Analysis of xx-top500-094-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .81.........4...5.....2.........18..5......2....3.....64....3..2...5.........7..1 initial

Autosolve

position: .81.........41..5.....2..1......18..5.....12.1..3.....64.1..3..21..5....8....7..1 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D8: 8,9 => CTR => D8: 6
* DIS # H7: 8,9 => CTR => H7: 7
* CNT   2 HDP CHAINS /   7 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 # D8: 8,9 => CTR => D8: 6
* DIS D8: 6 # F7: 2 => CTR => F7: 8,9
* DIS D8: 6 + F7: 8,9 # E5: 8,9 => CTR => E5: 6,7
* DIS D8: 6 + F7: 8,9 + E5: 6,7 # E6: 7 => CTR => E6: 8,9
* PRF D8: 6 + F7: 8,9 + E5: 6,7 + E6: 8,9 # D3: 7,9 => SOL
* STA D8: 6 + F7: 8,9 + E5: 6,7 + E6: 8,9 + D3: 7,9
* CNT   5 HDP CHAINS /   9 HYP OPENED

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

Details

Positions

.81.........4...5.....2.........18..5......2....3.....64....3..2...5.........7..1 initial
.81.........41..5.....2..1......18..5.....12.1..3.....64.1..3..21..5....8....7..1 autosolve
481735296392416758756928413924561837563874129178392645645189372217653984839247561 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
D4: 2,5
F6: 2,5
E7: 8,9
F8: 3,4
E9: 3,4
I7: 2,5
G9: 2,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B2,C2: 2.. / B2 = 2  =>  7 pairs (_) / C2 = 2  =>  7 pairs (_)
G1,I1: 2.. / G1 = 2  => 15 pairs (_) / I1 = 2  =>  0 pairs (X)
D4,F6: 2.. / D4 = 2  =>  0 pairs (X) / F6 = 2  => 15 pairs (_)
F7,D9: 2.. / F7 = 2  =>  0 pairs (X) / D9 = 2  => 15 pairs (_)
I7,G9: 2.. / I7 = 2  => 15 pairs (_) / G9 = 2  =>  0 pairs (X)
F7,I7: 2.. / F7 = 2  =>  0 pairs (X) / I7 = 2  => 15 pairs (_)
D9,G9: 2.. / D9 = 2  => 15 pairs (_) / G9 = 2  =>  0 pairs (X)
D4,D9: 2.. / D4 = 2  =>  0 pairs (X) / D9 = 2  => 15 pairs (_)
F6,F7: 2.. / F6 = 2  => 15 pairs (_) / F7 = 2  =>  0 pairs (X)
G1,G9: 2.. / G1 = 2  => 15 pairs (_) / G9 = 2  =>  0 pairs (X)
I1,I7: 2.. / I1 = 2  =>  0 pairs (X) / I7 = 2  => 15 pairs (_)
F8,E9: 3.. / F8 = 3  => 10 pairs (_) / E9 = 3  =>  0 pairs (X)
C8,F8: 3.. / C8 = 3  =>  0 pairs (X) / F8 = 3  => 10 pairs (_)
E1,E9: 3.. / E1 = 3  => 10 pairs (_) / E9 = 3  =>  0 pairs (X)
H1,H4: 3.. / H1 = 3  =>  0 pairs (X) / H4 = 3  =>  7 pairs (_)
F8,E9: 4.. / F8 = 4  =>  0 pairs (X) / E9 = 4  => 10 pairs (_)
E9,H9: 4.. / E9 = 4  => 10 pairs (_) / H9 = 4  =>  0 pairs (X)
F5,F8: 4.. / F5 = 4  => 10 pairs (_) / F8 = 4  =>  0 pairs (X)
B3,C3: 5.. / B3 = 5  =>  8 pairs (_) / C3 = 5  =>  0 pairs (X)
D1,F1: 5.. / D1 = 5  =>  0 pairs (X) / F1 = 5  => 15 pairs (_)
D4,F6: 5.. / D4 = 5  => 15 pairs (_) / F6 = 5  =>  0 pairs (X)
I7,G9: 5.. / I7 = 5  =>  0 pairs (X) / G9 = 5  => 15 pairs (_)
D4,I4: 5.. / D4 = 5  => 15 pairs (_) / I4 = 5  =>  0 pairs (X)
C7,I7: 5.. / C7 = 5  => 15 pairs (_) / I7 = 5  =>  0 pairs (X)
B3,B9: 5.. / B3 = 5  =>  8 pairs (_) / B9 = 5  =>  0 pairs (X)
D1,D4: 5.. / D1 = 5  =>  0 pairs (X) / D4 = 5  => 15 pairs (_)
F1,F6: 5.. / F1 = 5  => 15 pairs (_) / F6 = 5  =>  0 pairs (X)
G6,G9: 5.. / G6 = 5  =>  0 pairs (X) / G9 = 5  => 15 pairs (_)
D8,D9: 6.. / D8 = 6  => 11 pairs (_) / D9 = 6  =>  0 pairs (X)
D9,H9: 6.. / D9 = 6  =>  0 pairs (X) / H9 = 6  => 11 pairs (_)
C7,C8: 7.. / C7 = 7  =>  0 pairs (X) / C8 = 7  => 11 pairs (_)
C7,H7: 7.. / C7 = 7  =>  0 pairs (X) / H7 = 7  => 11 pairs (_)
I2,I3: 8.. / I2 = 8  =>  7 pairs (_) / I3 = 8  =>  9 pairs (_)
C5,C6: 8.. / C5 = 8  => 12 pairs (_) / C6 = 8  =>  7 pairs (_)
H7,H8: 8.. / H7 = 8  =>  0 pairs (X) / H8 = 8  =>  9 pairs (_)
F2,I2: 8.. / F2 = 8  =>  9 pairs (_) / I2 = 8  =>  7 pairs (_)
C6,E6: 8.. / C6 = 8  =>  7 pairs (_) / E6 = 8  => 12 pairs (_)
D8,H8: 8.. / D8 = 8  =>  0 pairs (X) / H8 = 8  =>  9 pairs (_)
* DURATION: 0:00:57.521279  START: 05:59:49.621148  END: 06:00:47.142427 2017-05-04
* CP COUNT: (38)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D4,E7,E9,F6,F8,G9,I7)
* .81.........41..5.....2..1......18..5.....12.1..3.....64.1..3..21..5....8....7..1
* PAIR E7: 8,9 BLK 8
F7: 8,9,2                                # reduction candidate for 8,9
F7: 8,9                                  # 15 pairs
D8: 8,9,6                                # reduction candidate for 8,9
D8: 8,9 => CTR
* .81.....2...41..5.....2..1....2.18.55.....12.1..3.....64.1..3..21..5....8..6.72.1
D8: 6                                    # 11 pairs
* PAIR E7: 8,9 ROW 7
H7: 8,9,7                                # reduction candidate for 8,9
H7: 8,9 => CTR
* .81.........41..5.....2..1......18..5.....12.1..3.....6471..3.521..5....8....72.1
H7: 7                                    # 11 pairs
* PAIR E7: 8,9 COL E
E5: 8,9,4,6,7                            # reduction candidate for 8,9
E5: 8,9                                  #  8 pairs
E6: 8,9,4,6,7                            # reduction candidate for 8,9
E6: 8,9                                  #  8 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-094-base-pr-000.dot
* REASONING
* DIS # D8: 8,9 => CTR => D8: 6
* DIS # H7: 8,9 => CTR => H7: 7
* CNT   2 HDP CHAINS /   7 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D4,E7,E9,F6,F8,G9,I7)
* .81.........41..5.....2..1......18..5.....12.1..3.....64.1..3..21..5....8....7..1
* PAIR E7: 8,9 BLK 8
F7: 8,9,2                                # reduction candidate for 8,9
F7: 8,9                                  # 15 pairs
D8: 8,9,6                                # reduction candidate for 8,9
D8: 8,9 => CTR
* .81.....2...41..5.....2..1....2.18.55.....12.1..3.....64.1..3..21..5....8..6.72.1
* RESTART
* PAIR E7: 8,9 BLK 8
F7: 8,9,2                                # reduction candidate for 8,9
F7: 2 => CTR
* .81.3.......41..5.....2..1......183.5....412.1..3.....64.1823.521.653.8.8..947.61
* PAIR E7: 8,9 COL E
E5: 8,9,6,7                              # reduction candidate for 8,9
E5: 8,9 => CTR
* 481735296...41.75.75..2..1....56183.5....412.1983726456451..372217653.84839247561
E6: 8,9,7                                # reduction candidate for 8,9
E6: 8,9                                  # 18 pairs
* RESTART
* PAIR E7: 8,9 COL E
E6: 8,9,7                                # reduction candidate for 8,9
E6: 7 => CTR
* 481735296...41.75.75.92.4139..5.183.5..8.412.1.8372645645189372217653.848..247561
* PAIR RESTART

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A4,B9,C9,D1,D5,E4,E5,E6,E7,F7,G2,G8,H1,H6,I2,I3,I5,I8)
* .81.352.6...41..5..5..2..1....5.183.5....412.17.3.26.56451..372217653.8.8..247561
* PAIR D1: 7,9 BLK 2
D3: 7,9,8                                # reduction candidate for 7,9
D3: 7,9 => SOLVED
* 481735296392416758756928413924561837563874129178392645645189372217653984839247561
* DURATION: 0:00:12.552672  START: 06:00:53.684394  END: 06:01:06.237066 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-094-base-pr-001.dot
* REASONING
* DIS # D8: 8,9 => CTR => D8: 6
* DIS D8: 6 # F7: 2 => CTR => F7: 8,9
* DIS D8: 6 + F7: 8,9 # E5: 8,9 => CTR => E5: 6,7
* DIS D8: 6 + F7: 8,9 + E5: 6,7 # E6: 7 => CTR => E6: 8,9
* PRF D8: 6 + F7: 8,9 + E5: 6,7 + E6: 8,9 # D3: 7,9 => SOL
* STA D8: 6 + F7: 8,9 + E5: 6,7 + E6: 8,9 + D3: 7,9
* CNT   5 HDP CHAINS /   9 HYP OPENED

Header Info

Top 500 Minimum 17 094

solution: 481735296392416758756928413924561837563874129178392645645189372217653984839247561
info: 1572     FNBTHXY  S8.f     39264

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

Solution

position: 481735296392416758756928413924561837563874129178392645645189372217653984839247561 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 # F7: 8,9 => UNS
* DIS # D8: 8,9 => CTR => D8: 6
* INC # D8: 6 => UNS
* DIS # H7: 8,9 => CTR => H7: 7
* INC # H7: 7 => UNS
* INC # E5: 8,9 => UNS
* INC # E6: 8,9 => UNS
* CNT   7 HDP CHAINS /   7 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F7: 8,9 => UNS
* DIS # D8: 8,9 => CTR => D8: 6
* INC D8: 6 # F7: 8,9 => UNS
* DIS D8: 6 # F7: 2 => CTR => F7: 8,9
* DIS D8: 6 + F7: 8,9 # E5: 8,9 => CTR => E5: 6,7
* INC D8: 6 + F7: 8,9 + E5: 6,7 # E6: 8,9 => UNS
* INC D8: 6 + F7: 8,9 + E5: 6,7 # E6: 8,9 => UNS
* DIS D8: 6 + F7: 8,9 + E5: 6,7 # E6: 7 => CTR => E6: 8,9
* PRF D8: 6 + F7: 8,9 + E5: 6,7 + E6: 8,9 # D3: 7,9 => SOL
* STA D8: 6 + F7: 8,9 + E5: 6,7 + E6: 8,9 + D3: 7,9
* CNT   9 HDP CHAINS /   9 HYP OPENED