Analysis of xx-top500-439-base.sdk
Contents
Original Sudoku
level: medium
position: ......23..1..5....7..6..........34.96...2......8.........8...61..2.......5....... initial
Autosolve
position: 56..8123.81325....72.63....2751634896.1.28.....8..5.....78.2561.825.6....563..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # H2: 4,7 => SOL * DIS # I2: 4,7 => CTR => I2: 6 * PRF # H2: 4,7 => SOL * DIS # I2: 4,7 => CTR => I2: 6 * DIS # I8: 4,7 => CTR => I8: 3 * DIS # I5: 3,7 => CTR => I5: 5 * DIS # I5: 3 => CTR => I5: 5,7 * CNT 7 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # H2: 4,7 => SOL * STA H2: 4,7 * CNT 1 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......23..1..5....7..6..........34.96...2......8.........8...61..2.......5....... | initial |
| 56..8123.81325....72.63....2751634896.1.28.....8..5.....78.2561.825.6....563..... | autosolve |
| 564981237813257946729634158275163489691428375348795612937842561482516793156379824 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) C1: 4,9 C3: 4,9 F2: 4,7 F3: 4,9 I1: 4,7 G3: 1,8 H3: 1,5 I3: 5,8 B5: 4,9 D5: 4,9 G5: 3,7 H5: 5,7 G6: 1,6 H6: 1,2 I6: 2,6 E7: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G3,H3: 1.. / G3 = 1 => 14 pairs (_) / H3 = 1 => 0 pairs (X) G6,H6: 1.. / G6 = 1 => 0 pairs (X) / H6 = 1 => 14 pairs (_) A8,A9: 1.. / A8 = 1 => 17 pairs (_) / A9 = 1 => 18 pairs (_) E8,E9: 1.. / E8 = 1 => 18 pairs (_) / E9 = 1 => 17 pairs (_) A8,E8: 1.. / A8 = 1 => 17 pairs (_) / E8 = 1 => 18 pairs (_) A9,E9: 1.. / A9 = 1 => 18 pairs (_) / E9 = 1 => 17 pairs (_) G3,G6: 1.. / G3 = 1 => 14 pairs (_) / G6 = 1 => 0 pairs (X) H3,H6: 1.. / H3 = 1 => 0 pairs (X) / H6 = 1 => 14 pairs (_) H6,I6: 2.. / H6 = 2 => 0 pairs (X) / I6 = 2 => 14 pairs (_) H9,I9: 2.. / H9 = 2 => 14 pairs (_) / I9 = 2 => 0 pairs (X) H6,H9: 2.. / H6 = 2 => 0 pairs (X) / H9 = 2 => 14 pairs (_) I6,I9: 2.. / I6 = 2 => 14 pairs (_) / I9 = 2 => 0 pairs (X) A6,B6: 3.. / A6 = 3 => 18 pairs (_) / B6 = 3 => 18 pairs (_) G5,I5: 3.. / G5 = 3 => 17 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 => 17 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 => 17 pairs (_) / G8 = 3 => 0 pairs (X) I5,I8: 3.. / I5 = 3 => 0 pairs (X) / I8 = 3 => 17 pairs (_) C1,C3: 4.. / C1 = 4 => 18 pairs (_) / C3 = 4 => 16 pairs (_) C3,F3: 4.. / C3 = 4 => 16 pairs (_) / F3 = 4 => 18 pairs (_) B5,D5: 4.. / B5 = 4 => 18 pairs (_) / D5 = 4 => 21 pairs (_) H3,I3: 5.. / H3 = 5 => 14 pairs (_) / I3 = 5 => 0 pairs (X) H5,I5: 5.. / H5 = 5 => 0 pairs (X) / I5 = 5 => 14 pairs (_) H3,H5: 5.. / H3 = 5 => 14 pairs (_) / H5 = 5 => 0 pairs (X) I3,I5: 5.. / I3 = 5 => 0 pairs (X) / I5 = 5 => 14 pairs (_) G2,I2: 6.. / G2 = 6 => 0 pairs (X) / I2 = 6 => 14 pairs (_) G6,I6: 6.. / G6 = 6 => 14 pairs (_) / I6 = 6 => 0 pairs (X) G2,G6: 6.. / G2 = 6 => 0 pairs (X) / G6 = 6 => 14 pairs (_) I2,I6: 6.. / I2 = 6 => 14 pairs (_) / I6 = 6 => 0 pairs (X) D1,F2: 7.. / D1 = 7 => 17 pairs (_) / F2 = 7 => 24 pairs (_) D6,E6: 7.. / D6 = 7 => 24 pairs (_) / E6 = 7 => 17 pairs (_) D1,I1: 7.. / D1 = 7 => 17 pairs (_) / I1 = 7 => 24 pairs (_) D1,D6: 7.. / D1 = 7 => 17 pairs (_) / D6 = 7 => 24 pairs (_) F2,F9: 7.. / F2 = 7 => 24 pairs (_) / F9 = 7 => 17 pairs (_) G3,I3: 8.. / G3 = 8 => 0 pairs (X) / I3 = 8 => 14 pairs (_) G9,I9: 8.. / G9 = 8 => 14 pairs (_) / I9 = 8 => 0 pairs (X) G3,G9: 8.. / G3 = 8 => 0 pairs (X) / G9 = 8 => 14 pairs (_) I3,I9: 8.. / I3 = 8 => 14 pairs (_) / I9 = 8 => 0 pairs (X) C1,C3: 9.. / C1 = 9 => 16 pairs (_) / C3 = 9 => 18 pairs (_) D1,F3: 9.. / D1 = 9 => 18 pairs (_) / F3 = 9 => 16 pairs (_) G2,H2: 9.. / G2 = 9 => 0 pairs (*) / H2 = 9 => 0 pairs (X) C1,D1: 9.. / C1 = 9 => 16 pairs (_) / D1 = 9 => 18 pairs (_) C3,F3: 9.. / C3 = 9 => 18 pairs (_) / F3 = 9 => 16 pairs (_) B5,D5: 9.. / B5 = 9 => 21 pairs (_) / D5 = 9 => 18 pairs (_) F3,F9: 9.. / F3 = 9 => 16 pairs (_) / F9 = 9 => 18 pairs (_) * DURATION: 0:01:22.271868 START: 17:45:53.173004 END: 17:47:15.444872 2017-05-04 * CP COUNT: (47) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,C1,C3,D5,E7,F2,F3,G3,G5,G6,H3,H5,H6,I1,I3,I6) * 56..8123.81325....72.63....2751634896.1.28.....8..5.....78.2561.825.6....563..... * PAIR C1: 4,9 ROW 1 D1: 4,9,7 # reduction candidate for 4,9 D1: 4,9 # 24 pairs D1: 7 # 17 pairs * PAIR F2: 4,7 BLK 2 D1: 4,7,9 # reduction candidate for 4,7 D1: 9 # 18 pairs D1: 4,7 # 16 pairs * PAIR F2: 4,7 ROW 2 H2: 4,7,9 # reduction candidate for 4,7 H2: 4,7 => SOLVED * 564981237813257946729634158275163489691428375348795612937842561482516793156379824 H2: 9 # 19 pairs I2: 4,7,6 # reduction candidate for 4,7 I2: 4,7 => CTR * 56..8123.81325.69.72.63.8152751634896.1.28.5...8..5126..78.2561.825.6....563....2 I2: 6 # 14 pairs * PAIR F2: 4,7 COL F F9: 4,7,9 # reduction candidate for 4,7 F9: 9 # 18 pairs F9: 4,7 # 16 pairs * PAIR F3: 4,9 BLK 2 D1: 4,9,7 # reduction candidate for 4,9 D1: 4,9 # 24 pairs D1: 7 # 17 pairs * PAIR F3: 4,9 COL F F9: 4,9,7 # reduction candidate for 4,9 F9: 4,9 # 24 pairs F9: 7 # 17 pairs * PAIR I1: 4,7 BLK 3 H2: 4,7,9 # reduction candidate for 4,7 H2: 4,7 => SOLVED * 564981237813257946729634158275163489691428375348795612937842561482516793156379824 H2: 9 # 19 pairs I2: 4,7,6 # reduction candidate for 4,7 I2: 4,7 => CTR * 56..8123.81325.69.72.63.8152751634896.1.28.5...8..5126..78.2561.825.6....563....2 I2: 6 # 14 pairs * PAIR I1: 4,7 ROW 1 D1: 4,7,9 # reduction candidate for 4,7 D1: 9 # 18 pairs D1: 4,7 # 16 pairs * PAIR I1: 4,7 COL I I8: 4,7,3 # reduction candidate for 4,7 I8: 4,7 => CTR * 56..8123.81325....72.63.8152751634896.1.28753..8..512...78.2561.825.63...563....8 I8: 3 # 17 pairs I9: 4,7,2,8 # reduction candidate for 4,7 I9: 4,7 # 14 pairs * PAIR B5: 4,9 BLK 4 A6: 4,9,3 # reduction candidate for 4,9 A6: 4,9 # 18 pairs B6: 4,9,3 # reduction candidate for 4,9 B6: 4,9 # 18 pairs * PAIR B5: 4,9 COL B B7: 4,9,3 # reduction candidate for 4,9 B7: 4,9 # 18 pairs B7: 3 # 18 pairs * PAIR D5: 4,9 BLK 5 D6: 4,9,7 # reduction candidate for 4,9 D6: 4,9 # 17 pairs E6: 4,9,7 # reduction candidate for 4,9 E6: 4,9 # 24 pairs * PAIR D5: 4,9 COL D D1: 4,9,7 # reduction candidate for 4,9 D1: 4,9 # 24 pairs D1: 7 # 17 pairs * PAIR G5: 3,7 BLK 6 I5: 3,7,5 # reduction candidate for 3,7 I5: 3,7 => CTR * 56..8123.81325....72.63.8152751634896.1.28.5...8..512...78.2561.825.6....563....8 I5: 5 # 14 pairs * PAIR G5: 3,7 COL G G8: 3,7,9 # reduction candidate for 3,7 G8: 9 # 20 pairs G8: 3,7 # 19 pairs * PAIR H5: 5,7 BLK 6 I5: 5,7,3 # reduction candidate for 5,7 I5: 3 => CTR * 56..8123.81325....72.63.8152751634896.1.28753..8..512...78.2561.825.63...563....8 I5: 5,7 # 17 pairs * PAIR E7: 4,9 BLK 8 E8: 4,9,1,7 # reduction candidate for 4,9 E8: 4,9 # 19 pairs E9: 4,9,1,7 # reduction candidate for 4,9 E9: 4,9 # 19 pairs F9: 4,9,7 # reduction candidate for 4,9 F9: 4,9 # 24 pairs * PAIR E7: 4,9 ROW 7 A7: 4,9,3 # reduction candidate for 4,9 A7: 4,9 # 18 pairs B7: 4,9,3 # reduction candidate for 4,9 B7: 4,9 # 18 pairs * PAIR E7: 4,9 COL E E6: 4,9,7 # reduction candidate for 4,9 E6: 4,9 # 24 pairs E6: 7 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-439-base-pr-000.dot * REASONING * PRF # H2: 4,7 => SOL * DIS # I2: 4,7 => CTR => I2: 6 * PRF # H2: 4,7 => SOL * DIS # I2: 4,7 => CTR => I2: 6 * DIS # I8: 4,7 => CTR => I8: 3 * DIS # I5: 3,7 => CTR => I5: 5 * DIS # I5: 3 => CTR => I5: 5,7 * CNT 7 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,C1,C3,D5,E7,F2,F3,G3,G5,G6,H3,H5,H6,I1,I3,I6) * 56..8123.81325....72.63....2751634896.1.28.....8..5.....78.2561.825.6....563..... * PAIR C1: 4,9 ROW 1 D1: 4,9,7 # reduction candidate for 4,9 D1: 4,9 # 24 pairs D1: 7 # 17 pairs * PAIR F2: 4,7 BLK 2 D1: 4,7,9 # reduction candidate for 4,7 D1: 9 # 18 pairs D1: 4,7 # 16 pairs * PAIR F2: 4,7 ROW 2 H2: 4,7,9 # reduction candidate for 4,7 H2: 4,7 => SOLVED * 564981237813257946729634158275163489691428375348795612937842561482516793156379824 * DURATION: 0:00:06.173597 START: 17:47:57.252106 END: 17:48:03.425703 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-439-base-pr-001.dot * REASONING * PRF # H2: 4,7 => SOL * STA H2: 4,7 * CNT 1 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 439 solution: 564981237813257946729634158275163489691428375348795612937842561482516793156379824 info: 95250 FNBTHXYK S8.f 45385 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 564981237813257946729634158275163489691428375348795612937842561482516793156379824 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: 4,9 => UNS * INC # D1: 7 => UNS * INC # D1: 4,7 => UNS * INC # D1: 9 => UNS * PRF # H2: 4,7 => SOL * INC # H2: 9 => UNS * DIS # I2: 4,7 => CTR => I2: 6 * INC # I2: 6 => UNS * INC # F9: 4,7 => UNS * INC # F9: 9 => UNS * INC # D1: 4,9 => UNS * INC # D1: 7 => UNS * INC # F9: 4,9 => UNS * INC # F9: 7 => UNS * PRF # H2: 4,7 => SOL * INC # H2: 9 => UNS * DIS # I2: 4,7 => CTR => I2: 6 * INC # I2: 6 => UNS * INC # D1: 4,7 => UNS * INC # D1: 9 => UNS * DIS # I8: 4,7 => CTR => I8: 3 * INC # I8: 3 => UNS * INC # I9: 4,7 => UNS * INC # A6: 4,9 => UNS * INC # B6: 4,9 => UNS * INC # B7: 4,9 => UNS * INC # B7: 3 => UNS * INC # D6: 4,9 => UNS * INC # E6: 4,9 => UNS * INC # D1: 4,9 => UNS * INC # D1: 7 => UNS * DIS # I5: 3,7 => CTR => I5: 5 * INC # I5: 5 => UNS * INC # G8: 3,7 => UNS * INC # G8: 9 => UNS * INC # I5: 5,7 => UNS * DIS # I5: 3 => CTR => I5: 5,7 * INC # E8: 4,9 => UNS * INC # E9: 4,9 => UNS * INC # F9: 4,9 => UNS * INC # A7: 4,9 => UNS * INC # B7: 4,9 => UNS * INC # E6: 4,9 => UNS * INC # E6: 7 => UNS * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D1: 4,9 => UNS * INC # D1: 7 => UNS * INC # D1: 4,7 => UNS * INC # D1: 9 => UNS * PRF # H2: 4,7 => SOL * STA H2: 4,7 * CNT 5 HDP CHAINS / 5 HYP OPENED