Analysis of xx-top500-494-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .6.41..7.......3.....6.....2...53....7.....6.........13.5...2..8..7.............. initial

Autosolve

position: 963412875.825..3.675.638..22.6.537...7.2...63.3.....213.5...2.78..7.563.6.73...5. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # H3: 1,4 => CTR => H3: 9
* PRF # C8: 9 => SOL
* DIS # H3: 1,4 => CTR => H3: 9
* PRF # G6: 9 => SOL
* DIS # B4: 4 => CTR => B4: 1,9
* PRF # C6: 4 => SOL
* DIS # D7: 1 => CTR => D7: 8,9
* DIS # G6: 4 => CTR => G6: 5,9
* DIS # B8: 4,9 => CTR => B8: 1,2
* DIS # B9: 4,9 => CTR => B9: 2
* DIS # B4: 1 => CTR => B4: 4,9
* DIS # G9: 4,9 => CTR => G9: 1
* DIS # B8: 4,9 => CTR => B8: 1,2
* DIS # E8: 4,9 => CTR => E8: 2
* CNT  14 HDP CHAINS /  47 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 # H3: 1,4 => CTR => H3: 9
* PRF H3: 9 # C8: 9 => SOL
* STA H3: 9 + C8: 9
* CNT   2 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

.6.41..7.......3.....6.....2...53....7.....6.........13.5...2..8..7.............. initial
963412875.825..3.675.638..22.6.537...7.2...63.3.....213.5...2.78..7.563.6.73...5. autosolve
963412875482597316751638492296153748178249563534876921345961287819725634627384159 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
A2: 1,4
C3: 1,4
E2: 7,9
F2: 7,9
H2: 1,4
A5: 1,5
A6: 4,5
D4: 1,9
D6: 8,9
E6: 6,7
F6: 6,7
G5: 5,9
B7: 4,9
I8: 4,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A2,C3: 1.. / A2 = 1  =>  0 pairs (X) / C3 = 1  => 15 pairs (_)
D4,F5: 1.. / D4 = 1  => 17 pairs (_) / F5 = 1  =>  0 pairs (X)
B8,C8: 1.. / B8 = 1  => 17 pairs (_) / C8 = 1  =>  0 pairs (X)
H7,G9: 1.. / H7 = 1  =>  0 pairs (X) / G9 = 1  => 16 pairs (_)
A2,H2: 1.. / A2 = 1  =>  0 pairs (X) / H2 = 1  => 15 pairs (_)
B4,D4: 1.. / B4 = 1  =>  0 pairs (X) / D4 = 1  => 17 pairs (_)
F9,G9: 1.. / F9 = 1  =>  0 pairs (X) / G9 = 1  => 16 pairs (_)
A2,A5: 1.. / A2 = 1  =>  0 pairs (X) / A5 = 1  => 15 pairs (_)
B4,B8: 1.. / B4 = 1  =>  0 pairs (X) / B8 = 1  => 17 pairs (_)
D4,D7: 1.. / D4 = 1  => 17 pairs (_) / D7 = 1  =>  0 pairs (X)
G3,G9: 1.. / G3 = 1  =>  0 pairs (X) / G9 = 1  => 16 pairs (_)
B8,B9: 2.. / B8 = 2  =>  0 pairs (X) / B9 = 2  => 14 pairs (_)
E8,E9: 2.. / E8 = 2  => 14 pairs (_) / E9 = 2  =>  0 pairs (X)
B8,E8: 2.. / B8 = 2  =>  0 pairs (X) / E8 = 2  => 14 pairs (_)
B9,E9: 2.. / B9 = 2  => 14 pairs (_) / E9 = 2  =>  0 pairs (X)
A2,C3: 4.. / A2 = 4  => 15 pairs (_) / C3 = 4  =>  0 pairs (X)
E5,F5: 4.. / E5 = 4  => 17 pairs (_) / F5 = 4  => 18 pairs (_)
A2,H2: 4.. / A2 = 4  => 15 pairs (_) / H2 = 4  =>  0 pairs (X)
A2,A6: 4.. / A2 = 4  => 15 pairs (_) / A6 = 4  =>  0 pairs (X)
A5,A6: 5.. / A5 = 5  =>  0 pairs (X) / A6 = 5  => 15 pairs (_)
G5,G6: 5.. / G5 = 5  => 15 pairs (_) / G6 = 5  =>  0 pairs (X)
A5,G5: 5.. / A5 = 5  =>  0 pairs (X) / G5 = 5  => 15 pairs (_)
A6,G6: 5.. / A6 = 5  => 15 pairs (_) / G6 = 5  =>  0 pairs (X)
E6,F6: 6.. / E6 = 6  => 12 pairs (_) / F6 = 6  => 12 pairs (_)
E7,F7: 6.. / E7 = 6  => 12 pairs (_) / F7 = 6  => 12 pairs (_)
E6,E7: 6.. / E6 = 6  => 12 pairs (_) / E7 = 6  => 12 pairs (_)
F6,F7: 6.. / F6 = 6  => 12 pairs (_) / F7 = 6  => 12 pairs (_)
E2,F2: 7.. / E2 = 7  => 12 pairs (_) / F2 = 7  => 12 pairs (_)
E6,F6: 7.. / E6 = 7  => 12 pairs (_) / F6 = 7  => 12 pairs (_)
E2,E6: 7.. / E2 = 7  => 12 pairs (_) / E6 = 7  => 12 pairs (_)
F2,F6: 7.. / F2 = 7  => 12 pairs (_) / F6 = 7  => 12 pairs (_)
C5,C6: 8.. / C5 = 8  => 16 pairs (_) / C6 = 8  => 19 pairs (_)
E5,D6: 8.. / E5 = 8  => 19 pairs (_) / D6 = 8  => 16 pairs (_)
H4,I4: 8.. / H4 = 8  => 15 pairs (_) / I4 = 8  => 20 pairs (_)
H7,I9: 8.. / H7 = 8  => 20 pairs (_) / I9 = 8  => 15 pairs (_)
C5,E5: 8.. / C5 = 8  => 16 pairs (_) / E5 = 8  => 19 pairs (_)
C6,D6: 8.. / C6 = 8  => 19 pairs (_) / D6 = 8  => 16 pairs (_)
E9,I9: 8.. / E9 = 8  => 20 pairs (_) / I9 = 8  => 15 pairs (_)
D6,D7: 8.. / D6 = 8  => 16 pairs (_) / D7 = 8  => 19 pairs (_)
H4,H7: 8.. / H4 = 8  => 15 pairs (_) / H7 = 8  => 20 pairs (_)
I4,I9: 8.. / I4 = 8  => 20 pairs (_) / I9 = 8  => 15 pairs (_)
E2,F2: 9.. / E2 = 9  => 12 pairs (_) / F2 = 9  => 12 pairs (_)
G3,H3: 9.. / G3 = 9  =>  0 pairs (X) / H3 = 9  => 16 pairs (_)
* DURATION: 0:01:19.059883  START: 19:32:42.104480  END: 19:34:01.164363 2017-05-04
* CP COUNT: (43)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,A6,B7,C3,D4,D6,E2,E6,F2,F6,G5,H2,I8)
* 963412875.825..3.675.638..22.6.537...7.2...63.3.....213.5...2.78..7.563.6.73...5.
* PAIR C3: 1,4 ROW 3
G3: 1,4,9                                # reduction candidate for 1,4
G3: 1,4                                  # 16 pairs
H3: 1,4,9                                # reduction candidate for 1,4
H3: 1,4 => CTR
* 9634128754825..3167516389422461537..17.2..56353....4213958..2.78..7.563.6.73..15.
H3: 9                                    # 16 pairs
* PAIR C3: 1,4 COL C
C8: 1,4,9                                # reduction candidate for 1,4
C8: 9 => SOLVED
* 963412875482597316751638492296153748178249563534876921345961287819725634627384159
C8: 1,4                                  # 19 pairs
* PAIR H2: 1,4 BLK 3
G3: 1,4,9                                # reduction candidate for 1,4
G3: 1,4                                  # 16 pairs
H3: 1,4,9                                # reduction candidate for 1,4
H3: 1,4 => CTR
* 9634128754825..3167516389422461537..17.2..56353....4213958..2.78..7.563.6.73..15.
H3: 9                                    # 16 pairs
* PAIR H2: 1,4 COL H
H7: 1,4,8,9                              # reduction candidate for 1,4
H7: 8,9                                  # 18 pairs
H7: 1,4                                  # 17 pairs
* PAIR A6: 4,5 ROW 6
G6: 4,5,9                                # reduction candidate for 4,5
G6: 9 => SOLVED
* 963412875482597316751638492296153748178249563534876921345961287819725634627384159
G6: 4,5                                  # 16 pairs
* PAIR D4: 1,9 BLK 5
F5: 1,9,4                                # reduction candidate for 1,9
F5: 4                                    # 18 pairs
F5: 1,9                                  # 17 pairs
* PAIR D4: 1,9 ROW 4
B4: 1,9,4                                # reduction candidate for 1,9
B4: 4 => CTR
* 963412875.825..3.675.638..22461537...7.2...6353....4213958..2.78147256396.73...5.
B4: 1,9                                  # 21 pairs
* PAIR D4: 1,9 COL D
D7: 1,9,8                                # reduction candidate for 1,9
D7: 8                                    # 19 pairs
D7: 1,9                                  # 16 pairs
* PAIR D6: 8,9 BLK 5
E5: 8,9,4                                # reduction candidate for 8,9
E5: 8,9                                  # 18 pairs
E5: 4                                    # 17 pairs
* PAIR D6: 8,9 ROW 6
C6: 8,9,4                                # reduction candidate for 8,9
C6: 4 => SOLVED
* 963412875482597316751638492296153748178249563534876921345961287819725634627384159
C6: 8,9                                  # 16 pairs
* PAIR D6: 8,9 COL D
D7: 8,9,1                                # reduction candidate for 8,9
D7: 1 => CTR
* 963412875.825..3.675.638..22169537..5782419634398..5213.51..2.78.17.563.6.73..15.
D7: 8,9                                  # 17 pairs
* PAIR G5: 5,9 BLK 6
G6: 5,9,4                                # reduction candidate for 5,9
G6: 4 => CTR
* 9634128754825..3167516389422461537..17.2..56353....4213958..2.78..7.563.6.73...5.
G6: 5,9                                  # 21 pairs
* PAIR B7: 4,9 BLK 7
B8: 4,9,1,2                              # reduction candidate for 4,9
B8: 4,9 => CTR
* 963412875.825..3.675.638..22169537..57.2.19634398..5213.51..2.78.172563.6273..15.
B8: 1,2                                  # 15 pairs
C8: 4,9,1                                # reduction candidate for 4,9
C8: 4,9                                  # 17 pairs
B9: 4,9,2                                # reduction candidate for 4,9
B9: 4,9 => CTR
* 9634128751825..346754638..221695378457.2.1963.3.....213.5...2.78217.563.6.732..58
B9: 2                                    # 14 pairs
* PAIR B7: 4,9 ROW 7
E7: 4,9,6,8                              # reduction candidate for 4,9
E7: 4,9                                  # 16 pairs
F7: 4,9,1,6                              # reduction candidate for 4,9
F7: 4,9                                  # 16 pairs
H7: 4,9,1,8                              # reduction candidate for 4,9
H7: 4,9                                  # 23 pairs
* PAIR B7: 4,9 COL B
B4: 4,9,1                                # reduction candidate for 4,9
B4: 1 => CTR
* 963412875.825..3.675.638..22169537..57.2.19634398..5213.51..2.78.17.563.6.73..15.
B4: 4,9                                  # 17 pairs
* PAIR I8: 4,9 BLK 9
H7: 4,9,1,8                              # reduction candidate for 4,9
H7: 4,9                                  # 23 pairs
G9: 4,9,1                                # reduction candidate for 4,9
G9: 4,9 => CTR
* 9634128751825..3467546381922.615378.5712849634389..5213.58..2178197256346.73.1.58
G9: 1                                    # 16 pairs
I9: 4,9,8                                # reduction candidate for 4,9
I9: 4,9                                  # 20 pairs
* PAIR I8: 4,9 ROW 8
B8: 4,9,1,2                              # reduction candidate for 4,9
B8: 4,9 => CTR
* 963412875.825..3.675.638..22169537..57.2.19634398..5213.51..2.78.172563.6273..15.
B8: 1,2                                  # 15 pairs
C8: 4,9,1                                # reduction candidate for 4,9
C8: 4,9                                  # 17 pairs
E8: 4,9,2                                # reduction candidate for 4,9
E8: 4,9 => CTR
* 9634128751825..346754638..221695378457.2.1963.3.....213.5...2.78217.563.6.732..58
E8: 2                                    # 14 pairs
* PAIR I8: 4,9 COL I
I4: 4,9,8                                # reduction candidate for 4,9
I4: 8                                    # 20 pairs
I4: 4,9                                  # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-494-base-pr-000.dot
* REASONING
* DIS # H3: 1,4 => CTR => H3: 9
* PRF # C8: 9 => SOL
* DIS # H3: 1,4 => CTR => H3: 9
* PRF # G6: 9 => SOL
* DIS # B4: 4 => CTR => B4: 1,9
* PRF # C6: 4 => SOL
* DIS # D7: 1 => CTR => D7: 8,9
* DIS # G6: 4 => CTR => G6: 5,9
* DIS # B8: 4,9 => CTR => B8: 1,2
* DIS # B9: 4,9 => CTR => B9: 2
* DIS # B4: 1 => CTR => B4: 4,9
* DIS # G9: 4,9 => CTR => G9: 1
* DIS # B8: 4,9 => CTR => B8: 1,2
* DIS # E8: 4,9 => CTR => E8: 2
* CNT  14 HDP CHAINS /  47 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,A6,B7,C3,D4,D6,E2,E6,F2,F6,G5,H2,I8)
* 963412875.825..3.675.638..22.6.537...7.2...63.3.....213.5...2.78..7.563.6.73...5.
* PAIR C3: 1,4 ROW 3
G3: 1,4,9                                # reduction candidate for 1,4
G3: 1,4                                  # 16 pairs
H3: 1,4,9                                # reduction candidate for 1,4
H3: 1,4 => CTR
* 9634128754825..3167516389422461537..17.2..56353....4213958..2.78..7.563.6.73..15.
* RESTART
* PAIR C3: 1,4 COL C
C8: 1,4,9                                # reduction candidate for 1,4
C8: 9 => SOLVED
* 963412875482597316751638492296153748178249563534876921345961287819725634627384159
* DURATION: 0:00:05.216425  START: 19:34:47.777368  END: 19:34:52.993793 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-494-base-pr-001.dot
* REASONING
* DIS # H3: 1,4 => CTR => H3: 9
* PRF H3: 9 # C8: 9 => SOL
* STA H3: 9 + C8: 9
* CNT   2 HDP CHAINS /   4 HYP OPENED

Header Info

Top 500 Minimum 17 494

solution: 963412875482597316751638492296153748178249563534876921345961287819725634627384159
info: 96272    FNBHYK   S8.f     21504

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

Solution

position: 963412875482597316751638492296153748178249563534876921345961287819725634627384159 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 # G3: 1,4 => UNS
* DIS # H3: 1,4 => CTR => H3: 9
* INC # H3: 9 => UNS
* INC # C8: 1,4 => UNS
* PRF # C8: 9 => SOL
* INC # G3: 1,4 => UNS
* DIS # H3: 1,4 => CTR => H3: 9
* INC # H3: 9 => UNS
* INC # H7: 1,4 => UNS
* INC # H7: 8,9 => UNS
* INC # G6: 4,5 => UNS
* PRF # G6: 9 => SOL
* INC # F5: 1,9 => UNS
* INC # F5: 4 => UNS
* INC # B4: 1,9 => UNS
* DIS # B4: 4 => CTR => B4: 1,9
* INC # D7: 1,9 => UNS
* INC # D7: 8 => UNS
* INC # E5: 8,9 => UNS
* INC # E5: 4 => UNS
* INC # C6: 8,9 => UNS
* PRF # C6: 4 => SOL
* INC # D7: 8,9 => UNS
* DIS # D7: 1 => CTR => D7: 8,9
* INC # G6: 5,9 => UNS
* DIS # G6: 4 => CTR => G6: 5,9
* DIS # B8: 4,9 => CTR => B8: 1,2
* INC # B8: 1,2 => UNS
* INC # C8: 4,9 => UNS
* DIS # B9: 4,9 => CTR => B9: 2
* INC # B9: 2 => UNS
* INC # E7: 4,9 => UNS
* INC # F7: 4,9 => UNS
* INC # H7: 4,9 => UNS
* INC # B4: 4,9 => UNS
* DIS # B4: 1 => CTR => B4: 4,9
* INC # H7: 4,9 => UNS
* DIS # G9: 4,9 => CTR => G9: 1
* INC # G9: 1 => UNS
* INC # I9: 4,9 => UNS
* DIS # B8: 4,9 => CTR => B8: 1,2
* INC # B8: 1,2 => UNS
* INC # C8: 4,9 => UNS
* DIS # E8: 4,9 => CTR => E8: 2
* INC # E8: 2 => UNS
* INC # I4: 4,9 => UNS
* INC # I4: 8 => UNS
* CNT  47 HDP CHAINS /  47 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G3: 1,4 => UNS
* DIS # H3: 1,4 => CTR => H3: 9
* INC H3: 9 # C8: 1,4 => UNS
* PRF H3: 9 # C8: 9 => SOL
* STA H3: 9 + C8: 9
* CNT   4 HDP CHAINS /   4 HYP OPENED