8,9 => CTR => D9: 1
* DIS # B4: 1,9 => CTR => B4: 6,8
* DIS # C4: 1,9 => CTR => C4: 6,8
* PRF # I7: 1,9 => SOL
* DIS # I7: 8 => CTR => I7: 1,9
* DIS # I9: 1,9 => CTR => I9: 8
* PRF # I9: 8 => SOL
* DIS # D9: 8,9 => CTR => D9: 1
* DIS # I9: 1 => CTR => I9: 8,9
* PRF # I7: 1,9 => SOL
* DIS # I7: 8 => CTR => I7: 1,9
* DIS # I9: 1,9 => CTR => I9: 8
* PRF # I9: 8 => SOL
* DIS # A7: 1,9 => CTR => A7: 8
* PRF # A7: 8 => SOL
* DIS # H2: 8 => CTR => H2: 1,9
* CNT  37 HDP CHAINS /  62 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 # E3: 8,9 => SOL
* STA E3: 8,9
* CNT   1 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

2.......6...7..3.......1...5...2..4..7.3..8............376.........4..25......... initial
2..4.5.76.547.63.27..2.15.45...27.43.7236485.34.51.267.376524..6...43725425.7.63. autosolve
218435976954786312763291584586927143172364859349518267837652491691843725425179638 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
E2: 8,9
G1: 1,9
H3: 8,9
A5: 1,9
C6: 8,9
D4: 8,9
F6: 8,9
G4: 1,9
I5: 1,9
F9: 8,9
H7: 1,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G1,H2: 1.. / G1 = 1  =>  0 pairs (X) / H2 = 1  =>  0 pairs (_)
G4,I5: 1.. / G4 = 1  =>  0 pairs (*) / I5 = 1  =>  0 pairs (X)
D8,D9: 1.. / D8 = 1  =>  0 pairs (X) / D9 = 1  => 14 pairs (_)
A2,H2: 1.. / A2 = 1  =>  0 pairs (X) / H2 = 1  =>  0 pairs (_)
A5,I5: 1.. / A5 = 1  =>  0 pairs (*) / I5 = 1  =>  0 pairs (X)
D9,I9: 1.. / D9 = 1  => 14 pairs (_) / I9 = 1  =>  0 pairs (X)
G1,G4: 1.. / G1 = 1  =>  0 pairs (X) / G4 = 1  =>  0 pairs (_)
H2,H7: 1.. / H2 = 1  =>  0 pairs (*) / H7 = 1  =>  0 pairs (X)
C1,C3: 3.. / C1 = 3  => 12 pairs (_) / C3 = 3  =>  0 pairs (*)
E1,E3: 3.. / E1 = 3  =>  0 pairs (*) / E3 = 3  =>  0 pairs (X)
C1,E1: 3.. / C1 = 3  => 12 pairs (_) / E1 = 3  =>  0 pairs (*)
C3,E3: 3.. / C3 = 3  =>  0 pairs (*) / E3 = 3  =>  0 pairs (X)
B3,C3: 6.. / B3 = 6  => 11 pairs (_) / C3 = 6  => 14 pairs (_)
B4,C4: 6.. / B4 = 6  => 14 pairs (_) / C4 = 6  => 11 pairs (_)
B3,B4: 6.. / B3 = 6  => 11 pairs (_) / B4 = 6  => 14 pairs (_)
C3,C4: 6.. / C3 = 6  => 14 pairs (_) / C4 = 6  => 11 pairs (_)
H2,H3: 8.. / H2 = 8  =>  0 pairs (X) / H3 = 8  => 13 pairs (_)
D4,F6: 8.. / D4 = 8  =>  0 pairs (X) / F6 = 8  =>  0 pairs (_)
I7,I9: 8.. / I7 = 8  =>  0 pairs (X) / I9 = 8  =>  0 pairs (_)
C6,F6: 8.. / C6 = 8  =>  0 pairs (X) / F6 = 8  =>  0 pairs (_)
A7,I7: 8.. / A7 = 8  =>  0 pairs (*) / I7 = 8  =>  0 pairs (X)
A2,A7: 8.. / A2 = 8  =>  0 pairs (X) / A7 = 8  =>  0 pairs (_)
F6,F9: 8.. / F6 = 8  =>  0 pairs (*) / F9 = 8  =>  0 pairs (X)
D4,F6: 9.. / D4 = 9  =>  0 pairs (*) / F6 = 9  =>  0 pairs (X)
G4,I5: 9.. / G4 = 9  =>  0 pairs (X) / I5 = 9  =>  0 pairs (_)
A5,I5: 9.. / A5 = 9  =>  0 pairs (X) / I5 = 9  =>  0 pairs (_)
C6,F6: 9.. / C6 = 9  =>  0 pairs (*) / F6 = 9  =>  0 pairs (X)
F6,F9: 9.. / F6 = 9  =>  0 pairs (X) / F9 = 9  =>  0 pairs (_)
G1,G4: 9.. / G1 = 9  =>  0 pairs (*) / G4 = 9  =>  0 pairs (X)
* DURATION: 0:00:53.601741  START: 13:40:48.532454  END: 13:41:42.134195 2017-05-04
* CP COUNT: (29)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C6,D4,E2,F6,F9,G1,G4,H3,H7,I5)
* 2..4.5.76.547.63.27..2.15.45...27.43.7236485.34.51.267.376524..6...43725425.7.63.
* PAIR E2: 8,9 BLK 2
E1: 8,9,3                                # reduction candidate for 8,9
E1: 8,9                                  # 12 pairs
E3: 8,9,3                                # reduction candidate for 8,9
E3: 8,9 => SOLVED
* 218435976954786312763291584586927143172364859349518267837652491691843725425179638
E3: 3                                    # 12 pairs
* PAIR E2: 8,9 ROW 2
A2: 8,9,1                                # reduction candidate for 8,9
A2: 8,9 => SOLVED
* 218435976954786312763291584586927143172364859349518267837652491691843725425179638
A2: 1 => CTR
* 2..4.5.761547.63.27..2.15.45...27.439723648513485192678376524196..843725425.7.63.
H2: 8,9,1                                # reduction candidate for 8,9
H2: 8,9 => CTR
* 2..4.51761547.63.27..2.15.45...279439723648513485192678376524196..843725425.7.63.
H2: 1 => SOLVED
* 218435976954786312763291584586927143172364859349518267837652491691843725425179638
* PAIR G1: 1,9 BLK 3
H2: 1,9,8                                # reduction candidate for 1,9
H2: 8 => CTR
* 2..4.51761547963827..2.15945...279439723648513485192678376524196..843725425.7.63.
H2: 1,9                                  # 13 pairs
* PAIR G1: 1,9 ROW 1
B1: 1,9,8                                # reduction candidate for 1,9
B1: 1,9                                  # 14 pairs
C1: 1,9,3,8                              # reduction candidate for 1,9
C1: 1,9 => CTR
* 28.435.76.547.63.27632.15.45.6827.43.7236485.3485192678376524..6...43725425.7863.
C1: 3,8                                  # 12 pairs
* PAIR H3: 8,9 BLK 3
H2: 8,9,1                                # reduction candidate for 8,9
H2: 8,9 => CTR
* 2..4.51761547.63.27..2.15.45...279439723648513485192678376524196..843725425.7.63.
H2: 1 => SOLVED
* 218435976954786312763291584586927143172364859349518267837652491691843725425179638
* PAIR H3: 8,9 ROW 3
B3: 8,9,6                                # reduction candidate for 8,9
B3: 8,9                                  # 14 pairs
C3: 8,9,3,6                              # reduction candidate for 8,9
C3: 8,9                                  # 17 pairs
E3: 8,9,3                                # reduction candidate for 8,9
E3: 8,9 => SOLVED
* 218435976954786312763291584586927143172364859349518267837652491691843725425179638
E3: 3                                    # 12 pairs
* PAIR A5: 1,9 BLK 4
B4: 1,9,6,8                              # reduction candidate for 1,9
B4: 1,9 => CTR
* 2..485.7685479631276.2315845.6827143172364859348519267.376524..68..43725425.7863.
B4: 6,8                                  # 12 pairs
C4: 1,9,6,8                              # reduction candidate for 1,9
C4: 1,9 => CTR
* 213485976854796312796231584569827143172364859348519267.376524..68..43725425.7863.
C4: 6,8                                  # 12 pairs
* PAIR A5: 1,9 COL A
A2: 1,9,8                                # reduction candidate for 1,9
A2: 1,9 => SOLVED
* 218435976954786312763291584586927143172364859349518267837652491691843725425179638
A2: 8 => CTR
* 2..4.5.768547963127..2.15845...2714317236485934.51.267.376524..6...43725425.7.63.
A7: 1,9,8                                # reduction candidate for 1,9
A7: 1,9 => CTR
* 2..4.5.768547963127..2.15845...2714317236485934.51.267.376524..6...43725425.7.63.
A7: 8 => SOLVED
* 218435976954786312763291584586927143172364859349518267837652491691843725425179638
* PAIR C6: 8,9 BLK 4
B4: 8,9,1,6                              # reduction candidate for 8,9
B4: 8,9 => SOLVED
* 218435976954786312763291584586927143172364859349518267837652491691843725425179638
B4: 1,6                                  # 13 pairs
C4: 8,9,1,6                              # reduction candidate for 8,9
C4: 8,9 => CTR
* 2.34.59769547863.27.62315.456..2714317236485934.51.267.376524916...43725425179638
C4: 1,6                                  # 12 pairs
* PAIR C6: 8,9 COL C
C1: 8,9,1,3                              # reduction candidate for 8,9
C1: 8,9 => SOLVED
* 218435976954786312763291584586927143172364859349518267837652491691843725425179638
C1: 1,3                                  # 12 pairs
C3: 8,9,3,6                              # reduction candidate for 8,9
C3: 8,9                                  # 17 pairs
C8: 8,9,1                                # reduction candidate for 8,9
C8: 8,9                                  # 15 pairs
* PAIR D4: 8,9 ROW 4
B4: 8,9,1,6                              # reduction candidate for 8,9
B4: 8,9 => SOLVED
* 218435976954786312763291584586927143172364859349518267837652491691843725425179638
B4: 1,6                                  # 13 pairs
C4: 8,9,1,6                              # reduction candidate for 8,9
C4: 8,9 => CTR
* 2.34.59769547863.27.62315.456..2714317236485934.51.267.376524916...43725425179638
C4: 1,6                                  # 12 pairs
* PAIR D4: 8,9 COL D
D8: 8,9,1                                # reduction candidate for 8,9
D8: 8,9                                  # 14 pairs
D9: 8,9,1                                # reduction candidate for 8,9
D9: 8,9 => CTR
* 2..4.5.76.547.63127..2.15845...2714317236485934.51.267.376524986..143725425.7.631
D9: 1                                    # 14 pairs
* PAIR G4: 1,9 ROW 4
B4: 1,9,6,8                              # reduction candidate for 1,9
B4: 1,9 => CTR
* 2..485.7685479631276.2315845.6827143172364859348519267.376524..68..43725425.7863.
B4: 6,8                                  # 12 pairs
C4: 1,9,6,8                              # reduction candidate for 1,9
C4: 1,9 => CTR
* 213485976854796312796231584569827143172364859348519267.376524..68..43725425.7863.
C4: 6,8                                  # 12 pairs
* PAIR I5: 1,9 COL I
I7: 1,9,8                                # reduction candidate for 1,9
I7: 1,9 => SOLVED
* 218435976954786312763291584586927143172364859349518267837652491691843725425179638
I7: 8 => CTR
* 2..4.5.768547963127..2.15845...2714317236485934.51.2679376524.86...43725425.7.63.
I9: 1,9,8                                # reduction candidate for 1,9
I9: 1,9 => CTR
* 2..4.5.768547963127..2.15845...2714317236485934.51.2679376524.86...43725425.7.63.
I9: 8 => SOLVED
* 218435976954786312763291584586927143172364859349518267837652491691843725425179638
* PAIR F9: 8,9 BLK 8
D8: 8,9,1                                # reduction candidate for 8,9
D8: 8,9                                  # 14 pairs
D9: 8,9,1                                # reduction candidate for 8,9
D9: 8,9 => CTR
* 2..4.5.76.547.63127..2.15845...2714317236485934.51.267.376524986..143725425.7.631
D9: 1                                    # 14 pairs
* PAIR F9: 8,9 ROW 9
I9: 8,9,1                                # reduction candidate for 8,9
I9: 1 => CTR
* 2..4.5.768547963127..2.15845...2714317236485934.51.2679376524.86...43725425.7.631
I9: 8,9                                  # 14 pairs
* PAIR H7: 1,9 BLK 9
I7: 1,9,8                                # reduction candidate for 1,9
I7: 1,9 => SOLVED
* 218435976954786312763291584586927143172364859349518267837652491691843725425179638
I7: 8 => CTR
* 2..4.5.768547963127..2.15845...2714317236485934.51.2679376524.86...43725425.7.63.
I9: 1,9,8                                # reduction candidate for 1,9
I9: 1,9 => CTR
* 2..4.5.768547963127..2.15845...2714317236485934.51.2679376524.86...43725425.7.63.
I9: 8 => SOLVED
* 218435976954786312763291584586927143172364859349518267837652491691843725425179638
* PAIR H7: 1,9 ROW 7
A7: 1,9,8                                # reduction candidate for 1,9
A7: 1,9 => CTR
* 2..4.5.768547963127..2.15845...2714317236485934.51.267.376524..6...43725425.7.63.
A7: 8 => SOLVED
* 218435976954786312763291584586927143172364859349518267837652491691843725425179638
* PAIR H7: 1,9 COL H
H2: 1,9,8                                # reduction candidate for 1,9
H2: 8 => CTR
* 2..4.51761547963827..2.15945...279439723648513485192678376524196..843725425.7.63.
H2: 1,9                                  # 13 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-313-base-pr-000.dot
* REASONING
* PRF # E3: 8,9 => SOL
* PRF # A2: 8,9 => SOL
* DIS # A2: 1 => CTR => A2: 8,9
* DIS # H2: 8,9 => CTR => H2: 1
* PRF # H2: 1 => SOL
* DIS # H2: 8 => CTR => H2: 1,9
* DIS # C1: 1,9 => CTR => C1: 3,8
* DIS # H2: 8,9 => CTR => H2: 1
* PRF # H2: 1 => SOL
* PRF # E3: 8,9 => SOL
* DIS # B4: 1,9 => CTR => B4: 6,8
* DIS # C4: 1,9 => CTR => C4: 6,8
* PRF # A2: 1,9 => SOL
* DIS # A2: 8 => CTR => A2: 1,9
* DIS # A7: 1,9 => CTR => A7: 8
* PRF # A7: 8 => SOL
* PRF # B4: 8,9 => SOL
* DIS # C4: 8,9 => CTR => C4: 1,6
* PRF # C1: 8,9 => SOL
* PRF # B4: 8,9 => SOL
* DIS # C4: 8,9 => CTR => C4: 1,6
* DIS # D9: 8,9 => CTR => D9: 1
* DIS # B4: 1,9 => CTR => B4: 6,8
* DIS # C4: 1,9 => CTR => C4: 6,8
* PRF # I7: 1,9 => SOL
* DIS # I7: 8 => CTR => I7: 1,9
* DIS # I9: 1,9 => CTR => I9: 8
* PRF # I9: 8 => SOL
* DIS # D9: 8,9 => CTR => D9: 1
* DIS # I9: 1 => CTR => I9: 8,9
* PRF # I7: 1,9 => SOL
* DIS # I7: 8 => CTR => I7: 1,9
* DIS # I9: 1,9 => CTR => I9: 8
* PRF # I9: 8 => SOL
* DIS # A7: 1,9 => CTR => A7: 8
* PRF # A7: 8 => SOL
* DIS # H2: 8 => CTR => H2: 1,9
* CNT  37 HDP CHAINS /  62 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C6,D4,E2,F6,F9,G1,G4,H3,H7,I5)
* 2..4.5.76.547.63.27..2.15.45...27.43.7236485.34.51.267.376524..6...43725425.7.63.
* PAIR E2: 8,9 BLK 2
E1: 8,9,3                                # reduction candidate for 8,9
E1: 8,9                                  # 12 pairs
E3: 8,9,3                                # reduction candidate for 8,9
E3: 8,9 => SOLVED
* 218435976954786312763291584586927143172364859349518267837652491691843725425179638
* DURATION: 0:00:03.090823  START: 13:42:49.456575  END: 13:42:52.547398 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-313-base-pr-001.dot
* REASONING
* PRF # E3: 8,9 => SOL
* STA E3: 8,9
* CNT   1 HDP CHAINS /   2 HYP OPENED

Header Info

Top 500 Minimum 17 313

solution: 218435976954786312763291584586927143172364859349518267837652491691843725425179638
info: 2847     FNBWX    S8.f     26681

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

Solution

position: 218435976954786312763291584586927143172364859349518267837652491691843725425179638 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 # E1: 8,9 => UNS
* PRF # E3: 8,9 => SOL
* INC # E3: 3 => UNS
* PRF # A2: 8,9 => SOL
* DIS # A2: 1 => CTR => A2: 8,9
* DIS # H2: 8,9 => CTR => H2: 1
* PRF # H2: 1 => SOL
* INC # H2: 1,9 => UNS
* DIS # H2: 8 => CTR => H2: 1,9
* INC # B1: 1,9 => UNS
* DIS # C1: 1,9 => CTR => C1: 3,8
* INC # C1: 3,8 => UNS
* DIS # H2: 8,9 => CTR => H2: 1
* PRF # H2: 1 => SOL
* INC # B3: 8,9 => UNS
* INC # C3: 8,9 => UNS
* PRF # E3: 8,9 => SOL
* INC # E3: 3 => UNS
* DIS # B4: 1,9 => CTR => B4: 6,8
* INC # B4: 6,8 => UNS
* DIS # C4: 1,9 => CTR => C4: 6,8
* INC # C4: 6,8 => UNS
* PRF # A2: 1,9 => SOL
* DIS # A2: 8 => CTR => A2: 1,9
* DIS # A7: 1,9 => CTR => A7: 8
* PRF # A7: 8 => SOL
* PRF # B4: 8,9 => SOL
* INC # B4: 1,6 => UNS
* DIS # C4: 8,9 => CTR => C4: 1,6
* INC # C4: 1,6 => UNS
* PRF # C1: 8,9 => SOL
* INC # C1: 1,3 => UNS
* INC # C3: 8,9 => UNS
* INC # C8: 8,9 => UNS
* PRF # B4: 8,9 => SOL
* INC # B4: 1,6 => UNS
* DIS # C4: 8,9 => CTR => C4: 1,6
* INC # C4: 1,6 => UNS
* INC # D8: 8,9 => UNS
* DIS # D9: 8,9 => CTR => D9: 1
* INC # D9: 1 => UNS
* DIS # B4: 1,9 => CTR => B4: 6,8
* INC # B4: 6,8 => UNS
* DIS # C4: 1,9 => CTR => C4: 6,8
* INC # C4: 6,8 => UNS
* PRF # I7: 1,9 => SOL
* DIS # I7: 8 => CTR => I7: 1,9
* DIS # I9: 1,9 => CTR => I9: 8
* PRF # I9: 8 => SOL
* INC # D8: 8,9 => UNS
* DIS # D9: 8,9 => CTR => D9: 1
* INC # D9: 1 => UNS
* INC # I9: 8,9 => UNS
* DIS # I9: 1 => CTR => I9: 8,9
* PRF # I7: 1,9 => SOL
* DIS # I7: 8 => CTR => I7: 1,9
* DIS # I9: 1,9 => CTR => I9: 8
* PRF # I9: 8 => SOL
* DIS # A7: 1,9 => CTR => A7: 8
* PRF # A7: 8 => SOL
* INC # H2: 1,9 => UNS
* DIS # H2: 8 => CTR => H2: 1,9
* CNT  62 HDP CHAINS /  62 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E1: 8,9 => UNS
* PRF # E3: 8,9 => SOL
* STA E3: 8,9
* CNT   2 HDP CHAINS /   2 HYP OPENED