Analysis of xx-top500-481-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 6.2.5.........4.3..........43...8....1....2........7..5..27...........81...6..... initial

Autosolve

position: 6.2.5.........4.32.....2...43..28....1....2........7..5..27...........81...68..27 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # I3: 4,9 => CTR => I3: 5,6
* DIS # I7: 6 => CTR => I7: 4,9
* DIS # B7: 4,9 => CTR => B7: 6,8
* DIS # C7: 4,9 => CTR => C7: 1,3,6,8
* DIS # G9: 4,9 => CTR => G9: 3,5
* DIS # G7: 6,9 => CTR => G7: 3,4
* DIS # I7: 6,9 => CTR => I7: 4
* DIS # C7: 6,9 => CTR => C7: 1,3,4,8
* PRF # H3: 6,9 => SOL
* CNT   9 HDP CHAINS /  30 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 # I3: 4,9 => CTR => I3: 5,6
* DIS I3: 5,6 # I7: 6 => CTR => I7: 4,9
* DIS I3: 5,6 + I7: 4,9 # B7: 4,9 => CTR => B7: 6,8
* DIS I3: 5,6 + I7: 4,9 + B7: 6,8 # C7: 4,9 => CTR => C7: 1,3,6,8
* DIS I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 # G7: 6,9 => CTR => G7: 3,4
* DIS I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 # G8: 3,5 => CTR => G8: 6,9
* DIS I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 # D1: 3,7 => CTR => D1: 1,8
* PRF I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 + D1: 1,8 => SOL
* STA I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 + D1: 1,8
* CNT   8 HDP CHAINS /  26 HYP OPENED

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

Details

Positions

6.2.5.........4.3..........43...8....1....2........7..5..27...........81...6..... initial
6.2.5.........4.32.....2...43..28....1....2........7..5..27...........81...68..27 autosolve
682153479951764832374892165437528916816947253295316748568271394729435681143689527 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
I1: 4,9
I5: 3,8
I6: 3,8
B9: 4,9
H7: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F7,F9: 1.. / F7 = 1  =>  5 pairs (_) / F9 = 1  =>  0 pairs (X)
C7,F7: 1.. / C7 = 1  =>  0 pairs (X) / F7 = 1  =>  5 pairs (_)
A6,B6: 2.. / A6 = 2  =>  5 pairs (_) / B6 = 2  =>  6 pairs (_)
A8,B8: 2.. / A8 = 2  =>  6 pairs (_) / B8 = 2  =>  5 pairs (_)
A6,A8: 2.. / A6 = 2  =>  5 pairs (_) / A8 = 2  =>  6 pairs (_)
B6,B8: 2.. / B6 = 2  =>  6 pairs (_) / B8 = 2  =>  5 pairs (_)
A3,C3: 3.. / A3 = 3  =>  6 pairs (_) / C3 = 3  =>  8 pairs (_)
D1,F1: 3.. / D1 = 3  =>  6 pairs (_) / F1 = 3  =>  0 pairs (*)
I5,I6: 3.. / I5 = 3  =>  5 pairs (_) / I6 = 3  =>  4 pairs (_)
H5,H6: 4.. / H5 = 4  =>  6 pairs (_) / H6 = 4  =>  5 pairs (_)
D8,E8: 4.. / D8 = 4  =>  6 pairs (_) / E8 = 4  =>  6 pairs (_)
B2,C2: 5.. / B2 = 5  =>  5 pairs (_) / C2 = 5  =>  0 pairs (X)
H3,I3: 5.. / H3 = 5  =>  0 pairs (X) / I3 = 5  =>  6 pairs (_)
G8,G9: 5.. / G8 = 5  =>  0 pairs (X) / G9 = 5  =>  5 pairs (_)
F9,G9: 5.. / F9 = 5  =>  0 pairs (X) / G9 = 5  =>  5 pairs (_)
B2,B6: 5.. / B2 = 5  =>  5 pairs (_) / B6 = 5  =>  0 pairs (X)
I3,I4: 5.. / I3 = 5  =>  6 pairs (_) / I4 = 5  =>  0 pairs (X)
E2,E3: 6.. / E2 = 6  =>  6 pairs (_) / E3 = 6  =>  0 pairs (X)
F5,F6: 6.. / F5 = 6  =>  0 pairs (X) / F6 = 6  =>  5 pairs (_)
E2,G2: 6.. / E2 = 6  =>  6 pairs (_) / G2 = 6  =>  0 pairs (X)
H1,H3: 7.. / H1 = 7  =>  0 pairs (*) / H3 = 7  =>  0 pairs (X)
C4,D4: 7.. / C4 = 7  =>  8 pairs (_) / D4 = 7  =>  0 pairs (X)
F1,F5: 7.. / F1 = 7  =>  0 pairs (X) / F5 = 7  =>  0 pairs (_)
I5,I6: 8.. / I5 = 8  =>  4 pairs (_) / I6 = 8  =>  5 pairs (_)
B7,C7: 8.. / B7 = 8  =>  0 pairs (X) / C7 = 8  =>  5 pairs (_)
* DURATION: 0:00:38.006575  START: 19:05:25.394869  END: 19:06:03.401444 2017-05-04
* CP COUNT: (25)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,H7,I1,I5,I6)
* 6.2.5.........4.32.....2...43..28....1....2........7..5..27...........81...68..27
* PAIR I1: 4,9 BLK 3
G1: 4,9,1,8                              # reduction candidate for 4,9
G1: 4,9                                  # 10 pairs
G3: 4,9,1,6,8                            # reduction candidate for 4,9
G3: 4,9                                  #  9 pairs
I3: 4,9,5,6                              # reduction candidate for 4,9
I3: 4,9 => CTR
* 6.2.5..7......4.32.....2.5.437.28965.165.724..25..671.5..27..96.6.....81...68..27
I3: 5,6                                  #  6 pairs
* PAIR I1: 4,9 ROW 1
B1: 4,9,7,8                              # reduction candidate for 4,9
B1: 4,9                                  # 11 pairs
B1: 7,8                                  #  6 pairs
* PAIR I1: 4,9 COL I
I7: 4,9,6                                # reduction candidate for 4,9
I7: 6 => CTR
* 6.2.5.....5.7.4.32.....2...437.28....1...72.......67..5..27..967......81...68..27
I7: 4,9                                  #  8 pairs
* PAIR B9: 4,9 BLK 7
B7: 4,9,6,8                              # reduction candidate for 4,9
B7: 4,9 => CTR
* 6.2.5....9517648323.4..2...437.28...81...72.326....7.85.82713..726....811.368..27
B7: 6,8                                  #  6 pairs
C7: 4,9,1,3,6,8                          # reduction candidate for 4,9
C7: 4,9 => CTR
* 6.2.5.....5.7.4.32.....2...437.28....1...72.......67..58.2713..7......81...68..27
C7: 1,3,6,8                              #  5 pairs
C9: 4,9,1,3                              # reduction candidate for 4,9
C9: 4,9                                  #  9 pairs
* PAIR B9: 4,9 ROW 9
G9: 4,9,3,5                              # reduction candidate for 4,9
G9: 4,9 => CTR
* 6.2.5.....5.7.4.32.....2...437.28....1...72.......67..5..2713..7.....581...685.27
G9: 3,5                                  #  6 pairs
* PAIR B9: 4,9 COL B
B1: 4,9,7,8                              # reduction candidate for 4,9
B1: 4,9                                  # 11 pairs
B3: 4,9,7,8                              # reduction candidate for 4,9
B3: 4,9                                  #  8 pairs
* PAIR H7: 6,9 BLK 9
G7: 6,9,3,4                              # reduction candidate for 6,9
G7: 6,9 => CTR
* 6.2.5...9.5.7.4.32.....2...437.28....1...72.......67..58.27...47......81...68..27
G7: 3,4                                  #  6 pairs
I7: 6,9,4                                # reduction candidate for 6,9
I7: 6,9 => CTR
* 6.2.5.....5.7.4.32.....2...437.28....1...72.......67..5..27....7......81...68..27
I7: 4                                    #  8 pairs
G8: 6,9,3,5                              # reduction candidate for 6,9
G8: 6,9                                  # 10 pairs
* PAIR H7: 6,9 ROW 7
B7: 6,9,4,8                              # reduction candidate for 6,9
B7: 6,9                                  # 10 pairs
C7: 6,9,1,3,4,8                          # reduction candidate for 6,9
C7: 6,9 => CTR
* 6.2.5...9.5.7.4.32.....2...437.28....1...72.......67..58.2713.47......81...68..27
C7: 1,3,4,8                              #  5 pairs
* PAIR H7: 6,9 COL H
H3: 6,9,1,5,7                            # reduction candidate for 6,9
H3: 6,9 => SOLVED
* 682153479951764832374892165437528916816947253295316748568271394729435681143689527
H3: 1,5,7                                #  5 pairs
H4: 6,9,1,5                              # reduction candidate for 6,9
H4: 6,9                                  #  9 pairs
H5: 6,9,4,5                              # reduction candidate for 6,9
H5: 6,9                                  #  9 pairs
H6: 6,9,1,4,5                            # reduction candidate for 6,9
H6: 6,9                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-481-base-pr-000.dot
* REASONING
* DIS # I3: 4,9 => CTR => I3: 5,6
* DIS # I7: 6 => CTR => I7: 4,9
* DIS # B7: 4,9 => CTR => B7: 6,8
* DIS # C7: 4,9 => CTR => C7: 1,3,6,8
* DIS # G9: 4,9 => CTR => G9: 3,5
* DIS # G7: 6,9 => CTR => G7: 3,4
* DIS # I7: 6,9 => CTR => I7: 4
* DIS # C7: 6,9 => CTR => C7: 1,3,4,8
* PRF # H3: 6,9 => SOL
* CNT   9 HDP CHAINS /  30 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,H7,I1,I5,I6)
* 6.2.5.........4.32.....2...43..28....1....2........7..5..27...........81...68..27
* PAIR I1: 4,9 BLK 3
G1: 4,9,1,8                              # reduction candidate for 4,9
G1: 4,9                                  # 10 pairs
G3: 4,9,1,6,8                            # reduction candidate for 4,9
G3: 4,9                                  #  9 pairs
I3: 4,9,5,6                              # reduction candidate for 4,9
I3: 4,9 => CTR
* 6.2.5..7......4.32.....2.5.437.28965.165.724..25..671.5..27..96.6.....81...68..27
* PAIR I1: 4,9 ROW 1
B1: 4,9,7,8                              # reduction candidate for 4,9
B1: 4,9                                  # 12 pairs
B1: 7,8                                  #  7 pairs
* PAIR I1: 4,9 COL I
I7: 4,9,6                                # reduction candidate for 4,9
I7: 6 => CTR
* 6.2.5...4.5.7.4.32.....2..5437.28..9.1...72.......67..5..27..967......81...68..27
* PAIR RESTART
* PAIR I1: 4,9 BLK 3
G1: 4,9,1,8                              # reduction candidate for 4,9
G1: 4,9                                  # 12 pairs
G3: 4,9,1,6,8                            # reduction candidate for 4,9
G3: 4,9                                  # 11 pairs
* PAIR I1: 4,9 ROW 1
B1: 4,9,7,8                              # reduction candidate for 4,9
B1: 4,9                                  # 14 pairs
B1: 7,8                                  #  9 pairs
* PAIR B9: 4,9 BLK 7
B7: 4,9,6,8                              # reduction candidate for 4,9
B7: 4,9 => CTR
* 6.2.5....9517648323.4..2...437.28...81...72.326....7.85.827136.726....811.368..27
C7: 4,9,1,3,6,8                          # reduction candidate for 4,9
C7: 4,9 => CTR
* 6.2.5.....5.7.4.32.....2...437.28....1...72.......67..58.27136.7......81...68..27
C9: 4,9,1,3                              # reduction candidate for 4,9
C9: 4,9                                  # 12 pairs
* RESTART
* PAIR B9: 4,9 BLK 7
C9: 4,9,1,3                              # reduction candidate for 4,9
C9: 4,9                                  # 12 pairs
C9: 1,3                                  # 11 pairs
* PAIR B9: 4,9 COL B
B1: 4,9,7,8                              # reduction candidate for 4,9
B1: 4,9                                  # 14 pairs
B3: 4,9,7,8                              # reduction candidate for 4,9
B3: 4,9                                  # 11 pairs
* PAIR H7: 6,9 BLK 9
G7: 6,9,3,4                              # reduction candidate for 6,9
G7: 6,9 => CTR
* 6.2.5...9.5.7.4.32.....2...437.28....1...72.......67..58.27...47......81...68..27
G8: 6,9,3,5                              # reduction candidate for 6,9
G8: 6,9                                  # 11 pairs
* RESTART
* PAIR H7: 6,9 BLK 9
G8: 6,9,3,5                              # reduction candidate for 6,9
G8: 3,5 => CTR
* 6.2.5.....5.7.4.32.....2...437.28....1...72.......67..58.27..697......81...68..27
* PAIR H7: 6,9 COL H
H4: 6,9,1,5                              # reduction candidate for 6,9
H4: 6,9                                  # 14 pairs
H5: 6,9,4,5                              # reduction candidate for 6,9
H5: 6,9                                  # 14 pairs
H6: 6,9,1,4,5                            # reduction candidate for 6,9
H6: 6,9                                  # 17 pairs

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (B7,B9,F1,F7,G8,H1,H7,I3,I4,I5,I6)
* 6.2.5...9.....4.32.....2...43..28....1....2........7..5..27.3.4.......81...68.527
* PAIR F1: 3,7 BLK 2
D1: 3,7,1,8                              # reduction candidate for 3,7
D1: 3,7 => CTR
* 642.5.819.....4632.9...2.7543..281.6.1....2........7..581279364......981...681527
D1: 1,8 => SOLVED
* 682153479951764832374892165437528916816947253295316748568271394729435681143689527
* DURATION: 0:00:25.259501  START: 19:06:27.470341  END: 19:06:52.729842 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-481-base-pr-001.dot
* REASONING
* DIS # I3: 4,9 => CTR => I3: 5,6
* DIS I3: 5,6 # I7: 6 => CTR => I7: 4,9
* DIS I3: 5,6 + I7: 4,9 # B7: 4,9 => CTR => B7: 6,8
* DIS I3: 5,6 + I7: 4,9 + B7: 6,8 # C7: 4,9 => CTR => C7: 1,3,6,8
* DIS I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 # G7: 6,9 => CTR => G7: 3,4
* DIS I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 # G8: 3,5 => CTR => G8: 6,9
* DIS I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 # D1: 3,7 => CTR => D1: 1,8
* PRF I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 + D1: 1,8 => SOL
* STA I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 + D1: 1,8
* CNT   8 HDP CHAINS /  26 HYP OPENED

Header Info

Top 500 Minimum 17 481

solution: 682153479951764832374892165437528916816947253295316748568271394729435681143689527
info: 95797    FNBHXYK  S8.f     35410

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

Solution

position: 682153479951764832374892165437528916816947253295316748568271394729435681143689527 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 # G1: 4,9 => UNS
* INC # G3: 4,9 => UNS
* DIS # I3: 4,9 => CTR => I3: 5,6
* INC # I3: 5,6 => UNS
* INC # B1: 4,9 => UNS
* INC # B1: 7,8 => UNS
* INC # I7: 4,9 => UNS
* DIS # I7: 6 => CTR => I7: 4,9
* DIS # B7: 4,9 => CTR => B7: 6,8
* INC # B7: 6,8 => UNS
* DIS # C7: 4,9 => CTR => C7: 1,3,6,8
* INC # C7: 1,3,6,8 => UNS
* INC # C9: 4,9 => UNS
* DIS # G9: 4,9 => CTR => G9: 3,5
* INC # G9: 3,5 => UNS
* INC # B1: 4,9 => UNS
* INC # B3: 4,9 => UNS
* DIS # G7: 6,9 => CTR => G7: 3,4
* INC # G7: 3,4 => UNS
* DIS # I7: 6,9 => CTR => I7: 4
* INC # I7: 4 => UNS
* INC # G8: 6,9 => UNS
* INC # B7: 6,9 => UNS
* DIS # C7: 6,9 => CTR => C7: 1,3,4,8
* INC # C7: 1,3,4,8 => UNS
* PRF # H3: 6,9 => SOL
* INC # H3: 1,5,7 => UNS
* INC # H4: 6,9 => UNS
* INC # H5: 6,9 => UNS
* INC # H6: 6,9 => UNS
* CNT  30 HDP CHAINS /  30 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G1: 4,9 => UNS
* INC # G3: 4,9 => UNS
* DIS # I3: 4,9 => CTR => I3: 5,6
* INC I3: 5,6 # B1: 4,9 => UNS
* INC I3: 5,6 # B1: 7,8 => UNS
* INC I3: 5,6 # I7: 4,9 => UNS
* DIS I3: 5,6 # I7: 6 => CTR => I7: 4,9
* INC I3: 5,6 + I7: 4,9 # G1: 4,9 => UNS
* INC I3: 5,6 + I7: 4,9 # G3: 4,9 => UNS
* INC I3: 5,6 + I7: 4,9 # B1: 4,9 => UNS
* INC I3: 5,6 + I7: 4,9 # B1: 7,8 => UNS
* DIS I3: 5,6 + I7: 4,9 # B7: 4,9 => CTR => B7: 6,8
* DIS I3: 5,6 + I7: 4,9 + B7: 6,8 # C7: 4,9 => CTR => C7: 1,3,6,8
* INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 # C9: 4,9 => UNS
* INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 # C9: 4,9 => UNS
* INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 # C9: 1,3 => UNS
* INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 # B1: 4,9 => UNS
* INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 # B3: 4,9 => UNS
* DIS I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 # G7: 6,9 => CTR => G7: 3,4
* INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 # G8: 6,9 => UNS
* INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 # G8: 6,9 => UNS
* DIS I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 # G8: 3,5 => CTR => G8: 6,9
* INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 # H4: 6,9 => UNS
* INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 # H5: 6,9 => UNS
* INC I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 # H6: 6,9 => UNS
* DIS I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 # D1: 3,7 => CTR => D1: 1,8
* PRF I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 + D1: 1,8 => SOL
* STA I3: 5,6 + I7: 4,9 + B7: 6,8 + C7: 1,3,6,8 + G7: 3,4 + G8: 6,9 + D1: 1,8
* CNT  27 HDP CHAINS /  26 HYP OPENED