Analysis of xx-top500-061-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...6.5...2.....4............76....4....1..2.....83...........57.....4..61...2.... initial

Autosolve

position: ...6.57.225....46.6..4.25...76259.415..14627.4..837695....6..577..5.4.2616572.9.4 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # I3: 8,9 => SOL
* DIS # I3: 3 => CTR => I3: 8,9
* DIS # E2: 8,9 => CTR => E2: 1,7
* DIS # A1: 3,8 => CTR => A1: 9
* DIS # I3: 9 => CTR => I3: 3,8
* PRF # A7: 8 => SOL
* CNT   6 HDP CHAINS /  26 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 # I3: 8,9 => SOL
* STA I3: 8,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

...6.5...2.....4............76....4....1..2.....83...........57.....4..61...2.... initial
...6.57.225....46.6..4.25...76259.415..14627.4..837695....6..577..5.4.2616572.9.4 autosolve
948615732251378469637492518376259841589146273412837695824961357793584126165723984 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (12)
D2: 3,9
I2: 8,9
A4: 3,8
B6: 1,2
C6: 1,2
G4: 3,8
I5: 3,8
B7: 2,4
C7: 2,4
D7: 3,9
F9: 3,8
H9: 3,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H3: 1.. / H1 = 1  => 14 pairs (_) / H3 = 1  => 14 pairs (_)
B6,C6: 1.. / B6 = 1  =>  8 pairs (_) / C6 = 1  =>  9 pairs (_)
F7,E8: 1.. / F7 = 1  => 18 pairs (_) / E8 = 1  => 17 pairs (_)
G7,G8: 1.. / G7 = 1  => 17 pairs (_) / G8 = 1  => 18 pairs (_)
F7,G7: 1.. / F7 = 1  => 18 pairs (_) / G7 = 1  => 17 pairs (_)
E8,G8: 1.. / E8 = 1  => 17 pairs (_) / G8 = 1  => 18 pairs (_)
F2,F7: 1.. / F2 = 1  => 17 pairs (_) / F7 = 1  => 18 pairs (_)
B6,C6: 2.. / B6 = 2  =>  9 pairs (_) / C6 = 2  =>  8 pairs (_)
B7,C7: 2.. / B7 = 2  =>  8 pairs (_) / C7 = 2  =>  9 pairs (_)
B6,B7: 2.. / B6 = 2  =>  9 pairs (_) / B7 = 2  =>  8 pairs (_)
C6,C7: 2.. / C6 = 2  =>  8 pairs (_) / C7 = 2  =>  9 pairs (_)
D2,F2: 3.. / D2 = 3  => 16 pairs (_) / F2 = 3  =>  0 pairs (X)
G4,I5: 3.. / G4 = 3  =>  0 pairs (X) / I5 = 3  =>  0 pairs (_)
A4,G4: 3.. / A4 = 3  =>  0 pairs (*) / G4 = 3  =>  0 pairs (X)
F9,H9: 3.. / F9 = 3  =>  0 pairs (*) / H9 = 3  =>  0 pairs (X)
D2,D7: 3.. / D2 = 3  => 16 pairs (_) / D7 = 3  =>  0 pairs (X)
I3,I5: 3.. / I3 = 3  =>  0 pairs (X) / I5 = 3  =>  0 pairs (_)
B1,C1: 4.. / B1 = 4  =>  8 pairs (_) / C1 = 4  =>  9 pairs (_)
B7,C7: 4.. / B7 = 4  =>  9 pairs (_) / C7 = 4  =>  8 pairs (_)
B1,B7: 4.. / B1 = 4  =>  8 pairs (_) / B7 = 4  =>  9 pairs (_)
C1,C7: 4.. / C1 = 4  =>  9 pairs (_) / C7 = 4  =>  8 pairs (_)
C2,C3: 7.. / C2 = 7  => 13 pairs (_) / C3 = 7  => 12 pairs (_)
E2,E3: 7.. / E2 = 7  => 12 pairs (_) / E3 = 7  => 13 pairs (_)
C2,E2: 7.. / C2 = 7  => 13 pairs (_) / E2 = 7  => 12 pairs (_)
C3,E3: 7.. / C3 = 7  => 12 pairs (_) / E3 = 7  => 13 pairs (_)
G4,I5: 8.. / G4 = 8  =>  0 pairs (*) / I5 = 8  =>  0 pairs (X)
A4,G4: 8.. / A4 = 8  =>  0 pairs (X) / G4 = 8  =>  0 pairs (_)
F9,H9: 8.. / F9 = 8  =>  0 pairs (X) / H9 = 8  =>  0 pairs (_)
I2,I3: 9.. / I2 = 9  => 15 pairs (_) / I3 = 9  =>  0 pairs (X)
B5,C5: 9.. / B5 = 9  => 14 pairs (_) / C5 = 9  => 14 pairs (_)
D7,E8: 9.. / D7 = 9  => 16 pairs (_) / E8 = 9  =>  0 pairs (X)
A7,D7: 9.. / A7 = 9  =>  0 pairs (X) / D7 = 9  => 16 pairs (_)
A1,A7: 9.. / A1 = 9  => 16 pairs (_) / A7 = 9  =>  0 pairs (X)
D2,D7: 9.. / D2 = 9  =>  0 pairs (X) / D7 = 9  => 16 pairs (_)
* DURATION: 0:01:01.816192  START: 04:45:04.716342  END: 04:46:06.532534 2017-05-04
* CP COUNT: (34)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B6,B7,C6,C7,D2,D7,F9,G4,H9,I2,I5)
* ...6.57.225....46.6..4.25...76259.415..14627.4..837695....6..577..5.4.2616572.9.4
* PAIR I2: 8,9 BLK 3
I3: 8,9,3                                # reduction candidate for 8,9
I3: 8,9 => SOLVED
* 948615732251378469637492518376259841589146273412837695824961357793584126165723984
I3: 3 => CTR
* 9..6.57.225.3..4696..4925.38762593415..1462784..8376953..96..577..5.4.26165728934
* PAIR I2: 8,9 ROW 2
C2: 8,9,1,7                              # reduction candidate for 8,9
C2: 8,9                                  # 20 pairs
E2: 8,9,1,7                              # reduction candidate for 8,9
E2: 8,9 => CTR
* 9..6857.22573914686..4725.9.762598415..1462734..8376958..9631577..51432616572.9.4
E2: 1,7                                  # 13 pairs
* PAIR A4: 3,8 BLK 4
B5: 3,8,9                                # reduction candidate for 3,8
B5: 3,8                                  # 14 pairs
C5: 3,8,9                                # reduction candidate for 3,8
C5: 3,8                                  # 14 pairs
* PAIR A4: 3,8 COL A
A1: 3,8,9                                # reduction candidate for 3,8
A1: 3,8 => CTR
* ...6.57.225.9.34686..4.25...76259.415..14627.4..8376959..36..577..594126165728934
A1: 9                                    # 16 pairs
A7: 3,8,9                                # reduction candidate for 3,8
A7: 3,8                                  # 16 pairs
* PAIR G4: 3,8 COL G
G7: 3,8,1                                # reduction candidate for 3,8
G7: 3,8                                  # 18 pairs
G8: 3,8,1                                # reduction candidate for 3,8
G8: 3,8                                  # 17 pairs
* PAIR I5: 3,8 ROW 5
B5: 3,8,9                                # reduction candidate for 3,8
B5: 3,8                                  # 14 pairs
C5: 3,8,9                                # reduction candidate for 3,8
C5: 3,8                                  # 14 pairs
* PAIR I5: 3,8 COL I
I3: 3,8,9                                # reduction candidate for 3,8
I3: 9 => CTR
* ...6.57.225....4686..4.25.93762598415..1462734..837695....681577..514326165723984
I3: 3,8                                  # 15 pairs
* PAIR D7: 3,9 ROW 7
A7: 3,9,8                                # reduction candidate for 3,9
A7: 8 => SOLVED
* 948615732251378469637492518376259841589146273412837695824961357793584126165723984
A7: 3,9                                  # 18 pairs
* PAIR F9: 3,8 BLK 8
F7: 3,8,1                                # reduction candidate for 3,8
F7: 1                                    # 18 pairs
F7: 3,8                                  # 17 pairs
* PAIR F9: 3,8 COL F
F2: 3,8,1                                # reduction candidate for 3,8
F2: 3,8                                  # 18 pairs
F2: 1                                    # 17 pairs
* PAIR H9: 3,8 BLK 9
G7: 3,8,1                                # reduction candidate for 3,8
G7: 3,8                                  # 18 pairs
G8: 3,8,1                                # reduction candidate for 3,8
G8: 3,8                                  # 17 pairs
* PAIR H9: 3,8 COL H
H1: 3,8,1                                # reduction candidate for 3,8
H1: 3,8                                  # 14 pairs
H3: 3,8,1                                # reduction candidate for 3,8
H3: 3,8                                  # 14 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-061-base-pr-000.dot
* REASONING
* PRF # I3: 8,9 => SOL
* DIS # I3: 3 => CTR => I3: 8,9
* DIS # E2: 8,9 => CTR => E2: 1,7
* DIS # A1: 3,8 => CTR => A1: 9
* DIS # I3: 9 => CTR => I3: 3,8
* PRF # A7: 8 => SOL
* CNT   6 HDP CHAINS /  26 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B6,B7,C6,C7,D2,D7,F9,G4,H9,I2,I5)
* ...6.57.225....46.6..4.25...76259.415..14627.4..837695....6..577..5.4.2616572.9.4
* PAIR I2: 8,9 BLK 3
I3: 8,9,3                                # reduction candidate for 8,9
I3: 8,9 => SOLVED
* 948615732251378469637492518376259841589146273412837695824961357793584126165723984
* DURATION: 0:00:02.389461  START: 04:46:33.343413  END: 04:46:35.732874 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-061-base-pr-001.dot
* REASONING
* PRF # I3: 8,9 => SOL
* STA I3: 8,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 061

solution: 948615732251378469637492518376259841589146273412837695824961357793584126165723984
info: 1437     FNBHWX   S8.f     10908

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

Solution

position: 948615732251378469637492518376259841589146273412837695824961357793584126165723984 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 # I3: 8,9 => SOL
* DIS # I3: 3 => CTR => I3: 8,9
* INC # C2: 8,9 => UNS
* DIS # E2: 8,9 => CTR => E2: 1,7
* INC # E2: 1,7 => UNS
* INC # B5: 3,8 => UNS
* INC # C5: 3,8 => UNS
* DIS # A1: 3,8 => CTR => A1: 9
* INC # A1: 9 => UNS
* INC # A7: 3,8 => UNS
* INC # G7: 3,8 => UNS
* INC # G8: 3,8 => UNS
* INC # B5: 3,8 => UNS
* INC # C5: 3,8 => UNS
* INC # I3: 3,8 => UNS
* DIS # I3: 9 => CTR => I3: 3,8
* INC # A7: 3,9 => UNS
* PRF # A7: 8 => SOL
* INC # F7: 3,8 => UNS
* INC # F7: 1 => UNS
* INC # F2: 3,8 => UNS
* INC # F2: 1 => UNS
* INC # G7: 3,8 => UNS
* INC # G8: 3,8 => UNS
* INC # H1: 3,8 => UNS
* INC # H3: 3,8 => UNS
* CNT  26 HDP CHAINS /  26 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # I3: 8,9 => SOL
* STA I3: 8,9
* CNT   1 HDP CHAINS /   1 HYP OPENED