Analysis of xx-top500-178-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ..7...2...1..8..........5.82.....3.....76.......1......64....1.5....3......2..... initial

Autosolve

position: 8573.62.1.12587.366.3.215782.1.5.367.3576.1..7.613...5364.75.1252.6137..17.2..653 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B4: 4,9 => CTR => B4: 8
* PRF # B4: 8 => SOL
* PRF # B6: 4,9 => SOL
* DIS # B6: 8 => CTR => B6: 4,9
* PRF # D4: 4,9 => SOL
* DIS # D4: 8 => CTR => D4: 4,9
* PRF # H6: 4,9 => SOL
* DIS # H6: 2,8 => CTR => H6: 4,9
* DIS # H8: 4,9 => CTR => H8: 8
* PRF # H8: 8 => SOL
* DIS # G6: 4,9 => CTR => G6: 8
* PRF # G6: 8 => SOL
* DIS # B4: 4,9 => CTR => B4: 8
* PRF # B4: 8 => SOL
* PRF # B6: 4,9 => SOL
* DIS # B6: 8 => CTR => B6: 4,9
* PRF # F6: 2,8 => SOL
* DIS # F6: 4,9 => CTR => F6: 2,8
* DIS # H6: 2,8 => CTR => H6: 4,9
* PRF # H6: 4,9 => SOL
* DIS # G6: 4,9 => CTR => G6: 8
* PRF # G6: 8 => SOL
* PRF # H6: 4,9 => SOL
* DIS # H6: 2,8 => CTR => H6: 4,9
* PRF # H8: 8,9 => SOL
* DIS # H8: 4 => CTR => H8: 8,9
* DIS # F9: 8,9 => CTR => F9: 4
* PRF # F9: 4 => SOL
* DIS # F9: 8,9 => CTR => F9: 4
* PRF # F9: 4 => SOL
* DIS # D4: 8,9 => CTR => D4: 4
* PRF # D4: 4 => SOL
* PRF # F9: 4,9 => SOL
* DIS # F9: 8 => CTR => F9: 4,9
* PRF # H8: 8,9 => SOL
* DIS # H8: 4 => CTR => H8: 8,9
* PRF # G6: 8,9 => SOL
* DIS # G6: 4 => CTR => G6: 8,9
* DIS # H8: 4,9 => CTR => H8: 8
* PRF # H8: 8 => SOL
* CNT  40 HDP CHAINS /  40 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: 8
* PRF B4: 8 => SOL
* STA B4: 8
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

..7...2...1..8..........5.82.....3.....76.......1......64....1.5....3......2..... initial
8573.62.1.12587.366.3.215782.1.5.367.3576.1..7.613...5364.75.1252.6137..17.2..653 autosolve
857346291912587436643921578281459367435768129796132845364875912529613784178294653 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
A2: 4,9
B3: 4,9
E1: 4,9
D3: 4,9
H1: 4,9
G2: 4,9
A5: 4,9
F5: 2,8
H5: 2,8
I5: 4,9
C8: 8,9
C9: 8,9
D7: 8,9
E9: 4,9
G7: 8,9
I8: 4,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F5,F6: 2.. / F5 = 2  =>  0 pairs (X) / F6 = 2  =>  0 pairs (_)
H5,H6: 2.. / H5 = 2  =>  0 pairs (*) / H6 = 2  =>  0 pairs (X)
F5,H5: 2.. / F5 = 2  =>  0 pairs (X) / H5 = 2  =>  0 pairs (_)
F6,H6: 2.. / F6 = 2  =>  0 pairs (*) / H6 = 2  =>  0 pairs (X)
A2,B3: 4.. / A2 = 4  =>  0 pairs (X) / B3 = 4  =>  0 pairs (_)
E1,D3: 4.. / E1 = 4  =>  0 pairs (*) / D3 = 4  =>  0 pairs (X)
H1,G2: 4.. / H1 = 4  =>  0 pairs (X) / G2 = 4  =>  0 pairs (_)
E9,F9: 4.. / E9 = 4  =>  0 pairs (X) / F9 = 4  =>  0 pairs (_)
H8,I8: 4.. / H8 = 4  =>  0 pairs (X) / I8 = 4  =>  0 pairs (_)
E1,H1: 4.. / E1 = 4  =>  0 pairs (*) / H1 = 4  =>  0 pairs (X)
A2,G2: 4.. / A2 = 4  =>  0 pairs (X) / G2 = 4  =>  0 pairs (_)
B3,D3: 4.. / B3 = 4  =>  0 pairs (*) / D3 = 4  =>  0 pairs (X)
A5,I5: 4.. / A5 = 4  =>  0 pairs (*) / I5 = 4  =>  0 pairs (X)
A2,A5: 4.. / A2 = 4  =>  0 pairs (X) / A5 = 4  =>  0 pairs (_)
D3,D4: 4.. / D3 = 4  =>  0 pairs (X) / D4 = 4  =>  0 pairs (_)
E1,E9: 4.. / E1 = 4  =>  0 pairs (*) / E9 = 4  =>  0 pairs (X)
G2,G6: 4.. / G2 = 4  =>  0 pairs (*) / G6 = 4  =>  0 pairs (X)
I5,I8: 4.. / I5 = 4  =>  0 pairs (X) / I8 = 4  =>  0 pairs (_)
B4,B6: 8.. / B4 = 8  =>  0 pairs (*) / B6 = 8  =>  0 pairs (X)
C8,C9: 8.. / C8 = 8  =>  0 pairs (X) / C9 = 8  =>  0 pairs (_)
D7,F9: 8.. / D7 = 8  =>  0 pairs (*) / F9 = 8  =>  0 pairs (X)
G7,H8: 8.. / G7 = 8  =>  0 pairs (X) / H8 = 8  =>  0 pairs (_)
F5,H5: 8.. / F5 = 8  =>  0 pairs (*) / H5 = 8  =>  0 pairs (X)
D7,G7: 8.. / D7 = 8  =>  0 pairs (*) / G7 = 8  =>  0 pairs (X)
C8,H8: 8.. / C8 = 8  =>  0 pairs (X) / H8 = 8  =>  0 pairs (_)
C9,F9: 8.. / C9 = 8  =>  0 pairs (*) / F9 = 8  =>  0 pairs (X)
D4,D7: 8.. / D4 = 8  =>  0 pairs (X) / D7 = 8  =>  0 pairs (_)
G6,G7: 8.. / G6 = 8  =>  0 pairs (*) / G7 = 8  =>  0 pairs (X)
A2,B3: 9.. / A2 = 9  =>  0 pairs (*) / B3 = 9  =>  0 pairs (X)
E1,D3: 9.. / E1 = 9  =>  0 pairs (X) / D3 = 9  =>  0 pairs (_)
H1,G2: 9.. / H1 = 9  =>  0 pairs (*) / G2 = 9  =>  0 pairs (X)
C8,C9: 9.. / C8 = 9  =>  0 pairs (*) / C9 = 9  =>  0 pairs (X)
E1,H1: 9.. / E1 = 9  =>  0 pairs (X) / H1 = 9  =>  0 pairs (_)
A2,G2: 9.. / A2 = 9  =>  0 pairs (*) / G2 = 9  =>  0 pairs (X)
B3,D3: 9.. / B3 = 9  =>  0 pairs (X) / D3 = 9  =>  0 pairs (_)
A5,I5: 9.. / A5 = 9  =>  0 pairs (X) / I5 = 9  =>  0 pairs (_)
D7,G7: 9.. / D7 = 9  =>  0 pairs (X) / G7 = 9  =>  0 pairs (_)
A2,A5: 9.. / A2 = 9  =>  0 pairs (*) / A5 = 9  =>  0 pairs (X)
E1,E9: 9.. / E1 = 9  =>  0 pairs (X) / E9 = 9  =>  0 pairs (_)
I5,I8: 9.. / I5 = 9  =>  0 pairs (*) / I8 = 9  =>  0 pairs (X)
* DURATION: 0:01:17.369792  START: 08:46:12.772566  END: 08:47:30.142358 2017-05-04
* CP COUNT: (40)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B3,C8,C9,D3,D7,E1,E9,F5,G2,G7,H1,H5,I5,I8)
* 8573.62.1.12587.366.3.215782.1.5.367.3576.1..7.613...5364.75.1252.6137..17.2..653
* PAIR B3: 4,9 COL B
B4: 4,9,8                                # reduction candidate for 4,9
B4: 4,9 => CTR
* 85739624141258793669342157824185936793576218.78613...5364.758125286137..179248653
B4: 8 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
B6: 4,9,8                                # reduction candidate for 4,9
B6: 4,9 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
B6: 8 => CTR
* 85739624141258793669342157824185936793576218.78613...5364.758125286137..179248653
* PAIR D3: 4,9 COL D
D4: 4,9,8                                # reduction candidate for 4,9
D4: 4,9 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
D4: 8 => CTR
* 857396241412587936693421578241859367.3576218.78613..253649758125286137..179248653
* PAIR H1: 4,9 COL H
H6: 4,9,2,8                              # reduction candidate for 4,9
H6: 4,9 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
H6: 2,8 => CTR
* 8573962414125879366934215782.185936793576.1..7.613...53649758125286137..179248653
H8: 4,9,8                                # reduction candidate for 4,9
H8: 4,9 => CTR
* 8573962414125879366934215782.185936793576218.7.613...5364.758125286137..179248653
H8: 8 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
* PAIR G2: 4,9 COL G
G6: 4,9,8                                # reduction candidate for 4,9
G6: 4,9 => CTR
* 8573962414125879366934215782.185936793576218.7.613...5364.758125286137..179248653
G6: 8 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
* PAIR A5: 4,9 BLK 4
B4: 4,9,8                                # reduction candidate for 4,9
B4: 4,9 => CTR
* 85739624141258793669342157824185936793576218.78613...5364.758125286137..179248653
B4: 8 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
B6: 4,9,8                                # reduction candidate for 4,9
B6: 4,9 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
B6: 8 => CTR
* 85739624141258793669342157824185936793576218.78613...5364.758125286137..179248653
* PAIR F5: 2,8 BLK 5
F6: 2,8,4,9                              # reduction candidate for 2,8
F6: 2,8 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
F6: 4,9 => CTR
* 85739624141258793669342157824185.367.3576218.78613..25364.758125286137..179248653
* PAIR H5: 2,8 BLK 6
H6: 2,8,4,9                              # reduction candidate for 2,8
H6: 2,8 => CTR
* 8573962414125879366934215782.185936793576.1..7.613...53649758125286137..179248653
H6: 4,9 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
* PAIR I5: 4,9 BLK 6
G6: 4,9,8                                # reduction candidate for 4,9
G6: 4,9 => CTR
* 8573962414125879366934215782.185936793576218.7.613...5364.758125286137..179248653
G6: 8 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
H6: 4,9,2,8                              # reduction candidate for 4,9
H6: 4,9 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
H6: 2,8 => CTR
* 8573962414125879366934215782.185936793576.1..7.613...53649758125286137..179248653
* PAIR C8: 8,9 ROW 8
H8: 8,9,4                                # reduction candidate for 8,9
H8: 8,9 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
H8: 4 => CTR
* 8573.62.1.12587.366.3.215782.1.5.367.3576.1..7.613...5364.7581252861374917924.653
* PAIR C9: 8,9 ROW 9
F9: 8,9,4                                # reduction candidate for 8,9
F9: 8,9 => CTR
* 8573962414125879366934215782.1.5.36793576.1.47.613...5364.75.1252.6137..17.24.653
F9: 4 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
* PAIR D7: 8,9 BLK 8
F9: 8,9,4                                # reduction candidate for 8,9
F9: 8,9 => CTR
* 8573962414125879366934215782.1.5.36793576.1.47.613...5364.75.1252.6137..17.24.653
F9: 4 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
* PAIR D7: 8,9 COL D
D4: 8,9,4                                # reduction candidate for 8,9
D4: 8,9 => CTR
* 8573962414125879366934215782.1.5.36793576.1.47.613...5364.75.1252.6137..17.24.653
D4: 4 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
* PAIR E9: 4,9 BLK 8
F9: 4,9,8                                # reduction candidate for 4,9
F9: 4,9 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
F9: 8 => CTR
* 8573962414125879366934215782.185936793576218.7.613...5364.75.1252.6137..17.248653
* PAIR G7: 8,9 BLK 9
H8: 8,9,4                                # reduction candidate for 8,9
H8: 8,9 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
H8: 4 => CTR
* 8573.62.1.12587.366.3.215782.1.5.367.3576.1..7.613...5364.7581252861374917924.653
* PAIR G7: 8,9 COL G
G6: 8,9,4                                # reduction candidate for 8,9
G6: 8,9 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
G6: 4 => CTR
* 85739624141258793669342157824185936793576.1..7.613.4.5364.758125286137.4179248653
* PAIR I8: 4,9 BLK 9
H8: 4,9,8                                # reduction candidate for 4,9
H8: 4,9 => CTR
* 8573962414125879366934215782.185936793576218.7.613...5364.758125286137..179248653
H8: 8 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
* INCONCLUSIVE
* SAVE PR GRAPH xx-top500-178-base-pr-000.dot
* REASONING
* DIS # B4: 4,9 => CTR => B4: 8
* PRF # B4: 8 => SOL
* PRF # B6: 4,9 => SOL
* DIS # B6: 8 => CTR => B6: 4,9
* PRF # D4: 4,9 => SOL
* DIS # D4: 8 => CTR => D4: 4,9
* PRF # H6: 4,9 => SOL
* DIS # H6: 2,8 => CTR => H6: 4,9
* DIS # H8: 4,9 => CTR => H8: 8
* PRF # H8: 8 => SOL
* DIS # G6: 4,9 => CTR => G6: 8
* PRF # G6: 8 => SOL
* DIS # B4: 4,9 => CTR => B4: 8
* PRF # B4: 8 => SOL
* PRF # B6: 4,9 => SOL
* DIS # B6: 8 => CTR => B6: 4,9
* PRF # F6: 2,8 => SOL
* DIS # F6: 4,9 => CTR => F6: 2,8
* DIS # H6: 2,8 => CTR => H6: 4,9
* PRF # H6: 4,9 => SOL
* DIS # G6: 4,9 => CTR => G6: 8
* PRF # G6: 8 => SOL
* PRF # H6: 4,9 => SOL
* DIS # H6: 2,8 => CTR => H6: 4,9
* PRF # H8: 8,9 => SOL
* DIS # H8: 4 => CTR => H8: 8,9
* DIS # F9: 8,9 => CTR => F9: 4
* PRF # F9: 4 => SOL
* DIS # F9: 8,9 => CTR => F9: 4
* PRF # F9: 4 => SOL
* DIS # D4: 8,9 => CTR => D4: 4
* PRF # D4: 4 => SOL
* PRF # F9: 4,9 => SOL
* DIS # F9: 8 => CTR => F9: 4,9
* PRF # H8: 8,9 => SOL
* DIS # H8: 4 => CTR => H8: 8,9
* PRF # G6: 8,9 => SOL
* DIS # G6: 4 => CTR => G6: 8,9
* DIS # H8: 4,9 => CTR => H8: 8
* PRF # H8: 8 => SOL
* CNT  40 HDP CHAINS /  40 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B3,C8,C9,D3,D7,E1,E9,F5,G2,G7,H1,H5,I5,I8)
* 8573.62.1.12587.366.3.215782.1.5.367.3576.1..7.613...5364.75.1252.6137..17.2..653
* PAIR B3: 4,9 COL B
B4: 4,9,8                                # reduction candidate for 4,9
B4: 4,9 => CTR
* 85739624141258793669342157824185936793576218.78613...5364.758125286137..179248653
B4: 8 => SOLVED
* 857346291912587436643921578281459367435768129796132845364875912529613784178294653
* DURATION: 0:00:01.983517  START: 08:48:24.018995  END: 08:48:26.002512 2017-05-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-top500-178-base-pr-001.dot
* REASONING
* DIS # B4: 4,9 => CTR => B4: 8
* PRF B4: 8 => SOL
* STA B4: 8
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

Top 500 Minimum 17 178

solution: 857346291912587436643921578281459367435768129796132845364875912529613784178294653
info: 1828     FNBTWX   S8.f     14261

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

Solution

position: 857346291912587436643921578281459367435768129796132845364875912529613784178294653 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: 8
* PRF # B4: 8 => SOL
* PRF # B6: 4,9 => SOL
* DIS # B6: 8 => CTR => B6: 4,9
* PRF # D4: 4,9 => SOL
* DIS # D4: 8 => CTR => D4: 4,9
* PRF # H6: 4,9 => SOL
* DIS # H6: 2,8 => CTR => H6: 4,9
* DIS # H8: 4,9 => CTR => H8: 8
* PRF # H8: 8 => SOL
* DIS # G6: 4,9 => CTR => G6: 8
* PRF # G6: 8 => SOL
* DIS # B4: 4,9 => CTR => B4: 8
* PRF # B4: 8 => SOL
* PRF # B6: 4,9 => SOL
* DIS # B6: 8 => CTR => B6: 4,9
* PRF # F6: 2,8 => SOL
* DIS # F6: 4,9 => CTR => F6: 2,8
* DIS # H6: 2,8 => CTR => H6: 4,9
* PRF # H6: 4,9 => SOL
* DIS # G6: 4,9 => CTR => G6: 8
* PRF # G6: 8 => SOL
* PRF # H6: 4,9 => SOL
* DIS # H6: 2,8 => CTR => H6: 4,9
* PRF # H8: 8,9 => SOL
* DIS # H8: 4 => CTR => H8: 8,9
* DIS # F9: 8,9 => CTR => F9: 4
* PRF # F9: 4 => SOL
* DIS # F9: 8,9 => CTR => F9: 4
* PRF # F9: 4 => SOL
* DIS # D4: 8,9 => CTR => D4: 4
* PRF # D4: 4 => SOL
* PRF # F9: 4,9 => SOL
* DIS # F9: 8 => CTR => F9: 4,9
* PRF # H8: 8,9 => SOL
* DIS # H8: 4 => CTR => H8: 8,9
* PRF # G6: 8,9 => SOL
* DIS # G6: 4 => CTR => G6: 8,9
* DIS # H8: 4,9 => CTR => H8: 8
* PRF # H8: 8 => SOL
* CNT  40 HDP CHAINS /  40 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B4: 4,9 => CTR => B4: 8
* PRF B4: 8 => SOL
* STA B4: 8
* CNT   2 HDP CHAINS /   1 HYP OPENED