Analysis of xx-top500-315-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...9...5.3....6....8....7....74..1........2..6........8......63...7...8.....1.... initial

Autosolve

position: 71.98365.3...7681..861..73..3746.1981.83.72466..8.1375871....63.6.73..81..3618.27 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # C6: 2,4 => SOL
* DIS # C6: 9 => CTR => C6: 2,4
* DIS # I2: 2,4 => CTR => I2: 9
* PRF # I2: 9 => SOL
* PRF # C8: 5,9 => SOL
* DIS # C8: 2 => CTR => C8: 5,9
* DIS # A8: 5,9 => CTR => A8: 2,4
* DIS # A9: 5,9 => CTR => A9: 4
* DIS # I2: 2,4 => CTR => I2: 9
* PRF # I2: 9 => SOL
* PRF # I2: 2,9 => SOL
* DIS # I2: 4 => CTR => I2: 2,9
* PRF # A8: 2,5 => SOL
* DIS # A8: 4,9 => CTR => A8: 2,5
* PRF # C6: 2,4 => SOL
* DIS # C6: 9 => CTR => C6: 2,4
* DIS # C6: 2,9 => CTR => C6: 4
* PRF # C6: 4 => SOL
* DIS # A8: 5,9 => CTR => A8: 2,4
* PRF # C8: 5,9 => SOL
* DIS # C8: 2 => CTR => C8: 5,9
* DIS # A9: 5,9 => CTR => A9: 4
* DIS # G9: 4 => CTR => G9: 5,9
* CNT  23 HDP CHAINS /  34 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 # C6: 2,4 => SOL
* STA C6: 2,4
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

...9...5.3....6....8....7....74..1........2..6........8......63...7...8.....1.... initial
71.98365.3...7681..861..73..3746.1981.83.72466..8.1375871....63.6.73..81..3618.27 autosolve
712983654345276819986145732537462198198357246624891375871529463269734581453618927 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
C1: 2,4
B2: 2,4
C2: 5,9
A3: 5,9
D2: 2,5
I1: 2,4
I3: 2,9
A4: 2,5
B5: 5,9
B6: 2,4
F4: 2,5
E5: 5,9
E6: 2,9
B9: 5,9
D7: 2,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C1,B2: 2.. / C1 = 2  =>  0 pairs (*) / B2 = 2  =>  0 pairs (X)
F4,E6: 2.. / F4 = 2  =>  0 pairs (*) / E6 = 2  =>  0 pairs (X)
A8,C8: 2.. / A8 = 2  =>  0 pairs (*) / C8 = 2  =>  0 pairs (X)
C1,I1: 2.. / C1 = 2  =>  0 pairs (*) / I1 = 2  =>  0 pairs (X)
A4,F4: 2.. / A4 = 2  =>  0 pairs (X) / F4 = 2  =>  0 pairs (_)
A4,A8: 2.. / A4 = 2  =>  0 pairs (X) / A8 = 2  =>  0 pairs (_)
B2,B6: 2.. / B2 = 2  =>  0 pairs (X) / B6 = 2  =>  0 pairs (_)
D2,D7: 2.. / D2 = 2  =>  0 pairs (*) / D7 = 2  =>  0 pairs (X)
C1,B2: 4.. / C1 = 4  =>  0 pairs (X) / B2 = 4  =>  0 pairs (_)
E3,F3: 4.. / E3 = 4  => 20 pairs (_) / F3 = 4  => 18 pairs (_)
I1,I2: 4.. / I1 = 4  =>  0 pairs (*) / I2 = 4  =>  0 pairs (X)
B6,C6: 4.. / B6 = 4  =>  0 pairs (X) / C6 = 4  =>  0 pairs (_)
A8,A9: 4.. / A8 = 4  =>  0 pairs (X) / A9 = 4  => 16 pairs (_)
C1,I1: 4.. / C1 = 4  =>  0 pairs (X) / I1 = 4  =>  0 pairs (_)
B2,I2: 4.. / B2 = 4  =>  0 pairs (*) / I2 = 4  =>  0 pairs (X)
A9,G9: 4.. / A9 = 4  => 16 pairs (_) / G9 = 4  =>  0 pairs (X)
B2,B6: 4.. / B2 = 4  =>  0 pairs (*) / B6 = 4  =>  0 pairs (X)
C1,C6: 4.. / C1 = 4  =>  0 pairs (X) / C6 = 4  =>  0 pairs (_)
E3,E7: 4.. / E3 = 4  => 20 pairs (_) / E7 = 4  => 18 pairs (_)
C2,A3: 5.. / C2 = 5  =>  0 pairs (*) / A3 = 5  =>  0 pairs (X)
A4,B5: 5.. / A4 = 5  =>  0 pairs (*) / B5 = 5  =>  0 pairs (X)
F4,E5: 5.. / F4 = 5  =>  0 pairs (X) / E5 = 5  =>  0 pairs (_)
C2,D2: 5.. / C2 = 5  =>  0 pairs (*) / D2 = 5  =>  0 pairs (X)
A4,F4: 5.. / A4 = 5  =>  0 pairs (*) / F4 = 5  =>  0 pairs (X)
B5,E5: 5.. / B5 = 5  =>  0 pairs (X) / E5 = 5  =>  0 pairs (_)
B5,B9: 5.. / B5 = 5  =>  0 pairs (X) / B9 = 5  =>  0 pairs (_)
C2,C8: 5.. / C2 = 5  =>  0 pairs (*) / C8 = 5  =>  0 pairs (X)
D2,D7: 5.. / D2 = 5  =>  0 pairs (X) / D7 = 5  =>  0 pairs (_)
C2,A3: 9.. / C2 = 9  =>  0 pairs (X) / A3 = 9  =>  0 pairs (_)
I2,I3: 9.. / I2 = 9  =>  0 pairs (*) / I3 = 9  =>  0 pairs (X)
B5,C6: 9.. / B5 = 9  =>  0 pairs (*) / C6 = 9  =>  0 pairs (X)
E5,E6: 9.. / E5 = 9  =>  0 pairs (X) / E6 = 9  =>  0 pairs (_)
F7,F8: 9.. / F7 = 9  => 17 pairs (_) / F8 = 9  => 18 pairs (_)
C2,I2: 9.. / C2 = 9  =>  0 pairs (X) / I2 = 9  =>  0 pairs (_)
A3,I3: 9.. / A3 = 9  =>  0 pairs (*) / I3 = 9  =>  0 pairs (X)
B5,E5: 9.. / B5 = 9  =>  0 pairs (*) / E5 = 9  =>  0 pairs (X)
C6,E6: 9.. / C6 = 9  =>  0 pairs (X) / E6 = 9  =>  0 pairs (_)
F7,G7: 9.. / F7 = 9  => 17 pairs (_) / G7 = 9  => 18 pairs (_)
B5,B9: 9.. / B5 = 9  =>  0 pairs (*) / B9 = 9  =>  0 pairs (X)
* DURATION: 0:01:23.547717  START: 13:45:31.329044  END: 13:46:54.876761 2017-05-04
* CP COUNT: (39)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B2,B5,B6,B9,C1,C2,D2,D7,E5,E6,F4,I1,I3)
* 71.98365.3...7681..861..73..3746.1981.83.72466..8.1375871....63.6.73..81..3618.27
* PAIR C1: 2,4 COL C
C6: 2,4,9                                # reduction candidate for 2,4
C6: 2,4 => SOLVED
* 712983654345276819986145732537462198198357246624891375871529463269734581453618927
C6: 9 => CTR
* 71498365232.5768145861..7392374651981583972466498.1375871....63.6.73..81..3618.27
* PAIR B2: 2,4 ROW 2
I2: 2,4,9                                # reduction candidate for 2,4
I2: 2,4 => CTR
* 71.98365.3.957681.5861..73923746.1981.83.72466..8.1375871....63.6.73..81..3618.27
I2: 9 => SOLVED
* 712983654345276819986145732537462198198357246624891375871529463269734581453618927
* PAIR C2: 5,9 COL C
C8: 5,9,2                                # reduction candidate for 5,9
C8: 5,9 => SOLVED
* 712983654345276819986145732537462198198357246624891375871529463269734581453618927
C8: 2 => CTR
* 71.98365.3.52768199861..732.3746.1981.83.724662.8.1375871....63.6.73..81..3618.27
* PAIR A3: 5,9 COL A
A8: 5,9,2,4                              # reduction candidate for 5,9
A8: 5,9 => CTR
* 71.98365.3...7681..861..73.237465198158397246649821375871....63.6273..81493618527
A8: 2,4                                  # 16 pairs
A9: 5,9,4                                # reduction candidate for 5,9
A9: 5,9 => CTR
* 714983652325.7681..861..73..3746.1981.83.72466..8.1375871....6346273..81..3618427
A9: 4                                    # 16 pairs
* PAIR D2: 2,5 BLK 2
E3: 2,5,4                                # reduction candidate for 2,5
E3: 2,5                                  # 18 pairs
F3: 2,5,4                                # reduction candidate for 2,5
F3: 2,5                                  # 20 pairs
* PAIR I1: 2,4 BLK 3
I2: 2,4,9                                # reduction candidate for 2,4
I2: 2,4 => CTR
* 71.98365.3.957681.5861..73923746.1981.83.72466..8.1375871....63.6.73..81..3618.27
I2: 9 => SOLVED
* 712983654345276819986145732537462198198357246624891375871529463269734581453618927
* PAIR I3: 2,9 BLK 3
I2: 2,9,4                                # reduction candidate for 2,9
I2: 2,9 => SOLVED
* 712983654345276819986145732537462198198357246624891375871529463269734581453618927
I2: 4 => CTR
* 71.98365.3.95768145861..73923746.1981.83.72466..8.1375871....63.6.73..81..3618.27
* PAIR A4: 2,5 COL A
A8: 2,5,4,9                              # reduction candidate for 2,5
A8: 2,5 => SOLVED
* 712983654345276819986145732537462198198357246624891375871529463269734581453618927
A8: 4,9 => CTR
* 71.98365.3...7681..861..73.237465198158397246649821375871....63.6273.581593618427
* PAIR B6: 2,4 BLK 4
C6: 2,4,9                                # reduction candidate for 2,4
C6: 2,4 => SOLVED
* 712983654345276819986145732537462198198357246624891375871529463269734581453618927
C6: 9 => CTR
* 71498365232.5768145861..7392374651981583972466498.1375871....63.6.73..81..3618.27
* PAIR F4: 2,5 COL F
F3: 2,5,4                                # reduction candidate for 2,5
F3: 2,5                                  # 20 pairs
F7: 2,5,4,9                              # reduction candidate for 2,5
F7: 2,5                                  # 20 pairs
* PAIR E6: 2,9 ROW 6
C6: 2,9,4                                # reduction candidate for 2,9
C6: 2,9 => CTR
* 71498365232.5768145861..7392374651981583972466498.1375871....63.6.73..81..3618.27
C6: 4 => SOLVED
* 712983654345276819986145732537462198198357246624891375871529463269734581453618927
* PAIR B9: 5,9 BLK 7
A8: 5,9,2,4                              # reduction candidate for 5,9
A8: 5,9 => CTR
* 71.98365.3...7681..861..73.237465198158397246649821375871....63.6273..81493618527
A8: 2,4                                  # 16 pairs
C8: 5,9,2                                # reduction candidate for 5,9
C8: 5,9 => SOLVED
* 712983654345276819986145732537462198198357246624891375871529463269734581453618927
C8: 2 => CTR
* 71.98365.3.52768199861..732.3746.1981.83.724662.8.1375871....63.6.73..81..3618.27
A9: 5,9,4                                # reduction candidate for 5,9
A9: 5,9 => CTR
* 714983652325.7681..861..73..3746.1981.83.72466..8.1375871....6346273..81..3618427
A9: 4                                    # 16 pairs
* PAIR B9: 5,9 ROW 9
G9: 5,9,4                                # reduction candidate for 5,9
G9: 4 => CTR
* 714983652325.7681..861..73..3746.1981.83.72466..8.1375871....6346273..81..3618427
G9: 5,9                                  # 16 pairs
* PAIR D7: 2,5 BLK 8
E7: 2,5,4                                # reduction candidate for 2,5
E7: 2,5                                  # 20 pairs
F7: 2,5,4,9                              # reduction candidate for 2,5
F7: 2,5                                  # 20 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-315-base-pr-000.dot
* REASONING
* PRF # C6: 2,4 => SOL
* DIS # C6: 9 => CTR => C6: 2,4
* DIS # I2: 2,4 => CTR => I2: 9
* PRF # I2: 9 => SOL
* PRF # C8: 5,9 => SOL
* DIS # C8: 2 => CTR => C8: 5,9
* DIS # A8: 5,9 => CTR => A8: 2,4
* DIS # A9: 5,9 => CTR => A9: 4
* DIS # I2: 2,4 => CTR => I2: 9
* PRF # I2: 9 => SOL
* PRF # I2: 2,9 => SOL
* DIS # I2: 4 => CTR => I2: 2,9
* PRF # A8: 2,5 => SOL
* DIS # A8: 4,9 => CTR => A8: 2,5
* PRF # C6: 2,4 => SOL
* DIS # C6: 9 => CTR => C6: 2,4
* DIS # C6: 2,9 => CTR => C6: 4
* PRF # C6: 4 => SOL
* DIS # A8: 5,9 => CTR => A8: 2,4
* PRF # C8: 5,9 => SOL
* DIS # C8: 2 => CTR => C8: 5,9
* DIS # A9: 5,9 => CTR => A9: 4
* DIS # G9: 4 => CTR => G9: 5,9
* CNT  23 HDP CHAINS /  34 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B2,B5,B6,B9,C1,C2,D2,D7,E5,E6,F4,I1,I3)
* 71.98365.3...7681..861..73..3746.1981.83.72466..8.1375871....63.6.73..81..3618.27
* PAIR C1: 2,4 COL C
C6: 2,4,9                                # reduction candidate for 2,4
C6: 2,4 => SOLVED
* 712983654345276819986145732537462198198357246624891375871529463269734581453618927
* DURATION: 0:00:02.332948  START: 13:47:41.158792  END: 13:47:43.491740 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-315-base-pr-001.dot
* REASONING
* PRF # C6: 2,4 => SOL
* STA C6: 2,4
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 315

solution: 712983654345276819986145732537462198198357246624891375871529463269734581453618927
info: 2893     FNBTWXY  S8.f     46549

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

Solution

position: 712983654345276819986145732537462198198357246624891375871529463269734581453618927 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 # C6: 2,4 => SOL
* DIS # C6: 9 => CTR => C6: 2,4
* DIS # I2: 2,4 => CTR => I2: 9
* PRF # I2: 9 => SOL
* PRF # C8: 5,9 => SOL
* DIS # C8: 2 => CTR => C8: 5,9
* DIS # A8: 5,9 => CTR => A8: 2,4
* INC # A8: 2,4 => UNS
* DIS # A9: 5,9 => CTR => A9: 4
* INC # A9: 4 => UNS
* INC # E3: 2,5 => UNS
* INC # F3: 2,5 => UNS
* DIS # I2: 2,4 => CTR => I2: 9
* PRF # I2: 9 => SOL
* PRF # I2: 2,9 => SOL
* DIS # I2: 4 => CTR => I2: 2,9
* PRF # A8: 2,5 => SOL
* DIS # A8: 4,9 => CTR => A8: 2,5
* PRF # C6: 2,4 => SOL
* DIS # C6: 9 => CTR => C6: 2,4
* INC # F3: 2,5 => UNS
* INC # F7: 2,5 => UNS
* DIS # C6: 2,9 => CTR => C6: 4
* PRF # C6: 4 => SOL
* DIS # A8: 5,9 => CTR => A8: 2,4
* INC # A8: 2,4 => UNS
* PRF # C8: 5,9 => SOL
* DIS # C8: 2 => CTR => C8: 5,9
* DIS # A9: 5,9 => CTR => A9: 4
* INC # A9: 4 => UNS
* INC # G9: 5,9 => UNS
* DIS # G9: 4 => CTR => G9: 5,9
* INC # E7: 2,5 => UNS
* INC # F7: 2,5 => UNS
* CNT  34 HDP CHAINS /  34 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # C6: 2,4 => SOL
* STA C6: 2,4
* CNT   1 HDP CHAINS /   1 HYP OPENED