Analysis of xx-top500-317-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .......218...4...........6..9.2.....7.....4.....5.1....15..........3.9..6.2...... initial

Autosolve

position: .......218...4...........64.9.2.4...7.....4.....5.1...915......4...3.9..632...... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A3: 3,5 => CTR => A3: 1,2
* DIS # F1: 3,5 => CTR => F1: 6,7,8,9
* DIS # G1: 3,5 => CTR => G1: 7,8
* PRF # A4: 3,5 => SOL
* DIS # A4: 1 => CTR => A4: 3,5
* PRF # I6: 2,3 => SOL
* DIS # A3: 2,3 => CTR => A3: 1,5
* PRF # A3: 1,5 => SOL
* DIS # D2: 3,7 => CTR => D2: 1,6
* DIS # H9: 1,5 => CTR => H9: 4,7,8
* DIS # H4: 1,5 => CTR => H4: 3,7,8
* CNT  11 HDP CHAINS /  21 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 # A3: 3,5 => CTR => A3: 1,2
* DIS A3: 1,2 # F1: 3,5 => CTR => F1: 6,7,8,9
* DIS A3: 1,2 + F1: 6,7,8,9 # G1: 3,5 => CTR => G1: 7,8
* PRF A3: 1,2 + F1: 6,7,8,9 + G1: 7,8 # A4: 3,5 => SOL
* STA A3: 1,2 + F1: 6,7,8,9 + G1: 7,8 + A4: 3,5
* CNT   4 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

.......218...4...........6..9.2.....7.....4.....5.1....15..........3.9..6.2...... initial
.......218...4...........64.9.2.4...7.....4.....5.1...915......4...3.9..632...... autosolve
349756821826143579157829364593264187761398452284571693915487236478632915632915748 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
A1: 3,5
A6: 2,3
B8: 7,8
C8: 7,8
D8: 1,6
H8: 1,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C2,D2: 1.. / C2 = 1  =>  0 pairs (X) / D2 = 1  =>  0 pairs (_)
C5,H5: 1.. / C5 = 1  =>  0 pairs (*) / H5 = 1  =>  0 pairs (X)
D8,H8: 1.. / D8 = 1  =>  0 pairs (X) / H8 = 1  =>  0 pairs (_)
A3,A4: 1.. / A3 = 1  =>  0 pairs (*) / A4 = 1  =>  0 pairs (X)
E3,E9: 1.. / E3 = 1  =>  0 pairs (X) / E9 = 1  =>  0 pairs (_)
G4,G9: 1.. / G4 = 1  =>  0 pairs (*) / G9 = 1  =>  0 pairs (X)
B2,F2: 2.. / B2 = 2  =>  0 pairs (*) / F2 = 2  =>  0 pairs (X)
B5,I5: 2.. / B5 = 2  =>  0 pairs (X) / I5 = 2  =>  0 pairs (_)
F8,I8: 2.. / F8 = 2  =>  0 pairs (*) / I8 = 2  =>  0 pairs (X)
A3,A6: 2.. / A3 = 2  =>  0 pairs (X) / A6 = 2  =>  0 pairs (_)
E3,E7: 2.. / E3 = 2  =>  0 pairs (*) / E7 = 2  =>  0 pairs (X)
G6,G7: 2.. / G6 = 2  =>  0 pairs (X) / G7 = 2  =>  0 pairs (_)
D5,F5: 3.. / D5 = 3  =>  6 pairs (_) / F5 = 3  =>  6 pairs (_)
B1,C1: 4.. / B1 = 4  =>  6 pairs (_) / C1 = 4  =>  6 pairs (_)
B6,C6: 4.. / B6 = 4  =>  6 pairs (_) / C6 = 4  =>  6 pairs (_)
D7,D9: 4.. / D7 = 4  =>  6 pairs (_) / D9 = 4  =>  8 pairs (_)
H7,H9: 4.. / H7 = 4  =>  8 pairs (_) / H9 = 4  =>  6 pairs (_)
D7,H7: 4.. / D7 = 4  =>  6 pairs (_) / H7 = 4  =>  8 pairs (_)
D9,H9: 4.. / D9 = 4  =>  8 pairs (_) / H9 = 4  =>  6 pairs (_)
B1,B6: 4.. / B1 = 4  =>  6 pairs (_) / B6 = 4  =>  6 pairs (_)
C1,C6: 4.. / C1 = 4  =>  6 pairs (_) / C6 = 4  =>  6 pairs (_)
A4,B5: 5.. / A4 = 5  =>  0 pairs (*) / B5 = 5  =>  0 pairs (X)
E4,E6: 7.. / E4 = 7  =>  6 pairs (_) / E6 = 7  =>  7 pairs (_)
B8,C8: 7.. / B8 = 7  =>  6 pairs (_) / C8 = 7  =>  4 pairs (_)
G1,G3: 8.. / G1 = 8  =>  6 pairs (_) / G3 = 8  =>  6 pairs (_)
B8,C8: 8.. / B8 = 8  =>  4 pairs (_) / C8 = 8  =>  6 pairs (_)
C1,C3: 9.. / C1 = 9  =>  6 pairs (_) / C3 = 9  =>  6 pairs (_)
H2,I2: 9.. / H2 = 9  =>  6 pairs (_) / I2 = 9  =>  6 pairs (_)
* DURATION: 0:00:39.841373  START: 13:49:16.178813  END: 13:49:56.020186 2017-05-04
* CP COUNT: (28)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B8,C8,D8,H8)
* .......218...4...........64.9.2.4...7.....4.....5.1...915......4...3.9..632......
* PAIR A1: 3,5 BLK 1
A3: 3,5,1,2                              # reduction candidate for 3,5
A3: 3,5 => CTR
* .......218...4...........6419.2.4...75....4122..5.1...915...2..4..132956632...1..
A3: 1,2                                  #  7 pairs
* PAIR A1: 3,5 ROW 1
F1: 3,5,6,7,8,9                          # reduction candidate for 3,5
F1: 3,5 => CTR
* 5....3.218...42...27.....6419.2.4...72.3..4153..5.12..915.2....487136952632.5.1..
F1: 6,7,8,9                              #  6 pairs
G1: 3,5,7,8                              # reduction candidate for 3,5
G1: 3,5 => CTR
* 5.....32186..42...27....86419.2.4...72....4153..5.12..915.2....487136952632.5.1..
G1: 7,8                                  #  7 pairs
* PAIR A1: 3,5 COL A
A4: 3,5,1                                # reduction candidate for 3,5
A4: 3,5 => SOLVED
* 349756821826143579157829364593264187761398452284571693915487236478632915632915748
A4: 1 => CTR
* .......218...4...........6419.2.4...75....412...5.1...915...2..4..132956632...1..
* PAIR A6: 2,3 ROW 6
G6: 2,3,6,7                              # reduction candidate for 2,3
G6: 2,3                                  #  7 pairs
I6: 2,3,6,7,8,9                          # reduction candidate for 2,3
I6: 2,3 => SOLVED
* 349756821826143579157829364593264187761398452284571693915487236478632915632915748
I6: 6,7,8,9                              #  6 pairs
* PAIR A6: 2,3 COL A
A3: 2,3,1,5                              # reduction candidate for 2,3
A3: 2,3 => CTR
* .......218...4...........6419.2.4...75....412...5.1...915...2..4..132956632...1..
A3: 1,5 => SOLVED
* 349756821826143579157829364593264187761398452284571693915487236478632915632915748
* PAIR D8: 1,6 COL D
D2: 1,6,3,7                              # reduction candidate for 1,6
D2: 3,7 => CTR
* .......218.1.4...........6419.2.4...75....412...5.1...915...2..4..132956632...1..
D2: 1,6                                  #  7 pairs
* PAIR H8: 1,5 BLK 9
G9: 1,5,7                                # reduction candidate for 1,5
G9: 1,5                                  #  9 pairs
H9: 1,5,4,7,8                            # reduction candidate for 1,5
H9: 1,5 => CTR
* .......218..14....1......64.9.2.41..7.1...4..2..5.1...915...2434..63.9..6324..7.8
H9: 4,7,8                                #  6 pairs
* PAIR H8: 1,5 COL H
H4: 1,5,3,7,8                            # reduction candidate for 1,5
H4: 1,5 => CTR
* .......2182.14.5..1...2..64.9.2.415.751...4.22..5.16..915.872.64..632915632915748
H4: 3,7,8                                #  6 pairs
H5: 1,5,8,9                              # reduction candidate for 1,5
H5: 1,5                                  #  7 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-317-base-pr-000.dot
* REASONING
* DIS # A3: 3,5 => CTR => A3: 1,2
* DIS # F1: 3,5 => CTR => F1: 6,7,8,9
* DIS # G1: 3,5 => CTR => G1: 7,8
* PRF # A4: 3,5 => SOL
* DIS # A4: 1 => CTR => A4: 3,5
* PRF # I6: 2,3 => SOL
* DIS # A3: 2,3 => CTR => A3: 1,5
* PRF # A3: 1,5 => SOL
* DIS # D2: 3,7 => CTR => D2: 1,6
* DIS # H9: 1,5 => CTR => H9: 4,7,8
* DIS # H4: 1,5 => CTR => H4: 3,7,8
* CNT  11 HDP CHAINS /  21 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B8,C8,D8,H8)
* .......218...4...........64.9.2.4...7.....4.....5.1...915......4...3.9..632......
* PAIR A1: 3,5 BLK 1
A3: 3,5,1,2                              # reduction candidate for 3,5
A3: 3,5 => CTR
* .......218...4...........6419.2.4...75....4122..5.1...915...2..4..132956632...1..
* PAIR A1: 3,5 ROW 1
F1: 3,5,6,7,8,9                          # reduction candidate for 3,5
F1: 3,5 => CTR
* 5....3.218...42...27.....6419.2.4...72.3..4153..5.12..915.2....487136952632.5.1..
G1: 3,5,7,8                              # reduction candidate for 3,5
G1: 3,5 => CTR
* 5.....32186..42...27....86419.2.4...72....4153..5.12..915.2....487136952632.5.1..
* RESTART
* PAIR A1: 3,5 COL A
A4: 3,5,1                                # reduction candidate for 3,5
A4: 3,5 => SOLVED
* 349756821826143579157829364593264187761398452284571693915487236478632915632915748
* DURATION: 0:00:05.913941  START: 13:50:13.348163  END: 13:50:19.262104 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-317-base-pr-001.dot
* REASONING
* DIS # A3: 3,5 => CTR => A3: 1,2
* DIS A3: 1,2 # F1: 3,5 => CTR => F1: 6,7,8,9
* DIS A3: 1,2 + F1: 6,7,8,9 # G1: 3,5 => CTR => G1: 7,8
* PRF A3: 1,2 + F1: 6,7,8,9 + G1: 7,8 # A4: 3,5 => SOL
* STA A3: 1,2 + F1: 6,7,8,9 + G1: 7,8 + A4: 3,5
* CNT   4 HDP CHAINS /   4 HYP OPENED

Header Info

Top 500 Minimum 17 317

solution: 349756821826143579157829364593264187761398452284571693915487236478632915632915748
info: 2899     FNBHWY   S8.f     125

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

Solution

position: 349756821826143579157829364593264187761398452284571693915487236478632915632915748 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 # A3: 3,5 => CTR => A3: 1,2
* INC # A3: 1,2 => UNS
* DIS # F1: 3,5 => CTR => F1: 6,7,8,9
* INC # F1: 6,7,8,9 => UNS
* DIS # G1: 3,5 => CTR => G1: 7,8
* INC # G1: 7,8 => UNS
* PRF # A4: 3,5 => SOL
* DIS # A4: 1 => CTR => A4: 3,5
* INC # G6: 2,3 => UNS
* PRF # I6: 2,3 => SOL
* INC # I6: 6,7,8,9 => UNS
* DIS # A3: 2,3 => CTR => A3: 1,5
* PRF # A3: 1,5 => SOL
* INC # D2: 1,6 => UNS
* DIS # D2: 3,7 => CTR => D2: 1,6
* INC # G9: 1,5 => UNS
* DIS # H9: 1,5 => CTR => H9: 4,7,8
* INC # H9: 4,7,8 => UNS
* DIS # H4: 1,5 => CTR => H4: 3,7,8
* INC # H4: 3,7,8 => UNS
* INC # H5: 1,5 => UNS
* CNT  21 HDP CHAINS /  21 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A3: 3,5 => CTR => A3: 1,2
* DIS A3: 1,2 # F1: 3,5 => CTR => F1: 6,7,8,9
* DIS A3: 1,2 + F1: 6,7,8,9 # G1: 3,5 => CTR => G1: 7,8
* PRF A3: 1,2 + F1: 6,7,8,9 + G1: 7,8 # A4: 3,5 => SOL
* STA A3: 1,2 + F1: 6,7,8,9 + G1: 7,8 + A4: 3,5
* CNT   4 HDP CHAINS /   4 HYP OPENED