Analysis of xx-top500-446-base.sdk
Contents
Original Sudoku
level: medium
position: ......23..1..5....4..6..........34.86...2......7.........7...61..2.......5....... initial
Autosolve
position: 56..7123.71325....42.63....2951634786.1.27.....7..5.....47.2561.725.6....563..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H2: 4,9 => CTR => H2: 8 * DIS # I2: 4,9 => CTR => I2: 6 * DIS # H2: 4,9 => CTR => H2: 8 * DIS # I2: 4,9 => CTR => I2: 6 * DIS # I8: 4,9 => CTR => I8: 3 * DIS # I5: 3,9 => CTR => I5: 5 * DIS # I5: 3 => CTR => I5: 5,9 * CNT 7 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H2: 4,9 => CTR => H2: 8 * DIS H2: 8 # I2: 4,9 => CTR => I2: 6 * PRF H2: 8 + I2: 6 => SOL * STA H2: 8 + I2: 6 * CNT 3 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......23..1..5....4..6..........34.86...2......7.........7...61..2.......5....... | initial |
| 56..7123.71325....42.63....2951634786.1.27.....7..5.....47.2561.725.6....563..... | autosolve |
| 569871234713254986428639157295163478681427395347985612834792561972516843156348729 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) C1: 8,9 C3: 8,9 F2: 4,9 F3: 8,9 I1: 4,9 G3: 1,7 H3: 1,5 I3: 5,7 B5: 4,8 A6: 3,8 D5: 4,8 G5: 3,9 H5: 5,9 G6: 1,6 H6: 1,2 I6: 2,6 B7: 3,8 E7: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G3,H3: 1.. / G3 = 1 => 16 pairs (_) / H3 = 1 => 0 pairs (X) G6,H6: 1.. / G6 = 1 => 0 pairs (X) / H6 = 1 => 16 pairs (_) A8,A9: 1.. / A8 = 1 => 19 pairs (_) / A9 = 1 => 19 pairs (_) E8,E9: 1.. / E8 = 1 => 19 pairs (_) / E9 = 1 => 19 pairs (_) A8,E8: 1.. / A8 = 1 => 19 pairs (_) / E8 = 1 => 19 pairs (_) A9,E9: 1.. / A9 = 1 => 19 pairs (_) / E9 = 1 => 19 pairs (_) G3,G6: 1.. / G3 = 1 => 16 pairs (_) / G6 = 1 => 0 pairs (X) H3,H6: 1.. / H3 = 1 => 0 pairs (X) / H6 = 1 => 16 pairs (_) H6,I6: 2.. / H6 = 2 => 0 pairs (X) / I6 = 2 => 16 pairs (_) H9,I9: 2.. / H9 = 2 => 16 pairs (_) / I9 = 2 => 0 pairs (X) H6,H9: 2.. / H6 = 2 => 0 pairs (X) / H9 = 2 => 16 pairs (_) I6,I9: 2.. / I6 = 2 => 16 pairs (_) / I9 = 2 => 0 pairs (X) A6,B6: 3.. / A6 = 3 => 18 pairs (_) / B6 = 3 => 18 pairs (_) G5,I5: 3.. / G5 = 3 => 19 pairs (_) / I5 = 3 => 0 pairs (X) A7,B7: 3.. / A7 = 3 => 18 pairs (_) / B7 = 3 => 18 pairs (_) G8,I8: 3.. / G8 = 3 => 0 pairs (X) / I8 = 3 => 19 pairs (_) A6,A7: 3.. / A6 = 3 => 18 pairs (_) / A7 = 3 => 18 pairs (_) B6,B7: 3.. / B6 = 3 => 18 pairs (_) / B7 = 3 => 18 pairs (_) G5,G8: 3.. / G5 = 3 => 19 pairs (_) / G8 = 3 => 0 pairs (X) I5,I8: 3.. / I5 = 3 => 0 pairs (X) / I8 = 3 => 19 pairs (_) D1,F2: 4.. / D1 = 4 => 18 pairs (_) / F2 = 4 => 24 pairs (_) B5,B6: 4.. / B5 = 4 => 18 pairs (_) / B6 = 4 => 22 pairs (_) D1,I1: 4.. / D1 = 4 => 18 pairs (_) / I1 = 4 => 24 pairs (_) B5,D5: 4.. / B5 = 4 => 18 pairs (_) / D5 = 4 => 22 pairs (_) F2,F9: 4.. / F2 = 4 => 24 pairs (_) / F9 = 4 => 18 pairs (_) H3,I3: 5.. / H3 = 5 => 16 pairs (_) / I3 = 5 => 0 pairs (X) H5,I5: 5.. / H5 = 5 => 0 pairs (X) / I5 = 5 => 16 pairs (_) H3,H5: 5.. / H3 = 5 => 16 pairs (_) / H5 = 5 => 0 pairs (X) I3,I5: 5.. / I3 = 5 => 0 pairs (X) / I5 = 5 => 16 pairs (_) G2,I2: 6.. / G2 = 6 => 0 pairs (X) / I2 = 6 => 16 pairs (_) G6,I6: 6.. / G6 = 6 => 16 pairs (_) / I6 = 6 => 0 pairs (X) G2,G6: 6.. / G2 = 6 => 0 pairs (X) / G6 = 6 => 16 pairs (_) I2,I6: 6.. / I2 = 6 => 16 pairs (_) / I6 = 6 => 0 pairs (X) G3,I3: 7.. / G3 = 7 => 0 pairs (X) / I3 = 7 => 16 pairs (_) G9,I9: 7.. / G9 = 7 => 16 pairs (_) / I9 = 7 => 0 pairs (X) G3,G9: 7.. / G3 = 7 => 0 pairs (X) / G9 = 7 => 16 pairs (_) I3,I9: 7.. / I3 = 7 => 16 pairs (_) / I9 = 7 => 0 pairs (X) C1,C3: 8.. / C1 = 8 => 18 pairs (_) / C3 = 8 => 16 pairs (_) D1,F3: 8.. / D1 = 8 => 16 pairs (_) / F3 = 8 => 18 pairs (_) G2,H2: 8.. / G2 = 8 => 0 pairs (X) / H2 = 8 => 21 pairs (_) C1,D1: 8.. / C1 = 8 => 18 pairs (_) / D1 = 8 => 16 pairs (_) C3,F3: 8.. / C3 = 8 => 16 pairs (_) / F3 = 8 => 18 pairs (_) B5,D5: 8.. / B5 = 8 => 22 pairs (_) / D5 = 8 => 18 pairs (_) F3,F9: 8.. / F3 = 8 => 18 pairs (_) / F9 = 8 => 16 pairs (_) C1,C3: 9.. / C1 = 9 => 16 pairs (_) / C3 = 9 => 18 pairs (_) D6,E6: 9.. / D6 = 9 => 21 pairs (_) / E6 = 9 => 21 pairs (_) C3,F3: 9.. / C3 = 9 => 18 pairs (_) / F3 = 9 => 16 pairs (_) A7,E7: 9.. / A7 = 9 => 18 pairs (_) / E7 = 9 => 23 pairs (_) D1,D6: 9.. / D1 = 9 => 21 pairs (_) / D6 = 9 => 21 pairs (_) * DURATION: 0:01:28.240684 START: 17:59:08.085785 END: 18:00:36.326469 2017-05-04 * CP COUNT: (49) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B5,B7,C1,C3,D5,E7,F2,F3,G3,G5,G6,H3,H5,H6,I1,I3,I6) * 56..7123.71325....42.63....2951634786.1.27.....7..5.....47.2561.725.6....563..... * PAIR C1: 8,9 ROW 1 D1: 8,9,4 # reduction candidate for 8,9 D1: 8,9 # 24 pairs D1: 4 # 18 pairs * PAIR F2: 4,9 BLK 2 D1: 4,9,8 # reduction candidate for 4,9 D1: 4,9 # 18 pairs D1: 8 # 16 pairs * PAIR F2: 4,9 ROW 2 H2: 4,9,8 # reduction candidate for 4,9 H2: 4,9 => CTR * 56..7123.71325.8.642.63.1572951634786.1.27.95..7..5612..47.2561.725.6.83.563..724 H2: 8 # 21 pairs I2: 4,9,6 # reduction candidate for 4,9 I2: 4,9 => CTR * 56..7123.71325.68.42.63.7152951634786.1.27.5...7..5126..47.2561.725.6....563....2 I2: 6 # 16 pairs * PAIR F2: 4,9 COL F F9: 4,9,8 # reduction candidate for 4,9 F9: 4,9 # 18 pairs F9: 8 # 16 pairs * PAIR F3: 8,9 BLK 2 D1: 8,9,4 # reduction candidate for 8,9 D1: 8,9 # 24 pairs D1: 4 # 18 pairs * PAIR F3: 8,9 COL F F9: 8,9,4 # reduction candidate for 8,9 F9: 8,9 # 24 pairs F9: 4 # 18 pairs * PAIR I1: 4,9 BLK 3 H2: 4,9,8 # reduction candidate for 4,9 H2: 4,9 => CTR * 56..7123.71325.8.642.63.1572951634786.1.27.95..7..5612..47.2561.725.6.83.563..724 H2: 8 # 21 pairs I2: 4,9,6 # reduction candidate for 4,9 I2: 4,9 => CTR * 56..7123.71325.68.42.63.7152951634786.1.27.5...7..5126..47.2561.725.6....563....2 I2: 6 # 16 pairs * PAIR I1: 4,9 ROW 1 D1: 4,9,8 # reduction candidate for 4,9 D1: 4,9 # 18 pairs D1: 8 # 16 pairs * PAIR I1: 4,9 COL I I8: 4,9,3 # reduction candidate for 4,9 I8: 4,9 => CTR * 56..7123.71325....42.63.7152951634786.1.27953..7..512...47.2561.725.63...563....7 I8: 3 # 19 pairs I9: 4,9,2,7 # reduction candidate for 4,9 I9: 4,9 # 16 pairs * PAIR B5: 4,8 BLK 4 B6: 4,8,3 # reduction candidate for 4,8 B6: 4,8 # 18 pairs B6: 3 # 18 pairs * PAIR A6: 3,8 BLK 4 B6: 3,8,4 # reduction candidate for 3,8 B6: 4 # 22 pairs B6: 3,8 # 18 pairs * PAIR A6: 3,8 COL A A7: 3,8,9 # reduction candidate for 3,8 A7: 3,8 # 23 pairs A7: 9 # 18 pairs * PAIR D5: 4,8 BLK 5 D6: 4,8,9 # reduction candidate for 4,8 D6: 4,8 # 21 pairs E6: 4,8,9 # reduction candidate for 4,8 E6: 4,8 # 21 pairs * PAIR D5: 4,8 COL D D1: 4,8,9 # reduction candidate for 4,8 D1: 9 # 21 pairs D1: 4,8 # 21 pairs * PAIR G5: 3,9 BLK 6 I5: 3,9,5 # reduction candidate for 3,9 I5: 3,9 => CTR * 56..7123.71325....42.63.7152951634786.1.27.5...7..512...47.2561.725.6....563....7 I5: 5 # 16 pairs * PAIR G5: 3,9 COL G G8: 3,9,8 # reduction candidate for 3,9 G8: 8 # 22 pairs G8: 3,9 # 21 pairs * PAIR H5: 5,9 BLK 6 I5: 5,9,3 # reduction candidate for 5,9 I5: 3 => CTR * 56..7123.71325....42.63.7152951634786.1.27953..7..512...47.2561.725.63...563....7 I5: 5,9 # 19 pairs * PAIR B7: 3,8 BLK 7 A7: 3,8,9 # reduction candidate for 3,8 A7: 3,8 # 23 pairs A7: 9 # 18 pairs * PAIR B7: 3,8 COL B B6: 3,8,4 # reduction candidate for 3,8 B6: 4 # 22 pairs B6: 3,8 # 18 pairs * PAIR E7: 8,9 BLK 8 E8: 8,9,1,4 # reduction candidate for 8,9 E8: 8,9 # 20 pairs E9: 8,9,1,4 # reduction candidate for 8,9 E9: 8,9 # 20 pairs F9: 8,9,4 # reduction candidate for 8,9 F9: 8,9 # 24 pairs * PAIR E7: 8,9 ROW 7 A7: 8,9,3 # reduction candidate for 8,9 A7: 8,9 # 18 pairs A7: 3 # 18 pairs * PAIR E7: 8,9 COL E E6: 8,9,4 # reduction candidate for 8,9 E6: 8,9 # 24 pairs E6: 4 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-446-base-pr-000.dot * REASONING * DIS # H2: 4,9 => CTR => H2: 8 * DIS # I2: 4,9 => CTR => I2: 6 * DIS # H2: 4,9 => CTR => H2: 8 * DIS # I2: 4,9 => CTR => I2: 6 * DIS # I8: 4,9 => CTR => I8: 3 * DIS # I5: 3,9 => CTR => I5: 5 * DIS # I5: 3 => CTR => I5: 5,9 * CNT 7 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B5,B7,C1,C3,D5,E7,F2,F3,G3,G5,G6,H3,H5,H6,I1,I3,I6) * 56..7123.71325....42.63....2951634786.1.27.....7..5.....47.2561.725.6....563..... * PAIR C1: 8,9 ROW 1 D1: 8,9,4 # reduction candidate for 8,9 D1: 8,9 # 24 pairs D1: 4 # 18 pairs * PAIR F2: 4,9 BLK 2 D1: 4,9,8 # reduction candidate for 4,9 D1: 4,9 # 18 pairs D1: 8 # 16 pairs * PAIR F2: 4,9 ROW 2 H2: 4,9,8 # reduction candidate for 4,9 H2: 4,9 => CTR * 56..7123.71325.8.642.63.1572951634786.1.27.95..7..5612..47.2561.725.6.83.563..724 I2: 4,9,6 # reduction candidate for 4,9 I2: 4,9 => CTR * 56..7123.71325.68.42.63.7152951634786.1.27.5...7..5126..47.2561.725.6....563....2 I2: 6 => SOLVED * 569871234713254986428639157295163478681427395347985612834792561972516843156348729 * DURATION: 0:00:06.861469 START: 18:01:24.864882 END: 18:01:31.726351 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-446-base-pr-001.dot * REASONING * DIS # H2: 4,9 => CTR => H2: 8 * DIS H2: 8 # I2: 4,9 => CTR => I2: 6 * PRF H2: 8 + I2: 6 => SOL * STA H2: 8 + I2: 6 * CNT 3 HDP CHAINS / 6 HYP OPENED
Header Info
Top 500 Minimum 17 446 solution: 569871234713254986428639157295163478681427395347985612834792561972516843156348729 info: 95340 FNBTHXK S8.f 45384 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 569871234713254986428639157295163478681427395347985612834792561972516843156348729 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 # D1: 8,9 => UNS * INC # D1: 4 => UNS * INC # D1: 4,9 => UNS * INC # D1: 8 => UNS * DIS # H2: 4,9 => CTR => H2: 8 * INC # H2: 8 => UNS * DIS # I2: 4,9 => CTR => I2: 6 * INC # I2: 6 => UNS * INC # F9: 4,9 => UNS * INC # F9: 8 => UNS * INC # D1: 8,9 => UNS * INC # D1: 4 => UNS * INC # F9: 8,9 => UNS * INC # F9: 4 => UNS * DIS # H2: 4,9 => CTR => H2: 8 * INC # H2: 8 => UNS * DIS # I2: 4,9 => CTR => I2: 6 * INC # I2: 6 => UNS * INC # D1: 4,9 => UNS * INC # D1: 8 => UNS * DIS # I8: 4,9 => CTR => I8: 3 * INC # I8: 3 => UNS * INC # I9: 4,9 => UNS * INC # B6: 4,8 => UNS * INC # B6: 3 => UNS * INC # B6: 3,8 => UNS * INC # B6: 4 => UNS * INC # A7: 3,8 => UNS * INC # A7: 9 => UNS * INC # D6: 4,8 => UNS * INC # E6: 4,8 => UNS * INC # D1: 4,8 => UNS * INC # D1: 9 => UNS * DIS # I5: 3,9 => CTR => I5: 5 * INC # I5: 5 => UNS * INC # G8: 3,9 => UNS * INC # G8: 8 => UNS * INC # I5: 5,9 => UNS * DIS # I5: 3 => CTR => I5: 5,9 * INC # A7: 3,8 => UNS * INC # A7: 9 => UNS * INC # B6: 3,8 => UNS * INC # B6: 4 => UNS * INC # E8: 8,9 => UNS * INC # E9: 8,9 => UNS * INC # F9: 8,9 => UNS * INC # A7: 8,9 => UNS * INC # A7: 3 => UNS * INC # E6: 8,9 => UNS * INC # E6: 4 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D1: 8,9 => UNS * INC # D1: 4 => UNS * INC # D1: 4,9 => UNS * INC # D1: 8 => UNS * DIS # H2: 4,9 => CTR => H2: 8 * DIS H2: 8 # I2: 4,9 => CTR => I2: 6 * PRF H2: 8 + I2: 6 => SOL * STA H2: 8 + I2: 6 * CNT 7 HDP CHAINS / 6 HYP OPENED