Analysis of xx-top500-178-base.sdk
Contents
Original Sudoku
level: medium
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
Pair Reduction Variants
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
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
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