Analysis of xx-top500-263-base.sdk
Contents
Original Sudoku
level: medium
position: 5.....72.....1....2...........2.3.8..9..........8.....4673...........9.13........ initial
Autosolve
position: 5.19..72.9...12..52....519.1..273689.9815.......8.951.467391.5.8....79313195284.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # I1: 3,8 => SOL * PRF # I1: 3,8 => SOL * DIS # B3: 3,8 => CTR => B3: 4,7 * PRF # I1: 3,8 => SOL * PRF # I3: 4,6 => SOL * CNT 5 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # I1: 3,8 => SOL * STA I1: 3,8 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5.....72.....1....2...........2.3.8..9..........8.....4673...........9.13........ | initial |
| 5.19..72.9...12..52....519.1..273689.9815.......8.951.467391.5.8....79313195284.. | autosolve |
| 541936728986712345273485196154273689698154273732869514467391852825647931319528467 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (25) E1: 3,8 F1: 4,6 E3: 3,8 G2: 3,8 H2: 4,6 B4: 4,5 C4: 4,5 A5: 6,7 A6: 6,7 B6: 2,3 C6: 2,3 F5: 4,6 E6: 4,6 G5: 2,3 H5: 4,7 I5: 2,3 I6: 4,7 B8: 2,5 C8: 2,5 D8: 4,6 E8: 4,6 G7: 2,8 I7: 2,8 H9: 6,7 I9: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B6,C6: 2.. / B6 = 2 => 26 pairs (_) / C6 = 2 => 22 pairs (_) G5,I5: 2.. / G5 = 2 => 23 pairs (_) / I5 = 2 => 22 pairs (_) B8,C8: 2.. / B8 = 2 => 22 pairs (_) / C8 = 2 => 26 pairs (_) G7,I7: 2.. / G7 = 2 => 22 pairs (_) / I7 = 2 => 23 pairs (_) B6,B8: 2.. / B6 = 2 => 26 pairs (_) / B8 = 2 => 22 pairs (_) C6,C8: 2.. / C6 = 2 => 22 pairs (_) / C8 = 2 => 26 pairs (_) G5,G7: 2.. / G5 = 2 => 23 pairs (_) / G7 = 2 => 22 pairs (_) I5,I7: 2.. / I5 = 2 => 22 pairs (_) / I7 = 2 => 23 pairs (_) E1,E3: 3.. / E1 = 3 => 24 pairs (_) / E3 = 3 => 27 pairs (_) B6,C6: 3.. / B6 = 3 => 22 pairs (_) / C6 = 3 => 26 pairs (_) G5,I5: 3.. / G5 = 3 => 22 pairs (_) / I5 = 3 => 23 pairs (_) G2,G5: 3.. / G2 = 3 => 23 pairs (_) / G5 = 3 => 22 pairs (_) B4,C4: 4.. / B4 = 4 => 26 pairs (_) / C4 = 4 => 22 pairs (_) F5,E6: 4.. / F5 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) H5,I6: 4.. / H5 = 4 => 0 pairs (X) / I6 = 4 => 0 pairs (_) D8,E8: 4.. / D8 = 4 => 0 pairs (X) / E8 = 4 => 0 pairs (_) F5,H5: 4.. / F5 = 4 => 0 pairs (*) / H5 = 4 => 0 pairs (X) E6,I6: 4.. / E6 = 4 => 0 pairs (X) / I6 = 4 => 0 pairs (_) E6,E8: 4.. / E6 = 4 => 0 pairs (X) / E8 = 4 => 0 pairs (_) F1,F5: 4.. / F1 = 4 => 0 pairs (X) / F5 = 4 => 0 pairs (_) H2,H5: 4.. / H2 = 4 => 0 pairs (*) / H5 = 4 => 0 pairs (X) B4,C4: 5.. / B4 = 5 => 22 pairs (_) / C4 = 5 => 26 pairs (_) B8,C8: 5.. / B8 = 5 => 26 pairs (_) / C8 = 5 => 22 pairs (_) B4,B8: 5.. / B4 = 5 => 22 pairs (_) / B8 = 5 => 26 pairs (_) C4,C8: 5.. / C4 = 5 => 26 pairs (_) / C8 = 5 => 22 pairs (_) C2,C3: 6.. / C2 = 6 => 0 pairs (*) / C3 = 6 => 0 pairs (X) A5,A6: 6.. / A5 = 6 => 0 pairs (*) / A6 = 6 => 0 pairs (X) F5,E6: 6.. / F5 = 6 => 0 pairs (X) / E6 = 6 => 0 pairs (_) D8,E8: 6.. / D8 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) H9,I9: 6.. / H9 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) F1,I1: 6.. / F1 = 6 => 0 pairs (*) / I1 = 6 => 0 pairs (X) A5,F5: 6.. / A5 = 6 => 0 pairs (*) / F5 = 6 => 0 pairs (X) A6,E6: 6.. / A6 = 6 => 0 pairs (X) / E6 = 6 => 0 pairs (_) E6,E8: 6.. / E6 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) F1,F5: 6.. / F1 = 6 => 0 pairs (*) / F5 = 6 => 0 pairs (X) H2,H9: 6.. / H2 = 6 => 0 pairs (X) / H9 = 6 => 0 pairs (_) B2,B3: 7.. / B2 = 7 => 18 pairs (_) / B3 = 7 => 26 pairs (_) D2,D3: 7.. / D2 = 7 => 26 pairs (_) / D3 = 7 => 18 pairs (_) A5,A6: 7.. / A5 = 7 => 0 pairs (X) / A6 = 7 => 0 pairs (_) H5,I6: 7.. / H5 = 7 => 0 pairs (*) / I6 = 7 => 0 pairs (X) H9,I9: 7.. / H9 = 7 => 0 pairs (X) / I9 = 7 => 0 pairs (_) B2,D2: 7.. / B2 = 7 => 18 pairs (_) / D2 = 7 => 26 pairs (_) B3,D3: 7.. / B3 = 7 => 26 pairs (_) / D3 = 7 => 18 pairs (_) A5,H5: 7.. / A5 = 7 => 0 pairs (X) / H5 = 7 => 0 pairs (_) A6,I6: 7.. / A6 = 7 => 0 pairs (*) / I6 = 7 => 0 pairs (X) H5,H9: 7.. / H5 = 7 => 0 pairs (*) / H9 = 7 => 0 pairs (X) I6,I9: 7.. / I6 = 7 => 0 pairs (X) / I9 = 7 => 0 pairs (_) E1,E3: 8.. / E1 = 8 => 27 pairs (_) / E3 = 8 => 24 pairs (_) G7,I7: 8.. / G7 = 8 => 23 pairs (_) / I7 = 8 => 22 pairs (_) B2,G2: 8.. / B2 = 8 => 23 pairs (_) / G2 = 8 => 22 pairs (_) G2,G7: 8.. / G2 = 8 => 22 pairs (_) / G7 = 8 => 23 pairs (_) * DURATION: 0:01:58.209494 START: 11:50:26.544625 END: 11:52:24.754119 2017-05-04 * CP COUNT: (51) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B4,B6,B8,C4,C6,C8,D8,E1,E3,E6,E8,F1,F5,G2,G5,G7,H2,H5,H9,I5,I6,I7,I9) * 5.19..72.9...12..52....519.1..273689.9815.......8.951.467391.5.8....79313195284.. * PAIR E1: 3,8 ROW 1 B1: 3,8,4 # reduction candidate for 3,8 B1: 3,8 # 30 pairs I1: 3,8,4,6 # reduction candidate for 3,8 I1: 3,8 => SOLVED * 541936728986712345273485196154273689698154273732869514467391852825647931319528467 I1: 4,6 # 30 pairs * PAIR F1: 4,6 BLK 2 D2: 4,6,7 # reduction candidate for 4,6 D2: 4,6 # 18 pairs D3: 4,6,7 # reduction candidate for 4,6 D3: 4,6 # 26 pairs * PAIR F1: 4,6 ROW 1 I1: 4,6,3,8 # reduction candidate for 4,6 I1: 3,8 => SOLVED * 541936728986712345273485196154273689698154273732869514467391852825647931319528467 I1: 4,6 # 30 pairs * PAIR E3: 3,8 ROW 3 B3: 3,8,4,7 # reduction candidate for 3,8 B3: 3,8 => CTR * 5.19..72.973.128.52867351941.4273689.9815.342.32849517467391258825467931319528476 B3: 4,7 # 26 pairs I3: 3,8,4,6 # reduction candidate for 3,8 I3: 3,8 # 30 pairs * PAIR G2: 3,8 BLK 3 I1: 3,8,4,6 # reduction candidate for 3,8 I1: 3,8 => SOLVED * 541936728986712345273485196154273689698154273732869514467391852825647931319528467 I1: 4,6 # 30 pairs I3: 3,8,4,6 # reduction candidate for 3,8 I3: 3,8 # 30 pairs * PAIR G2: 3,8 ROW 2 B2: 3,8,4,7 # reduction candidate for 3,8 B2: 3,8 # 28 pairs B2: 4,7 # 18 pairs * PAIR H2: 4,6 BLK 3 I1: 4,6,3,8 # reduction candidate for 4,6 I1: 4,6 # 30 pairs I3: 4,6,3,8 # reduction candidate for 4,6 I3: 4,6 => SOLVED * 541936728986712345273485196154273689698154273732869514467391852825647931319528467 I3: 3,8 # 30 pairs * PAIR H2: 4,6 ROW 2 C2: 4,6,3 # reduction candidate for 4,6 C2: 4,6 # 28 pairs D2: 4,6,7 # reduction candidate for 4,6 D2: 4,6 # 18 pairs * PAIR D8: 4,6 COL D D2: 4,6,7 # reduction candidate for 4,6 D2: 4,6 # 18 pairs D3: 4,6,7 # reduction candidate for 4,6 D3: 4,6 # 26 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-263-base-pr-000.dot * REASONING * PRF # I1: 3,8 => SOL * PRF # I1: 3,8 => SOL * DIS # B3: 3,8 => CTR => B3: 4,7 * PRF # I1: 3,8 => SOL * PRF # I3: 4,6 => SOL * CNT 5 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B4,B6,B8,C4,C6,C8,D8,E1,E3,E6,E8,F1,F5,G2,G5,G7,H2,H5,H9,I5,I6,I7,I9) * 5.19..72.9...12..52....519.1..273689.9815.......8.951.467391.5.8....79313195284.. * PAIR E1: 3,8 ROW 1 B1: 3,8,4 # reduction candidate for 3,8 B1: 3,8 # 30 pairs I1: 3,8,4,6 # reduction candidate for 3,8 I1: 3,8 => SOLVED * 541936728986712345273485196154273689698154273732869514467391852825647931319528467 * DURATION: 0:00:03.673145 START: 11:52:56.290155 END: 11:52:59.963300 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-263-base-pr-001.dot * REASONING * PRF # I1: 3,8 => SOL * STA I1: 3,8 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 263 solution: 541936728986712345273485196154273689698154273732869514467391852825647931319528467 info: 2097 FNBTWXY S8.f 32160 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 541936728986712345273485196154273689698154273732869514467391852825647931319528467 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 # B1: 3,8 => UNS * PRF # I1: 3,8 => SOL * INC # I1: 4,6 => UNS * INC # D2: 4,6 => UNS * INC # D3: 4,6 => UNS * INC # I1: 4,6 => UNS * PRF # I1: 3,8 => SOL * DIS # B3: 3,8 => CTR => B3: 4,7 * INC # B3: 4,7 => UNS * INC # I3: 3,8 => UNS * PRF # I1: 3,8 => SOL * INC # I1: 4,6 => UNS * INC # I3: 3,8 => UNS * INC # B2: 3,8 => UNS * INC # B2: 4,7 => UNS * INC # I1: 4,6 => UNS * PRF # I3: 4,6 => SOL * INC # I3: 3,8 => UNS * INC # C2: 4,6 => UNS * INC # D2: 4,6 => UNS * INC # D2: 4,6 => UNS * INC # D3: 4,6 => UNS * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 3,8 => UNS * PRF # I1: 3,8 => SOL * STA I1: 3,8 * CNT 2 HDP CHAINS / 2 HYP OPENED