Analysis of xx-top500-010-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .8..9.1..6......3...........2....9.8...4.3......6.....8.1.........7...2.59....... initial

Autosolve

position: .83.961.46.9.4.83..4.83.69.324.7.96896.48321...86294.3871952346436718529592364781 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A3: 2,7 => SOL
* DIS # A3: 1 => CTR => A3: 2,7
* PRF # D2: 1,5 => SOL
* DIS # D2: 2 => CTR => D2: 1,5
* DIS # F2: 1,5 => CTR => F2: 7
* DIS # F3: 5,7 => CTR => F3: 1
* PRF # F3: 1 => SOL
* PRF # I3: 5,7 => SOL
* DIS # I3: 2 => CTR => I3: 5,7
* DIS # D2: 1 => CTR => D2: 2,5
* DIS # I2: 5,7 => CTR => I2: 2
* PRF # I2: 2 => SOL
* PRF # I3: 5,7 => SOL
* DIS # I3: 2 => CTR => I3: 5,7
* DIS # A3: 1,7 => CTR => A3: 2
* PRF # A3: 2 => SOL
* PRF # D2: 1,5 => SOL
* DIS # D2: 2 => CTR => D2: 1,5
* DIS # F2: 1,5 => CTR => F2: 7
* DIS # I2: 5,7 => CTR => I2: 2
* PRF # I2: 2 => SOL
* PRF # I3: 5,7 => SOL
* DIS # I3: 2 => CTR => I3: 5,7
* CNT  23 HDP CHAINS /  27 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 # A3: 2,7 => SOL
* STA A3: 2,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

.8..9.1..6......3...........2....9.8...4.3......6.....8.1.........7...2.59....... initial
.83.961.46.9.4.83..4.83.69.324.7.96896.48321...86294.3871952346436718529592364781 autosolve
783296154619547832245831697324175968967483215158629473871952346436718529592364781 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (12)
A1: 2,7
B2: 1,5
C3: 5,7
D1: 2,5
H1: 5,7
C5: 5,7
A6: 1,7
B6: 1,5
D4: 1,5
F4: 1,5
I5: 5,7
H6: 5,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B2,A3: 1.. / B2 = 1  =>  0 pairs (*) / A3 = 1  =>  0 pairs (X)
A6,B6: 1.. / A6 = 1  =>  0 pairs (*) / B6 = 1  =>  0 pairs (X)
D4,F4: 1.. / D4 = 1  => 13 pairs (_) / F4 = 1  =>  0 pairs (X)
A3,F3: 1.. / A3 = 1  =>  0 pairs (X) / F3 = 1  =>  0 pairs (_)
A3,A6: 1.. / A3 = 1  =>  0 pairs (X) / A6 = 1  =>  0 pairs (_)
B2,B6: 1.. / B2 = 1  =>  0 pairs (*) / B6 = 1  =>  0 pairs (X)
D2,D4: 1.. / D2 = 1  =>  0 pairs (X) / D4 = 1  => 13 pairs (_)
A1,A3: 2.. / A1 = 2  =>  0 pairs (X) / A3 = 2  =>  0 pairs (_)
D1,D2: 2.. / D1 = 2  =>  0 pairs (*) / D2 = 2  =>  0 pairs (X)
I2,I3: 2.. / I2 = 2  =>  0 pairs (*) / I3 = 2  =>  0 pairs (X)
A1,D1: 2.. / A1 = 2  =>  0 pairs (X) / D1 = 2  =>  0 pairs (_)
D2,I2: 2.. / D2 = 2  =>  0 pairs (X) / I2 = 2  =>  0 pairs (_)
A3,I3: 2.. / A3 = 2  =>  0 pairs (*) / I3 = 2  =>  0 pairs (X)
B2,C3: 5.. / B2 = 5  =>  0 pairs (X) / C3 = 5  =>  0 pairs (_)
C5,B6: 5.. / C5 = 5  =>  0 pairs (X) / B6 = 5  =>  0 pairs (_)
D4,F4: 5.. / D4 = 5  =>  0 pairs (X) / F4 = 5  => 13 pairs (_)
I5,H6: 5.. / I5 = 5  =>  0 pairs (*) / H6 = 5  =>  0 pairs (X)
D1,H1: 5.. / D1 = 5  =>  0 pairs (X) / H1 = 5  =>  0 pairs (_)
C5,I5: 5.. / C5 = 5  =>  0 pairs (X) / I5 = 5  =>  0 pairs (_)
B6,H6: 5.. / B6 = 5  =>  0 pairs (*) / H6 = 5  =>  0 pairs (X)
B2,B6: 5.. / B2 = 5  =>  0 pairs (X) / B6 = 5  =>  0 pairs (_)
C3,C5: 5.. / C3 = 5  =>  0 pairs (*) / C5 = 5  =>  0 pairs (X)
H1,H6: 5.. / H1 = 5  =>  0 pairs (*) / H6 = 5  =>  0 pairs (X)
F2,F3: 7.. / F2 = 7  => 14 pairs (_) / F3 = 7  =>  0 pairs (X)
C5,A6: 7.. / C5 = 7  =>  0 pairs (*) / A6 = 7  =>  0 pairs (X)
I5,H6: 7.. / I5 = 7  =>  0 pairs (X) / H6 = 7  =>  0 pairs (_)
A1,H1: 7.. / A1 = 7  =>  0 pairs (*) / H1 = 7  =>  0 pairs (X)
F2,I2: 7.. / F2 = 7  => 14 pairs (_) / I2 = 7  =>  0 pairs (X)
C5,I5: 7.. / C5 = 7  =>  0 pairs (*) / I5 = 7  =>  0 pairs (X)
A6,H6: 7.. / A6 = 7  =>  0 pairs (X) / H6 = 7  =>  0 pairs (_)
C3,C5: 7.. / C3 = 7  =>  0 pairs (X) / C5 = 7  =>  0 pairs (_)
H1,H6: 7.. / H1 = 7  =>  0 pairs (X) / H6 = 7  =>  0 pairs (_)
* DURATION: 0:01:04.470238  START: 02:56:22.161949  END: 02:57:26.632187 2017-05-04
* CP COUNT: (32)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B2,B6,C3,C5,D1,D4,F4,H1,H6,I5)
* .83.961.46.9.4.83..4.83.69.324.7.96896.48321...86294.3871952346436718529592364781
* PAIR A1: 2,7 BLK 1
A3: 2,7,1                                # reduction candidate for 2,7
A3: 2,7 => SOLVED
* 783296154619547832245831697324175968967483215158629473871952346436718529592364781
A3: 1 => CTR
* 2835961746.924783514.83.69.324.7.96896.48321...86294.3871952346436718529592364781
* PAIR B2: 1,5 ROW 2
D2: 1,5,2                                # reduction candidate for 1,5
D2: 1,5 => SOLVED
* 783296154619547832245831697324175968967483215158629473871952346436718529592364781
D2: 2 => CTR
* 2835961746.9247835.4583169232417596896748321...86294.3871952346436718529592364781
F2: 1,5,7                                # reduction candidate for 1,5
F2: 1,5 => CTR
* .83.961.46.9.4.837.4.837692324.7.9689674832151.86294.3871952346436718529592364781
F2: 7                                    # 14 pairs
* PAIR C3: 5,7 ROW 3
F3: 5,7,1                                # reduction candidate for 5,7
F3: 5,7 => CTR
* 283596174659.4.83.14.83.692324.7.96896.48321.718629453871952346436718529592364781
F3: 1 => SOLVED
* 783296154619547832245831697324175968967483215158629473871952346436718529592364781
I3: 5,7,2                                # reduction candidate for 5,7
I3: 5,7 => SOLVED
* 783296154619547832245831697324175968967483215158629473871952346436718529592364781
I3: 2 => CTR
* 2835961746.9247835.4583169232417596896748321...86294.3871952346436718529592364781
* PAIR D1: 2,5 BLK 2
D2: 2,5,1                                # reduction candidate for 2,5
D2: 1 => CTR
* .832961546.914.832.4.83.69.324.7.96896.48321...86294.3871952346436718529592364781
D2: 2,5                                  # 13 pairs
* PAIR H1: 5,7 BLK 3
I2: 5,7,2                                # reduction candidate for 5,7
I2: 5,7 => CTR
* 2835961746.9247835.4583169232417596896748321...86294.3871952346436718529592364781
I2: 2 => SOLVED
* 783296154619547832245831697324175968967483215158629473871952346436718529592364781
I3: 5,7,2                                # reduction candidate for 5,7
I3: 5,7 => SOLVED
* 783296154619547832245831697324175968967483215158629473871952346436718529592364781
I3: 2 => CTR
* 2835961746.9247835.4583169232417596896748321...86294.3871952346436718529592364781
* PAIR A6: 1,7 COL A
A3: 1,7,2                                # reduction candidate for 1,7
A3: 1,7 => CTR
* 2835961746.9247835.4583169232417596896748321...86294.3871952346436718529592364781
A3: 2 => SOLVED
* 783296154619547832245831697324175968967483215158629473871952346436718529592364781
* PAIR D4: 1,5 COL D
D2: 1,5,2                                # reduction candidate for 1,5
D2: 1,5 => SOLVED
* 783296154619547832245831697324175968967483215158629473871952346436718529592364781
D2: 2 => CTR
* 2835961746.9247835.4583169232417596896748321...86294.3871952346436718529592364781
* PAIR F4: 1,5 COL F
F2: 1,5,7                                # reduction candidate for 1,5
F2: 1,5 => CTR
* .83.961.46.9.4.837.4.837692324.7.9689674832151.86294.3871952346436718529592364781
F2: 7                                    # 14 pairs
F3: 1,5,7                                # reduction candidate for 1,5
F3: 1,5                                  # 14 pairs
* PAIR I5: 5,7 COL I
I2: 5,7,2                                # reduction candidate for 5,7
I2: 5,7 => CTR
* 2835961746.9247835.4583169232417596896748321...86294.3871952346436718529592364781
I2: 2 => SOLVED
* 783296154619547832245831697324175968967483215158629473871952346436718529592364781
I3: 5,7,2                                # reduction candidate for 5,7
I3: 5,7 => SOLVED
* 783296154619547832245831697324175968967483215158629473871952346436718529592364781
I3: 2 => CTR
* 2835961746.9247835.4583169232417596896748321...86294.3871952346436718529592364781
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-010-base-pr-000.dot
* REASONING
* PRF # A3: 2,7 => SOL
* DIS # A3: 1 => CTR => A3: 2,7
* PRF # D2: 1,5 => SOL
* DIS # D2: 2 => CTR => D2: 1,5
* DIS # F2: 1,5 => CTR => F2: 7
* DIS # F3: 5,7 => CTR => F3: 1
* PRF # F3: 1 => SOL
* PRF # I3: 5,7 => SOL
* DIS # I3: 2 => CTR => I3: 5,7
* DIS # D2: 1 => CTR => D2: 2,5
* DIS # I2: 5,7 => CTR => I2: 2
* PRF # I2: 2 => SOL
* PRF # I3: 5,7 => SOL
* DIS # I3: 2 => CTR => I3: 5,7
* DIS # A3: 1,7 => CTR => A3: 2
* PRF # A3: 2 => SOL
* PRF # D2: 1,5 => SOL
* DIS # D2: 2 => CTR => D2: 1,5
* DIS # F2: 1,5 => CTR => F2: 7
* DIS # I2: 5,7 => CTR => I2: 2
* PRF # I2: 2 => SOL
* PRF # I3: 5,7 => SOL
* DIS # I3: 2 => CTR => I3: 5,7
* CNT  23 HDP CHAINS /  27 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B2,B6,C3,C5,D1,D4,F4,H1,H6,I5)
* .83.961.46.9.4.83..4.83.69.324.7.96896.48321...86294.3871952346436718529592364781
* PAIR A1: 2,7 BLK 1
A3: 2,7,1                                # reduction candidate for 2,7
A3: 2,7 => SOLVED
* 783296154619547832245831697324175968967483215158629473871952346436718529592364781
* DURATION: 0:00:01.976090  START: 02:58:02.778388  END: 02:58:04.754478 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-010-base-pr-001.dot
* REASONING
* PRF # A3: 2,7 => SOL
* STA A3: 2,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 010

solution: 783296154619547832245831697324175968967483215158629473871952346436718529592364781
info: 1308     FNBWXY   S8.f     23628

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

Solution

position: 783296154619547832245831697324175968967483215158629473871952346436718529592364781 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:

* PRF # A3: 2,7 => SOL
* DIS # A3: 1 => CTR => A3: 2,7
* PRF # D2: 1,5 => SOL
* DIS # D2: 2 => CTR => D2: 1,5
* DIS # F2: 1,5 => CTR => F2: 7
* INC # F2: 7 => UNS
* DIS # F3: 5,7 => CTR => F3: 1
* PRF # F3: 1 => SOL
* PRF # I3: 5,7 => SOL
* DIS # I3: 2 => CTR => I3: 5,7
* INC # D2: 2,5 => UNS
* DIS # D2: 1 => CTR => D2: 2,5
* DIS # I2: 5,7 => CTR => I2: 2
* PRF # I2: 2 => SOL
* PRF # I3: 5,7 => SOL
* DIS # I3: 2 => CTR => I3: 5,7
* DIS # A3: 1,7 => CTR => A3: 2
* PRF # A3: 2 => SOL
* PRF # D2: 1,5 => SOL
* DIS # D2: 2 => CTR => D2: 1,5
* DIS # F2: 1,5 => CTR => F2: 7
* INC # F2: 7 => UNS
* INC # F3: 1,5 => UNS
* DIS # I2: 5,7 => CTR => I2: 2
* PRF # I2: 2 => SOL
* PRF # I3: 5,7 => SOL
* DIS # I3: 2 => CTR => I3: 5,7
* CNT  27 HDP CHAINS /  27 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # A3: 2,7 => SOL
* STA A3: 2,7
* CNT   1 HDP CHAINS /   1 HYP OPENED