Analysis of xx-top500-375-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 1.9.........7...4.6............9.6.1.7.3.......8.......3....87......69......2.... initial

Autosolve

position: 1.963.7.8.8.719.466.7.8.319....97681.71368.9.9681...37.369.187.81..769.379.82316. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # G5: 2,5 => SOL
* DIS # A4: 2,5 => CTR => A4: 3,4
* PRF # C4: 2,5 => SOL
* PRF # D4: 4 => SOL
* DIS # F6: 4,5 => CTR => F6: 2
* DIS # G6: 2 => CTR => G6: 4,5
* PRF # G5: 2,5 => SOL
* PRF # A5: 4 => SOL
* DIS # I7: 4 => CTR => I7: 2,5
* DIS # A7: 4,5 => CTR => A7: 2
* PRF # A7: 2 => SOL
* PRF # C8: 4,5 => SOL
* DIS # C8: 2 => CTR => C8: 4,5
* DIS # C4: 4,5 => CTR => C4: 2,3
* DIS # A7: 4,5 => CTR => A7: 2
* PRF # A7: 2 => SOL
* PRF # I7: 4,5 => SOL
* DIS # I7: 2 => CTR => I7: 4,5
* PRF # C8: 4,5 => SOL
* DIS # C8: 2 => CTR => C8: 4,5
* DIS # D3: 4,5 => CTR => D3: 2
* DIS # I7: 4 => CTR => I7: 2,5
* PRF # C8: 4 => SOL
* PRF # I7: 4,5 => SOL
* DIS # I7: 2 => CTR => I7: 4,5
* CNT  25 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:

* PRF # G5: 2,5 => SOL
* STA G5: 2,5
* CNT   1 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

1.9.........7...4.6............9.6.1.7.3.......8.......3....87......69......2.... initial
1.963.7.8.8.719.466.7.8.319....97681.71368.9.9681...37.369.187.81..769.379.82316. autosolve
129634758583719246647285319352497681471368592968152437236941875814576923795823164 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
H1: 2,5
G2: 2,5
B4: 2,5
E6: 4,5
I5: 2,5
C9: 4,5
E7: 4,5
D8: 4,5
H8: 2,5
I9: 4,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,G2: 2.. / H1 = 2  =>  0 pairs (X) / G2 = 2  =>  0 pairs (_)
D4,F6: 2.. / D4 = 2  =>  0 pairs (X) / F6 = 2  => 16 pairs (_)
A7,C8: 2.. / A7 = 2  =>  0 pairs (*) / C8 = 2  =>  0 pairs (X)
I7,H8: 2.. / I7 = 2  =>  0 pairs (X) / H8 = 2  =>  0 pairs (_)
F6,G6: 2.. / F6 = 2  => 16 pairs (_) / G6 = 2  =>  0 pairs (X)
A7,I7: 2.. / A7 = 2  =>  0 pairs (*) / I7 = 2  =>  0 pairs (X)
C8,H8: 2.. / C8 = 2  =>  0 pairs (X) / H8 = 2  =>  0 pairs (_)
D3,D4: 2.. / D3 = 2  => 16 pairs (_) / D4 = 2  =>  0 pairs (X)
H1,H8: 2.. / H1 = 2  =>  0 pairs (X) / H8 = 2  =>  0 pairs (_)
I5,I7: 2.. / I5 = 2  =>  0 pairs (*) / I7 = 2  =>  0 pairs (X)
A2,C2: 3.. / A2 = 3  => 12 pairs (_) / C2 = 3  => 11 pairs (_)
A4,C4: 3.. / A4 = 3  => 11 pairs (_) / C4 = 3  => 12 pairs (_)
A2,A4: 3.. / A2 = 3  => 12 pairs (_) / A4 = 3  => 11 pairs (_)
C2,C4: 3.. / C2 = 3  => 11 pairs (_) / C4 = 3  => 12 pairs (_)
B1,B3: 4.. / B1 = 4  => 12 pairs (_) / B3 = 4  => 14 pairs (_)
G5,G6: 4.. / G5 = 4  => 15 pairs (_) / G6 = 4  =>  0 pairs (*)
E7,D8: 4.. / E7 = 4  =>  0 pairs (*) / D8 = 4  =>  0 pairs (X)
I7,I9: 4.. / I7 = 4  =>  0 pairs (X) / I9 = 4  => 12 pairs (_)
B1,F1: 4.. / B1 = 4  => 12 pairs (_) / F1 = 4  => 14 pairs (_)
A5,G5: 4.. / A5 = 4  =>  0 pairs (*) / G5 = 4  =>  0 pairs (X)
C8,D8: 4.. / C8 = 4  =>  0 pairs (*) / D8 = 4  =>  0 pairs (X)
C9,I9: 4.. / C9 = 4  =>  0 pairs (X) / I9 = 4  => 12 pairs (_)
E6,E7: 4.. / E6 = 4  => 18 pairs (_) / E7 = 4  =>  0 pairs (*)
H1,G2: 5.. / H1 = 5  =>  0 pairs (*) / G2 = 5  =>  0 pairs (X)
E7,D8: 5.. / E7 = 5  => 18 pairs (_) / D8 = 5  =>  0 pairs (*)
C9,I9: 5.. / C9 = 5  => 12 pairs (_) / I9 = 5  =>  0 pairs (X)
E6,E7: 5.. / E6 = 5  =>  0 pairs (*) / E7 = 5  =>  0 pairs (X)
H1,H8: 5.. / H1 = 5  =>  0 pairs (*) / H8 = 5  =>  0 pairs (X)
* DURATION: 0:01:01.151814  START: 15:42:11.430307  END: 15:43:12.582121 2017-05-04
* CP COUNT: (28)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C9,D8,E6,E7,G2,H1,H8,I5,I9)
* 1.963.7.8.8.719.466.7.8.319....97681.71368.9.9681...37.369.187.81..769.379.82316.
* PAIR H1: 2,5 ROW 1
B1: 2,5,4                                # reduction candidate for 2,5
B1: 2,5                                  # 14 pairs
F1: 2,5,4                                # reduction candidate for 2,5
F1: 2,5                                  # 12 pairs
* PAIR G2: 2,5 ROW 2
A2: 2,5,3                                # reduction candidate for 2,5
A2: 2,5                                  # 11 pairs
C2: 2,5,3                                # reduction candidate for 2,5
C2: 2,5                                  # 12 pairs
* PAIR G2: 2,5 COL G
G5: 2,5,4                                # reduction candidate for 2,5
G5: 2,5 => SOLVED
* 129634758583719246647285319352497681471368592968152437236941875814576923795823164
G5: 4                                    # 15 pairs
G6: 2,5,4                                # reduction candidate for 2,5
G6: 2,5                                  # 15 pairs
* PAIR B4: 2,5 BLK 4
A4: 2,5,3,4                              # reduction candidate for 2,5
A4: 2,5 => CTR
* 1.963.7.838.719.466.7.8.319..3497681471368.9.968152437.3694187.814576923795823164
A4: 3,4                                  # 11 pairs
C4: 2,5,3,4                              # reduction candidate for 2,5
C4: 2,5 => SOLVED
* 129634758583719246647285319352497681471368592968152437236941875814576923795823164
C4: 3,4                                  # 11 pairs
A5: 2,5,4                                # reduction candidate for 2,5
A5: 2,5                                  # 15 pairs
* PAIR B4: 2,5 ROW 4
D4: 2,5,4                                # reduction candidate for 2,5
D4: 4 => SOLVED
* 129634758583719246647285319352497681471368592968152437236941875814576923795823164
D4: 2,5                                  # 15 pairs
* PAIR B4: 2,5 COL B
B1: 2,5,4                                # reduction candidate for 2,5
B1: 2,5                                  # 14 pairs
B3: 2,5,4                                # reduction candidate for 2,5
B3: 2,5                                  # 12 pairs
* PAIR E6: 4,5 BLK 5
D4: 4,5,2                                # reduction candidate for 4,5
D4: 4,5                                  # 16 pairs
F6: 4,5,2                                # reduction candidate for 4,5
F6: 4,5 => CTR
* 1.963.7.8.8.719.466.7.8.319...2976812713684959681..237.369.1872812476953795823164
F6: 2                                    # 16 pairs
* PAIR E6: 4,5 ROW 6
G6: 4,5,2                                # reduction candidate for 4,5
G6: 2 => CTR
* 1.963.72828.719.466.7.8.319....97681.713684959681..237.369.1872812476953795823164
G6: 4,5                                  # 16 pairs
* PAIR I5: 2,5 BLK 6
G5: 2,5,4                                # reduction candidate for 2,5
G5: 2,5 => SOLVED
* 129634758583719246647285319352497681471368592968152437236941875814576923795823164
G5: 4                                    # 15 pairs
G6: 2,5,4                                # reduction candidate for 2,5
G6: 2,5                                  # 15 pairs
* PAIR I5: 2,5 ROW 5
A5: 2,5,4                                # reduction candidate for 2,5
A5: 4 => SOLVED
* 129634758583719246647285319352497681471368592968152437236941875814576923795823164
A5: 2,5                                  # 15 pairs
* PAIR I5: 2,5 COL I
I7: 2,5,4                                # reduction candidate for 2,5
I7: 4 => CTR
* 129634758.8.71924664728531945..97681.71368.929681.2.3723695187481.476923794823165
I7: 2,5                                  # 12 pairs
* PAIR C9: 4,5 BLK 7
A7: 4,5,2                                # reduction candidate for 4,5
A7: 4,5 => CTR
* 1.963.7282837195466.7.8.319324597681571368.9.9681...37.369.1872812476953795823164
A7: 2 => SOLVED
* 129634758583719246647285319352497681471368592968152437236941875814576923795823164
C8: 4,5,2                                # reduction candidate for 4,5
C8: 4,5 => SOLVED
* 129634758583719246647285319352497681471368592968152437236941875814576923795823164
C8: 2 => CTR
* 1.963.7282837195466.7.8.3193245976815713684929681...37.369.187.812476953795823164
* PAIR C9: 4,5 COL C
C4: 4,5,2,3                              # reduction candidate for 4,5
C4: 4,5 => CTR
* 1.963.7282837195466.7.8.3193245976815713684929681...37.369.187.812476953795823164
C4: 2,3                                  # 12 pairs
* PAIR E7: 4,5 ROW 7
A7: 4,5,2                                # reduction candidate for 4,5
A7: 4,5 => CTR
* 1.963.7282837195466.7.8.319324597681571368.9.9681...37.369.1872812476953795823164
A7: 2 => SOLVED
* 129634758583719246647285319352497681471368592968152437236941875814576923795823164
I7: 4,5,2                                # reduction candidate for 4,5
I7: 4,5 => SOLVED
* 129634758583719246647285319352497681471368592968152437236941875814576923795823164
I7: 2 => CTR
* 1.963.7282837195466.7.8.319324597681571368.9.9681...37.369.1872812476953795823164
* PAIR D8: 4,5 ROW 8
C8: 4,5,2                                # reduction candidate for 4,5
C8: 4,5 => SOLVED
* 129634758583719246647285319352497681471368592968152437236941875814576923795823164
C8: 2 => CTR
* 1.963.7282837195466.7.8.3193245976815713684929681...37.369.187.812476953795823164
* PAIR D8: 4,5 COL D
D3: 4,5,2                                # reduction candidate for 4,5
D3: 4,5 => CTR
* 1.963.7.8.8.719.466.7.8.319...2976812713684959681..237.369.1872812476953795823164
D3: 2                                    # 16 pairs
D4: 4,5,2                                # reduction candidate for 4,5
D4: 4,5                                  # 16 pairs
* PAIR H8: 2,5 BLK 9
I7: 2,5,4                                # reduction candidate for 2,5
I7: 4 => CTR
* 129634758.8.71924664728531945..97681.71368.929681.2.3723695187481.476923794823165
I7: 2,5                                  # 12 pairs
* PAIR H8: 2,5 ROW 8
C8: 2,5,4                                # reduction candidate for 2,5
C8: 4 => SOLVED
* 129634758583719246647285319352497681471368592968152437236941875814576923795823164
C8: 2,5                                  # 18 pairs
* PAIR I9: 4,5 BLK 9
I7: 4,5,2                                # reduction candidate for 4,5
I7: 4,5 => SOLVED
* 129634758583719246647285319352497681471368592968152437236941875814576923795823164
I7: 2 => CTR
* 1.963.7282837195466.7.8.319324597681571368.9.9681...37.369.1872812476953795823164
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-375-base-pr-000.dot
* REASONING
* PRF # G5: 2,5 => SOL
* DIS # A4: 2,5 => CTR => A4: 3,4
* PRF # C4: 2,5 => SOL
* PRF # D4: 4 => SOL
* DIS # F6: 4,5 => CTR => F6: 2
* DIS # G6: 2 => CTR => G6: 4,5
* PRF # G5: 2,5 => SOL
* PRF # A5: 4 => SOL
* DIS # I7: 4 => CTR => I7: 2,5
* DIS # A7: 4,5 => CTR => A7: 2
* PRF # A7: 2 => SOL
* PRF # C8: 4,5 => SOL
* DIS # C8: 2 => CTR => C8: 4,5
* DIS # C4: 4,5 => CTR => C4: 2,3
* DIS # A7: 4,5 => CTR => A7: 2
* PRF # A7: 2 => SOL
* PRF # I7: 4,5 => SOL
* DIS # I7: 2 => CTR => I7: 4,5
* PRF # C8: 4,5 => SOL
* DIS # C8: 2 => CTR => C8: 4,5
* DIS # D3: 4,5 => CTR => D3: 2
* DIS # I7: 4 => CTR => I7: 2,5
* PRF # C8: 4 => SOL
* PRF # I7: 4,5 => SOL
* DIS # I7: 2 => CTR => I7: 4,5
* CNT  25 HDP CHAINS /  49 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C9,D8,E6,E7,G2,H1,H8,I5,I9)
* 1.963.7.8.8.719.466.7.8.319....97681.71368.9.9681...37.369.187.81..769.379.82316.
* PAIR H1: 2,5 ROW 1
B1: 2,5,4                                # reduction candidate for 2,5
B1: 2,5                                  # 14 pairs
F1: 2,5,4                                # reduction candidate for 2,5
F1: 2,5                                  # 12 pairs
* PAIR G2: 2,5 ROW 2
A2: 2,5,3                                # reduction candidate for 2,5
A2: 2,5                                  # 11 pairs
C2: 2,5,3                                # reduction candidate for 2,5
C2: 2,5                                  # 12 pairs
* PAIR G2: 2,5 COL G
G5: 2,5,4                                # reduction candidate for 2,5
G5: 2,5 => SOLVED
* 129634758583719246647285319352497681471368592968152437236941875814576923795823164
* DURATION: 0:00:07.053847  START: 15:44:18.167611  END: 15:44:25.221458 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-375-base-pr-001.dot
* REASONING
* PRF # G5: 2,5 => SOL
* STA G5: 2,5
* CNT   1 HDP CHAINS /   5 HYP OPENED

Header Info

Top 500 Minimum 17 375

solution: 129634758583719246647285319352497681471368592968152437236941875814576923795823164
info: 7907     FNBHWX   S8.f     26269

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

Solution

position: 129634758583719246647285319352497681471368592968152437236941875814576923795823164 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 # B1: 2,5 => UNS
* INC # F1: 2,5 => UNS
* INC # A2: 2,5 => UNS
* INC # C2: 2,5 => UNS
* PRF # G5: 2,5 => SOL
* INC # G5: 4 => UNS
* INC # G6: 2,5 => UNS
* DIS # A4: 2,5 => CTR => A4: 3,4
* INC # A4: 3,4 => UNS
* PRF # C4: 2,5 => SOL
* INC # C4: 3,4 => UNS
* INC # A5: 2,5 => UNS
* INC # D4: 2,5 => UNS
* PRF # D4: 4 => SOL
* INC # B1: 2,5 => UNS
* INC # B3: 2,5 => UNS
* INC # D4: 4,5 => UNS
* DIS # F6: 4,5 => CTR => F6: 2
* INC # F6: 2 => UNS
* INC # G6: 4,5 => UNS
* DIS # G6: 2 => CTR => G6: 4,5
* PRF # G5: 2,5 => SOL
* INC # G5: 4 => UNS
* INC # G6: 2,5 => UNS
* INC # A5: 2,5 => UNS
* PRF # A5: 4 => SOL
* INC # I7: 2,5 => UNS
* DIS # I7: 4 => CTR => I7: 2,5
* DIS # A7: 4,5 => CTR => A7: 2
* PRF # A7: 2 => SOL
* PRF # C8: 4,5 => SOL
* DIS # C8: 2 => CTR => C8: 4,5
* DIS # C4: 4,5 => CTR => C4: 2,3
* INC # C4: 2,3 => UNS
* DIS # A7: 4,5 => CTR => A7: 2
* PRF # A7: 2 => SOL
* PRF # I7: 4,5 => SOL
* DIS # I7: 2 => CTR => I7: 4,5
* PRF # C8: 4,5 => SOL
* DIS # C8: 2 => CTR => C8: 4,5
* DIS # D3: 4,5 => CTR => D3: 2
* INC # D3: 2 => UNS
* INC # D4: 4,5 => UNS
* INC # I7: 2,5 => UNS
* DIS # I7: 4 => CTR => I7: 2,5
* INC # C8: 2,5 => UNS
* PRF # C8: 4 => SOL
* PRF # I7: 4,5 => SOL
* DIS # I7: 2 => CTR => I7: 4,5
* CNT  49 HDP CHAINS /  49 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 2,5 => UNS
* INC # F1: 2,5 => UNS
* INC # A2: 2,5 => UNS
* INC # C2: 2,5 => UNS
* PRF # G5: 2,5 => SOL
* STA G5: 2,5
* CNT   5 HDP CHAINS /   5 HYP OPENED