Analysis of xx-top500-351-base.sdk
Contents
Original Sudoku
level: medium
position: 7..9...2...8.1.............9..2.7...2.....1........5...54...8.....7....3.1....... initial
Autosolve
position: 7..985.21598.127..1.2.7.9859.1257..82758.41..48.19.572.54.298178297.1.53.175.82.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B1: 3,6 => SOL * PRF # G1: 4 => SOL * PRF # D3: 3,6 => SOL * PRF # B3: 4 => SOL * PRF # G1: 4,6 => SOL * DIS # G1: 3 => CTR => G1: 4,6 * DIS # H2: 4,6 => CTR => H2: 3 * PRF # H2: 3 => SOL * PRF # D2: 4,6 => SOL * DIS # D2: 3 => CTR => D2: 4,6 * DIS # I9: 9 => CTR => I9: 4,6 * DIS # H4: 3,6 => CTR => H4: 4 * PRF # B1: 3,6 => SOL * DIS # H5: 9 => CTR => H5: 3,6 * DIS # E9: 4 => CTR => E9: 3,6 * PRF # H5: 6,9 => SOL * DIS # H5: 3 => CTR => H5: 6,9 * DIS # E9: 4 => CTR => E9: 3,6 * DIS # E9: 4 => CTR => E9: 3,6 * PRF # D3: 3,6 => SOL * PRF # E9: 4,6 => SOL * DIS # E9: 3 => CTR => E9: 4,6 * DIS # H9: 4,6 => CTR => H9: 9 * PRF # G1: 4,6 => SOL * DIS # G1: 3 => CTR => G1: 4,6 * DIS # G4: 4,6 => CTR => G4: 3 * PRF # G4: 3 => SOL * CNT 27 HDP CHAINS / 48 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B1: 3,6 => SOL * STA B1: 3,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7..9...2...8.1.............9..2.7...2.....1........5...54...8.....7....3.1....... | initial |
| 7..985.21598.127..1.2.7.9859.1257..82758.41..48.19.572.54.298178297.1.53.175.82.. | autosolve |
| 736985421598412736142673985961257348275834169483196572654329817829741653317568294 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) C1: 3,6 F3: 3,6 I2: 4,6 B4: 3,6 C6: 3,6 E5: 3,6 F6: 3,6 I5: 6,9 A7: 3,6 A9: 3,6 D7: 3,6 E8: 4,6 G8: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,H2: 3.. / G1 = 3 => 0 pairs (X) / H2 = 3 => 0 pairs (_) B4,C6: 3.. / B4 = 3 => 0 pairs (X) / C6 = 3 => 0 pairs (_) E5,F6: 3.. / E5 = 3 => 0 pairs (*) / F6 = 3 => 0 pairs (X) A7,A9: 3.. / A7 = 3 => 0 pairs (X) / A9 = 3 => 0 pairs (_) D7,E9: 3.. / D7 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) D2,H2: 3.. / D2 = 3 => 0 pairs (X) / H2 = 3 => 0 pairs (_) E5,H5: 3.. / E5 = 3 => 0 pairs (*) / H5 = 3 => 0 pairs (X) C6,F6: 3.. / C6 = 3 => 0 pairs (*) / F6 = 3 => 0 pairs (X) A7,D7: 3.. / A7 = 3 => 0 pairs (X) / D7 = 3 => 0 pairs (_) A9,E9: 3.. / A9 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) C1,C6: 3.. / C1 = 3 => 0 pairs (X) / C6 = 3 => 0 pairs (_) E5,E9: 3.. / E5 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) F3,F6: 3.. / F3 = 3 => 0 pairs (*) / F6 = 3 => 0 pairs (X) G1,G4: 3.. / G1 = 3 => 0 pairs (X) / G4 = 3 => 0 pairs (_) B1,B3: 4.. / B1 = 4 => 16 pairs (_) / B3 = 4 => 0 pairs (*) D2,D3: 4.. / D2 = 4 => 0 pairs (*) / D3 = 4 => 0 pairs (X) G4,H4: 4.. / G4 = 4 => 0 pairs (X) / H4 = 4 => 16 pairs (_) E8,E9: 4.. / E8 = 4 => 18 pairs (_) / E9 = 4 => 0 pairs (X) B1,G1: 4.. / B1 = 4 => 16 pairs (_) / G1 = 4 => 0 pairs (*) B3,D3: 4.. / B3 = 4 => 0 pairs (*) / D3 = 4 => 0 pairs (X) E8,G8: 4.. / E8 = 4 => 18 pairs (_) / G8 = 4 => 0 pairs (X) I2,I9: 4.. / I2 = 4 => 17 pairs (_) / I9 = 4 => 16 pairs (_) B4,C6: 6.. / B4 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) E5,F6: 6.. / E5 = 6 => 0 pairs (X) / F6 = 6 => 0 pairs (_) A7,A9: 6.. / A7 = 6 => 0 pairs (*) / A9 = 6 => 0 pairs (X) C6,F6: 6.. / C6 = 6 => 0 pairs (X) / F6 = 6 => 0 pairs (_) A7,D7: 6.. / A7 = 6 => 0 pairs (*) / D7 = 6 => 0 pairs (X) E8,G8: 6.. / E8 = 6 => 0 pairs (X) / G8 = 6 => 18 pairs (_) C1,C6: 6.. / C1 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) F3,F6: 6.. / F3 = 6 => 0 pairs (X) / F6 = 6 => 0 pairs (_) H5,I5: 9.. / H5 = 9 => 0 pairs (X) / I5 = 9 => 14 pairs (_) H9,I9: 9.. / H9 = 9 => 14 pairs (_) / I9 = 9 => 0 pairs (X) H5,H9: 9.. / H5 = 9 => 0 pairs (X) / H9 = 9 => 14 pairs (_) I5,I9: 9.. / I5 = 9 => 14 pairs (_) / I9 = 9 => 0 pairs (X) * DURATION: 0:01:05.697630 START: 14:44:37.343660 END: 14:45:43.041290 2017-05-04 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,B4,C1,C6,D7,E5,E8,F3,F6,G8,I2,I5) * 7..985.21598.127..1.2.7.9859.1257..82758.41..48.19.572.54.298178297.1.53.175.82.. * PAIR C1: 3,6 BLK 1 B1: 3,6,4 # reduction candidate for 3,6 B1: 3,6 => SOLVED * 736985421598412736142673985961257348275834169483196572654329817829741653317568294 B1: 4 # 16 pairs B3: 3,6,4 # reduction candidate for 3,6 B3: 3,6 # 16 pairs * PAIR C1: 3,6 ROW 1 G1: 3,6,4 # reduction candidate for 3,6 G1: 4 => SOLVED * 736985421598412736142673985961257348275834169483196572654329817829741653317568294 G1: 3,6 # 16 pairs * PAIR F3: 3,6 BLK 2 D2: 3,6,4 # reduction candidate for 3,6 D2: 3,6 # 16 pairs D3: 3,6,4 # reduction candidate for 3,6 D3: 3,6 => SOLVED * 736985421598412736142673985961257348275834169483196572654329817829741653317568294 D3: 4 # 16 pairs * PAIR F3: 3,6 ROW 3 B3: 3,6,4 # reduction candidate for 3,6 B3: 4 => SOLVED * 736985421598412736142673985961257348275834169483196572654329817829741653317568294 B3: 3,6 # 16 pairs * PAIR I2: 4,6 BLK 3 G1: 4,6,3 # reduction candidate for 4,6 G1: 4,6 => SOLVED * 736985421598412736142673985961257348275834169483196572654329817829741653317568294 G1: 3 => CTR * 7469853215983127..1324769859.1257..82758.41..48.19.572.54.298178297.1.53.175.82.. H2: 4,6,3 # reduction candidate for 4,6 H2: 4,6 => CTR * 7..9853215983127..132476985961257..82758.41..48.19.572.54.298178297.1.53.175.82.. H2: 3 => SOLVED * 736985421598412736142673985961257348275834169483196572654329817829741653317568294 * PAIR I2: 4,6 ROW 2 D2: 4,6,3 # reduction candidate for 4,6 D2: 4,6 => SOLVED * 736985421598412736142673985961257348275834169483196572654329817829741653317568294 D2: 3 => CTR * 7..985.215983127..132476985961257..82758.41..48.19.572.54.298178297.1.53.175.82.. * PAIR I2: 4,6 COL I I9: 4,6,9 # reduction candidate for 4,6 I9: 9 => CTR * 746985321598.127.41.247.9859.1257..82758.41.648.196572.54.298178297.1.53.175.82.9 I9: 4,6 # 14 pairs * PAIR B4: 3,6 ROW 4 G4: 3,6,4 # reduction candidate for 3,6 G4: 3,6 # 16 pairs H4: 3,6,4 # reduction candidate for 3,6 H4: 3,6 => CTR * 7469853215983127..1324769859.12574.82758.41..48.19.572.54.29817829741653.175.82.. H4: 4 # 16 pairs * PAIR B4: 3,6 COL B B1: 3,6,4 # reduction candidate for 3,6 B1: 3,6 => SOLVED * 736985421598412736142673985961257348275834169483196572654329817829741653317568294 B1: 4 # 16 pairs B3: 3,6,4 # reduction candidate for 3,6 B3: 3,6 # 16 pairs * PAIR E5: 3,6 ROW 5 H5: 3,6,9 # reduction candidate for 3,6 H5: 9 => CTR * 7.6985.21598.127..1.2.7.9859.1257..8275834196483196572.543298178297.1.533175.82.9 H5: 3,6 # 14 pairs * PAIR E5: 3,6 COL E E9: 3,6,4 # reduction candidate for 3,6 E9: 4 => CTR * 746985321598.127.4132.7.9859.1257..82758341..483196572.543298178297614533175482.. E9: 3,6 # 18 pairs * PAIR I5: 6,9 BLK 6 H5: 6,9,3 # reduction candidate for 6,9 H5: 6,9 => SOLVED * 736985421598412736142673985961257348275834169483196572654329817829741653317568294 H5: 3 => CTR * 7.3985.215983127461.2.7.9859.1257..82758.413948.193572.54.298178297.1.53.17538294 * PAIR I5: 6,9 COL I I9: 6,9,4 # reduction candidate for 6,9 I9: 6,9 # 17 pairs I9: 4 # 16 pairs * PAIR A9: 3,6 ROW 9 E9: 3,6,4 # reduction candidate for 3,6 E9: 4 => CTR * 746985321598.127.4132.7.9859.1257..82758341..483196572.543298178297614533175482.. E9: 3,6 # 18 pairs * PAIR D7: 3,6 BLK 8 E9: 3,6,4 # reduction candidate for 3,6 E9: 4 => CTR * 746985321598.127.4132.7.9859.1257..82758341..483196572.543298178297614533175482.. E9: 3,6 # 18 pairs * PAIR D7: 3,6 COL D D2: 3,6,4 # reduction candidate for 3,6 D2: 3,6 # 16 pairs D3: 3,6,4 # reduction candidate for 3,6 D3: 3,6 => SOLVED * 736985421598412736142673985961257348275834169483196572654329817829741653317568294 D3: 4 # 16 pairs * PAIR E8: 4,6 BLK 8 E9: 4,6,3 # reduction candidate for 4,6 E9: 4,6 => SOLVED * 736985421598412736142673985961257348275834169483196572654329817829741653317568294 E9: 3 => CTR * 763985.21598.127..1.2.7.9859.1257..8275864139486193572354629817829741653617538294 * PAIR G8: 4,6 BLK 9 H9: 4,6,9 # reduction candidate for 4,6 H9: 4,6 => CTR * 7.6985.21598.127641.2.7.9859.1257..82758.419648.196572.54.298178297.1.53.175.82.9 H9: 9 # 14 pairs I9: 4,6,9 # reduction candidate for 4,6 I9: 4,6 # 14 pairs * PAIR G8: 4,6 COL G G1: 4,6,3 # reduction candidate for 4,6 G1: 4,6 => SOLVED * 736985421598412736142673985961257348275834169483196572654329817829741653317568294 G1: 3 => CTR * 7469853215983127..1324769859.1257..82758.41..48.19.572.54.298178297.1.53.175.82.. G4: 4,6,3 # reduction candidate for 4,6 G4: 4,6 => CTR * 7..9853215983127..132476985961257..82758.41..48.19.572.54.298178297.1.53.175.82.. G4: 3 => SOLVED * 736985421598412736142673985961257348275834169483196572654329817829741653317568294 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-351-base-pr-000.dot * REASONING * PRF # B1: 3,6 => SOL * PRF # G1: 4 => SOL * PRF # D3: 3,6 => SOL * PRF # B3: 4 => SOL * PRF # G1: 4,6 => SOL * DIS # G1: 3 => CTR => G1: 4,6 * DIS # H2: 4,6 => CTR => H2: 3 * PRF # H2: 3 => SOL * PRF # D2: 4,6 => SOL * DIS # D2: 3 => CTR => D2: 4,6 * DIS # I9: 9 => CTR => I9: 4,6 * DIS # H4: 3,6 => CTR => H4: 4 * PRF # B1: 3,6 => SOL * DIS # H5: 9 => CTR => H5: 3,6 * DIS # E9: 4 => CTR => E9: 3,6 * PRF # H5: 6,9 => SOL * DIS # H5: 3 => CTR => H5: 6,9 * DIS # E9: 4 => CTR => E9: 3,6 * DIS # E9: 4 => CTR => E9: 3,6 * PRF # D3: 3,6 => SOL * PRF # E9: 4,6 => SOL * DIS # E9: 3 => CTR => E9: 4,6 * DIS # H9: 4,6 => CTR => H9: 9 * PRF # G1: 4,6 => SOL * DIS # G1: 3 => CTR => G1: 4,6 * DIS # G4: 4,6 => CTR => G4: 3 * PRF # G4: 3 => SOL * CNT 27 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,B4,C1,C6,D7,E5,E8,F3,F6,G8,I2,I5) * 7..985.21598.127..1.2.7.9859.1257..82758.41..48.19.572.54.298178297.1.53.175.82.. * PAIR C1: 3,6 BLK 1 B1: 3,6,4 # reduction candidate for 3,6 B1: 3,6 => SOLVED * 736985421598412736142673985961257348275834169483196572654329817829741653317568294 * DURATION: 0:00:02.126665 START: 14:46:40.048071 END: 14:46:42.174736 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-351-base-pr-001.dot * REASONING * PRF # B1: 3,6 => SOL * STA B1: 3,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 351 solution: 736985421598412736142673985961257348275834169483196572654329817829741653317568294 info: 4883 FNBWX S8.f 37164 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 736985421598412736142673985961257348275834169483196572654329817829741653317568294 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:
* PRF # B1: 3,6 => SOL * INC # B1: 4 => UNS * INC # B3: 3,6 => UNS * INC # G1: 3,6 => UNS * PRF # G1: 4 => SOL * INC # D2: 3,6 => UNS * PRF # D3: 3,6 => SOL * INC # D3: 4 => UNS * INC # B3: 3,6 => UNS * PRF # B3: 4 => SOL * PRF # G1: 4,6 => SOL * DIS # G1: 3 => CTR => G1: 4,6 * DIS # H2: 4,6 => CTR => H2: 3 * PRF # H2: 3 => SOL * PRF # D2: 4,6 => SOL * DIS # D2: 3 => CTR => D2: 4,6 * INC # I9: 4,6 => UNS * DIS # I9: 9 => CTR => I9: 4,6 * INC # G4: 3,6 => UNS * DIS # H4: 3,6 => CTR => H4: 4 * INC # H4: 4 => UNS * PRF # B1: 3,6 => SOL * INC # B1: 4 => UNS * INC # B3: 3,6 => UNS * INC # H5: 3,6 => UNS * DIS # H5: 9 => CTR => H5: 3,6 * INC # E9: 3,6 => UNS * DIS # E9: 4 => CTR => E9: 3,6 * PRF # H5: 6,9 => SOL * DIS # H5: 3 => CTR => H5: 6,9 * INC # I9: 6,9 => UNS * INC # I9: 4 => UNS * INC # E9: 3,6 => UNS * DIS # E9: 4 => CTR => E9: 3,6 * INC # E9: 3,6 => UNS * DIS # E9: 4 => CTR => E9: 3,6 * INC # D2: 3,6 => UNS * PRF # D3: 3,6 => SOL * INC # D3: 4 => UNS * PRF # E9: 4,6 => SOL * DIS # E9: 3 => CTR => E9: 4,6 * DIS # H9: 4,6 => CTR => H9: 9 * INC # H9: 9 => UNS * INC # I9: 4,6 => UNS * PRF # G1: 4,6 => SOL * DIS # G1: 3 => CTR => G1: 4,6 * DIS # G4: 4,6 => CTR => G4: 3 * PRF # G4: 3 => SOL * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # B1: 3,6 => SOL * STA B1: 3,6 * CNT 1 HDP CHAINS / 1 HYP OPENED