Analysis of xx-top500-050-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .784...........1.....6.....1.....34....7....52.........6.....843...1.........2... initial

Autosolve

position: 6784.1.2.4..2..1...126..4..1.7...3428..72..152..1..8...613..28432.81.7..78...2.31 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E1: 3 => CTR => E1: 5,9
* DIS # I3: 3,9 => CTR => I3: 7,8
* DIS # E1: 5 => CTR => E1: 3,9
* PRF # E6: 5,9 => SOL
* DIS # C5: 3 => CTR => C5: 6,9
* DIS # G9: 5 => CTR => G9: 6,9
* DIS # H8: 6,9 => CTR => H8: 5
* CNT   7 HDP CHAINS /  41 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 # E1: 3 => CTR => E1: 5,9
* PRF E1: 5,9 # E6: 5,9 => SOL
* STA E1: 5,9 + E6: 5,9
* CNT   2 HDP CHAINS /  20 HYP OPENED

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

Details

Positions

.784...........1.....6.....1.....34....7....52.........6.....843...1.........2... initial
6784.1.2.4..2..1...126..4..1.7...3428..72..152..1..8...613..28432.81.7..78...2.31 autosolve
678491523435287196912635478157968342846723915293154867561379284324816759789542631 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
A3: 5,9
G1: 5,9
I1: 3,9
B4: 5,9
D4: 5,9
E4: 6,8
F4: 6,8
G5: 6,9
A7: 5,9
F8: 4,6
D9: 5,9
E9: 4,6
I8: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B2,C2: 3.. / B2 = 3  => 17 pairs (_) / C2 = 3  => 18 pairs (_)
I1,I3: 3.. / I1 = 3  => 13 pairs (_) / I3 = 3  =>  0 pairs (X)
E1,I1: 3.. / E1 = 3  =>  0 pairs (X) / I1 = 3  => 13 pairs (_)
B5,B6: 4.. / B5 = 4  => 14 pairs (_) / B6 = 4  => 15 pairs (_)
C8,C9: 4.. / C8 = 4  => 15 pairs (_) / C9 = 4  => 17 pairs (_)
F8,E9: 4.. / F8 = 4  => 17 pairs (_) / E9 = 4  => 15 pairs (_)
B5,F5: 4.. / B5 = 4  => 14 pairs (_) / F5 = 4  => 15 pairs (_)
C8,F8: 4.. / C8 = 4  => 15 pairs (_) / F8 = 4  => 17 pairs (_)
C9,E9: 4.. / C9 = 4  => 17 pairs (_) / E9 = 4  => 15 pairs (_)
E6,E9: 4.. / E6 = 4  => 17 pairs (_) / E9 = 4  => 15 pairs (_)
H8,G9: 5.. / H8 = 5  => 16 pairs (_) / G9 = 5  =>  0 pairs (X)
E1,G1: 5.. / E1 = 5  =>  0 pairs (X) / G1 = 5  => 16 pairs (_)
B4,D4: 5.. / B4 = 5  => 22 pairs (_) / D4 = 5  => 17 pairs (_)
C8,H8: 5.. / C8 = 5  =>  0 pairs (X) / H8 = 5  => 16 pairs (_)
A3,A7: 5.. / A3 = 5  => 17 pairs (_) / A7 = 5  => 22 pairs (_)
D4,D9: 5.. / D4 = 5  => 17 pairs (_) / D9 = 5  => 22 pairs (_)
G1,G9: 5.. / G1 = 5  => 16 pairs (_) / G9 = 5  =>  0 pairs (X)
H2,I2: 6.. / H2 = 6  => 15 pairs (_) / I2 = 6  => 16 pairs (_)
C5,C6: 6.. / C5 = 6  => 15 pairs (_) / C6 = 6  => 17 pairs (_)
E4,F4: 6.. / E4 = 6  => 15 pairs (_) / F4 = 6  => 17 pairs (_)
F8,E9: 6.. / F8 = 6  => 15 pairs (_) / E9 = 6  => 17 pairs (_)
C5,G5: 6.. / C5 = 6  => 15 pairs (_) / G5 = 6  => 17 pairs (_)
E9,G9: 6.. / E9 = 6  => 17 pairs (_) / G9 = 6  => 15 pairs (_)
E4,E9: 6.. / E4 = 6  => 15 pairs (_) / E9 = 6  => 17 pairs (_)
F4,F8: 6.. / F4 = 6  => 17 pairs (_) / F8 = 6  => 15 pairs (_)
G5,G9: 6.. / G5 = 6  => 17 pairs (_) / G9 = 6  => 15 pairs (_)
H6,I6: 7.. / H6 = 7  => 18 pairs (_) / I6 = 7  => 14 pairs (_)
E7,F7: 7.. / E7 = 7  => 14 pairs (_) / F7 = 7  => 14 pairs (_)
I2,I3: 8.. / I2 = 8  => 15 pairs (_) / I3 = 8  => 13 pairs (_)
E4,F4: 8.. / E4 = 8  => 17 pairs (_) / F4 = 8  => 15 pairs (_)
B4,D4: 9.. / B4 = 9  => 17 pairs (_) / D4 = 9  => 22 pairs (_)
A3,A7: 9.. / A3 = 9  => 22 pairs (_) / A7 = 9  => 17 pairs (_)
D4,D9: 9.. / D4 = 9  => 22 pairs (_) / D9 = 9  => 17 pairs (_)
* DURATION: 0:01:05.786062  START: 04:22:03.889868  END: 04:23:09.675930 2017-05-04
* CP COUNT: (33)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A7,B4,D4,D9,E4,E9,F4,F8,G1,G5,I1,I8)
* 6784.1.2.4..2..1...126..4..1.7...3428..72..152..1..8...613..28432.81.7..78...2.31
* PAIR A3: 5,9 BLK 1
B2: 5,9,3                                # reduction candidate for 5,9
B2: 5,9                                  # 18 pairs
C2: 5,9,3                                # reduction candidate for 5,9
C2: 5,9                                  # 17 pairs
* PAIR A3: 5,9 ROW 3
E3: 5,9,3,7,8                            # reduction candidate for 5,9
E3: 5,9                                  # 17 pairs
F3: 5,9,3,7,8                            # reduction candidate for 5,9
F3: 5,9                                  # 17 pairs
H3: 5,9,7                                # reduction candidate for 5,9
H3: 5,9                                  # 16 pairs
* PAIR G1: 5,9 BLK 3
H2: 5,9,6,7                              # reduction candidate for 5,9
H2: 5,9                                  # 19 pairs
H3: 5,9,7                                # reduction candidate for 5,9
H3: 5,9                                  # 16 pairs
* PAIR G1: 5,9 ROW 1
E1: 5,9,3                                # reduction candidate for 5,9
E1: 3 => CTR
* 6784315294..2..168.126..4731.79863428..72.6152.6145897.613..284329814756784562931
E1: 5,9                                  # 13 pairs
* PAIR G1: 5,9 COL G
G9: 5,9,6                                # reduction candidate for 5,9
G9: 5,9                                  # 17 pairs
G9: 6                                    # 15 pairs
* PAIR I1: 3,9 BLK 3
I3: 3,9,7,8                              # reduction candidate for 3,9
I3: 3,9 => CTR
* 6784.152.4.52..1689126584731579863428..72.6152.614.897.613..284329814756784562931
I3: 7,8                                  # 14 pairs
* PAIR I1: 3,9 ROW 1
E1: 3,9,5                                # reduction candidate for 3,9
E1: 5 => CTR
* 6784519234..2..1565126394..1.75863428..72.6152561438...613.52843258147..784962531
E1: 3,9                                  # 16 pairs
* PAIR B4: 5,9 BLK 4
B6: 5,9,3,4                              # reduction candidate for 5,9
B6: 5,9                                  # 18 pairs
C6: 5,9,3,6                              # reduction candidate for 5,9
C6: 5,9                                  # 18 pairs
* PAIR B4: 5,9 COL B
B2: 5,9,3                                # reduction candidate for 5,9
B2: 5,9                                  # 18 pairs
B2: 3                                    # 17 pairs
* PAIR D4: 5,9 BLK 5
E6: 5,9,3,4                              # reduction candidate for 5,9
E6: 5,9 => SOLVED
* 678491523435287196912635478157968342846723915293154867561379284324816759789542631
E6: 3,4                                  # 14 pairs
F6: 5,9,3,4                              # reduction candidate for 5,9
F6: 5,9                                  # 16 pairs
* PAIR G5: 6,9 BLK 6
H6: 6,9,7                                # reduction candidate for 6,9
H6: 6,9                                  # 14 pairs
I6: 6,9,7                                # reduction candidate for 6,9
I6: 6,9                                  # 18 pairs
* PAIR G5: 6,9 ROW 5
C5: 6,9,3                                # reduction candidate for 6,9
C5: 3 => CTR
* 67845192343.2..1...1263.4..1975863428437296152561438..9613752843258147..784962531
C5: 6,9                                  # 16 pairs
* PAIR G5: 6,9 COL G
G9: 6,9,5                                # reduction candidate for 6,9
G9: 5 => CTR
* 6784519234..2..1565126394..1.75863428..72.6152561438...613.52843258147..784962531
G9: 6,9                                  # 16 pairs
* PAIR A7: 5,9 BLK 7
C8: 5,9,4                                # reduction candidate for 5,9
C8: 5,9                                  # 17 pairs
C9: 5,9,4                                # reduction candidate for 5,9
C9: 5,9                                  # 15 pairs
* PAIR A7: 5,9 ROW 7
E7: 5,9,7                                # reduction candidate for 5,9
E7: 5,9                                  # 14 pairs
F7: 5,9,7                                # reduction candidate for 5,9
F7: 5,9                                  # 14 pairs
* PAIR D9: 5,9 BLK 8
E7: 5,9,7                                # reduction candidate for 5,9
E7: 5,9                                  # 14 pairs
F7: 5,9,7                                # reduction candidate for 5,9
F7: 5,9                                  # 14 pairs
* PAIR D9: 5,9 ROW 9
C9: 5,9,4                                # reduction candidate for 5,9
C9: 5,9                                  # 15 pairs
G9: 5,9,6                                # reduction candidate for 5,9
G9: 5,9                                  # 17 pairs
* PAIR I8: 6,9 BLK 9
H8: 6,9,5                                # reduction candidate for 6,9
H8: 6,9 => CTR
* 6784519234..2..1..5126..4781.758634284.72.6152561438979613752843258147..784.62531
H8: 5                                    # 16 pairs
G9: 6,9,5                                # reduction candidate for 6,9
G9: 6,9                                  # 16 pairs
* PAIR I8: 6,9 COL I
I2: 6,9,7,8                              # reduction candidate for 6,9
I2: 6,9                                  # 15 pairs
I6: 6,9,7                                # reduction candidate for 6,9
I6: 6,9                                  # 18 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-050-base-pr-000.dot
* REASONING
* DIS # E1: 3 => CTR => E1: 5,9
* DIS # I3: 3,9 => CTR => I3: 7,8
* DIS # E1: 5 => CTR => E1: 3,9
* PRF # E6: 5,9 => SOL
* DIS # C5: 3 => CTR => C5: 6,9
* DIS # G9: 5 => CTR => G9: 6,9
* DIS # H8: 6,9 => CTR => H8: 5
* CNT   7 HDP CHAINS /  41 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A7,B4,D4,D9,E4,E9,F4,F8,G1,G5,I1,I8)
* 6784.1.2.4..2..1...126..4..1.7...3428..72..152..1..8...613..28432.81.7..78...2.31
* PAIR A3: 5,9 BLK 1
B2: 5,9,3                                # reduction candidate for 5,9
B2: 5,9                                  # 18 pairs
C2: 5,9,3                                # reduction candidate for 5,9
C2: 5,9                                  # 17 pairs
* PAIR A3: 5,9 ROW 3
E3: 5,9,3,7,8                            # reduction candidate for 5,9
E3: 5,9                                  # 17 pairs
F3: 5,9,3,7,8                            # reduction candidate for 5,9
F3: 5,9                                  # 17 pairs
H3: 5,9,7                                # reduction candidate for 5,9
H3: 5,9                                  # 16 pairs
* PAIR G1: 5,9 BLK 3
H2: 5,9,6,7                              # reduction candidate for 5,9
H2: 5,9                                  # 19 pairs
H3: 5,9,7                                # reduction candidate for 5,9
H3: 5,9                                  # 16 pairs
* PAIR G1: 5,9 ROW 1
E1: 5,9,3                                # reduction candidate for 5,9
E1: 3 => CTR
* 6784315294..2..168.126..4731.79863428..72.6152.6145897.613..284329814756784562931
* PAIR G1: 5,9 COL G
G9: 5,9,6                                # reduction candidate for 5,9
G9: 5,9                                  # 17 pairs
G9: 6                                    # 15 pairs
* PAIR RESTART
* PAIR G1: 5,9 BLK 3
H2: 5,9,6,7                              # reduction candidate for 5,9
H2: 5,9                                  # 19 pairs
H3: 5,9,7                                # reduction candidate for 5,9
H3: 5,9                                  # 16 pairs
* PAIR G1: 5,9 COL G
G9: 5,9,6                                # reduction candidate for 5,9
G9: 5,9                                  # 17 pairs
G9: 6                                    # 15 pairs
* PAIR B4: 5,9 BLK 4
B6: 5,9,3,4                              # reduction candidate for 5,9
B6: 5,9                                  # 18 pairs
C6: 5,9,3,6                              # reduction candidate for 5,9
C6: 5,9                                  # 18 pairs
* PAIR B4: 5,9 COL B
B2: 5,9,3                                # reduction candidate for 5,9
B2: 5,9                                  # 18 pairs
B2: 3                                    # 17 pairs
* PAIR D4: 5,9 BLK 5
E6: 5,9,3,4                              # reduction candidate for 5,9
E6: 5,9 => SOLVED
* 678491523435287196912635478157968342846723915293154867561379284324816759789542631
* DURATION: 0:00:21.618535  START: 04:23:52.106618  END: 04:24:13.725153 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-050-base-pr-001.dot
* REASONING
* DIS # E1: 3 => CTR => E1: 5,9
* PRF E1: 5,9 # E6: 5,9 => SOL
* STA E1: 5,9 + E6: 5,9
* CNT   2 HDP CHAINS /  20 HYP OPENED

Header Info

Top 500 Minimum 17 050

solution: 678491523435287196912635478157968342846723915293154867561379284324816759789542631
info: 1386     FNBTHXY  S8.f     23211

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

Solution

position: 678491523435287196912635478157968342846723915293154867561379284324816759789542631 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:

* INC # B2: 5,9 => UNS
* INC # C2: 5,9 => UNS
* INC # E3: 5,9 => UNS
* INC # F3: 5,9 => UNS
* INC # H3: 5,9 => UNS
* INC # H2: 5,9 => UNS
* INC # H3: 5,9 => UNS
* INC # E1: 5,9 => UNS
* DIS # E1: 3 => CTR => E1: 5,9
* INC # G9: 5,9 => UNS
* INC # G9: 6 => UNS
* DIS # I3: 3,9 => CTR => I3: 7,8
* INC # I3: 7,8 => UNS
* INC # E1: 3,9 => UNS
* DIS # E1: 5 => CTR => E1: 3,9
* INC # B6: 5,9 => UNS
* INC # C6: 5,9 => UNS
* INC # B2: 5,9 => UNS
* INC # B2: 3 => UNS
* PRF # E6: 5,9 => SOL
* INC # E6: 3,4 => UNS
* INC # F6: 5,9 => UNS
* INC # H6: 6,9 => UNS
* INC # I6: 6,9 => UNS
* INC # C5: 6,9 => UNS
* DIS # C5: 3 => CTR => C5: 6,9
* INC # G9: 6,9 => UNS
* DIS # G9: 5 => CTR => G9: 6,9
* INC # C8: 5,9 => UNS
* INC # C9: 5,9 => UNS
* INC # E7: 5,9 => UNS
* INC # F7: 5,9 => UNS
* INC # E7: 5,9 => UNS
* INC # F7: 5,9 => UNS
* INC # C9: 5,9 => UNS
* INC # G9: 5,9 => UNS
* DIS # H8: 6,9 => CTR => H8: 5
* INC # H8: 5 => UNS
* INC # G9: 6,9 => UNS
* INC # I2: 6,9 => UNS
* INC # I6: 6,9 => UNS
* CNT  41 HDP CHAINS /  41 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 5,9 => UNS
* INC # C2: 5,9 => UNS
* INC # E3: 5,9 => UNS
* INC # F3: 5,9 => UNS
* INC # H3: 5,9 => UNS
* INC # H2: 5,9 => UNS
* INC # H3: 5,9 => UNS
* INC # E1: 5,9 => UNS
* DIS # E1: 3 => CTR => E1: 5,9
* INC E1: 5,9 # G9: 5,9 => UNS
* INC E1: 5,9 # G9: 6 => UNS
* INC E1: 5,9 # H2: 5,9 => UNS
* INC E1: 5,9 # H3: 5,9 => UNS
* INC E1: 5,9 # G9: 5,9 => UNS
* INC E1: 5,9 # G9: 6 => UNS
* INC E1: 5,9 # B6: 5,9 => UNS
* INC E1: 5,9 # C6: 5,9 => UNS
* INC E1: 5,9 # B2: 5,9 => UNS
* INC E1: 5,9 # B2: 3 => UNS
* PRF E1: 5,9 # E6: 5,9 => SOL
* STA E1: 5,9 + E6: 5,9
* CNT  20 HDP CHAINS /  20 HYP OPENED