Analysis of xx-top500-345-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 1...2..6.7.5................8.....1....5.3.....47........4..7..2.....5...6..1.... initial

Autosolve

position: 1...2..6.7.5................8.....1....5.3.....47.1......4..7..2.....5...6..1.... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # F3: 5,7 => CTR => F3: 4,8,9
* DIS # F9: 2,8,9 => CTR => F9: 5,7
* DIS # I3: 5,7 => CTR => I3: 2,3,4,8,9
* DIS # I4: 3,4,9 => CTR => I4: 5,7
* DIS # A4: 6,9 => CTR => A4: 3,5
* PRF # C4: 6,9 => SOL
* DIS # C4: 3,7 => CTR => C4: 6,9
* DIS # C5: 6,9 => CTR => C5: 1,2,7
* DIS # A6: 6,9 => CTR => A6: 3,5
* PRF # A3: 6,9 => SOL
* DIS # A3: 3,4,8 => CTR => A3: 6,9
* CNT  11 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 # F3: 5,7 => CTR => F3: 4,8,9
* DIS F3: 4,8,9 # F9: 2,8,9 => CTR => F9: 5,7
* DIS F3: 4,8,9 + F9: 5,7 # I3: 5,7 => CTR => I3: 2,3,4,8,9
* DIS F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 # I4: 3,4,9 => CTR => I4: 5,7
* DIS F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 + I4: 5,7 # A4: 6,9 => CTR => A4: 3,5
* PRF F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 + I4: 5,7 + A4: 3,5 # C4: 6,9 => SOL
* STA F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 + I4: 5,7 + A4: 3,5 + C4: 6,9
* CNT   6 HDP CHAINS /  10 HYP OPENED

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

Details

Positions

1...2..6.7.5................8.....1....5.3.....47........4..7..2.....5...6..1.... initial
1...2..6.7.5................8.....1....5.3.....47.1......4..7..2.....5...6..1.... autosolve
198327465745698132632154978586942317971563284324781659859436721213879546467215893 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
F1: 5,7
I1: 5,7
A5: 6,9
I7: 1,6
I8: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,D3: 1.. / D2 = 1  =>  5 pairs (_) / D3 = 1  =>  5 pairs (_)
G2,G3: 1.. / G2 = 1  =>  5 pairs (_) / G3 = 1  =>  5 pairs (_)
B5,C5: 1.. / B5 = 1  =>  0 pairs (X) / C5 = 1  =>  0 pairs (_)
I7,I8: 1.. / I7 = 1  =>  0 pairs (*) / I8 = 1  =>  0 pairs (X)
D2,G2: 1.. / D2 = 1  =>  5 pairs (_) / G2 = 1  =>  5 pairs (_)
D3,G3: 1.. / D3 = 1  =>  5 pairs (_) / G3 = 1  =>  5 pairs (_)
D4,F4: 2.. / D4 = 2  =>  5 pairs (_) / F4 = 2  =>  6 pairs (_)
F7,H7: 2.. / F7 = 2  =>  5 pairs (_) / H7 = 2  =>  5 pairs (_)
C3,C5: 2.. / C3 = 2  =>  0 pairs (*) / C5 = 2  =>  0 pairs (X)
D4,D9: 2.. / D4 = 2  =>  5 pairs (_) / D9 = 2  =>  6 pairs (_)
B8,A9: 4.. / B8 = 4  =>  0 pairs (X) / A9 = 4  =>  0 pairs (_)
B1,G1: 4.. / B1 = 4  =>  0 pairs (X) / G1 = 4  =>  6 pairs (_)
B8,H8: 4.. / B8 = 4  =>  0 pairs (X) / H8 = 4  =>  0 pairs (_)
A3,A9: 4.. / A3 = 4  =>  0 pairs (X) / A9 = 4  =>  0 pairs (_)
F1,I1: 5.. / F1 = 5  =>  0 pairs (X) / I1 = 5  =>  0 pairs (_)
A4,I4: 5.. / A4 = 5  =>  0 pairs (*) / I4 = 5  =>  0 pairs (X)
A9,F9: 5.. / A9 = 5  =>  0 pairs (X) / F9 = 5  =>  0 pairs (_)
B6,B7: 5.. / B6 = 5  =>  0 pairs (X) / B7 = 5  =>  0 pairs (_)
E3,E7: 5.. / E3 = 5  =>  0 pairs (*) / E7 = 5  =>  0 pairs (X)
H3,H6: 5.. / H3 = 5  =>  0 pairs (X) / H6 = 5  =>  0 pairs (_)
A3,C3: 6.. / A3 = 6  =>  0 pairs (*) / C3 = 6  =>  0 pairs (X)
I7,I8: 6.. / I7 = 6  =>  3 pairs (_) / I8 = 6  =>  0 pairs (*)
F1,I1: 7.. / F1 = 7  =>  0 pairs (*) / I1 = 7  =>  0 pairs (X)
C4,I4: 7.. / C4 = 7  =>  0 pairs (X) / I4 = 7  =>  0 pairs (_)
C9,F9: 7.. / C9 = 7  =>  0 pairs (*) / F9 = 7  =>  0 pairs (X)
B5,B8: 7.. / B5 = 7  =>  0 pairs (*) / B8 = 7  =>  0 pairs (X)
E3,E8: 7.. / E3 = 7  =>  0 pairs (X) / E8 = 7  =>  0 pairs (_)
H3,H5: 7.. / H3 = 7  =>  0 pairs (*) / H5 = 7  =>  0 pairs (X)
E5,E6: 8.. / E5 = 8  =>  6 pairs (_) / E6 = 8  =>  5 pairs (_)
* DURATION: 0:00:49.285408  START: 14:31:28.340028  END: 14:32:17.625436 2017-05-04
* CP COUNT: (29)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,F1,I1,I7,I8)
* 1...2..6.7.5................8.....1....5.3.....47.1......4..7..2.....5...6..1....
* PAIR F1: 5,7 BLK 2
E3: 5,7,3,4,9                            # reduction candidate for 5,7
E3: 5,7                                  #  6 pairs
F3: 5,7,4,8,9                            # reduction candidate for 5,7
F3: 5,7 => CTR
* 1...2..6.7.5................8.....1....5.3.....47.1......45.7..2...7.5..567.1....
F3: 4,8,9                                #  6 pairs
* PAIR F1: 5,7 COL F
F9: 5,7,2,8,9                            # reduction candidate for 5,7
F9: 2,8,9 => CTR
* 1...2..6.7.5................8.....1....5.3.....47.1......4..7..2.....5..567.1....
F9: 5,7                                  #  7 pairs
* PAIR I1: 5,7 BLK 3
H3: 5,7,2,3,4,8,9                        # reduction candidate for 5,7
H3: 5,7                                  #  6 pairs
I3: 5,7,2,3,4,8,9                        # reduction candidate for 5,7
I3: 5,7 => CTR
* 1...2..6.7.5...............587....1....5.3.7...47.1.5..5.4..7..27....54.46..1....
I3: 2,3,4,8,9                            #  6 pairs
* PAIR I1: 5,7 COL I
I4: 5,7,3,4,9                            # reduction candidate for 5,7
I4: 3,4,9 => CTR
* 1...2..6.7.5...............587....1....5.3.....47.1....5.4..7..27....54.46..1....
I4: 5,7                                  #  7 pairs
* PAIR A5: 6,9 BLK 4
A4: 6,9,3,5                              # reduction candidate for 6,9
A4: 6,9 => CTR
* 1...25.677.5.............5..87...315...5.3.7...47.1......45.7..27....54..6..1....
A4: 3,5                                  #  6 pairs
C4: 6,9,3,7                              # reduction candidate for 6,9
C4: 6,9 => SOLVED
* 198327465745698132632154978586942317971563284324781659859436721213879546467215893
C4: 3,7 => CTR
* 1...2..6.7.5................8.....1..1.5.3.....47.1......4..7..27....54.46..1....
C5: 6,9,1,2,7                            # reduction candidate for 6,9
C5: 6,9 => CTR
* 1...2..6.7.5........2.......8.....1..1.5.3....247.1....5.4..7..27....54.46..1....
C5: 1,2,7                                #  5 pairs
A6: 6,9,3,5                              # reduction candidate for 6,9
A6: 6,9 => CTR
* 1...2..6.7.5........6.......8.....1..125.3.....47.1......4..7..27....54.46..1....
A6: 3,5                                  #  6 pairs
* PAIR A5: 6,9 ROW 5
E5: 6,9,4,8                              # reduction candidate for 6,9
E5: 6,9                                  #  6 pairs
G5: 6,9,2,4,8                            # reduction candidate for 6,9
G5: 6,9                                  #  7 pairs
* PAIR A5: 6,9 COL A
A3: 6,9,3,4,8                            # reduction candidate for 6,9
A3: 6,9 => SOLVED
* 198327465745698132632154978586942317971563284324781659859436721213879546467215893
A3: 3,4,8 => CTR
* 1...2..6.7.5........6.......8.....1..125.3.....47.1......4..7..27....54.46..1....
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-345-base-pr-000.dot
* REASONING
* DIS # F3: 5,7 => CTR => F3: 4,8,9
* DIS # F9: 2,8,9 => CTR => F9: 5,7
* DIS # I3: 5,7 => CTR => I3: 2,3,4,8,9
* DIS # I4: 3,4,9 => CTR => I4: 5,7
* DIS # A4: 6,9 => CTR => A4: 3,5
* PRF # C4: 6,9 => SOL
* DIS # C4: 3,7 => CTR => C4: 6,9
* DIS # C5: 6,9 => CTR => C5: 1,2,7
* DIS # A6: 6,9 => CTR => A6: 3,5
* PRF # A3: 6,9 => SOL
* DIS # A3: 3,4,8 => CTR => A3: 6,9
* CNT  11 HDP CHAINS /  22 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,F1,I1,I7,I8)
* 1...2..6.7.5................8.....1....5.3.....47.1......4..7..2.....5...6..1....
* PAIR F1: 5,7 BLK 2
E3: 5,7,3,4,9                            # reduction candidate for 5,7
E3: 5,7                                  #  6 pairs
F3: 5,7,4,8,9                            # reduction candidate for 5,7
F3: 5,7 => CTR
* 1...2..6.7.5................8.....1....5.3.....47.1......45.7..2...7.5..567.1....
* RESTART
* PAIR F1: 5,7 COL F
F9: 5,7,2,8,9                            # reduction candidate for 5,7
F9: 2,8,9 => CTR
* 1...2..6.7.5................8.....1....5.3.....47.1......4..7..2.....5..567.1....
* PAIR RESTART
* PAIR I1: 5,7 BLK 3
H3: 5,7,2,3,4,8,9                        # reduction candidate for 5,7
H3: 5,7                                  #  8 pairs
I3: 5,7,2,3,4,8,9                        # reduction candidate for 5,7
I3: 5,7 => CTR
* 1...2..6.7.5...............587....1....5.3.7...47.1.5..5.4..7..27....54.46..1....
* RESTART
* PAIR I1: 5,7 COL I
I4: 5,7,3,4,9                            # reduction candidate for 5,7
I4: 3,4,9 => CTR
* 1...2..6.7.5...............587....1....5.3.....47.1....5.4..7..27....54.46..1....
* PAIR RESTART
* PAIR A5: 6,9 BLK 4
A4: 6,9,3,5                              # reduction candidate for 6,9
A4: 6,9 => CTR
* 1...2..6.7.5................8.....15...5.3.7...47.1......4..7..27....54.46..1....
C4: 6,9,3,7                              # reduction candidate for 6,9
C4: 6,9 => SOLVED
* 198327465745698132632154978586942317971563284324781659859436721213879546467215893
* DURATION: 0:00:09.908188  START: 14:32:34.881706  END: 14:32:44.789894 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-345-base-pr-001.dot
* REASONING
* DIS # F3: 5,7 => CTR => F3: 4,8,9
* DIS F3: 4,8,9 # F9: 2,8,9 => CTR => F9: 5,7
* DIS F3: 4,8,9 + F9: 5,7 # I3: 5,7 => CTR => I3: 2,3,4,8,9
* DIS F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 # I4: 3,4,9 => CTR => I4: 5,7
* DIS F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 + I4: 5,7 # A4: 6,9 => CTR => A4: 3,5
* PRF F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 + I4: 5,7 + A4: 3,5 # C4: 6,9 => SOL
* STA F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 + I4: 5,7 + A4: 3,5 + C4: 6,9
* CNT   6 HDP CHAINS /  10 HYP OPENED

Header Info

Top 500 Minimum 17 345

solution: 198327465745698132632154978586942317971563284324781659859436721213879546467215893
info: 3476     FNBHWXY  S8.f     25213

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

Solution

position: 198327465745698132632154978586942317971563284324781659859436721213879546467215893 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 # E3: 5,7 => UNS
* DIS # F3: 5,7 => CTR => F3: 4,8,9
* INC # F3: 4,8,9 => UNS
* INC # F9: 5,7 => UNS
* DIS # F9: 2,8,9 => CTR => F9: 5,7
* INC # H3: 5,7 => UNS
* DIS # I3: 5,7 => CTR => I3: 2,3,4,8,9
* INC # I3: 2,3,4,8,9 => UNS
* INC # I4: 5,7 => UNS
* DIS # I4: 3,4,9 => CTR => I4: 5,7
* DIS # A4: 6,9 => CTR => A4: 3,5
* INC # A4: 3,5 => UNS
* PRF # C4: 6,9 => SOL
* DIS # C4: 3,7 => CTR => C4: 6,9
* DIS # C5: 6,9 => CTR => C5: 1,2,7
* INC # C5: 1,2,7 => UNS
* DIS # A6: 6,9 => CTR => A6: 3,5
* INC # A6: 3,5 => UNS
* INC # E5: 6,9 => UNS
* INC # G5: 6,9 => UNS
* PRF # A3: 6,9 => SOL
* DIS # A3: 3,4,8 => CTR => A3: 6,9
* CNT  22 HDP CHAINS /  22 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E3: 5,7 => UNS
* DIS # F3: 5,7 => CTR => F3: 4,8,9
* INC F3: 4,8,9 # F9: 5,7 => UNS
* DIS F3: 4,8,9 # F9: 2,8,9 => CTR => F9: 5,7
* INC F3: 4,8,9 + F9: 5,7 # H3: 5,7 => UNS
* DIS F3: 4,8,9 + F9: 5,7 # I3: 5,7 => CTR => I3: 2,3,4,8,9
* INC F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 # I4: 5,7 => UNS
* DIS F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 # I4: 3,4,9 => CTR => I4: 5,7
* DIS F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 + I4: 5,7 # A4: 6,9 => CTR => A4: 3,5
* PRF F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 + I4: 5,7 + A4: 3,5 # C4: 6,9 => SOL
* STA F3: 4,8,9 + F9: 5,7 + I3: 2,3,4,8,9 + I4: 5,7 + A4: 3,5 + C4: 6,9
* CNT  10 HDP CHAINS /  10 HYP OPENED