Analysis of xx-top500-225-base.sdk
Contents
Original Sudoku
level: medium
position: 2.1.........1....7......58.....423...5..6.....8.....4.3.....6.....8........7..... initial
Autosolve
position: 271.85...8.51....7......581....423.845..6871..8.....4.3.8...67....8..1.....7..8.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 6,9 => CTR => B3: 3,4 * DIS # C3: 6,9 => CTR => C3: 4 * DIS # D3: 2 => CTR => D3: 4,6 * DIS # E3: 3,9 => CTR => E3: 2,7 * DIS # F3: 3,9 => CTR => F3: 4,7 * DIS # B2: 3,9 => CTR => B2: 4,6 * PRF # D6: 5,9 => SOL * DIS # D6: 3 => CTR => D6: 5,9 * PRF # D6: 3,9 => SOL * DIS # D6: 5 => CTR => D6: 3,9 * DIS # D3: 2,4 => CTR => D3: 6 * PRF # D3: 6 => SOL * CNT 12 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 6,9 => CTR => B3: 3,4 * DIS B3: 3,4 # C3: 6,9 => CTR => C3: 4 * PRF B3: 3,4 + C3: 4 # F2: 3,9 => SOL * STA B3: 3,4 + C3: 4 + F2: 3,9 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2.1.........1....7......58.....423...5..6.....8.....4.3.....6.....8........7..... | initial |
| 271.85...8.51....7......581....423.845..6871..8.....4.3.8...67....8..1.....7..8.. | autosolve |
| 271485936865193427934627581197542368452368719683971245318259674749836152526714893 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (21) A3: 6,9 D1: 4,6 E2: 3,9 G1: 4,9 G2: 2,4 H2: 2,6 A4: 1,7 C5: 2,3 A6: 6,9 C6: 2,3 D4: 5,9 D5: 3,9 E6: 1,7 F6: 1,7 H4: 5,6 I5: 2,9 G6: 2,9 I6: 5,6 A8: 5,7 A9: 1,5 D7: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A4,B4: 1.. / A4 = 1 => 19 pairs (_) / B4 = 1 => 19 pairs (_) E6,F6: 1.. / E6 = 1 => 0 pairs (X) / F6 = 1 => 20 pairs (_) A4,A9: 1.. / A4 = 1 => 19 pairs (_) / A9 = 1 => 19 pairs (_) D3,E3: 2.. / D3 = 2 => 0 pairs (X) / E3 = 2 => 22 pairs (_) G2,H2: 2.. / G2 = 2 => 0 pairs (X) / H2 = 2 => 0 pairs (_) C5,C6: 2.. / C5 = 2 => 0 pairs (*) / C6 = 2 => 0 pairs (X) I5,G6: 2.. / I5 = 2 => 0 pairs (X) / G6 = 2 => 0 pairs (_) C5,I5: 2.. / C5 = 2 => 0 pairs (*) / I5 = 2 => 0 pairs (X) C6,G6: 2.. / C6 = 2 => 0 pairs (X) / G6 = 2 => 0 pairs (_) D3,D7: 2.. / D3 = 2 => 0 pairs (X) / D7 = 2 => 22 pairs (_) G2,G6: 2.. / G2 = 2 => 0 pairs (X) / G6 = 2 => 0 pairs (_) B2,B3: 3.. / B2 = 3 => 0 pairs (X) / B3 = 3 => 21 pairs (_) H1,I1: 3.. / H1 = 3 => 22 pairs (_) / I1 = 3 => 0 pairs (X) C5,C6: 3.. / C5 = 3 => 0 pairs (X) / C6 = 3 => 0 pairs (_) D5,D6: 3.. / D5 = 3 => 0 pairs (*) / D6 = 3 => 0 pairs (X) C5,D5: 3.. / C5 = 3 => 0 pairs (X) / D5 = 3 => 0 pairs (_) C6,D6: 3.. / C6 = 3 => 0 pairs (*) / D6 = 3 => 0 pairs (X) G1,G2: 4.. / G1 = 4 => 0 pairs (X) / G2 = 4 => 0 pairs (_) D1,G1: 4.. / D1 = 4 => 0 pairs (*) / G1 = 4 => 0 pairs (X) D4,D6: 5.. / D4 = 5 => 0 pairs (*) / D6 = 5 => 0 pairs (X) H4,I6: 5.. / H4 = 5 => 0 pairs (X) / I6 = 5 => 0 pairs (_) A8,A9: 5.. / A8 = 5 => 19 pairs (_) / A9 = 5 => 19 pairs (_) D4,H4: 5.. / D4 = 5 => 0 pairs (*) / H4 = 5 => 0 pairs (X) D6,I6: 5.. / D6 = 5 => 0 pairs (X) / I6 = 5 => 0 pairs (_) E7,I7: 5.. / E7 = 5 => 21 pairs (_) / I7 = 5 => 0 pairs (X) D1,D3: 6.. / D1 = 6 => 0 pairs (X) / D3 = 6 => 0 pairs (_) H4,I6: 6.. / H4 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) F8,F9: 6.. / F8 = 6 => 21 pairs (_) / F9 = 6 => 22 pairs (_) B2,H2: 6.. / B2 = 6 => 0 pairs (*) / H2 = 6 => 0 pairs (X) A6,I6: 6.. / A6 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) A3,A6: 6.. / A3 = 6 => 0 pairs (X) / A6 = 6 => 0 pairs (_) I1,I6: 6.. / I1 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) E3,F3: 7.. / E3 = 7 => 0 pairs (X) / F3 = 7 => 20 pairs (_) A4,C4: 7.. / A4 = 7 => 19 pairs (_) / C4 = 7 => 19 pairs (_) E6,F6: 7.. / E6 = 7 => 20 pairs (_) / F6 = 7 => 0 pairs (X) A8,C8: 7.. / A8 = 7 => 19 pairs (_) / C8 = 7 => 19 pairs (_) A4,A8: 7.. / A4 = 7 => 19 pairs (_) / A8 = 7 => 19 pairs (_) C4,C8: 7.. / C4 = 7 => 19 pairs (_) / C8 = 7 => 19 pairs (_) E3,E6: 7.. / E3 = 7 => 0 pairs (X) / E6 = 7 => 20 pairs (_) F3,F6: 7.. / F3 = 7 => 20 pairs (_) / F6 = 7 => 0 pairs (X) I5,G6: 9.. / I5 = 9 => 0 pairs (*) / G6 = 9 => 0 pairs (X) D5,I5: 9.. / D5 = 9 => 0 pairs (X) / I5 = 9 => 0 pairs (_) A3,A6: 9.. / A3 = 9 => 0 pairs (*) / A6 = 9 => 0 pairs (X) G1,G6: 9.. / G1 = 9 => 0 pairs (*) / G6 = 9 => 0 pairs (X) * DURATION: 0:01:32.327269 START: 10:32:02.404778 END: 10:33:34.732047 2017-05-04 * CP COUNT: (44) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A6,A8,A9,C5,C6,D1,D4,D5,D7,E2,E6,F6,G1,G2,G6,H2,H4,I5,I6) * 271.85...8.51....7......581....423.845..6871..8.....4.3.8...67....8..1.....7..8.. * PAIR A3: 6,9 BLK 1 B2: 6,9,3,4 # reduction candidate for 6,9 B2: 6,9 # 25 pairs B3: 6,9,3,4 # reduction candidate for 6,9 B3: 6,9 => CTR * 271.85...835194267..4...581....4235845..68712.82....4.3.8...67....8..1.....7..8.. B3: 3,4 # 22 pairs C3: 6,9,4 # reduction candidate for 6,9 C3: 6,9 => CTR * 2716854..8.51..267......581....4235845..68712.82....4.3.8...67....8..1.....7..8.. C3: 4 # 23 pairs * PAIR D1: 4,6 BLK 2 D3: 4,6,2 # reduction candidate for 4,6 D3: 2 => CTR * 2716854..8.51..267...2..581....4235845..68712.82....4.3.8...67....8..1.....7..8.. D3: 4,6 # 22 pairs * PAIR E2: 3,9 BLK 2 F2: 3,9,4 # reduction candidate for 3,9 F2: 3,9 # 25 pairs E3: 3,9,2,7 # reduction candidate for 3,9 E3: 3,9 => CTR * 2716854..8.51.4267...2.7581....4235845..68712.82.71.4.3.84.967....8..1.....7..8.. E3: 2,7 # 22 pairs F3: 3,9,4,7 # reduction candidate for 3,9 F3: 3,9 => CTR * 2716854..8.51.4267...27.581....4235845..68712.82.17.4.3.84..67....8..1.....7..8.. F3: 4,7 # 22 pairs * PAIR E2: 3,9 ROW 2 B2: 3,9,4,6 # reduction candidate for 3,9 B2: 3,9 => CTR * 2716854..8.51.42676..2..581...94235845.36871..8.5...463.8...67....8..1.....7..8.. B2: 4,6 # 25 pairs * PAIR E2: 3,9 COL E E8: 3,9,2,5 # reduction candidate for 3,9 E8: 3,9 # 23 pairs E9: 3,9,1,2,5 # reduction candidate for 3,9 E9: 3,9 # 24 pairs * PAIR A6: 6,9 BLK 4 B4: 6,9,1 # reduction candidate for 6,9 B4: 6,9 # 19 pairs C4: 6,9,7 # reduction candidate for 6,9 C4: 6,9 # 19 pairs * PAIR D4: 5,9 BLK 5 D6: 5,9,3 # reduction candidate for 5,9 D6: 5,9 => SOLVED * 271485936865193427934627581197542368452368719683971245318259674749836152526714893 D6: 3 => CTR * 271.854.68.51....7......581...54236845.9687126823..9453.8.5.67....8..1.....7..8.. * PAIR D5: 3,9 BLK 5 D6: 3,9,5 # reduction candidate for 3,9 D6: 3,9 => SOLVED * 271485936865193427934627581197542368452368719683971245318259674749836152526714893 D6: 5 => CTR * 271.859.38.51..4276.....581...9423.845.3687199835..2463.8...67....8..1.....7..8.. * PAIR I5: 2,9 COL I I7: 2,9,4,5 # reduction candidate for 2,9 I7: 2,9 # 23 pairs I8: 2,9,3,4,5 # reduction candidate for 2,9 I8: 2,9 # 24 pairs I9: 2,9,3,4,5 # reduction candidate for 2,9 I9: 2,9 # 24 pairs * PAIR A9: 1,5 ROW 9 E9: 1,5,2,3,9 # reduction candidate for 1,5 E9: 1,5 # 22 pairs E9: 2,3,9 # 21 pairs * PAIR D7: 2,4 ROW 7 B7: 2,4,1,9 # reduction candidate for 2,4 B7: 2,4 # 24 pairs I7: 2,4,5,9 # reduction candidate for 2,4 I7: 2,4 # 24 pairs * PAIR D7: 2,4 COL D D3: 2,4,6 # reduction candidate for 2,4 D3: 2,4 => CTR * 2716854..8.51..267......581....4235845..68712.82....4.3.8...67....8..1.....7..8.. D3: 6 => SOLVED * 271485936865193427934627581197542368452368719683971245318259674749836152526714893 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-225-base-pr-000.dot * REASONING * DIS # B3: 6,9 => CTR => B3: 3,4 * DIS # C3: 6,9 => CTR => C3: 4 * DIS # D3: 2 => CTR => D3: 4,6 * DIS # E3: 3,9 => CTR => E3: 2,7 * DIS # F3: 3,9 => CTR => F3: 4,7 * DIS # B2: 3,9 => CTR => B2: 4,6 * PRF # D6: 5,9 => SOL * DIS # D6: 3 => CTR => D6: 5,9 * PRF # D6: 3,9 => SOL * DIS # D6: 5 => CTR => D6: 3,9 * DIS # D3: 2,4 => CTR => D3: 6 * PRF # D3: 6 => SOL * CNT 12 HDP CHAINS / 31 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A6,A8,A9,C5,C6,D1,D4,D5,D7,E2,E6,F6,G1,G2,G6,H2,H4,I5,I6) * 271.85...8.51....7......581....423.845..6871..8.....4.3.8...67....8..1.....7..8.. * PAIR A3: 6,9 BLK 1 B2: 6,9,3,4 # reduction candidate for 6,9 B2: 6,9 # 25 pairs B3: 6,9,3,4 # reduction candidate for 6,9 B3: 6,9 => CTR * 271.85...835194267..4...581....4235845..68712.82....4.3.8...67....8..1.....7..8.. C3: 6,9,4 # reduction candidate for 6,9 C3: 6,9 => CTR * 2716854..8.51..267......581....4235845..68712.82....4.3.8...67....8..1.....7..8.. * RESTART * PAIR E2: 3,9 BLK 2 F2: 3,9,4 # reduction candidate for 3,9 F2: 3,9 => SOLVED * 271485936865193427934627581197542368452368719683971245318259674749836152526714893 * DURATION: 0:00:06.215198 START: 10:34:11.255416 END: 10:34:17.470614 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-225-base-pr-001.dot * REASONING * DIS # B3: 6,9 => CTR => B3: 3,4 * DIS B3: 3,4 # C3: 6,9 => CTR => C3: 4 * PRF B3: 3,4 + C3: 4 # F2: 3,9 => SOL * STA B3: 3,4 + C3: 4 + F2: 3,9 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 225 solution: 271485936865193427934627581197542368452368719683971245318259674749836152526714893 info: 2040 FNBTHWY S8.f 27982 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 271485936865193427934627581197542368452368719683971245318259674749836152526714893 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 # B2: 6,9 => UNS * DIS # B3: 6,9 => CTR => B3: 3,4 * INC # B3: 3,4 => UNS * DIS # C3: 6,9 => CTR => C3: 4 * INC # C3: 4 => UNS * INC # D3: 4,6 => UNS * DIS # D3: 2 => CTR => D3: 4,6 * INC # F2: 3,9 => UNS * DIS # E3: 3,9 => CTR => E3: 2,7 * INC # E3: 2,7 => UNS * DIS # F3: 3,9 => CTR => F3: 4,7 * INC # F3: 4,7 => UNS * DIS # B2: 3,9 => CTR => B2: 4,6 * INC # B2: 4,6 => UNS * INC # E8: 3,9 => UNS * INC # E9: 3,9 => UNS * INC # B4: 6,9 => UNS * INC # C4: 6,9 => UNS * PRF # D6: 5,9 => SOL * DIS # D6: 3 => CTR => D6: 5,9 * PRF # D6: 3,9 => SOL * DIS # D6: 5 => CTR => D6: 3,9 * INC # I7: 2,9 => UNS * INC # I8: 2,9 => UNS * INC # I9: 2,9 => UNS * INC # E9: 1,5 => UNS * INC # E9: 2,3,9 => UNS * INC # B7: 2,4 => UNS * INC # I7: 2,4 => UNS * DIS # D3: 2,4 => CTR => D3: 6 * PRF # D3: 6 => SOL * CNT 31 HDP CHAINS / 31 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 6,9 => UNS * DIS # B3: 6,9 => CTR => B3: 3,4 * DIS B3: 3,4 # C3: 6,9 => CTR => C3: 4 * PRF B3: 3,4 + C3: 4 # F2: 3,9 => SOL * STA B3: 3,4 + C3: 4 + F2: 3,9 * CNT 4 HDP CHAINS / 4 HYP OPENED