Analysis of xx-top500-325-base.sdk
Contents
Original Sudoku
level: medium
position: ....3.9..4.8......1.........3..7...5..2....1........48.6....2..5..8........1..... initial
Autosolve
position: ....3.9..4.8......1.3.......3..7.625..2....19.......48.6....2..5..8........1..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F2: 1,5 => CTR => F2: 2,6,7,9 * DIS # F4: 8,9 => CTR => F4: 1,4 * PRF # F4: 1,4 => SOL * DIS # A7: 8,9 => CTR => A7: 3 * PRF # A7: 3 => SOL * DIS # A9: 8,9 => CTR => A9: 2,3 * PRF # E6: 5,6 => SOL * DIS # F4: 4,9 => CTR => F4: 1,8 * PRF # C4: 4,9 => SOL * DIS # C4: 1 => CTR => C4: 4,9 * DIS # D3: 4,9 => CTR => D3: 2,5,6,7 * DIS # D7: 4,9 => CTR => D7: 3,5,7 * DIS # I8: 1,4 => CTR => I8: 3,6,7 * DIS # C8: 1,4 => CTR => C8: 7,9 * CNT 14 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F2: 1,5 => CTR => F2: 2,6,7,9 * DIS F2: 2,6,7,9 # E2: 2,6,9 => CTR => E2: 1,5 * DIS F2: 2,6,7,9 + E2: 1,5 # F4: 8,9 => CTR => F4: 1,4 * PRF F2: 2,6,7,9 + E2: 1,5 + F4: 1,4 => SOL * STA F2: 2,6,7,9 + E2: 1,5 + F4: 1,4 * CNT 4 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....3.9..4.8......1.........3..7...5..2....1........48.6....2..5..8........1..... | initial |
| ....3.9..4.8......1.3.......3..7.625..2....19.......48.6....2..5..8........1..... | autosolve |
| 625438971498716532173295864834971625752684319916352748361549287547823196289167453 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) C1: 5,6 G2: 1,5 A4: 8,9 C6: 5,6 D4: 4,9 G5: 3,7 G6: 3,7 G8: 1,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C4,B6: 1.. / C4 = 1 => 0 pairs (X) / B6 = 1 => 0 pairs (_) F1,I1: 1.. / F1 = 1 => 0 pairs (X) / I1 = 1 => 0 pairs (_) C4,F4: 1.. / C4 = 1 => 0 pairs (X) / F4 = 1 => 0 pairs (_) C7,I7: 1.. / C7 = 1 => 0 pairs (*) / I7 = 1 => 0 pairs (X) B6,B8: 1.. / B6 = 1 => 0 pairs (*) / B8 = 1 => 0 pairs (X) E2,E6: 1.. / E2 = 1 => 0 pairs (*) / E6 = 1 => 0 pairs (X) G2,G8: 1.. / G2 = 1 => 0 pairs (X) / G8 = 1 => 0 pairs (_) A1,A9: 2.. / A1 = 2 => 0 pairs (X) / A9 = 2 => 0 pairs (_) H2,I2: 3.. / H2 = 3 => 8 pairs (_) / I2 = 3 => 11 pairs (_) G5,G6: 3.. / G5 = 3 => 8 pairs (_) / G6 = 3 => 7 pairs (_) A7,A9: 3.. / A7 = 3 => 0 pairs (*) / A9 = 3 => 0 pairs (X) C4,B5: 4.. / C4 = 4 => 0 pairs (*) / B5 = 4 => 0 pairs (X) C1,C6: 5.. / C1 = 5 => 0 pairs (*) / C6 = 5 => 0 pairs (X) A1,C1: 6.. / A1 = 6 => 0 pairs (*) / C1 = 6 => 0 pairs (X) C1,C6: 6.. / C1 = 6 => 8 pairs (_) / C6 = 6 => 0 pairs (*) G5,G6: 7.. / G5 = 7 => 7 pairs (_) / G6 = 7 => 8 pairs (_) F1,H1: 8.. / F1 = 8 => 0 pairs (*) / H1 = 8 => 0 pairs (X) A4,F4: 8.. / A4 = 8 => 0 pairs (*) / F4 = 8 => 0 pairs (X) A7,H7: 8.. / A7 = 8 => 0 pairs (X) / H7 = 8 => 0 pairs (_) B5,B9: 8.. / B5 = 8 => 0 pairs (X) / B9 = 8 => 0 pairs (_) E3,E5: 8.. / E3 = 8 => 0 pairs (X) / E5 = 8 => 0 pairs (_) G3,G9: 8.. / G3 = 8 => 0 pairs (*) / G9 = 8 => 0 pairs (X) B2,B3: 9.. / B2 = 9 => 8 pairs (_) / B3 = 9 => 8 pairs (_) * DURATION: 0:00:37.238349 START: 13:59:09.072680 END: 13:59:46.311029 2017-05-04 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,C1,C6,D4,G2,G5,G6,G8) * ....3.9..4.8......1.3.......3..7.625..2....19.......48.6....2..5..8........1..... * PAIR G2: 1,5 ROW 2 E2: 1,5,2,6,9 # reduction candidate for 1,5 E2: 1,5 # 9 pairs F2: 1,5,2,6,7,9 # reduction candidate for 1,5 F2: 1,5 => CTR * ....3198.4.8...1..1.3.......31.7.625.42....19....1..48.6....2.151.8..4...8.1..5.. F2: 2,6,7,9 # 8 pairs * PAIR A4: 8,9 ROW 4 F4: 8,9,1,4 # reduction candidate for 8,9 F4: 8,9 => CTR * ....3198.4.8......1.3.......3147.625.42....19.......48.6....2.151.8..4...8.1..5.. F4: 1,4 => SOLVED * 625438971498716532173295864834971625752684319916352748361549287547823196289167453 * PAIR A4: 8,9 COL A A7: 8,9,3 # reduction candidate for 8,9 A7: 8,9 => CTR * 2.6.389714.8.1.5..1.3...864839471625.42.8..19.15....48961...28.5248..19.3871..456 A7: 3 => SOLVED * 625438971498716532173295864834971625752684319916352748361549287547823196289167453 A9: 8,9,2,3 # reduction candidate for 8,9 A9: 8,9 => CTR * 2.64389714.8...5.21.3...864839.7.625..2.8..19..5....48361...2875..8..1..98.1..45. A9: 2,3 # 9 pairs * PAIR C6: 5,6 ROW 6 D6: 5,6,2,3,9 # reduction candidate for 5,6 D6: 5,6 # 11 pairs E6: 5,6,1,2,9 # reduction candidate for 5,6 E6: 5,6 => SOLVED * 625438971498716532173295864834971625752684319916352748361549287547823196289167453 E6: 1,2,9 # 8 pairs F6: 5,6,1,2,3,9 # reduction candidate for 5,6 F6: 5,6 # 11 pairs * PAIR D4: 4,9 BLK 5 F4: 4,9,1,8 # reduction candidate for 4,9 F4: 4,9 => CTR * ....3.9..4.8......1.3......831.7.625.42....199......4836....28151.8..4..28.1..5.. F4: 1,8 # 9 pairs * PAIR D4: 4,9 ROW 4 C4: 4,9,1 # reduction candidate for 4,9 C4: 4,9 => SOLVED * 625438971498716532173295864834971625752684319916352748361549287547823196289167453 C4: 1 => CTR * ....3198.4.8......1.3.......31.7.625.42....19.......48.6....2.151.8..4...8.1..5.. * PAIR D4: 4,9 COL D D3: 4,9,2,5,6,7 # reduction candidate for 4,9 D3: 4,9 => CTR * 2.6.3.98.4.8......1.3......93.478625..2....19.......4886....2..5..8.....3..1..8.. D3: 2,5,6,7 # 8 pairs D7: 4,9,3,5,7 # reduction candidate for 4,9 D7: 4,9 => CTR * 2.6.3.98.4.8......1.3......93.478625..2....19.......4886....2..5..8.....3..1..8.. D7: 3,5,7 # 8 pairs * PAIR G8: 1,4 BLK 9 I7: 1,4,3,7 # reduction candidate for 1,4 I7: 1,4 # 10 pairs I8: 1,4,3,6,7 # reduction candidate for 1,4 I8: 1,4 => CTR * 2.6.3.9.14.8.1.5..1.3...4..83..71625.42....19.15....48.61...2..52.8..1.4...1..8.. I8: 3,6,7 # 8 pairs * PAIR G8: 1,4 ROW 8 B8: 1,4,2 # reduction candidate for 1,4 B8: 1,4 # 13 pairs C8: 1,4,7,9 # reduction candidate for 1,4 C8: 1,4 => CTR * 2.6.389714.8.1.5..1.3...864839471625.42.8..19.15....48.61.4.28.5248..19..871..45. C8: 7,9 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-325-base-pr-000.dot * REASONING * DIS # F2: 1,5 => CTR => F2: 2,6,7,9 * DIS # F4: 8,9 => CTR => F4: 1,4 * PRF # F4: 1,4 => SOL * DIS # A7: 8,9 => CTR => A7: 3 * PRF # A7: 3 => SOL * DIS # A9: 8,9 => CTR => A9: 2,3 * PRF # E6: 5,6 => SOL * DIS # F4: 4,9 => CTR => F4: 1,8 * PRF # C4: 4,9 => SOL * DIS # C4: 1 => CTR => C4: 4,9 * DIS # D3: 4,9 => CTR => D3: 2,5,6,7 * DIS # D7: 4,9 => CTR => D7: 3,5,7 * DIS # I8: 1,4 => CTR => I8: 3,6,7 * DIS # C8: 1,4 => CTR => C8: 7,9 * CNT 14 HDP CHAINS / 27 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,C1,C6,D4,G2,G5,G6,G8) * ....3.9..4.8......1.3.......3..7.625..2....19.......48.6....2..5..8........1..... * PAIR G2: 1,5 ROW 2 E2: 1,5,2,6,9 # reduction candidate for 1,5 E2: 1,5 # 9 pairs F2: 1,5,2,6,7,9 # reduction candidate for 1,5 F2: 1,5 => CTR * ....3198.4.8...1..1.3.......31.7.625.42....19....1..48.6....2.151.8..4...8.1..5.. * RESTART * PAIR G2: 1,5 ROW 2 E2: 1,5,2,6,9 # reduction candidate for 1,5 E2: 2,6,9 => CTR * ....3198.4.8......1.3.......31.7.625.42....19....1..4886....2.151.8..4..32.1..8.. * PAIR RESTART * PAIR A4: 8,9 ROW 4 F4: 8,9,1,4 # reduction candidate for 8,9 F4: 8,9 => CTR * ....3198.4.8......1.3.......3147.625.42....19.......48.6....2.151.8..4...8.1..5.. F4: 1,4 => SOLVED * 625438971498716532173295864834971625752684319916352748361549287547823196289167453 * DURATION: 0:00:06.247884 START: 14:00:08.476834 END: 14:00:14.724718 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-325-base-pr-001.dot * REASONING * DIS # F2: 1,5 => CTR => F2: 2,6,7,9 * DIS F2: 2,6,7,9 # E2: 2,6,9 => CTR => E2: 1,5 * DIS F2: 2,6,7,9 + E2: 1,5 # F4: 8,9 => CTR => F4: 1,4 * PRF F2: 2,6,7,9 + E2: 1,5 + F4: 1,4 => SOL * STA F2: 2,6,7,9 + E2: 1,5 + F4: 1,4 * CNT 4 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 325 solution: 625438971498716532173295864834971625752684319916352748361549287547823196289167453 info: 2963 FNBHWY S8.f 3942 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 625438971498716532173295864834971625752684319916352748361549287547823196289167453 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:
* INC # E2: 1,5 => UNS * DIS # F2: 1,5 => CTR => F2: 2,6,7,9 * INC # F2: 2,6,7,9 => UNS * DIS # F4: 8,9 => CTR => F4: 1,4 * PRF # F4: 1,4 => SOL * DIS # A7: 8,9 => CTR => A7: 3 * PRF # A7: 3 => SOL * DIS # A9: 8,9 => CTR => A9: 2,3 * INC # A9: 2,3 => UNS * INC # D6: 5,6 => UNS * PRF # E6: 5,6 => SOL * INC # E6: 1,2,9 => UNS * INC # F6: 5,6 => UNS * DIS # F4: 4,9 => CTR => F4: 1,8 * INC # F4: 1,8 => UNS * PRF # C4: 4,9 => SOL * DIS # C4: 1 => CTR => C4: 4,9 * DIS # D3: 4,9 => CTR => D3: 2,5,6,7 * INC # D3: 2,5,6,7 => UNS * DIS # D7: 4,9 => CTR => D7: 3,5,7 * INC # D7: 3,5,7 => UNS * INC # I7: 1,4 => UNS * DIS # I8: 1,4 => CTR => I8: 3,6,7 * INC # I8: 3,6,7 => UNS * INC # B8: 1,4 => UNS * DIS # C8: 1,4 => CTR => C8: 7,9 * INC # C8: 7,9 => UNS * CNT 27 HDP CHAINS / 27 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E2: 1,5 => UNS * DIS # F2: 1,5 => CTR => F2: 2,6,7,9 * INC F2: 2,6,7,9 # E2: 1,5 => UNS * DIS F2: 2,6,7,9 # E2: 2,6,9 => CTR => E2: 1,5 * DIS F2: 2,6,7,9 + E2: 1,5 # F4: 8,9 => CTR => F4: 1,4 * PRF F2: 2,6,7,9 + E2: 1,5 + F4: 1,4 => SOL * STA F2: 2,6,7,9 + E2: 1,5 + F4: 1,4 * CNT 6 HDP CHAINS / 5 HYP OPENED