Analysis of xx-top500-273-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .836.........7..4...........6.1.8..........27...3.....4.2.5....7.....8........1.. initial

Autosolve

position: .836.........7..48.74.8.....671.8..........27...3.7.814.285....7.....8.....7..1.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # G1: 5,9 => CTR => G1: 2,7
* PRF # G2: 5,9 => SOL
* DIS # I3: 5,9 => CTR => I3: 3,6
* DIS # F1: 5,9 => CTR => F1: 1,2,4
* DIS # I4: 3 => CTR => I4: 5,9
* DIS # A4: 5,9 => CTR => A4: 2,3
* DIS # B6: 5,9 => CTR => B6: 2,4
* DIS # G6: 5,9 => CTR => G6: 4,6
* DIS # C8: 5,9 => CTR => C8: 1,6
* PRF # C9: 5,9 => SOL
* DIS # G4: 3,9 => CTR => G4: 4,5
* DIS # I4: 3,9 => CTR => I4: 5
* DIS # A4: 2,5 => CTR => A4: 3,9
* PRF # H3: 3,9 => SOL
* DIS # H7: 3,9 => CTR => H7: 6,7
* DIS # F8: 2,4 => CTR => F8: 1,6,9
* DIS # F9: 6,9 => CTR => F9: 2,4
* CNT  17 HDP CHAINS /  42 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 # G1: 5,9 => CTR => G1: 2,7
* PRF G1: 2,7 # G2: 5,9 => SOL
* STA G1: 2,7 + G2: 5,9
* CNT   2 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

.836.........7..4...........6.1.8..........27...3.....4.2.5....7.....8........1.. initial
.836.........7..48.74.8.....671.8..........27...3.7.814.285....7.....8.....7..1.. autosolve
583642719621973548974581236367128495198465327245397681412856973736219854859734162 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
I1: 5,9
C6: 5,9
H4: 3,9
I8: 2,4
I9: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H3: 1.. / H1 = 1  =>  0 pairs (*) / H3 = 1  =>  0 pairs (X)
B7,F7: 1.. / B7 = 1  =>  8 pairs (_) / F7 = 1  =>  0 pairs (X)
E1,E8: 1.. / E1 = 1  =>  0 pairs (X) / E8 = 1  =>  0 pairs (_)
E4,E6: 2.. / E4 = 2  =>  5 pairs (_) / E6 = 2  =>  0 pairs (X)
I8,I9: 2.. / I8 = 2  =>  4 pairs (_) / I9 = 2  => 10 pairs (_)
A4,E4: 2.. / A4 = 2  =>  0 pairs (X) / E4 = 2  =>  5 pairs (_)
F9,I9: 2.. / F9 = 2  =>  4 pairs (_) / I9 = 2  => 10 pairs (_)
B2,B6: 2.. / B2 = 2  =>  6 pairs (_) / B6 = 2  =>  0 pairs (X)
F2,F3: 3.. / F2 = 3  =>  0 pairs (*) / F3 = 3  =>  0 pairs (X)
E8,E9: 3.. / E8 = 3  =>  0 pairs (X) / E9 = 3  =>  7 pairs (_)
F2,G2: 3.. / F2 = 3  =>  0 pairs (*) / G2 = 3  =>  0 pairs (X)
E1,F1: 4.. / E1 = 4  =>  0 pairs (*) / F1 = 4  =>  0 pairs (X)
B5,B6: 4.. / B5 = 4  =>  0 pairs (X) / B6 = 4  =>  6 pairs (_)
I8,I9: 4.. / I8 = 4  => 10 pairs (_) / I9 = 4  =>  4 pairs (_)
E4,G4: 4.. / E4 = 4  =>  0 pairs (X) / G4 = 4  =>  6 pairs (_)
D5,D8: 4.. / D5 = 4  => 11 pairs (_) / D8 = 4  =>  4 pairs (_)
D5,F5: 5.. / D5 = 5  =>  6 pairs (_) / F5 = 5  =>  6 pairs (_)
H8,H9: 5.. / H8 = 5  =>  5 pairs (_) / H9 = 5  =>  6 pairs (_)
A2,C2: 6.. / A2 = 6  =>  5 pairs (_) / C2 = 6  =>  0 pairs (X)
H3,I3: 6.. / H3 = 6  =>  0 pairs (X) / I3 = 6  =>  6 pairs (_)
G5,G6: 6.. / G5 = 6  =>  0 pairs (X) / G6 = 6  =>  5 pairs (_)
E6,G6: 6.. / E6 = 6  =>  0 pairs (X) / G6 = 6  =>  5 pairs (_)
A2,A9: 6.. / A2 = 6  =>  5 pairs (_) / A9 = 6  =>  0 pairs (X)
I3,I7: 6.. / I3 = 6  =>  6 pairs (_) / I7 = 6  =>  0 pairs (X)
G1,H1: 7.. / G1 = 7  =>  7 pairs (_) / H1 = 7  =>  0 pairs (X)
G7,H7: 7.. / G7 = 7  =>  0 pairs (X) / H7 = 7  =>  7 pairs (_)
G1,G7: 7.. / G1 = 7  =>  7 pairs (_) / G7 = 7  =>  0 pairs (X)
H1,H7: 7.. / H1 = 7  =>  0 pairs (X) / H7 = 7  =>  7 pairs (_)
A5,C5: 8.. / A5 = 8  =>  6 pairs (_) / C5 = 8  =>  5 pairs (_)
A9,C9: 8.. / A9 = 8  =>  5 pairs (_) / C9 = 8  =>  6 pairs (_)
A5,A9: 8.. / A5 = 8  =>  6 pairs (_) / A9 = 8  =>  5 pairs (_)
C5,C9: 8.. / C5 = 8  =>  5 pairs (_) / C9 = 8  =>  6 pairs (_)
* DURATION: 0:00:51.235247  START: 12:15:10.921703  END: 12:16:02.156950 2017-05-04
* CP COUNT: (32)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C6,H4,I1,I8,I9)
* .836.........7..48.74.8.....671.8..........27...3.7.814.285....7.....8.....7..1..
* PAIR I1: 5,9 BLK 3
G1: 5,9,2,7                              # reduction candidate for 5,9
G1: 5,9 => CTR
* 183642.7.62..71348.74.83216.671.84..3....5.27.4.3.7.8141285.7..7..21.8.4...7341.2
G1: 2,7                                  #  6 pairs
G2: 5,9,2,3                              # reduction candidate for 5,9
G2: 5,9 => SOLVED
* 583642719621973548974581236367128495198465327245397681412856973736219854859734162
G2: 2,3                                  #  6 pairs
G3: 5,9,2,3                              # reduction candidate for 5,9
G3: 5,9                                  # 10 pairs
I3: 5,9,3,6                              # reduction candidate for 5,9
I3: 5,9 => CTR
* .836..71.....7..48.74.8..6..671.8.933.8....27...3.7.81412859.767...1.8.....73.1..
I3: 3,6                                  #  6 pairs
* PAIR I1: 5,9 ROW 1
A1: 5,9,1,2                              # reduction candidate for 5,9
A1: 5,9                                  #  9 pairs
F1: 5,9,1,2,4                            # reduction candidate for 5,9
F1: 5,9 => CTR
* .8364.27..2..7..48.74.8..16.671.84...9..6.327.453.768141285.73973..1.85..5.73.16.
F1: 1,2,4                                #  5 pairs
* PAIR I1: 5,9 COL I
I4: 5,9,3                                # reduction candidate for 5,9
I4: 3 => CTR
* .836.....62..71348.74.83....671.8.93.......27.4.3.7.81412856.397.6...8.....7..1..
I4: 5,9                                  #  8 pairs
* PAIR C6: 5,9 BLK 4
A4: 5,9,2,3                              # reduction candidate for 5,9
A4: 5,9 => CTR
* .836.....62..71348.74.83....671284.........2724.3.7.8141285....7.6.1.8....873.1..
A4: 2,3                                  #  6 pairs
A6: 5,9,2                                # reduction candidate for 5,9
A6: 5,9                                  # 10 pairs
B6: 5,9,2,4                              # reduction candidate for 5,9
B6: 5,9 => CTR
* .836.427..2..7..48.7428..16.671.8...34.....27...3.7.814.285.7..7..4..8.2...7.21.4
B6: 2,4                                  #  6 pairs
* PAIR C6: 5,9 ROW 6
G6: 5,9,4,6                              # reduction candidate for 5,9
G6: 5,9 => CTR
* .836.....62..71348.74.83....671284........62724.367.8141285....7.6.1.8....873.1..
G6: 4,6                                  #  6 pairs
* PAIR C6: 5,9 COL C
C2: 5,9,1,6                              # reduction candidate for 5,9
C2: 5,9                                  #  9 pairs
C8: 5,9,1,6                              # reduction candidate for 5,9
C8: 5,9 => CTR
* .8364.719....73.48.74.81.36367128495....6.327.4.39768141285697373..1.86....73.15.
C8: 1,6                                  #  6 pairs
C9: 5,9,6,8                              # reduction candidate for 5,9
C9: 5,9 => SOLVED
* 583642719621973548974581236367128495198465327245397681412856973736219854859734162
C9: 6,8                                  #  6 pairs
* PAIR H4: 3,9 BLK 6
G4: 3,9,4,5                              # reduction candidate for 3,9
G4: 3,9 => CTR
* 583614279.2..7..4897428..16267148..5......427.4.3276814.285.7.37..4..8.2...7.21.4
G4: 4,5                                  #  6 pairs
I4: 3,9,5                                # reduction candidate for 3,9
I4: 3,9 => CTR
* .836.....62..71348.74.83....671.8..........27.4.3.7.8141285....7.6.1.8....873.1..
I4: 5                                    #  8 pairs
G5: 3,9,4,6                              # reduction candidate for 3,9
G5: 3,9                                  # 10 pairs
* PAIR H4: 3,9 ROW 4
A4: 3,9,2,5                              # reduction candidate for 3,9
A4: 2,5 => CTR
* .836.....62..71348.74.83....671.8..........27.4.3.7.8141285....7.6.1.8....873.1..
A4: 3,9                                  # 10 pairs
* PAIR H4: 3,9 COL H
H3: 3,9,1,6                              # reduction candidate for 3,9
H3: 3,9 => SOLVED
* 583642719621973548974581236367128495198465327245397681412856973736219854859734162
H3: 1,6                                  #  6 pairs
H7: 3,9,6,7                              # reduction candidate for 3,9
H7: 3,9 => CTR
* 1836...7.62..71348.74.83.16.671.8...831....27.4.3.7.814128567..7.....8.....7..1..
H7: 6,7                                  #  6 pairs
H8: 3,9,5,6                              # reduction candidate for 3,9
H8: 3,9                                  # 11 pairs
H9: 3,9,5,6                              # reduction candidate for 3,9
H9: 3,9                                  # 10 pairs
* PAIR I8: 2,4 ROW 8
D8: 2,4,9                                # reduction candidate for 2,4
D8: 2,4                                  #  6 pairs
F8: 2,4,1,6,9                            # reduction candidate for 2,4
F8: 2,4 => CTR
* 5836..279.2.57.348974283516.671.8435...4.5.272453.7.814.285.7.37..9..8.....7..1..
F8: 1,6,9                                #  5 pairs
* PAIR I9: 2,4 ROW 9
F9: 2,4,6,9                              # reduction candidate for 2,4
F9: 6,9 => CTR
* .8361427..2..7..48.74.8..16.671.84.....4.5.27.4.3.7.814.285.7..7...3.8.4...74.1.2
F9: 2,4                                  #  6 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-273-base-pr-000.dot
* REASONING
* DIS # G1: 5,9 => CTR => G1: 2,7
* PRF # G2: 5,9 => SOL
* DIS # I3: 5,9 => CTR => I3: 3,6
* DIS # F1: 5,9 => CTR => F1: 1,2,4
* DIS # I4: 3 => CTR => I4: 5,9
* DIS # A4: 5,9 => CTR => A4: 2,3
* DIS # B6: 5,9 => CTR => B6: 2,4
* DIS # G6: 5,9 => CTR => G6: 4,6
* DIS # C8: 5,9 => CTR => C8: 1,6
* PRF # C9: 5,9 => SOL
* DIS # G4: 3,9 => CTR => G4: 4,5
* DIS # I4: 3,9 => CTR => I4: 5
* DIS # A4: 2,5 => CTR => A4: 3,9
* PRF # H3: 3,9 => SOL
* DIS # H7: 3,9 => CTR => H7: 6,7
* DIS # F8: 2,4 => CTR => F8: 1,6,9
* DIS # F9: 6,9 => CTR => F9: 2,4
* CNT  17 HDP CHAINS /  42 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C6,H4,I1,I8,I9)
* .836.........7..48.74.8.....671.8..........27...3.7.814.285....7.....8.....7..1..
* PAIR I1: 5,9 BLK 3
G1: 5,9,2,7                              # reduction candidate for 5,9
G1: 5,9 => CTR
* 183642.7.62..71348.74.83216.671.84..3....5.27.4.3.7.8141285.7..7..21.8.4...7341.2
G2: 5,9,2,3                              # reduction candidate for 5,9
G2: 5,9 => SOLVED
* 583642719621973548974581236367128495198465327245397681412856973736219854859734162
* DURATION: 0:00:04.008084  START: 12:16:40.186596  END: 12:16:44.194680 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-273-base-pr-001.dot
* REASONING
* DIS # G1: 5,9 => CTR => G1: 2,7
* PRF G1: 2,7 # G2: 5,9 => SOL
* STA G1: 2,7 + G2: 5,9
* CNT   2 HDP CHAINS /   2 HYP OPENED

Header Info

Top 500 Minimum 17 273

solution: 583642719621973548974581236367128495198465327245397681412856973736219854859734162
info: 2201     FNBHXYK  S8.f     24153

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

Solution

position: 583642719621973548974581236367128495198465327245397681412856973736219854859734162 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 # G1: 5,9 => CTR => G1: 2,7
* INC # G1: 2,7 => UNS
* PRF # G2: 5,9 => SOL
* INC # G2: 2,3 => UNS
* INC # G3: 5,9 => UNS
* DIS # I3: 5,9 => CTR => I3: 3,6
* INC # I3: 3,6 => UNS
* INC # A1: 5,9 => UNS
* DIS # F1: 5,9 => CTR => F1: 1,2,4
* INC # F1: 1,2,4 => UNS
* INC # I4: 5,9 => UNS
* DIS # I4: 3 => CTR => I4: 5,9
* DIS # A4: 5,9 => CTR => A4: 2,3
* INC # A4: 2,3 => UNS
* INC # A6: 5,9 => UNS
* DIS # B6: 5,9 => CTR => B6: 2,4
* INC # B6: 2,4 => UNS
* DIS # G6: 5,9 => CTR => G6: 4,6
* INC # G6: 4,6 => UNS
* INC # C2: 5,9 => UNS
* DIS # C8: 5,9 => CTR => C8: 1,6
* INC # C8: 1,6 => UNS
* PRF # C9: 5,9 => SOL
* INC # C9: 6,8 => UNS
* DIS # G4: 3,9 => CTR => G4: 4,5
* INC # G4: 4,5 => UNS
* DIS # I4: 3,9 => CTR => I4: 5
* INC # I4: 5 => UNS
* INC # G5: 3,9 => UNS
* INC # A4: 3,9 => UNS
* DIS # A4: 2,5 => CTR => A4: 3,9
* PRF # H3: 3,9 => SOL
* INC # H3: 1,6 => UNS
* DIS # H7: 3,9 => CTR => H7: 6,7
* INC # H7: 6,7 => UNS
* INC # H8: 3,9 => UNS
* INC # H9: 3,9 => UNS
* INC # D8: 2,4 => UNS
* DIS # F8: 2,4 => CTR => F8: 1,6,9
* INC # F8: 1,6,9 => UNS
* INC # F9: 2,4 => UNS
* DIS # F9: 6,9 => CTR => F9: 2,4
* CNT  42 HDP CHAINS /  42 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # G1: 5,9 => CTR => G1: 2,7
* PRF G1: 2,7 # G2: 5,9 => SOL
* STA G1: 2,7 + G2: 5,9
* CNT   2 HDP CHAINS /   2 HYP OPENED