Analysis of xx-top500-053-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ......52.8..1.....2.....7...53....6....4....1.7..8........5.3..4..6.............. initial

Autosolve

position: 3178..52.8.51....324.5.37189537..8646..4359711749862357..25.3..43.6..15.5..3..... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # C7: 6,9 => SOL
* PRF # E1: 4,9 => SOL
* DIS # E1: 6 => CTR => E1: 4,9
* PRF # F9: 4,9 => SOL
* DIS # E1: 6,9 => CTR => E1: 4
* PRF # E1: 4 => SOL
* DIS # E1: 6,9 => CTR => E1: 4
* PRF # E1: 4 => SOL
* DIS # H9: 4,9 => CTR => H9: 8
* DIS # C9: 2,8 => CTR => C9: 1,6,9
* PRF # E9: 7,9 => SOL
* PRF # C7: 6,9 => SOL
* CNT  12 HDP CHAINS /  29 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # C7: 6,9 => SOL
* STA C7: 6,9
* CNT   1 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

......52.8..1.....2.....7...53....6....4....1.7..8........5.3..4..6.............. initial
3178..52.8.51....324.5.37189537..8646..4359711749862357..25.3..43.6..15.5..3..... autosolve
317849526865127493249563718953712864628435971174986235786251349432698157591374682 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (18)
B2: 6,9
C3: 6,9
F1: 4,9
E2: 2,7
F2: 2,7
E3: 6,9
I1: 6,9
G2: 4,6
H2: 4,9
B5: 2,8
C5: 2,8
E4: 1,2
F4: 1,2
E8: 7,9
I7: 6,9
I8: 2,7
G9: 4,6
I9: 2,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E4,F4: 1.. / E4 = 1  => 15 pairs (_) / F4 = 1  =>  0 pairs (X)
C7,C9: 1.. / C7 = 1  => 18 pairs (_) / C9 = 1  =>  0 pairs (*)
C7,F7: 1.. / C7 = 1  => 18 pairs (_) / F7 = 1  =>  0 pairs (*)
E4,E9: 1.. / E4 = 1  => 15 pairs (_) / E9 = 1  =>  0 pairs (X)
E2,F2: 2.. / E2 = 2  => 15 pairs (_) / F2 = 2  =>  0 pairs (X)
B5,C5: 2.. / B5 = 2  => 17 pairs (_) / C5 = 2  => 18 pairs (_)
E4,F4: 2.. / E4 = 2  =>  0 pairs (X) / F4 = 2  => 15 pairs (_)
I8,I9: 2.. / I8 = 2  => 17 pairs (_) / I9 = 2  =>  0 pairs (*)
C8,I8: 2.. / C8 = 2  =>  0 pairs (*) / I8 = 2  =>  0 pairs (X)
B5,B9: 2.. / B5 = 2  => 17 pairs (_) / B9 = 2  => 18 pairs (_)
E2,E4: 2.. / E2 = 2  => 15 pairs (_) / E4 = 2  =>  0 pairs (X)
F2,F4: 2.. / F2 = 2  =>  0 pairs (X) / F4 = 2  => 15 pairs (_)
E1,F1: 4.. / E1 = 4  =>  0 pairs (*) / F1 = 4  =>  0 pairs (X)
G2,H2: 4.. / G2 = 4  =>  0 pairs (*) / H2 = 4  =>  0 pairs (X)
F7,H7: 4.. / F7 = 4  =>  0 pairs (X) / H7 = 4  =>  0 pairs (_)
E1,E9: 4.. / E1 = 4  =>  0 pairs (*) / E9 = 4  =>  0 pairs (X)
G2,G9: 4.. / G2 = 4  =>  0 pairs (*) / G9 = 4  =>  0 pairs (X)
B2,C3: 6.. / B2 = 6  =>  0 pairs (*) / C3 = 6  =>  0 pairs (X)
E1,E3: 6.. / E1 = 6  =>  0 pairs (X) / E3 = 6  =>  0 pairs (_)
I1,G2: 6.. / I1 = 6  =>  0 pairs (*) / G2 = 6  =>  0 pairs (X)
I7,G9: 6.. / I7 = 6  =>  0 pairs (X) / G9 = 6  =>  0 pairs (_)
E1,I1: 6.. / E1 = 6  =>  0 pairs (X) / I1 = 6  =>  0 pairs (_)
B2,G2: 6.. / B2 = 6  =>  0 pairs (*) / G2 = 6  =>  0 pairs (X)
C3,E3: 6.. / C3 = 6  =>  0 pairs (X) / E3 = 6  =>  0 pairs (_)
G2,G9: 6.. / G2 = 6  =>  0 pairs (X) / G9 = 6  =>  0 pairs (_)
I1,I7: 6.. / I1 = 6  =>  0 pairs (*) / I7 = 6  =>  0 pairs (X)
E2,F2: 7.. / E2 = 7  =>  0 pairs (X) / F2 = 7  => 15 pairs (_)
I8,I9: 7.. / I8 = 7  =>  0 pairs (*) / I9 = 7  =>  0 pairs (X)
B5,C5: 8.. / B5 = 8  => 18 pairs (_) / C5 = 8  => 17 pairs (_)
H7,H9: 8.. / H7 = 8  =>  0 pairs (X) / H9 = 8  => 20 pairs (_)
C8,F8: 8.. / C8 = 8  => 20 pairs (_) / F8 = 8  => 19 pairs (_)
B2,C3: 9.. / B2 = 9  =>  0 pairs (X) / C3 = 9  =>  0 pairs (_)
I1,H2: 9.. / I1 = 9  =>  0 pairs (X) / H2 = 9  =>  0 pairs (_)
B2,H2: 9.. / B2 = 9  =>  0 pairs (X) / H2 = 9  =>  0 pairs (_)
C3,E3: 9.. / C3 = 9  =>  0 pairs (*) / E3 = 9  =>  0 pairs (X)
I1,I7: 9.. / I1 = 9  =>  0 pairs (X) / I7 = 9  =>  0 pairs (_)
* DURATION: 0:01:16.170308  START: 04:28:10.228915  END: 04:29:26.399223 2017-05-04
* CP COUNT: (36)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B5,C3,C5,E2,E3,E4,E8,F1,F2,F4,G2,G9,H2,I1,I7,I8,I9)
* 3178..52.8.51....324.5.37189537..8646..4359711749862357..25.3..43.6..15.5..3.....
* PAIR B2: 6,9 COL B
B7: 6,9,8                                # reduction candidate for 6,9
B7: 6,9                                  # 22 pairs
B9: 6,9,2,8                              # reduction candidate for 6,9
B9: 6,9                                  # 21 pairs
* PAIR C3: 6,9 COL C
C7: 6,9,1,8                              # reduction candidate for 6,9
C7: 6,9 => SOLVED
* 317849526865127493249563718953712864628435971174986235786251349432698157591374682
C7: 1,8                                  # 19 pairs
C9: 6,9,1,2,8                            # reduction candidate for 6,9
C9: 6,9                                  # 21 pairs
* PAIR F1: 4,9 BLK 2
E1: 4,9,6                                # reduction candidate for 4,9
E1: 4,9 => SOLVED
* 317849526865127493249563718953712864628435971174986235786251349432698157591374682
E1: 6 => CTR
* 3178645298951..6432465937189537..8646..4359711749862357..25.3.643.67.15256234....
* PAIR F1: 4,9 COL F
F7: 4,9,1,8                              # reduction candidate for 4,9
F7: 4,9                                  # 20 pairs
F9: 4,9,1,7,8                            # reduction candidate for 4,9
F9: 4,9 => SOLVED
* 317849526865127493249563718953712864628435971174986235786251349432698157591374682
F9: 1,7,8                                # 18 pairs
* PAIR E3: 6,9 BLK 2
E1: 6,9,4                                # reduction candidate for 6,9
E1: 6,9 => CTR
* 3178.45268651..4932495637189537128646..4359711749862357.625134943.6.815.59134768.
E1: 4 => SOLVED
* 317849526865127493249563718953712864628435971174986235786251349432698157591374682
* PAIR I1: 6,9 ROW 1
E1: 6,9,4                                # reduction candidate for 6,9
E1: 6,9 => CTR
* 3178.45268651..4932495637189537128646..4359711749862357.625134943.6.815.59134768.
E1: 4 => SOLVED
* 317849526865127493249563718953712864628435971174986235786251349432698157591374682
* PAIR H2: 4,9 COL H
H7: 4,9,8                                # reduction candidate for 4,9
H7: 4,9                                  # 20 pairs
H9: 4,9,8                                # reduction candidate for 4,9
H9: 4,9 => CTR
* 3178495268651..4932495.37189537..8646..4359711749862357..25438.43.6..15.5..3.....
H9: 8                                    # 20 pairs
* PAIR B5: 2,8 COL B
B9: 2,8,6,9                              # reduction candidate for 2,8
B9: 2,8                                  # 22 pairs
B9: 6,9                                  # 21 pairs
* PAIR C5: 2,8 COL C
C8: 2,8,9                                # reduction candidate for 2,8
C8: 2,8                                  # 19 pairs
C9: 2,8,1,6,9                            # reduction candidate for 2,8
C9: 2,8 => CTR
* 3178645298951276432465937189537128646..4359711749862357.12593864396781525..3....7
C9: 1,6,9                                # 18 pairs
* PAIR E8: 7,9 BLK 8
F8: 7,9,8                                # reduction candidate for 7,9
F8: 7,9                                  # 20 pairs
E9: 7,9,1,4                              # reduction candidate for 7,9
E9: 7,9 => SOLVED
* 317849526865127493249563718953712864628435971174986235786251349432698157591374682
E9: 1,4                                  # 19 pairs
F9: 7,9,1,4,8                            # reduction candidate for 7,9
F9: 7,9                                  # 22 pairs
* PAIR I7: 6,9 ROW 7
B7: 6,9,8                                # reduction candidate for 6,9
B7: 6,9                                  # 22 pairs
C7: 6,9,1,8                              # reduction candidate for 6,9
C7: 6,9 => SOLVED
* 317849526865127493249563718953712864628435971174986235786251349432698157591374682
C7: 1,8                                  # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-053-base-pr-000.dot
* REASONING
* PRF # C7: 6,9 => SOL
* PRF # E1: 4,9 => SOL
* DIS # E1: 6 => CTR => E1: 4,9
* PRF # F9: 4,9 => SOL
* DIS # E1: 6,9 => CTR => E1: 4
* PRF # E1: 4 => SOL
* DIS # E1: 6,9 => CTR => E1: 4
* PRF # E1: 4 => SOL
* DIS # H9: 4,9 => CTR => H9: 8
* DIS # C9: 2,8 => CTR => C9: 1,6,9
* PRF # E9: 7,9 => SOL
* PRF # C7: 6,9 => SOL
* CNT  12 HDP CHAINS /  29 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B5,C3,C5,E2,E3,E4,E8,F1,F2,F4,G2,G9,H2,I1,I7,I8,I9)
* 3178..52.8.51....324.5.37189537..8646..4359711749862357..25.3..43.6..15.5..3.....
* PAIR B2: 6,9 COL B
B7: 6,9,8                                # reduction candidate for 6,9
B7: 6,9                                  # 22 pairs
B9: 6,9,2,8                              # reduction candidate for 6,9
B9: 6,9                                  # 21 pairs
* PAIR C3: 6,9 COL C
C7: 6,9,1,8                              # reduction candidate for 6,9
C7: 6,9 => SOLVED
* 317849526865127493249563718953712864628435971174986235786251349432698157591374682
* DURATION: 0:00:04.609826  START: 04:30:03.555755  END: 04:30:08.165581 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-053-base-pr-001.dot
* REASONING
* PRF # C7: 6,9 => SOL
* STA C7: 6,9
* CNT   1 HDP CHAINS /   3 HYP OPENED

Header Info

Top 500 Minimum 17 053

solution: 317849526865127493249563718953712864628435971174986235786251349432698157591374682
info: 1398     FNBTHWXY S8.f     1399

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

Solution

position: 317849526865127493249563718953712864628435971174986235786251349432698157591374682 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 # B7: 6,9 => UNS
* INC # B9: 6,9 => UNS
* PRF # C7: 6,9 => SOL
* INC # C7: 1,8 => UNS
* INC # C9: 6,9 => UNS
* PRF # E1: 4,9 => SOL
* DIS # E1: 6 => CTR => E1: 4,9
* INC # F7: 4,9 => UNS
* PRF # F9: 4,9 => SOL
* INC # F9: 1,7,8 => UNS
* DIS # E1: 6,9 => CTR => E1: 4
* PRF # E1: 4 => SOL
* DIS # E1: 6,9 => CTR => E1: 4
* PRF # E1: 4 => SOL
* INC # H7: 4,9 => UNS
* DIS # H9: 4,9 => CTR => H9: 8
* INC # H9: 8 => UNS
* INC # B9: 2,8 => UNS
* INC # B9: 6,9 => UNS
* INC # C8: 2,8 => UNS
* DIS # C9: 2,8 => CTR => C9: 1,6,9
* INC # C9: 1,6,9 => UNS
* INC # F8: 7,9 => UNS
* PRF # E9: 7,9 => SOL
* INC # E9: 1,4 => UNS
* INC # F9: 7,9 => UNS
* INC # B7: 6,9 => UNS
* PRF # C7: 6,9 => SOL
* INC # C7: 1,8 => UNS
* CNT  29 HDP CHAINS /  29 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B7: 6,9 => UNS
* INC # B9: 6,9 => UNS
* PRF # C7: 6,9 => SOL
* STA C7: 6,9
* CNT   3 HDP CHAINS /   3 HYP OPENED