Analysis of xx-top500-269-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 18.4.........9.6..3.........7...3.8...9.2...........1.6....1......5..9........2.. initial

Autosolve

position: 182436.9....1986233962..14827.613.89.19.2.3...63..9.1262.9.183..3.5.29..9..3..2.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C2: 4,5 => CTR => C2: 7
* DIS # G6: 5,7 => CTR => G6: 4
* PRF # G6: 4 => SOL
* DIS # I5: 5,7 => CTR => I5: 6
* DIS # I9: 5,7 => CTR => I9: 1,4,6
* PRF # A5: 4,5 => SOL
* DIS # A5: 8 => CTR => A5: 4,5
* DIS # A6: 4,5 => CTR => A6: 8
* PRF # A6: 8 => SOL
* DIS # C2: 4,5 => CTR => C2: 7
* PRF # A5: 4,5 => SOL
* DIS # A5: 8 => CTR => A5: 4,5
* DIS # A6: 4,5 => CTR => A6: 8
* PRF # A6: 8 => SOL
* PRF # G6: 4,5 => SOL
* DIS # G6: 7 => CTR => G6: 4,5
* PRF # G6: 4,5 => SOL
* DIS # G6: 7 => CTR => G6: 4,5
* DIS # C7: 4,7 => CTR => C7: 5
* PRF # C7: 5 => SOL
* DIS # I8: 1,6 => CTR => I8: 4,7
* PRF # A2: 4,7 => SOL
* DIS # A2: 5 => CTR => A2: 4,7
* DIS # C7: 7 => CTR => C7: 4,5
* DIS # I9: 4,5 => CTR => I9: 1,6,7
* DIS # C7: 4,7 => CTR => C7: 5
* PRF # C7: 5 => SOL
* PRF # I7: 4,7 => SOL
* DIS # I7: 5 => CTR => I7: 4,7
* DIS # I9: 4,7 => CTR => I9: 1,5,6
* DIS # I8: 6,7 => CTR => I8: 1,4
* DIS # H9: 6,7 => CTR => H9: 5
* PRF # H9: 5 => SOL
* DIS # I9: 6,7 => CTR => I9: 1,4,5
* PRF # H5: 6,7 => SOL
* DIS # H5: 5 => CTR => H5: 6,7
* CNT  36 HDP CHAINS /  49 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 # C2: 4,5 => CTR => C2: 7
* DIS C2: 7 # G6: 5,7 => CTR => G6: 4
* PRF C2: 7 + G6: 4 => SOL
* STA C2: 7 + G6: 4
* CNT   3 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

18.4.........9.6..3.........7...3.8...9.2...........1.6....1......5..9........2.. initial
182436.9....1986233962..14827.613.89.19.2.3...63..9.1262.9.183..3.5.29..9..3..2.. autosolve
182436795457198623396275148274613589519824376863759412625941837731582964948367251 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (20)
B2: 4,5
E3: 5,7
F3: 5,7
G1: 5,7
I1: 5,7
C4: 4,5
D5: 7,8
F5: 4,5
D6: 7,8
E6: 4,5
G4: 4,5
A8: 4,7
C8: 1,8
B9: 4,5
C9: 1,8
E7: 4,7
E8: 6,8
E9: 6,8
F9: 4,7
H8: 6,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C8,C9: 1.. / C8 = 1  => 17 pairs (_) / C9 = 1  =>  0 pairs (X)
I8,I9: 1.. / I8 = 1  =>  0 pairs (X) / I9 = 1  => 17 pairs (_)
C8,I8: 1.. / C8 = 1  => 17 pairs (_) / I8 = 1  =>  0 pairs (X)
C9,I9: 1.. / C9 = 1  =>  0 pairs (X) / I9 = 1  => 17 pairs (_)
F5,E6: 4.. / F5 = 4  => 23 pairs (_) / E6 = 4  =>  0 pairs (X)
G4,G6: 4.. / G4 = 4  =>  0 pairs (X) / G6 = 4  =>  0 pairs (_)
E7,F9: 4.. / E7 = 4  => 23 pairs (_) / F9 = 4  =>  0 pairs (X)
C4,G4: 4.. / C4 = 4  =>  0 pairs (*) / G4 = 4  =>  0 pairs (X)
A5,F5: 4.. / A5 = 4  =>  0 pairs (X) / F5 = 4  => 23 pairs (_)
A8,I8: 4.. / A8 = 4  =>  0 pairs (X) / I8 = 4  => 19 pairs (_)
B2,B9: 4.. / B2 = 4  =>  0 pairs (X) / B9 = 4  =>  0 pairs (_)
E6,E7: 4.. / E6 = 4  =>  0 pairs (X) / E7 = 4  => 23 pairs (_)
F5,F9: 4.. / F5 = 4  => 23 pairs (_) / F9 = 4  =>  0 pairs (X)
E3,F3: 5.. / E3 = 5  =>  0 pairs (X) / F3 = 5  => 23 pairs (_)
G1,I1: 5.. / G1 = 5  =>  0 pairs (X) / I1 = 5  =>  0 pairs (_)
F5,E6: 5.. / F5 = 5  =>  0 pairs (X) / E6 = 5  => 23 pairs (_)
C7,B9: 5.. / C7 = 5  =>  0 pairs (*) / B9 = 5  =>  0 pairs (X)
C4,G4: 5.. / C4 = 5  =>  0 pairs (X) / G4 = 5  =>  0 pairs (_)
C7,I7: 5.. / C7 = 5  =>  0 pairs (*) / I7 = 5  =>  0 pairs (X)
B2,B9: 5.. / B2 = 5  =>  0 pairs (*) / B9 = 5  =>  0 pairs (X)
E3,E6: 5.. / E3 = 5  =>  0 pairs (X) / E6 = 5  => 23 pairs (_)
F3,F5: 5.. / F3 = 5  => 23 pairs (_) / F5 = 5  =>  0 pairs (X)
H5,H9: 5.. / H5 = 5  =>  0 pairs (X) / H9 = 5  =>  0 pairs (_)
H5,I5: 6.. / H5 = 6  =>  0 pairs (X) / I5 = 6  => 21 pairs (_)
E8,E9: 6.. / E8 = 6  =>  0 pairs (X) / E9 = 6  => 17 pairs (_)
A2,C2: 7.. / A2 = 7  =>  0 pairs (X) / C2 = 7  => 19 pairs (_)
E3,F3: 7.. / E3 = 7  => 23 pairs (_) / F3 = 7  =>  0 pairs (X)
G1,I1: 7.. / G1 = 7  =>  0 pairs (*) / I1 = 7  =>  0 pairs (X)
D5,D6: 7.. / D5 = 7  =>  0 pairs (X) / D6 = 7  =>  0 pairs (_)
C7,A8: 7.. / C7 = 7  =>  0 pairs (X) / A8 = 7  => 19 pairs (_)
E7,F9: 7.. / E7 = 7  =>  0 pairs (X) / F9 = 7  => 23 pairs (_)
D6,G6: 7.. / D6 = 7  =>  0 pairs (*) / G6 = 7  =>  0 pairs (X)
A2,A8: 7.. / A2 = 7  =>  0 pairs (X) / A8 = 7  => 19 pairs (_)
C2,C7: 7.. / C2 = 7  => 19 pairs (_) / C7 = 7  =>  0 pairs (X)
E3,E7: 7.. / E3 = 7  => 23 pairs (_) / E7 = 7  =>  0 pairs (X)
F3,F9: 7.. / F3 = 7  =>  0 pairs (X) / F9 = 7  => 23 pairs (_)
G1,G6: 7.. / G1 = 7  =>  0 pairs (*) / G6 = 7  =>  0 pairs (X)
A5,A6: 8.. / A5 = 8  =>  0 pairs (X) / A6 = 8  =>  0 pairs (_)
D5,D6: 8.. / D5 = 8  =>  0 pairs (*) / D6 = 8  =>  0 pairs (X)
C8,C9: 8.. / C8 = 8  =>  0 pairs (X) / C9 = 8  => 17 pairs (_)
E8,E9: 8.. / E8 = 8  => 17 pairs (_) / E9 = 8  =>  0 pairs (X)
A5,D5: 8.. / A5 = 8  =>  0 pairs (X) / D5 = 8  =>  0 pairs (_)
A6,D6: 8.. / A6 = 8  =>  0 pairs (*) / D6 = 8  =>  0 pairs (X)
C8,E8: 8.. / C8 = 8  =>  0 pairs (X) / E8 = 8  => 17 pairs (_)
C9,E9: 8.. / C9 = 8  => 17 pairs (_) / E9 = 8  =>  0 pairs (X)
* DURATION: 0:01:26.709085  START: 12:05:47.169278  END: 12:07:13.878363 2017-05-04
* CP COUNT: (45)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B2,B9,C4,C8,C9,D5,D6,E3,E6,E7,E8,E9,F3,F5,F9,G1,G4,H8,I1)
* 182436.9....1986233962..14827.613.89.19.2.3...63..9.1262.9.183..3.5.29..9..3..2..
* PAIR B2: 4,5 BLK 1
A2: 4,5,7                                # reduction candidate for 4,5
A2: 4,5                                  # 19 pairs
C2: 4,5,7                                # reduction candidate for 4,5
C2: 4,5 => CTR
* 1824365977451986233962..14827.613.89.19.2.3...63..9.1262794183543.5.29..95.3.7264
C2: 7                                    # 19 pairs
* PAIR G1: 5,7 COL G
G6: 5,7,4                                # reduction candidate for 5,7
G6: 5,7 => CTR
* 1824365975471986233962..148275613489.19.2.356.63.597126249.1835.3.5.29..95.3..2..
G6: 4 => SOLVED
* 182436795457198623396275148274613589519824376863759412625941837731582964948367251
* PAIR I1: 5,7 COL I
I5: 5,7,6                                # reduction candidate for 5,7
I5: 5,7 => CTR
* 182436.9....1986233962..14827.613.89.19.2.36..63..9.1262.9.183..3.5.297.9..3.725.
I5: 6                                    # 21 pairs
I7: 5,7,4                                # reduction candidate for 5,7
I7: 5,7                                  # 24 pairs
I9: 5,7,1,4,6                            # reduction candidate for 5,7
I9: 5,7 => CTR
* 182436.9....1986233962..14827.613.89.19.2.356.63.5971262.94183.4385.29.19.138.26.
I9: 1,4,6                                # 20 pairs
* PAIR C4: 4,5 BLK 4
A5: 4,5,8                                # reduction candidate for 4,5
A5: 4,5 => SOLVED
* 182436795457198623396275148274613589519824376863759412625941837731582964948367251
A5: 8 => CTR
* 1824365975471986233962..14827.613.898197243...6385971262.94183..3.5.29..9..3.72..
A6: 4,5,8                                # reduction candidate for 4,5
A6: 4,5 => CTR
* 1824365975471986233962..14827.613.898197243...6385971262.94183..3.5.29..9..3.72..
A6: 8 => SOLVED
* 182436795457198623396275148274613589519824376863759412625941837731582964948367251
* PAIR C4: 4,5 COL C
C2: 4,5,7                                # reduction candidate for 4,5
C2: 4,5 => CTR
* 1824365977451986233962..14827.613.89.19.2.3...63..9.1262794183543.5.29..95.3.7264
C2: 7                                    # 19 pairs
C7: 4,5,7                                # reduction candidate for 4,5
C7: 4,5                                  # 19 pairs
* PAIR F5: 4,5 ROW 5
A5: 4,5,8                                # reduction candidate for 4,5
A5: 4,5 => SOLVED
* 182436795457198623396275148274613589519824376863759412625941837731582964948367251
A5: 8 => CTR
* 1824365975471986233962..14827.613.898197243...6385971262.94183..3.5.29..9..3.72..
* PAIR E6: 4,5 ROW 6
A6: 4,5,8                                # reduction candidate for 4,5
A6: 4,5 => CTR
* 1824365975471986233962..14827.613.898197243...6385971262.94183..3.5.29..9..3.72..
A6: 8 => SOLVED
* 182436795457198623396275148274613589519824376863759412625941837731582964948367251
G6: 4,5,7                                # reduction candidate for 4,5
G6: 4,5 => SOLVED
* 182436795457198623396275148274613589519824376863759412625941837731582964948367251
G6: 7 => CTR
* 18243659754.1986233962..148275613489.1972.3...6385971262.941835.3.5.29..95.3.7264
* PAIR G4: 4,5 BLK 6
G6: 4,5,7                                # reduction candidate for 4,5
G6: 4,5 => SOLVED
* 182436795457198623396275148274613589519824376863759412625941837731582964948367251
G6: 7 => CTR
* 18243659754.1986233962..148275613489.1972.3...6385971262.941835.3.5.29..95.3.7264
* PAIR A8: 4,7 BLK 7
C7: 4,7,5                                # reduction candidate for 4,7
C7: 4,7 => CTR
* 182436597.4.1986233962..148275613489.19.2.356.63.59712624971835.3.5.29..95.3..2..
C7: 5 => SOLVED
* 182436795457198623396275148274613589519824376863759412625941837731582964948367251
* PAIR A8: 4,7 ROW 8
I8: 4,7,1,6                              # reduction candidate for 4,7
I8: 1,6 => CTR
* 182436.9.745198623396275148274613589.19.2.3...63..9.1262.9.183.43.5.297.95.3.7264
I8: 4,7                                  # 18 pairs
* PAIR A8: 4,7 COL A
A2: 4,7,5                                # reduction candidate for 4,7
A2: 4,7 => SOLVED
* 182436795457198623396275148274613589519824376863759412625941837731582964948367251
A2: 5 => CTR
* 182436.9.5471986233962..148275613489.19.2.3...63..9.1262497183573.5.296495.364271
* PAIR B9: 4,5 BLK 7
C7: 4,5,7                                # reduction candidate for 4,5
C7: 7 => CTR
* 1824365977451986233962..14827.613.89.19.2.3...63..9.1262794183543.5.29..95.3.7264
C7: 4,5                                  # 19 pairs
* PAIR B9: 4,5 ROW 9
I9: 4,5,1,6,7                            # reduction candidate for 4,5
I9: 4,5 => CTR
* 182436.9....1986233962..14827.613.89.19.2.356.63.5971262.94183.4385.29.19.138.26.
I9: 1,6,7                                # 20 pairs
* PAIR E7: 4,7 ROW 7
C7: 4,7,5                                # reduction candidate for 4,7
C7: 4,7 => CTR
* 182436597.4.1986233962..148275613489.19.2.356.63.59712624971835.3.5.29..95.3..2..
C7: 5 => SOLVED
* 182436795457198623396275148274613589519824376863759412625941837731582964948367251
I7: 4,7,5                                # reduction candidate for 4,7
I7: 4,7 => SOLVED
* 182436795457198623396275148274613589519824376863759412625941837731582964948367251
I7: 5 => CTR
* 182436597.4.1986233962..148275613489.19.2.356.63.59712624971835.3.5.29..95.3..2..
* PAIR F9: 4,7 ROW 9
I9: 4,7,1,5,6                            # reduction candidate for 4,7
I9: 4,7 => CTR
* 182436.9....1986233962..14827.613.89.19.2.356.63.5971262.9418354385.29.19.138.26.
I9: 1,5,6                                # 20 pairs
* PAIR H8: 6,7 BLK 9
I8: 6,7,1,4                              # reduction candidate for 6,7
I8: 6,7 => CTR
* 182436.9....1986233962..14827.613.89.19.2.3...63..9.1262.9.183.4315829..95836.271
I8: 1,4                                  # 21 pairs
H9: 6,7,5                                # reduction candidate for 6,7
H9: 6,7 => CTR
* 1824365975471986233962..14827.613.89.19.2.356.63.5971262.94183..3.5.29..9..3.726.
H9: 5 => SOLVED
* 182436795457198623396275148274613589519824376863759412625941837731582964948367251
I9: 6,7,1,4,5                            # reduction candidate for 6,7
I9: 6,7 => CTR
* 182436.9....1986233962..14827.613.89.19.2.3...63..9.1262.9.18344385.29.19.138.2..
I9: 1,4,5                                # 20 pairs
* PAIR H8: 6,7 COL H
H5: 6,7,5                                # reduction candidate for 6,7
H5: 6,7 => SOLVED
* 182436795457198623396275148274613589519824376863759412625941837731582964948367251
H5: 5 => CTR
* 1824365975471986233962..14827.613.89.19.2.356.63.5971262.94183..3.5.29..9..3.726.
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-269-base-pr-000.dot
* REASONING
* DIS # C2: 4,5 => CTR => C2: 7
* DIS # G6: 5,7 => CTR => G6: 4
* PRF # G6: 4 => SOL
* DIS # I5: 5,7 => CTR => I5: 6
* DIS # I9: 5,7 => CTR => I9: 1,4,6
* PRF # A5: 4,5 => SOL
* DIS # A5: 8 => CTR => A5: 4,5
* DIS # A6: 4,5 => CTR => A6: 8
* PRF # A6: 8 => SOL
* DIS # C2: 4,5 => CTR => C2: 7
* PRF # A5: 4,5 => SOL
* DIS # A5: 8 => CTR => A5: 4,5
* DIS # A6: 4,5 => CTR => A6: 8
* PRF # A6: 8 => SOL
* PRF # G6: 4,5 => SOL
* DIS # G6: 7 => CTR => G6: 4,5
* PRF # G6: 4,5 => SOL
* DIS # G6: 7 => CTR => G6: 4,5
* DIS # C7: 4,7 => CTR => C7: 5
* PRF # C7: 5 => SOL
* DIS # I8: 1,6 => CTR => I8: 4,7
* PRF # A2: 4,7 => SOL
* DIS # A2: 5 => CTR => A2: 4,7
* DIS # C7: 7 => CTR => C7: 4,5
* DIS # I9: 4,5 => CTR => I9: 1,6,7
* DIS # C7: 4,7 => CTR => C7: 5
* PRF # C7: 5 => SOL
* PRF # I7: 4,7 => SOL
* DIS # I7: 5 => CTR => I7: 4,7
* DIS # I9: 4,7 => CTR => I9: 1,5,6
* DIS # I8: 6,7 => CTR => I8: 1,4
* DIS # H9: 6,7 => CTR => H9: 5
* PRF # H9: 5 => SOL
* DIS # I9: 6,7 => CTR => I9: 1,4,5
* PRF # H5: 6,7 => SOL
* DIS # H5: 5 => CTR => H5: 6,7
* CNT  36 HDP CHAINS /  49 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B2,B9,C4,C8,C9,D5,D6,E3,E6,E7,E8,E9,F3,F5,F9,G1,G4,H8,I1)
* 182436.9....1986233962..14827.613.89.19.2.3...63..9.1262.9.183..3.5.29..9..3..2..
* PAIR B2: 4,5 BLK 1
A2: 4,5,7                                # reduction candidate for 4,5
A2: 4,5                                  # 19 pairs
C2: 4,5,7                                # reduction candidate for 4,5
C2: 4,5 => CTR
* 1824365977451986233962..14827.613.89.19.2.3...63..9.1262794183543.5.29..95.3.7264
* RESTART
* PAIR G1: 5,7 COL G
G6: 5,7,4                                # reduction candidate for 5,7
G6: 5,7 => CTR
* 182436.9...71986233962..14827.613489.19.2.3.6.63..9.12624971835731582964958364271
G6: 4 => SOLVED
* 182436795457198623396275148274613589519824376863759412625941837731582964948367251
* DURATION: 0:00:05.605290  START: 12:08:09.258754  END: 12:08:14.864044 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-269-base-pr-001.dot
* REASONING
* DIS # C2: 4,5 => CTR => C2: 7
* DIS C2: 7 # G6: 5,7 => CTR => G6: 4
* PRF C2: 7 + G6: 4 => SOL
* STA C2: 7 + G6: 4
* CNT   3 HDP CHAINS /   3 HYP OPENED

Header Info

Top 500 Minimum 17 269

solution: 182436795457198623396275148274613589519824376863759412625941837731582964948367251
info: 2143     FNBTHWXY S8.f     26636

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

Solution

position: 182436795457198623396275148274613589519824376863759412625941837731582964948367251 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 # A2: 4,5 => UNS
* DIS # C2: 4,5 => CTR => C2: 7
* INC # C2: 7 => UNS
* DIS # G6: 5,7 => CTR => G6: 4
* PRF # G6: 4 => SOL
* DIS # I5: 5,7 => CTR => I5: 6
* INC # I5: 6 => UNS
* INC # I7: 5,7 => UNS
* DIS # I9: 5,7 => CTR => I9: 1,4,6
* INC # I9: 1,4,6 => UNS
* PRF # A5: 4,5 => SOL
* DIS # A5: 8 => CTR => A5: 4,5
* DIS # A6: 4,5 => CTR => A6: 8
* PRF # A6: 8 => SOL
* DIS # C2: 4,5 => CTR => C2: 7
* INC # C2: 7 => UNS
* INC # C7: 4,5 => UNS
* PRF # A5: 4,5 => SOL
* DIS # A5: 8 => CTR => A5: 4,5
* DIS # A6: 4,5 => CTR => A6: 8
* PRF # A6: 8 => SOL
* PRF # G6: 4,5 => SOL
* DIS # G6: 7 => CTR => G6: 4,5
* PRF # G6: 4,5 => SOL
* DIS # G6: 7 => CTR => G6: 4,5
* DIS # C7: 4,7 => CTR => C7: 5
* PRF # C7: 5 => SOL
* INC # I8: 4,7 => UNS
* DIS # I8: 1,6 => CTR => I8: 4,7
* PRF # A2: 4,7 => SOL
* DIS # A2: 5 => CTR => A2: 4,7
* INC # C7: 4,5 => UNS
* DIS # C7: 7 => CTR => C7: 4,5
* DIS # I9: 4,5 => CTR => I9: 1,6,7
* INC # I9: 1,6,7 => UNS
* DIS # C7: 4,7 => CTR => C7: 5
* PRF # C7: 5 => SOL
* PRF # I7: 4,7 => SOL
* DIS # I7: 5 => CTR => I7: 4,7
* DIS # I9: 4,7 => CTR => I9: 1,5,6
* INC # I9: 1,5,6 => UNS
* DIS # I8: 6,7 => CTR => I8: 1,4
* INC # I8: 1,4 => UNS
* DIS # H9: 6,7 => CTR => H9: 5
* PRF # H9: 5 => SOL
* DIS # I9: 6,7 => CTR => I9: 1,4,5
* INC # I9: 1,4,5 => UNS
* PRF # H5: 6,7 => SOL
* DIS # H5: 5 => CTR => H5: 6,7
* CNT  49 HDP CHAINS /  49 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 4,5 => UNS
* DIS # C2: 4,5 => CTR => C2: 7
* DIS C2: 7 # G6: 5,7 => CTR => G6: 4
* PRF C2: 7 + G6: 4 => SOL
* STA C2: 7 + G6: 4
* CNT   4 HDP CHAINS /   3 HYP OPENED