Analysis of xx-top500-160-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ....68.1..25...............1..5........2..7....6....4.6...1...2.7....3.....4..... initial

Autosolve

position: ....68215.251.46...61.52..41.75.6.2....2.17562568..14.6...154.2574629381.1248.56. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 3,9 => CTR => A1: 4,7
* DIS # B1: 3,9 => CTR => B1: 4
* DIS # A2: 3,9 => CTR => A2: 7,8
* PRF # A2: 7,8 => SOL
* PRF # A3: 3,9 => SOL
* DIS # D1: 7 => CTR => D1: 3,9
* PRF # D1: 3,7 => SOL
* DIS # D1: 9 => CTR => D1: 3,7
* DIS # D3: 3,7 => CTR => D3: 9
* PRF # D3: 9 => SOL
* DIS # A2: 3,7 => CTR => A2: 8,9
* PRF # H2: 3,7 => SOL
* DIS # H2: 9 => CTR => H2: 3,7
* DIS # E6: 3,7 => CTR => E6: 9
* PRF # E6: 9 => SOL
* PRF # I2: 8,9 => SOL
* DIS # I2: 7 => CTR => I2: 8,9
* DIS # A3: 8,9 => CTR => A3: 3,7
* PRF # A3: 3,7 => SOL
* DIS # E6: 3,7 => CTR => E6: 9
* PRF # E6: 9 => SOL
* PRF # I4: 8,9 => SOL
* DIS # I4: 3 => CTR => I4: 8,9
* DIS # I4: 3,9 => CTR => I4: 8
* PRF # I4: 8 => SOL
* PRF # E6: 3,9 => SOL
* DIS # E6: 7 => CTR => E6: 3,9
* DIS # A1: 3,9 => CTR => A1: 4,7
* DIS # A2: 3,9 => CTR => A2: 7,8
* PRF # A2: 7,8 => SOL
* PRF # A3: 3,9 => SOL
* DIS # A5: 3,9 => CTR => A5: 4
* PRF # D1: 3,7 => SOL
* DIS # D1: 9 => CTR => D1: 3,7
* DIS # D3: 3,7 => CTR => D3: 9
* PRF # D3: 9 => SOL
* DIS # H2: 7,9 => CTR => H2: 3
* PRF # H2: 3 => SOL
* PRF # H3: 7,9 => SOL
* DIS # H3: 3 => CTR => H3: 7,9
* PRF # I2: 7,9 => SOL
* DIS # I2: 8 => CTR => I2: 7,9
* CNT  42 HDP CHAINS /  54 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 # A1: 3,9 => CTR => A1: 4,7
* DIS A1: 4,7 # B1: 3,9 => CTR => B1: 4
* DIS A1: 4,7 + B1: 4 # A2: 3,9 => CTR => A2: 8
* PRF A1: 4,7 + B1: 4 + A2: 8 => SOL
* STA A1: 4,7 + B1: 4 + A2: 8
* CNT   4 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

....68.1..25...............1..5........2..7....6....4.6...1...2.7....3.....4..... initial
....68215.251.46...61.52..41.75.6.2....2.17562568..14.6...154.2574629381.1248.56. autosolve
749368215825174639361952874137546928498231756256897143683715492574629381912483567 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
C1: 3,9
E2: 3,7
G3: 8,9
F6: 3,7
G4: 8,9
I6: 3,9
A9: 3,9
D7: 3,7
F9: 3,7
H7: 7,9
I9: 7,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H2,H3: 3.. / H2 = 3  =>  0 pairs (*) / H3 = 3  =>  0 pairs (X)
I4,I6: 3.. / I4 = 3  =>  0 pairs (X) / I6 = 3  =>  0 pairs (_)
D7,F9: 3.. / D7 = 3  =>  0 pairs (X) / F9 = 3  =>  0 pairs (_)
A9,F9: 3.. / A9 = 3  =>  0 pairs (X) / F9 = 3  =>  0 pairs (_)
F6,F9: 3.. / F6 = 3  =>  0 pairs (X) / F9 = 3  =>  0 pairs (_)
A1,B1: 4.. / A1 = 4  =>  0 pairs (X) / B1 = 4  => 13 pairs (_)
E4,E5: 4.. / E4 = 4  => 13 pairs (_) / E5 = 4  =>  0 pairs (X)
B4,E4: 4.. / B4 = 4  =>  0 pairs (X) / E4 = 4  => 13 pairs (_)
A1,A5: 4.. / A1 = 4  =>  0 pairs (X) / A5 = 4  => 13 pairs (_)
E6,F6: 7.. / E6 = 7  =>  0 pairs (X) / F6 = 7  =>  0 pairs (_)
D7,F9: 7.. / D7 = 7  =>  0 pairs (*) / F9 = 7  =>  0 pairs (X)
H7,I9: 7.. / H7 = 7  =>  0 pairs (X) / I9 = 7  =>  0 pairs (_)
A1,D1: 7.. / A1 = 7  => 14 pairs (_) / D1 = 7  =>  0 pairs (X)
D7,H7: 7.. / D7 = 7  =>  0 pairs (*) / H7 = 7  =>  0 pairs (X)
F9,I9: 7.. / F9 = 7  =>  0 pairs (X) / I9 = 7  =>  0 pairs (_)
E2,E6: 7.. / E2 = 7  =>  0 pairs (*) / E6 = 7  =>  0 pairs (X)
F6,F9: 7.. / F6 = 7  =>  0 pairs (*) / F9 = 7  =>  0 pairs (X)
I2,I9: 7.. / I2 = 7  =>  0 pairs (X) / I9 = 7  =>  0 pairs (_)
A2,A3: 8.. / A2 = 8  =>  0 pairs (*) / A3 = 8  =>  0 pairs (X)
I2,G3: 8.. / I2 = 8  =>  0 pairs (X) / G3 = 8  =>  0 pairs (_)
B5,C5: 8.. / B5 = 8  => 13 pairs (_) / C5 = 8  => 12 pairs (_)
G4,I4: 8.. / G4 = 8  =>  0 pairs (X) / I4 = 8  =>  0 pairs (_)
B7,C7: 8.. / B7 = 8  => 12 pairs (_) / C7 = 8  => 13 pairs (_)
A2,I2: 8.. / A2 = 8  =>  0 pairs (*) / I2 = 8  =>  0 pairs (X)
A3,G3: 8.. / A3 = 8  =>  0 pairs (X) / G3 = 8  =>  0 pairs (_)
B5,B7: 8.. / B5 = 8  => 13 pairs (_) / B7 = 8  => 12 pairs (_)
C5,C7: 8.. / C5 = 8  => 12 pairs (_) / C7 = 8  => 13 pairs (_)
G3,G4: 8.. / G3 = 8  =>  0 pairs (*) / G4 = 8  =>  0 pairs (X)
I2,I4: 8.. / I2 = 8  =>  0 pairs (X) / I4 = 8  =>  0 pairs (_)
D1,D3: 9.. / D1 = 9  =>  0 pairs (X) / D3 = 9  =>  0 pairs (_)
H7,I9: 9.. / H7 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
E6,I6: 9.. / E6 = 9  =>  0 pairs (*) / I6 = 9  =>  0 pairs (X)
A9,I9: 9.. / A9 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
G3,G4: 9.. / G3 = 9  =>  0 pairs (X) / G4 = 9  =>  0 pairs (_)
* DURATION: 0:00:56.869682  START: 08:12:56.856763  END: 08:13:53.726445 2017-05-04
* CP COUNT: (34)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,C1,D7,E2,F6,F9,G3,G4,H7,I6,I9)
* ....68215.251.46...61.52..41.75.6.2....2.17562568..14.6...154.2574629381.1248.56.
* PAIR C1: 3,9 BLK 1
A1: 3,9,4,7                              # reduction candidate for 3,9
A1: 3,9 => CTR
* .4.768215.251346...619528341.75469284..2917562568..14.6...154.2574629381.1248.56.
A1: 4,7                                  # 12 pairs
B1: 3,9,4                                # reduction candidate for 3,9
B1: 3,9 => CTR
* 4..768215.251346...619528341.75.6928...2.17562568..14.6...154.2574629381.1248.56.
B1: 4                                    # 13 pairs
A2: 3,9,7,8                              # reduction candidate for 3,9
A2: 3,9 => CTR
* ....68215.251.46.8861.529.41.75.682....2.17562568..14.6...15492574629381912483567
A2: 7,8 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
A3: 3,9,7,8                              # reduction candidate for 3,9
A3: 3,9 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
A3: 7,8                                  # 12 pairs
* PAIR C1: 3,9 ROW 1
D1: 3,9,7                                # reduction candidate for 3,9
D1: 7 => CTR
* ...768215.251346...619528341.75.6928...2.17562568..14.6...154.2574629381.1248.56.
D1: 3,9                                  # 14 pairs
* PAIR C1: 3,9 COL C
C5: 3,9,8                                # reduction candidate for 3,9
C5: 3,9                                  # 13 pairs
C7: 3,9,8                                # reduction candidate for 3,9
C7: 3,9                                  # 12 pairs
* PAIR E2: 3,7 BLK 2
D1: 3,7,9                                # reduction candidate for 3,7
D1: 3,7 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
D1: 9 => CTR
* 743968215.251.46...61.52..41.7546.2.4..2.17562568..14.6...154.2574629381312487569
D3: 3,7,9                                # reduction candidate for 3,7
D3: 3,7 => CTR
* 743968215.251.46...61.52..41.7546.2.4..2.17562568..14.6...154.2574629381312487569
D3: 9 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
* PAIR E2: 3,7 ROW 2
A2: 3,7,8,9                              # reduction candidate for 3,7
A2: 3,7 => CTR
* ....68215.251.46.8861.529.41.75.682....2.17562568..14.6...15492574629381912483567
A2: 8,9                                  # 12 pairs
H2: 3,7,9                                # reduction candidate for 3,7
H2: 3,7 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
H2: 9 => CTR
* ....68215.251.469..61.528341.75.6928...2.17562568971436...154.2574629381.1248.56.
* PAIR E2: 3,7 COL E
E6: 3,7,9                                # reduction candidate for 3,7
E6: 3,7 => CTR
* ....68215.251.46...61.52..41.75.6.2....2.17562568..1496...15492574629381912483567
E6: 9 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
* PAIR G3: 8,9 BLK 3
I2: 8,9,7                                # reduction candidate for 8,9
I2: 8,9 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
I2: 7 => CTR
* ....682158251.4697.61.528341.75.6928...2.17562568..14.6...154.2574629381.1248.56.
* PAIR G3: 8,9 ROW 3
A3: 8,9,3,7                              # reduction candidate for 8,9
A3: 8,9 => CTR
* 743968215.251.46...61.52..41.7546.2.4..2.17562568..14.6...154.2574629381312487569
A3: 3,7 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
* PAIR F6: 3,7 BLK 5
E6: 3,7,9                                # reduction candidate for 3,7
E6: 3,7 => CTR
* ....68215.251.46...61.52..41.75.6.2....2.17562568..1496...15492574629381912483567
E6: 9 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
* PAIR G4: 8,9 BLK 6
I4: 8,9,3                                # reduction candidate for 8,9
I4: 8,9 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
I4: 3 => CTR
* ....68215.251.46.8861.529.41.75.6823...2.17562568..1496...15492574629381912483567
* PAIR I6: 3,9 BLK 6
I4: 3,9,8                                # reduction candidate for 3,9
I4: 3,9 => CTR
* ....68215.251.46.8861.529.41.75.682....2.17562568..14.6...15492574629381912483567
I4: 8 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
* PAIR I6: 3,9 ROW 6
E6: 3,9,7                                # reduction candidate for 3,9
E6: 3,9 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
E6: 7 => CTR
* ....68215.251.46...61.52..41.75.6.2....2.17562568731496..3154.2574629381.1248.56.
* PAIR A9: 3,9 BLK 7
B7: 3,9,8                                # reduction candidate for 3,9
B7: 3,9                                  # 13 pairs
C7: 3,9,8                                # reduction candidate for 3,9
C7: 3,9                                  # 12 pairs
* PAIR A9: 3,9 COL A
A1: 3,9,4,7                              # reduction candidate for 3,9
A1: 3,9 => CTR
* .4.768215.251346...619528341.75469284..2917562568..14.6...154.2574629381.1248.56.
A1: 4,7                                  # 12 pairs
A2: 3,9,7,8                              # reduction candidate for 3,9
A2: 3,9 => CTR
* ....68215.251.46.8861.529.41.75.682....2.17562568..14.6...15492574629381912483567
A2: 7,8 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
A3: 3,9,7,8                              # reduction candidate for 3,9
A3: 3,9 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
A3: 7,8                                  # 12 pairs
A5: 3,9,4                                # reduction candidate for 3,9
A5: 3,9 => CTR
* 4..768215.251346...619528341.75.6928...2.17562568..14.6...154.2574629381.1248.56.
A5: 4                                    # 13 pairs
* PAIR D7: 3,7 COL D
D1: 3,7,9                                # reduction candidate for 3,7
D1: 3,7 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
D1: 9 => CTR
* 743968215.251.46...61.52..41.7546.2.4..2.17562568..14.6...154.2574629381312487569
D3: 3,7,9                                # reduction candidate for 3,7
D3: 3,7 => CTR
* 743968215.251.46...61.52..41.7546.2.4..2.17562568..14.6...154.2574629381312487569
D3: 9 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
* PAIR H7: 7,9 COL H
H2: 7,9,3                                # reduction candidate for 7,9
H2: 7,9 => CTR
* ....68215.251346...61.52.341.75.6.2....2.17562568731496..3154.2574629381.1248.56.
H2: 3 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
H3: 7,9,3                                # reduction candidate for 7,9
H3: 7,9 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
H3: 3 => CTR
* ....68215.251346...61.52.341.75.6.2....2.17562568731496..3154.2574629381.1248.56.
* PAIR I9: 7,9 COL I
I2: 7,9,8                                # reduction candidate for 7,9
I2: 7,9 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
I2: 8 => CTR
* ....68215.251.46.8861.529.41.75.682....2.17562568..14.6...15492574629381912483567
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-160-base-pr-000.dot
* REASONING
* DIS # A1: 3,9 => CTR => A1: 4,7
* DIS # B1: 3,9 => CTR => B1: 4
* DIS # A2: 3,9 => CTR => A2: 7,8
* PRF # A2: 7,8 => SOL
* PRF # A3: 3,9 => SOL
* DIS # D1: 7 => CTR => D1: 3,9
* PRF # D1: 3,7 => SOL
* DIS # D1: 9 => CTR => D1: 3,7
* DIS # D3: 3,7 => CTR => D3: 9
* PRF # D3: 9 => SOL
* DIS # A2: 3,7 => CTR => A2: 8,9
* PRF # H2: 3,7 => SOL
* DIS # H2: 9 => CTR => H2: 3,7
* DIS # E6: 3,7 => CTR => E6: 9
* PRF # E6: 9 => SOL
* PRF # I2: 8,9 => SOL
* DIS # I2: 7 => CTR => I2: 8,9
* DIS # A3: 8,9 => CTR => A3: 3,7
* PRF # A3: 3,7 => SOL
* DIS # E6: 3,7 => CTR => E6: 9
* PRF # E6: 9 => SOL
* PRF # I4: 8,9 => SOL
* DIS # I4: 3 => CTR => I4: 8,9
* DIS # I4: 3,9 => CTR => I4: 8
* PRF # I4: 8 => SOL
* PRF # E6: 3,9 => SOL
* DIS # E6: 7 => CTR => E6: 3,9
* DIS # A1: 3,9 => CTR => A1: 4,7
* DIS # A2: 3,9 => CTR => A2: 7,8
* PRF # A2: 7,8 => SOL
* PRF # A3: 3,9 => SOL
* DIS # A5: 3,9 => CTR => A5: 4
* PRF # D1: 3,7 => SOL
* DIS # D1: 9 => CTR => D1: 3,7
* DIS # D3: 3,7 => CTR => D3: 9
* PRF # D3: 9 => SOL
* DIS # H2: 7,9 => CTR => H2: 3
* PRF # H2: 3 => SOL
* PRF # H3: 7,9 => SOL
* DIS # H3: 3 => CTR => H3: 7,9
* PRF # I2: 7,9 => SOL
* DIS # I2: 8 => CTR => I2: 7,9
* CNT  42 HDP CHAINS /  54 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,C1,D7,E2,F6,F9,G3,G4,H7,I6,I9)
* ....68215.251.46...61.52..41.75.6.2....2.17562568..14.6...154.2574629381.1248.56.
* PAIR C1: 3,9 BLK 1
A1: 3,9,4,7                              # reduction candidate for 3,9
A1: 3,9 => CTR
* .4.768215.251346...619528341.75469284..2917562568..14.6...154.2574629381.1248.56.
B1: 3,9,4                                # reduction candidate for 3,9
B1: 3,9 => CTR
* 4..768215.251346...619528341.75.6928...2.17562568..14.6...154.2574629381.1248.56.
A2: 3,9,8                                # reduction candidate for 3,9
A2: 3,9 => CTR
* 74..68215.251.46.8861.529.41.754682.4..2.17562568..14.6...15492574629381912483567
A2: 8 => SOLVED
* 749368215825174639361952874137546928498231756256897143683715492574629381912483567
* DURATION: 0:00:03.705195  START: 08:14:49.145963  END: 08:14:52.851158 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-160-base-pr-001.dot
* REASONING
* DIS # A1: 3,9 => CTR => A1: 4,7
* DIS A1: 4,7 # B1: 3,9 => CTR => B1: 4
* DIS A1: 4,7 + B1: 4 # A2: 3,9 => CTR => A2: 8
* PRF A1: 4,7 + B1: 4 + A2: 8 => SOL
* STA A1: 4,7 + B1: 4 + A2: 8
* CNT   4 HDP CHAINS /   3 HYP OPENED

Header Info

Top 500 Minimum 17 160

solution: 749368215825174639361952874137546928498231756256897143683715492574629381912483567
info: 1819     FNBWX    S8.f     41545

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

Solution

position: 749368215825174639361952874137546928498231756256897143683715492574629381912483567 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:

* DIS # A1: 3,9 => CTR => A1: 4,7
* INC # A1: 4,7 => UNS
* DIS # B1: 3,9 => CTR => B1: 4
* INC # B1: 4 => UNS
* DIS # A2: 3,9 => CTR => A2: 7,8
* PRF # A2: 7,8 => SOL
* PRF # A3: 3,9 => SOL
* INC # A3: 7,8 => UNS
* INC # D1: 3,9 => UNS
* DIS # D1: 7 => CTR => D1: 3,9
* INC # C5: 3,9 => UNS
* INC # C7: 3,9 => UNS
* PRF # D1: 3,7 => SOL
* DIS # D1: 9 => CTR => D1: 3,7
* DIS # D3: 3,7 => CTR => D3: 9
* PRF # D3: 9 => SOL
* DIS # A2: 3,7 => CTR => A2: 8,9
* INC # A2: 8,9 => UNS
* PRF # H2: 3,7 => SOL
* DIS # H2: 9 => CTR => H2: 3,7
* DIS # E6: 3,7 => CTR => E6: 9
* PRF # E6: 9 => SOL
* PRF # I2: 8,9 => SOL
* DIS # I2: 7 => CTR => I2: 8,9
* DIS # A3: 8,9 => CTR => A3: 3,7
* PRF # A3: 3,7 => SOL
* DIS # E6: 3,7 => CTR => E6: 9
* PRF # E6: 9 => SOL
* PRF # I4: 8,9 => SOL
* DIS # I4: 3 => CTR => I4: 8,9
* DIS # I4: 3,9 => CTR => I4: 8
* PRF # I4: 8 => SOL
* PRF # E6: 3,9 => SOL
* DIS # E6: 7 => CTR => E6: 3,9
* INC # B7: 3,9 => UNS
* INC # C7: 3,9 => UNS
* DIS # A1: 3,9 => CTR => A1: 4,7
* INC # A1: 4,7 => UNS
* DIS # A2: 3,9 => CTR => A2: 7,8
* PRF # A2: 7,8 => SOL
* PRF # A3: 3,9 => SOL
* INC # A3: 7,8 => UNS
* DIS # A5: 3,9 => CTR => A5: 4
* INC # A5: 4 => UNS
* PRF # D1: 3,7 => SOL
* DIS # D1: 9 => CTR => D1: 3,7
* DIS # D3: 3,7 => CTR => D3: 9
* PRF # D3: 9 => SOL
* DIS # H2: 7,9 => CTR => H2: 3
* PRF # H2: 3 => SOL
* PRF # H3: 7,9 => SOL
* DIS # H3: 3 => CTR => H3: 7,9
* PRF # I2: 7,9 => SOL
* DIS # I2: 8 => CTR => I2: 7,9
* CNT  54 HDP CHAINS /  54 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 3,9 => CTR => A1: 4,7
* DIS A1: 4,7 # B1: 3,9 => CTR => B1: 4
* DIS A1: 4,7 + B1: 4 # A2: 3,9 => CTR => A2: 8
* PRF A1: 4,7 + B1: 4 + A2: 8 => SOL
* STA A1: 4,7 + B1: 4 + A2: 8
* CNT   4 HDP CHAINS /   3 HYP OPENED