Analysis of xx-top500-482-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 6.2.5.........3.4..........43...8....1....2........7..5..27...........81...6..... initial

Autosolve

position: 6.2.5.........3.42.....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 # G1: 1,8 => CTR => G1: 3,9
* DIS # I7: 6 => CTR => I7: 3,9
* DIS # B7: 4,9 => CTR => B7: 6,8
* DIS # C7: 4,9 => CTR => C7: 1,3,6,8
* DIS # B8: 4,9 => CTR => B8: 2,6,7
* PRF # C8: 4,9 => SOL
* DIS # C9: 4,9 => CTR => C9: 1,3
* DIS # G9: 4,9 => CTR => G9: 3,5
* DIS # G7: 6,9 => CTR => G7: 3,4
* DIS # I7: 6,9 => CTR => I7: 3
* DIS # C7: 6,9 => CTR => C7: 1,3,4,8
* PRF # H3: 6,9 => SOL
* CNT  12 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 # G1: 1,8 => CTR => G1: 3,9
* DIS G1: 3,9 # I7: 6 => CTR => I7: 3,9
* DIS G1: 3,9 + I7: 3,9 # B7: 4,9 => CTR => B7: 6,8
* DIS G1: 3,9 + I7: 3,9 + B7: 6,8 # C7: 4,9 => CTR => C7: 1,3,6,8
* DIS G1: 3,9 + I7: 3,9 + B7: 6,8 + C7: 1,3,6,8 # B8: 4,9 => CTR => B8: 2,6,7
* PRF G1: 3,9 + I7: 3,9 + B7: 6,8 + C7: 1,3,6,8 + B8: 2,6,7 # C8: 4,9 => SOL
* STA G1: 3,9 + I7: 3,9 + B7: 6,8 + C7: 1,3,6,8 + B8: 2,6,7 + C8: 4,9
* CNT   6 HDP CHAINS /   8 HYP OPENED

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

Details

Positions

6.2.5.........3.4..........43...8....1....2........7..5..27...........81...6..... initial
6.2.5.........3.42.....2...43..28....1....2........7..5..27...........81...68..27 autosolve
682154379951763842374892165437528916816937254295416738568271493729345681143689527 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
I1: 3,9
I5: 4,8
I6: 4,8
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  =>  6 pairs (_) / B6 = 2  =>  6 pairs (_)
A8,B8: 2.. / A8 = 2  =>  6 pairs (_) / B8 = 2  =>  6 pairs (_)
A6,A8: 2.. / A6 = 2  =>  6 pairs (_) / A8 = 2  =>  6 pairs (_)
B6,B8: 2.. / B6 = 2  =>  6 pairs (_) / B8 = 2  =>  6 pairs (_)
A3,C3: 3.. / A3 = 3  =>  6 pairs (_) / C3 = 3  =>  8 pairs (_)
G1,I1: 3.. / G1 = 3  =>  8 pairs (_) / I1 = 3  =>  0 pairs (X)
H5,H6: 3.. / H5 = 3  =>  6 pairs (_) / H6 = 3  =>  5 pairs (_)
D8,E8: 3.. / D8 = 3  =>  6 pairs (_) / E8 = 3  =>  6 pairs (_)
A3,A9: 3.. / A3 = 3  =>  6 pairs (_) / A9 = 3  =>  8 pairs (_)
I1,I7: 3.. / I1 = 3  =>  0 pairs (X) / I7 = 3  =>  8 pairs (_)
I5,I6: 4.. / I5 = 4  =>  5 pairs (_) / I6 = 4  =>  4 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  =>  5 pairs (_) / E3 = 6  =>  0 pairs (X)
F5,F6: 6.. / F5 = 6  =>  0 pairs (X) / F6 = 6  =>  5 pairs (_)
E2,G2: 6.. / E2 = 6  =>  5 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  =>  7 pairs (_)
* DURATION: 0:00:38.800785  START: 19:07:08.928984  END: 19:07:47.729769 2017-05-04
* CP COUNT: (27)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,H7,I1,I5,I6)
* 6.2.5.........3.42.....2...43..28....1....2........7..5..27...........81...68..27
* PAIR I1: 3,9 BLK 3
G1: 3,9,1,8                              # reduction candidate for 3,9
G1: 1,8 => CTR
* 6.2.5...3.5.7.3.42.....2...437.28....1...72.......67..5..27....7......81...68..27
G1: 3,9                                  #  9 pairs
* PAIR I1: 3,9 COL I
I7: 3,9,6                                # reduction candidate for 3,9
I7: 6 => CTR
* 6.2.5...3.5.7.3.42.....2...437.28....1...72.......67..5..27..967......81...68..27
I7: 3,9                                  #  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....9517638423.4..2...437.28...81...72.426....7.85.8271...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.....5.7.3.42.....2...437.28....1...72.......67..58.271...7......81...68..27
C7: 1,3,6,8                              #  5 pairs
B8: 4,9,2,6,7                            # reduction candidate for 4,9
B8: 4,9 => CTR
* 6.2.5.3.9.5..63.42.....2...43.72891.71....2.882....7.45682714932.7...681...68.527
B8: 2,6,7                                #  5 pairs
C8: 4,9,6,7                              # reduction candidate for 4,9
C8: 4,9 => SOLVED
* 682154379951763842374892165437528916816937254295416738568271493729345681143689527
C8: 6,7                                  #  6 pairs
C9: 4,9,1,3                              # reduction candidate for 4,9
C9: 4,9 => CTR
* 6.2.5.....5.7.3.42.....2...437.28....1...72.......67..58.27....7......81...68..27
C9: 1,3                                  #  6 pairs
* PAIR B9: 4,9 ROW 9
F9: 4,9,1,5                              # reduction candidate for 4,9
F9: 4,9                                  #  8 pairs
G9: 4,9,3,5                              # reduction candidate for 4,9
G9: 4,9 => CTR
* 6.2.5.....5.7.3.42.....2...437.28....1...72.......67..5..271...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                                  #  8 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
* 6.2.5.3.9.5.7.3.42.....2...437.28....1...72.......67..5..27...37......81...68..27
G7: 3,4                                  #  6 pairs
I7: 6,9,3                                # reduction candidate for 6,9
I7: 6,9 => CTR
* 6.2.5...3.5.7.3.42.....2...437.28....1...72.......67..5..27....7......81...68..27
I7: 3                                    #  8 pairs
G8: 6,9,4,5                              # 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                                  # 12 pairs
C7: 6,9,1,3,4,8                          # reduction candidate for 6,9
C7: 6,9 => CTR
* 672854319...7.3.42.94162875437.281.6.1...72......167..5892714637......81.4.68..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
* 682154379951763842374892165437528916816937254295416738568271493729345681143689527
H3: 1,5,7                                #  5 pairs
H4: 6,9,1,5                              # reduction candidate for 6,9
H4: 6,9                                  #  9 pairs
H5: 6,9,3,5                              # reduction candidate for 6,9
H5: 6,9                                  #  9 pairs
H6: 6,9,1,3,5                            # reduction candidate for 6,9
H6: 6,9                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-482-base-pr-000.dot
* REASONING
* DIS # G1: 1,8 => CTR => G1: 3,9
* DIS # I7: 6 => CTR => I7: 3,9
* DIS # B7: 4,9 => CTR => B7: 6,8
* DIS # C7: 4,9 => CTR => C7: 1,3,6,8
* DIS # B8: 4,9 => CTR => B8: 2,6,7
* PRF # C8: 4,9 => SOL
* DIS # C9: 4,9 => CTR => C9: 1,3
* DIS # G9: 4,9 => CTR => G9: 3,5
* DIS # G7: 6,9 => CTR => G7: 3,4
* DIS # I7: 6,9 => CTR => I7: 3
* DIS # C7: 6,9 => CTR => C7: 1,3,4,8
* PRF # H3: 6,9 => SOL
* CNT  12 HDP CHAINS /  32 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,H7,I1,I5,I6)
* 6.2.5.........3.42.....2...43..28....1....2........7..5..27...........81...68..27
* PAIR I1: 3,9 BLK 3
G1: 3,9,1,8                              # reduction candidate for 3,9
G1: 1,8 => CTR
* 6.2.5...3.5.7.3.42.....2...437.28....1...72.......67..5..27....7......81...68..27
* PAIR I1: 3,9 COL I
I7: 3,9,6                                # reduction candidate for 3,9
I7: 6 => CTR
* 6.2.5.9.3.5.7.3.42.....2..5437.28..9.1...72.......67..5..27..967......81...68..27
* PAIR RESTART
* PAIR B9: 4,9 BLK 7
B7: 4,9,6,8                              # reduction candidate for 4,9
B7: 4,9 => CTR
* 6.2.5....9517638423.4..2...437.28...81...72.426....7.85.8271...726....811.368..27
C7: 4,9,1,3,6,8                          # reduction candidate for 4,9
C7: 4,9 => CTR
* 672854.1..5.7.3.42.....2.75437.281.6.1...72.......67..58.271.6.7......81...68..27
B8: 4,9,2,6,7                            # reduction candidate for 4,9
B8: 4,9 => CTR
* 6.2.5.3.9.5..63.42.....2...43.72891.71....2.882....7.45682714932.7...681...68.527
C8: 4,9,6,7                              # reduction candidate for 4,9
C8: 4,9 => SOLVED
* 682154379951763842374892165437528916816937254295416738568271493729345681143689527
* DURATION: 0:00:09.976087  START: 19:08:14.546764  END: 19:08:24.522851 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-482-base-pr-001.dot
* REASONING
* DIS # G1: 1,8 => CTR => G1: 3,9
* DIS G1: 3,9 # I7: 6 => CTR => I7: 3,9
* DIS G1: 3,9 + I7: 3,9 # B7: 4,9 => CTR => B7: 6,8
* DIS G1: 3,9 + I7: 3,9 + B7: 6,8 # C7: 4,9 => CTR => C7: 1,3,6,8
* DIS G1: 3,9 + I7: 3,9 + B7: 6,8 + C7: 1,3,6,8 # B8: 4,9 => CTR => B8: 2,6,7
* PRF G1: 3,9 + I7: 3,9 + B7: 6,8 + C7: 1,3,6,8 + B8: 2,6,7 # C8: 4,9 => SOL
* STA G1: 3,9 + I7: 3,9 + B7: 6,8 + C7: 1,3,6,8 + B8: 2,6,7 + C8: 4,9
* CNT   6 HDP CHAINS /   8 HYP OPENED

Header Info

Top 500 Minimum 17 482

solution: 682154379951763842374892165437528916816937254295416738568271493729345681143689527
info: 95799    FNBTHXYK S8.f     35409

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

Solution

position: 682154379951763842374892165437528916816937254295416738568271493729345681143689527 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: 3,9 => UNS
* DIS # G1: 1,8 => CTR => G1: 3,9
* INC # I7: 3,9 => UNS
* DIS # I7: 6 => CTR => I7: 3,9
* 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
* DIS # B8: 4,9 => CTR => B8: 2,6,7
* INC # B8: 2,6,7 => UNS
* PRF # C8: 4,9 => SOL
* INC # C8: 6,7 => UNS
* DIS # C9: 4,9 => CTR => C9: 1,3
* INC # C9: 1,3 => UNS
* INC # F9: 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: 3
* INC # I7: 3 => 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  32 HDP CHAINS /  32 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G1: 3,9 => UNS
* DIS # G1: 1,8 => CTR => G1: 3,9
* INC G1: 3,9 # I7: 3,9 => UNS
* DIS G1: 3,9 # I7: 6 => CTR => I7: 3,9
* DIS G1: 3,9 + I7: 3,9 # B7: 4,9 => CTR => B7: 6,8
* DIS G1: 3,9 + I7: 3,9 + B7: 6,8 # C7: 4,9 => CTR => C7: 1,3,6,8
* DIS G1: 3,9 + I7: 3,9 + B7: 6,8 + C7: 1,3,6,8 # B8: 4,9 => CTR => B8: 2,6,7
* PRF G1: 3,9 + I7: 3,9 + B7: 6,8 + C7: 1,3,6,8 + B8: 2,6,7 # C8: 4,9 => SOL
* STA G1: 3,9 + I7: 3,9 + B7: 6,8 + C7: 1,3,6,8 + B8: 2,6,7 + C8: 4,9
* CNT   8 HDP CHAINS /   8 HYP OPENED