Analysis of xx-top500-114-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .316.........4..5...........7.1.6..........28...3.....4.2.5....5.....6........1.. initial

Autosolve

position: .316.54..6...43.51....1..63.7.1.65941.657.328...3..716462.51.3.51..3.6.2....6.1.5 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B6: 4,5 => CTR => B6: 2,8,9
* PRF # B6: 2,8,9 => SOL
* DIS # H9: 7,8 => CTR => H9: 4
* PRF # A4: 3,8 => SOL
* DIS # A4: 2 => CTR => A4: 3,8
* DIS # C9: 7,9 => CTR => C9: 3,8
* DIS # B6: 4,9 => CTR => B6: 2,5,8
* DIS # B6: 4,5 => CTR => B6: 2,8,9
* PRF # B6: 2,8,9 => SOL
* PRF # E6: 2,8 => SOL
* DIS # E6: 9 => CTR => E6: 2,8
* DIS # F6: 2,8 => CTR => F6: 4,9
* PRF # F6: 4,9 => SOL
* DIS # A4: 2,8 => CTR => A4: 3
* PRF # A4: 3 => SOL
* DIS # E1: 2,8 => CTR => E1: 9
* PRF # E1: 9 => SOL
* PRF # F6: 4,9 => SOL
* DIS # F6: 2,8 => CTR => F6: 4,9
* DIS # A9: 8,9 => CTR => A9: 3,7
* DIS # C9: 8,9 => CTR => C9: 3,7
* PRF # D9: 8,9 => SOL
* DIS # F9: 8,9 => CTR => F9: 2,7
* PRF # B2: 8,9 => SOL
* DIS # B2: 2 => CTR => B2: 8,9
* DIS # B6: 8,9 => CTR => B6: 2,4,5
* DIS # D8: 7,8 => CTR => D8: 4,9
* DIS # D9: 7,8 => CTR => D9: 2,4,9
* DIS # F9: 7,8 => CTR => F9: 2,9
* DIS # D3: 7,8 => CTR => D3: 2,9
* PRF # G3: 8,9 => SOL
* CNT  31 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 # B6: 4,5 => CTR => B6: 2,8,9
* PRF B6: 2,8,9 => SOL
* STA B6: 2,8,9
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

.316.........4..5...........7.1.6..........28...3.....4.2.5....5.....6........1.. initial
.316.54..6...43.51....1..63.7.1.65941.657.328...3..716462.51.3.51..3.6.2....6.1.5 autosolve
231695487697843251854217963378126594146579328925384716462751839519438672783962145 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
B3: 4,5
C3: 4,5
H1: 7,8
I1: 7,9
C4: 3,8
B5: 4,9
C6: 4,5
E4: 2,8
F5: 4,9
B9: 8,9
D7: 7,8
G7: 8,9
I7: 7,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,G3: 2.. / G2 = 2  =>  0 pairs (*) / G3 = 2  =>  0 pairs (X)
D9,F9: 2.. / D9 = 2  =>  0 pairs (X) / F9 = 2  =>  0 pairs (_)
A1,E1: 2.. / A1 = 2  =>  0 pairs (*) / E1 = 2  =>  0 pairs (X)
A4,E4: 2.. / A4 = 2  =>  0 pairs (X) / E4 = 2  =>  0 pairs (_)
B2,B6: 2.. / B2 = 2  =>  0 pairs (X) / B6 = 2  =>  0 pairs (_)
A4,C4: 3.. / A4 = 3  =>  0 pairs (*) / C4 = 3  =>  0 pairs (X)
A9,C9: 3.. / A9 = 3  =>  0 pairs (X) / C9 = 3  =>  0 pairs (_)
A4,A9: 3.. / A4 = 3  =>  0 pairs (*) / A9 = 3  =>  0 pairs (X)
C4,C9: 3.. / C4 = 3  =>  0 pairs (X) / C9 = 3  =>  0 pairs (_)
B3,C3: 4.. / B3 = 4  =>  0 pairs (X) / C3 = 4  => 10 pairs (_)
F5,F6: 4.. / F5 = 4  =>  0 pairs (X) / F6 = 4  =>  0 pairs (_)
D8,D9: 4.. / D8 = 4  => 14 pairs (_) / D9 = 4  =>  0 pairs (X)
H8,H9: 4.. / H8 = 4  =>  0 pairs (X) / H9 = 4  => 14 pairs (_)
B5,F5: 4.. / B5 = 4  =>  0 pairs (*) / F5 = 4  =>  0 pairs (X)
D8,H8: 4.. / D8 = 4  => 14 pairs (_) / H8 = 4  =>  0 pairs (X)
D9,H9: 4.. / D9 = 4  =>  0 pairs (X) / H9 = 4  => 14 pairs (_)
C3,C6: 4.. / C3 = 4  => 10 pairs (_) / C6 = 4  =>  0 pairs (X)
B3,C3: 5.. / B3 = 5  => 10 pairs (_) / C3 = 5  =>  0 pairs (X)
B6,C6: 5.. / B6 = 5  =>  0 pairs (X) / C6 = 5  => 10 pairs (_)
B3,B6: 5.. / B3 = 5  => 10 pairs (_) / B6 = 5  =>  0 pairs (X)
C3,C6: 5.. / C3 = 5  =>  0 pairs (X) / C6 = 5  => 10 pairs (_)
C2,A3: 7.. / C2 = 7  =>  0 pairs (*) / A3 = 7  =>  0 pairs (X)
H1,I1: 7.. / H1 = 7  =>  0 pairs (X) / I1 = 7  =>  0 pairs (_)
C2,D2: 7.. / C2 = 7  =>  0 pairs (*) / D2 = 7  =>  0 pairs (X)
D7,I7: 7.. / D7 = 7  =>  0 pairs (*) / I7 = 7  =>  0 pairs (X)
A3,A9: 7.. / A3 = 7  =>  0 pairs (X) / A9 = 7  =>  0 pairs (_)
I1,I7: 7.. / I1 = 7  =>  0 pairs (*) / I7 = 7  =>  0 pairs (X)
D7,G7: 8.. / D7 = 8  =>  0 pairs (X) / G7 = 8  =>  0 pairs (_)
G7,I7: 9.. / G7 = 9  =>  0 pairs (X) / I7 = 9  =>  0 pairs (_)
B5,F5: 9.. / B5 = 9  =>  0 pairs (X) / F5 = 9  =>  0 pairs (_)
E1,E6: 9.. / E1 = 9  =>  0 pairs (*) / E6 = 9  =>  0 pairs (X)
I1,I7: 9.. / I1 = 9  =>  0 pairs (X) / I7 = 9  =>  0 pairs (_)
* DURATION: 0:01:05.800193  START: 06:39:20.540253  END: 06:40:26.340446 2017-05-04
* CP COUNT: (32)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B5,B9,C3,C4,C6,D7,E4,F5,G7,H1,I1,I7)
* .316.54..6...43.51....1..63.7.1.65941.657.328...3..716462.51.3.51..3.6.2....6.1.5
* PAIR B3: 4,5 COL B
B6: 4,5,2,8,9                            # reduction candidate for 4,5
B6: 4,5 => CTR
* 9316254876287439517..9182632731865941965743288..392716462851.3.51.43.6.238.26.145
B6: 2,8,9 => SOLVED
* 231695487697843251854217963378126594146579328925384716462751839519438672783962145
* PAIR H1: 7,8 COL H
H8: 7,8,4                                # reduction candidate for 7,8
H8: 7,8                                  # 14 pairs
H9: 7,8,4                                # reduction candidate for 7,8
H9: 7,8 => CTR
* 2316954876...43.51.54.1.963.7.126594146579328925384716462751839517938642...462175
H9: 4                                    # 14 pairs
* PAIR C4: 3,8 BLK 4
A4: 3,8,2                                # reduction candidate for 3,8
A4: 3,8 => SOLVED
* 231695487697843251854217963378126594146579328925384716462751839519438672783962145
A4: 2 => CTR
* 9316254876287439517...1.2632731865941965743288..392716462851.3.51..3.6.23..26.145
* PAIR C4: 3,8 COL C
C9: 3,8,7,9                              # reduction candidate for 3,8
C9: 7,9 => CTR
* .316.54796..743.517...1..63.731.65941.657.3289..3..71646285193751..3.6.23...6.1.5
C9: 3,8                                  # 17 pairs
* PAIR B5: 4,9 BLK 4
B6: 4,9,2,5,8                            # reduction candidate for 4,9
B6: 4,9 => CTR
* 931625487628743951754918263273186594196574328845392716462851.3.51.43.6.238.26.145
B6: 2,5,8                                # 13 pairs
* PAIR C6: 4,5 BLK 4
B6: 4,5,2,8,9                            # reduction candidate for 4,5
B6: 4,5 => CTR
* 9316254876287439517..9182632731865941965743288..392716462851.3.51.43.6.238.26.145
B6: 2,8,9 => SOLVED
* 231695487697843251854217963378126594146579328925384716462751839519438672783962145
* PAIR E4: 2,8 BLK 5
E6: 2,8,9                                # reduction candidate for 2,8
E6: 2,8 => SOLVED
* 231695487697843251854217963378126594146579328925384716462751839519438672783962145
E6: 9 => CTR
* 9316254876287439517..9182632731865941965743288..392716462851.3.51.43.6.238.26.145
F6: 2,8,4,9                              # reduction candidate for 2,8
F6: 2,8 => CTR
* 9316254876287439517..9182632731865941965743288..392716462851.3.51.43.6.238.26.145
F6: 4,9 => SOLVED
* 231695487697843251854217963378126594146579328925384716462751839519438672783962145
* PAIR E4: 2,8 ROW 4
A4: 2,8,3                                # reduction candidate for 2,8
A4: 2,8 => CTR
* .316.54796..743.517...1..63.731.65941.657.3289..3..71646285193751..3.6.23...6.1.5
A4: 3 => SOLVED
* 231695487697843251854217963378126594146579328925384716462751839519438672783962145
* PAIR E4: 2,8 COL E
E1: 2,8,9                                # reduction candidate for 2,8
E1: 2,8 => CTR
* 9316254876287439517..9182632731865941965743288..392716462851.3.51.43.6.238.26.145
E1: 9 => SOLVED
* 231695487697843251854217963378126594146579328925384716462751839519438672783962145
* PAIR F5: 4,9 BLK 5
F6: 4,9,2,8                              # reduction candidate for 4,9
F6: 4,9 => SOLVED
* 231695487697843251854217963378126594146579328925384716462751839519438672783962145
F6: 2,8 => CTR
* 9316254876287439517..9182632731865941965743288..392716462851.3.51.43.6.238.26.145
* PAIR B9: 8,9 BLK 7
C8: 8,9,7                                # reduction candidate for 8,9
C8: 8,9                                  # 17 pairs
A9: 8,9,3,7                              # reduction candidate for 8,9
A9: 8,9 => CTR
* 2316.54..6897432517...1..633781265941.657.328925384716462851937517.396.2..3.6.1.5
A9: 3,7                                  # 14 pairs
C9: 8,9,3,7                              # reduction candidate for 8,9
C9: 8,9 => CTR
* .316.54796..743.517...1..63.731.65941.657.3289..3..716462851937517.396823..267145
C9: 3,7                                  # 14 pairs
* PAIR B9: 8,9 ROW 9
D9: 8,9,2,4,7                            # reduction candidate for 8,9
D9: 8,9 => SOLVED
* 231695487697843251854217963378126594146579328925384716462751839519438672783962145
D9: 2,4,7                                # 13 pairs
F9: 8,9,2,7                              # reduction candidate for 8,9
F9: 8,9 => CTR
* 9316254876287439517..9182632731865941965743288..392716462.51.3.51943.6.2387269145
F9: 2,7                                  # 14 pairs
* PAIR B9: 8,9 COL B
B2: 8,9,2                                # reduction candidate for 8,9
B2: 8,9 => SOLVED
* 231695487697843251854217963378126594146579328925384716462751839519438672783962145
B2: 2 => CTR
* 9316254876287439517..9182632731865941965743288..392716462851.3.51.43.6.238.26.145
B6: 8,9,2,4,5                            # reduction candidate for 8,9
B6: 8,9 => CTR
* .316.54..62..43.51.54.1.263.7.1.6594146579328..53.4716462.51.3.51..3.6.2...26.145
B6: 2,4,5                                # 13 pairs
* PAIR D7: 7,8 BLK 8
D8: 7,8,4,9                              # reduction candidate for 7,8
D8: 7,8 => CTR
* .316.54..6...43.51....17.63.7.1.6594196574328...398716462.51.3.51..3964278.4621.5
D8: 4,9                                  # 14 pairs
F8: 7,8,9                                # reduction candidate for 7,8
F8: 7,8                                  # 16 pairs
D9: 7,8,2,4,9                            # reduction candidate for 7,8
D9: 7,8 => CTR
* .316.54..6...43.51....17.63.7.1.6594196574328...398716462.51.3.51.4396.278..62145
D9: 2,4,9                                # 13 pairs
F9: 7,8,2,9                              # reduction candidate for 7,8
F9: 7,8 => CTR
* .316254796297438517..91826327.1.6594196574328...392716462851937517439682.8.267145
F9: 2,9                                  # 14 pairs
* PAIR D7: 7,8 COL D
D2: 7,8,2,9                              # reduction candidate for 7,8
D2: 7,8                                  # 16 pairs
D3: 7,8,2,9                              # reduction candidate for 7,8
D3: 7,8 => CTR
* 2316.54..6972438518..71926337812659414657.328...3..716462.51.3.51943.6.2783.6.145
D3: 2,9                                  # 14 pairs
* PAIR G7: 8,9 COL G
G2: 8,9,2                                # reduction candidate for 8,9
G2: 8,9                                  # 14 pairs
G3: 8,9,2                                # reduction candidate for 8,9
G3: 8,9 => SOLVED
* 231695487697843251854217963378126594146579328925384716462751839519438672783962145
G3: 2                                    # 14 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-114-base-pr-000.dot
* REASONING
* DIS # B6: 4,5 => CTR => B6: 2,8,9
* PRF # B6: 2,8,9 => SOL
* DIS # H9: 7,8 => CTR => H9: 4
* PRF # A4: 3,8 => SOL
* DIS # A4: 2 => CTR => A4: 3,8
* DIS # C9: 7,9 => CTR => C9: 3,8
* DIS # B6: 4,9 => CTR => B6: 2,5,8
* DIS # B6: 4,5 => CTR => B6: 2,8,9
* PRF # B6: 2,8,9 => SOL
* PRF # E6: 2,8 => SOL
* DIS # E6: 9 => CTR => E6: 2,8
* DIS # F6: 2,8 => CTR => F6: 4,9
* PRF # F6: 4,9 => SOL
* DIS # A4: 2,8 => CTR => A4: 3
* PRF # A4: 3 => SOL
* DIS # E1: 2,8 => CTR => E1: 9
* PRF # E1: 9 => SOL
* PRF # F6: 4,9 => SOL
* DIS # F6: 2,8 => CTR => F6: 4,9
* DIS # A9: 8,9 => CTR => A9: 3,7
* DIS # C9: 8,9 => CTR => C9: 3,7
* PRF # D9: 8,9 => SOL
* DIS # F9: 8,9 => CTR => F9: 2,7
* PRF # B2: 8,9 => SOL
* DIS # B2: 2 => CTR => B2: 8,9
* DIS # B6: 8,9 => CTR => B6: 2,4,5
* DIS # D8: 7,8 => CTR => D8: 4,9
* DIS # D9: 7,8 => CTR => D9: 2,4,9
* DIS # F9: 7,8 => CTR => F9: 2,9
* DIS # D3: 7,8 => CTR => D3: 2,9
* PRF # G3: 8,9 => SOL
* CNT  31 HDP CHAINS /  49 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B5,B9,C3,C4,C6,D7,E4,F5,G7,H1,I1,I7)
* .316.54..6...43.51....1..63.7.1.65941.657.328...3..716462.51.3.51..3.6.2....6.1.5
* PAIR B3: 4,5 COL B
B6: 4,5,2,8,9                            # reduction candidate for 4,5
B6: 4,5 => CTR
* 9316254876287439517..9182632731865941965743288..392716462851.3.51.43.6.238.26.145
B6: 2,8,9 => SOLVED
* 231695487697843251854217963378126594146579328925384716462751839519438672783962145
* DURATION: 0:00:03.513379  START: 06:41:22.942058  END: 06:41:26.455437 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-114-base-pr-001.dot
* REASONING
* DIS # B6: 4,5 => CTR => B6: 2,8,9
* PRF B6: 2,8,9 => SOL
* STA B6: 2,8,9
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 114

solution: 231695487697843251854217963378126594146579328925384716462751839519438672783962145
info: 1702     FNBTHWXY S8.f     18249

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

Solution

position: 231695487697843251854217963378126594146579328925384716462751839519438672783962145 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 # B6: 4,5 => CTR => B6: 2,8,9
* PRF # B6: 2,8,9 => SOL
* INC # H8: 7,8 => UNS
* DIS # H9: 7,8 => CTR => H9: 4
* INC # H9: 4 => UNS
* PRF # A4: 3,8 => SOL
* DIS # A4: 2 => CTR => A4: 3,8
* INC # C9: 3,8 => UNS
* DIS # C9: 7,9 => CTR => C9: 3,8
* DIS # B6: 4,9 => CTR => B6: 2,5,8
* INC # B6: 2,5,8 => UNS
* DIS # B6: 4,5 => CTR => B6: 2,8,9
* PRF # B6: 2,8,9 => SOL
* PRF # E6: 2,8 => SOL
* DIS # E6: 9 => CTR => E6: 2,8
* DIS # F6: 2,8 => CTR => F6: 4,9
* PRF # F6: 4,9 => SOL
* DIS # A4: 2,8 => CTR => A4: 3
* PRF # A4: 3 => SOL
* DIS # E1: 2,8 => CTR => E1: 9
* PRF # E1: 9 => SOL
* PRF # F6: 4,9 => SOL
* DIS # F6: 2,8 => CTR => F6: 4,9
* INC # C8: 8,9 => UNS
* DIS # A9: 8,9 => CTR => A9: 3,7
* INC # A9: 3,7 => UNS
* DIS # C9: 8,9 => CTR => C9: 3,7
* INC # C9: 3,7 => UNS
* PRF # D9: 8,9 => SOL
* INC # D9: 2,4,7 => UNS
* DIS # F9: 8,9 => CTR => F9: 2,7
* INC # F9: 2,7 => UNS
* PRF # B2: 8,9 => SOL
* DIS # B2: 2 => CTR => B2: 8,9
* DIS # B6: 8,9 => CTR => B6: 2,4,5
* INC # B6: 2,4,5 => UNS
* DIS # D8: 7,8 => CTR => D8: 4,9
* INC # D8: 4,9 => UNS
* INC # F8: 7,8 => UNS
* DIS # D9: 7,8 => CTR => D9: 2,4,9
* INC # D9: 2,4,9 => UNS
* DIS # F9: 7,8 => CTR => F9: 2,9
* INC # F9: 2,9 => UNS
* INC # D2: 7,8 => UNS
* DIS # D3: 7,8 => CTR => D3: 2,9
* INC # D3: 2,9 => UNS
* INC # G2: 8,9 => UNS
* PRF # G3: 8,9 => SOL
* INC # G3: 2 => UNS
* CNT  49 HDP CHAINS /  49 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B6: 4,5 => CTR => B6: 2,8,9
* PRF B6: 2,8,9 => SOL
* STA B6: 2,8,9
* CNT   2 HDP CHAINS /   1 HYP OPENED