Analysis of xx-top500-152-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...67.5..4.......1.3.8.....1.5...2..2..3............8.....51....6.....3.......... initial

Autosolve

position: 9126735484865923715378146291.5...2.32.83..15.6.3125.8.32..518..7612...3585..36.12 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B4: 4,9 => CTR => B4: 7
* PRF # B4: 7 => SOL
* DIS # D7: 4,9 => CTR => D7: 7
* PRF # E4: 4,6 => SOL
* DIS # E4: 8 => CTR => E4: 4,6
* DIS # I5: 7 => CTR => I5: 4,6
* DIS # F4: 7,9 => CTR => F4: 8
* PRF # F4: 8 => SOL
* DIS # B5: 4 => CTR => B5: 7,9
* PRF # I5: 4,7 => SOL
* DIS # I5: 6 => CTR => I5: 4,7
* DIS # G6: 4,7 => CTR => G6: 9
* PRF # G6: 9 => SOL
* PRF # B6: 4,7 => SOL
* DIS # B6: 9 => CTR => B6: 4,7
* DIS # I7: 4,7 => CTR => I7: 6
* PRF # I7: 6 => SOL
* DIS # D7: 4,9 => CTR => D7: 7
* DIS # G9: 4,9 => CTR => G9: 7
* PRF # E4: 4,8 => SOL
* DIS # E4: 6 => CTR => E4: 4,8
* PRF # F4: 8,9 => SOL
* DIS # F4: 7 => CTR => F4: 8,9
* DIS # G9: 4,9 => CTR => G9: 7
* DIS # G6: 7 => CTR => G6: 4,9
* CNT  25 HDP CHAINS /  34 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 # B4: 4,9 => CTR => B4: 7
* PRF B4: 7 => SOL
* STA B4: 7
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

...67.5..4.......1.3.8.....1.5...2..2..3............8.....51....6.....3.......... initial
9126735484865923715378146291.5...2.32.83..15.6.3125.8.32..518..7612...3585..36.12 autosolve
912673548486592371537814629175948263298367154643125987324751896761289435859436712 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
D4: 4,9
E5: 4,6
F5: 7,9
H4: 6,9
I6: 4,7
C7: 4,9
C9: 4,9
E8: 4,8
F8: 8,9
H7: 6,9
G8: 4,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C7,C9: 4.. / C7 = 4  => 14 pairs (_) / C9 = 4  =>  0 pairs (X)
E8,G8: 4.. / E8 = 4  =>  0 pairs (X) / G8 = 4  =>  0 pairs (_)
E4,E5: 6.. / E4 = 6  =>  0 pairs (X) / E5 = 6  =>  0 pairs (_)
H4,I5: 6.. / H4 = 6  =>  0 pairs (*) / I5 = 6  =>  0 pairs (X)
H7,I7: 6.. / H7 = 6  =>  0 pairs (X) / I7 = 6  =>  0 pairs (_)
E4,H4: 6.. / E4 = 6  =>  0 pairs (X) / H4 = 6  =>  0 pairs (_)
E5,I5: 6.. / E5 = 6  =>  0 pairs (*) / I5 = 6  =>  0 pairs (X)
H4,H7: 6.. / H4 = 6  =>  0 pairs (*) / H7 = 6  =>  0 pairs (X)
I5,I7: 6.. / I5 = 6  =>  0 pairs (X) / I7 = 6  =>  0 pairs (_)
F4,F5: 7.. / F4 = 7  =>  0 pairs (X) / F5 = 7  =>  0 pairs (_)
D7,D9: 7.. / D7 = 7  => 14 pairs (_) / D9 = 7  =>  0 pairs (X)
I7,G9: 7.. / I7 = 7  =>  0 pairs (X) / G9 = 7  => 14 pairs (_)
B4,F4: 7.. / B4 = 7  =>  0 pairs (*) / F4 = 7  =>  0 pairs (X)
D7,I7: 7.. / D7 = 7  => 14 pairs (_) / I7 = 7  =>  0 pairs (X)
D9,G9: 7.. / D9 = 7  =>  0 pairs (X) / G9 = 7  => 14 pairs (_)
G6,G9: 7.. / G6 = 7  =>  0 pairs (X) / G9 = 7  => 14 pairs (_)
E4,F4: 8.. / E4 = 8  =>  0 pairs (X) / F4 = 8  =>  0 pairs (_)
E8,F8: 8.. / E8 = 8  =>  0 pairs (*) / F8 = 8  =>  0 pairs (X)
E4,E8: 8.. / E4 = 8  =>  0 pairs (X) / E8 = 8  =>  0 pairs (_)
F4,F8: 8.. / F4 = 8  =>  0 pairs (*) / F8 = 8  =>  0 pairs (X)
H4,G6: 9.. / H4 = 9  =>  0 pairs (X) / G6 = 9  =>  0 pairs (_)
C7,C9: 9.. / C7 = 9  =>  0 pairs (X) / C9 = 9  => 14 pairs (_)
B5,F5: 9.. / B5 = 9  =>  0 pairs (*) / F5 = 9  =>  0 pairs (X)
B6,G6: 9.. / B6 = 9  =>  0 pairs (X) / G6 = 9  =>  0 pairs (_)
F8,G8: 9.. / F8 = 9  =>  0 pairs (*) / G8 = 9  =>  0 pairs (X)
H4,H7: 9.. / H4 = 9  =>  0 pairs (X) / H7 = 9  =>  0 pairs (_)
* DURATION: 0:00:48.664094  START: 07:57:08.694167  END: 07:57:57.358261 2017-05-04
* CP COUNT: (26)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C7,C9,D4,E5,E8,F5,F8,G8,H4,H7,I6)
* 9126735484865923715378146291.5...2.32.83..15.6.3125.8.32..518..7612...3585..36.12
* PAIR D4: 4,9 ROW 4
B4: 4,9,7                                # reduction candidate for 4,9
B4: 4,9 => CTR
* 9126735484865923715378146291.54872.32.83.915.6.3125.8.32..518..7612.893585..36.12
B4: 7 => SOLVED
* 912673548486592371537814629175948263298367154643125987324751896761289435859436712
* PAIR D4: 4,9 COL D
D7: 4,9,7                                # reduction candidate for 4,9
D7: 4,9 => CTR
* 9126735484865923715378146291.5.682932.834.1566.312578432..518677612...3585.736.12
D7: 7                                    # 14 pairs
D9: 4,9,7                                # reduction candidate for 4,9
D9: 4,9                                  # 14 pairs
* PAIR E5: 4,6 BLK 5
E4: 4,6,8                                # reduction candidate for 4,6
E4: 4,6 => SOLVED
* 912673548486592371537814629175948263298367154643125987324751896761289435859436712
E4: 8 => CTR
* 9126735484865923715378146291.5.8.2632.836.15.6.312598.32..5189676124..3585..36.12
* PAIR E5: 4,6 ROW 5
I5: 4,6,7                                # reduction candidate for 4,6
I5: 7 => CTR
* 9126735484865923715378146291.5...2632.836.15767312598432.7518967612.9.3585..36.12
I5: 4,6                                  # 14 pairs
* PAIR F5: 7,9 BLK 5
F4: 7,9,8                                # reduction candidate for 7,9
F4: 7,9 => CTR
* 9126735484865923715378146291.5.8.2632.836.15.6.312598.32..5189676124..3585..36.12
F4: 8 => SOLVED
* 912673548486592371537814629175948263298367154643125987324751896761289435859436712
* PAIR F5: 7,9 ROW 5
B5: 7,9,4                                # reduction candidate for 7,9
B5: 4 => CTR
* 9126735484865923715378146291.5...2.324836915767312598432.7518967612.843585..36.12
B5: 7,9                                  # 14 pairs
* PAIR I6: 4,7 BLK 6
I5: 4,7,6                                # reduction candidate for 4,7
I5: 4,7 => SOLVED
* 912673548486592371537814629175948263298367154643125987324751896761289435859436712
I5: 6 => CTR
* 9126735484865923715378146291.5.682932.834.1566.3125.8.32..5186.7612...3585..36.12
G6: 4,7,9                                # reduction candidate for 4,7
G6: 4,7 => CTR
* 9126735484865923715378146291.5...2932.83.9156693125.8.32..5186.7612.893585..36.12
G6: 9 => SOLVED
* 912673548486592371537814629175948263298367154643125987324751896761289435859436712
* PAIR I6: 4,7 ROW 6
B6: 4,7,9                                # reduction candidate for 4,7
B6: 4,7 => SOLVED
* 912673548486592371537814629175948263298367154643125987324751896761289435859436712
B6: 9 => CTR
* 9126735484865923715378146291.5...2932.83.9156693125.8.32..5186.7612.893585..36.12
* PAIR I6: 4,7 COL I
I7: 4,7,6                                # reduction candidate for 4,7
I7: 4,7 => CTR
* 9126735484865923715378146291.5.682932.834.1566.3125.8.32..5186.7612...3585..36.12
I7: 6 => SOLVED
* 912673548486592371537814629175948263298367154643125987324751896761289435859436712
* PAIR C7: 4,9 ROW 7
D7: 4,9,7                                # reduction candidate for 4,9
D7: 4,9 => CTR
* 9126735484865923715378146291.5.682932.834.1566.312578432..518677612...3585.736.12
D7: 7                                    # 14 pairs
* PAIR C9: 4,9 ROW 9
D9: 4,9,7                                # reduction candidate for 4,9
D9: 4,9                                  # 14 pairs
G9: 4,9,7                                # reduction candidate for 4,9
G9: 4,9 => CTR
* 9126735484865923715378146291.5...2932.83.915669312578432.95186776124..3585.736.12
G9: 7                                    # 14 pairs
* PAIR E8: 4,8 COL E
E4: 4,8,6                                # reduction candidate for 4,8
E4: 4,8 => SOLVED
* 912673548486592371537814629175948263298367154643125987324751896761289435859436712
E4: 6 => CTR
* 9126735484865923715378146291.5.682932.834.15.6.3125.8.32..518..7612...3585..36.12
* PAIR F8: 8,9 COL F
F4: 8,9,7                                # reduction candidate for 8,9
F4: 8,9 => SOLVED
* 912673548486592371537814629175948263298367154643125987324751896761289435859436712
F4: 7 => CTR
* 9126735484865923715378146291.5.872632.836915.6.312598.32..5189676124..3585..36.12
* PAIR G8: 4,9 BLK 9
G9: 4,9,7                                # reduction candidate for 4,9
G9: 4,9 => CTR
* 9126735484865923715378146291.5...2932.83.915669312578432.95186776124..3585.736.12
G9: 7                                    # 14 pairs
* PAIR G8: 4,9 COL G
G6: 4,9,7                                # reduction candidate for 4,9
G6: 7 => CTR
* 9126735484865923715378146291.5...2932.83.915669312578432..518677612.893585.736412
G6: 4,9                                  # 14 pairs
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-152-base-pr-000.dot
* REASONING
* DIS # B4: 4,9 => CTR => B4: 7
* PRF # B4: 7 => SOL
* DIS # D7: 4,9 => CTR => D7: 7
* PRF # E4: 4,6 => SOL
* DIS # E4: 8 => CTR => E4: 4,6
* DIS # I5: 7 => CTR => I5: 4,6
* DIS # F4: 7,9 => CTR => F4: 8
* PRF # F4: 8 => SOL
* DIS # B5: 4 => CTR => B5: 7,9
* PRF # I5: 4,7 => SOL
* DIS # I5: 6 => CTR => I5: 4,7
* DIS # G6: 4,7 => CTR => G6: 9
* PRF # G6: 9 => SOL
* PRF # B6: 4,7 => SOL
* DIS # B6: 9 => CTR => B6: 4,7
* DIS # I7: 4,7 => CTR => I7: 6
* PRF # I7: 6 => SOL
* DIS # D7: 4,9 => CTR => D7: 7
* DIS # G9: 4,9 => CTR => G9: 7
* PRF # E4: 4,8 => SOL
* DIS # E4: 6 => CTR => E4: 4,8
* PRF # F4: 8,9 => SOL
* DIS # F4: 7 => CTR => F4: 8,9
* DIS # G9: 4,9 => CTR => G9: 7
* DIS # G6: 7 => CTR => G6: 4,9
* CNT  25 HDP CHAINS /  34 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C7,C9,D4,E5,E8,F5,F8,G8,H4,H7,I6)
* 9126735484865923715378146291.5...2.32.83..15.6.3125.8.32..518..7612...3585..36.12
* PAIR D4: 4,9 ROW 4
B4: 4,9,7                                # reduction candidate for 4,9
B4: 4,9 => CTR
* 9126735484865923715378146291.54872.32.83.915.6.3125.8.32..518..7612.893585..36.12
B4: 7 => SOLVED
* 912673548486592371537814629175948263298367154643125987324751896761289435859436712
* DURATION: 0:00:02.915061  START: 07:58:36.940044  END: 07:58:39.855105 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-152-base-pr-001.dot
* REASONING
* DIS # B4: 4,9 => CTR => B4: 7
* PRF B4: 7 => SOL
* STA B4: 7
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 152

solution: 912673548486592371537814629175948263298367154643125987324751896761289435859436712
info: 1817     FNBWY    S8.f     11177

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

Solution

position: 912673548486592371537814629175948263298367154643125987324751896761289435859436712 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 # B4: 4,9 => CTR => B4: 7
* PRF # B4: 7 => SOL
* DIS # D7: 4,9 => CTR => D7: 7
* INC # D7: 7 => UNS
* INC # D9: 4,9 => UNS
* PRF # E4: 4,6 => SOL
* DIS # E4: 8 => CTR => E4: 4,6
* INC # I5: 4,6 => UNS
* DIS # I5: 7 => CTR => I5: 4,6
* DIS # F4: 7,9 => CTR => F4: 8
* PRF # F4: 8 => SOL
* INC # B5: 7,9 => UNS
* DIS # B5: 4 => CTR => B5: 7,9
* PRF # I5: 4,7 => SOL
* DIS # I5: 6 => CTR => I5: 4,7
* DIS # G6: 4,7 => CTR => G6: 9
* PRF # G6: 9 => SOL
* PRF # B6: 4,7 => SOL
* DIS # B6: 9 => CTR => B6: 4,7
* DIS # I7: 4,7 => CTR => I7: 6
* PRF # I7: 6 => SOL
* DIS # D7: 4,9 => CTR => D7: 7
* INC # D7: 7 => UNS
* INC # D9: 4,9 => UNS
* DIS # G9: 4,9 => CTR => G9: 7
* INC # G9: 7 => UNS
* PRF # E4: 4,8 => SOL
* DIS # E4: 6 => CTR => E4: 4,8
* PRF # F4: 8,9 => SOL
* DIS # F4: 7 => CTR => F4: 8,9
* DIS # G9: 4,9 => CTR => G9: 7
* INC # G9: 7 => UNS
* INC # G6: 4,9 => UNS
* DIS # G6: 7 => CTR => G6: 4,9
* CNT  34 HDP CHAINS /  34 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B4: 4,9 => CTR => B4: 7
* PRF B4: 7 => SOL
* STA B4: 7
* CNT   2 HDP CHAINS /   1 HYP OPENED