Analysis of xx-top500-036-base.sdk
Contents
Original Sudoku
level: medium
position: 1......6....2...........7.....8..2.7.7....4..3.............6.31.2..3..5...8...... initial
Autosolve
position: 1.2..736.7.32..14.8..3..72..168.329727.6..48338..72516..7.26831.21738.54.381...72 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E3: 4,5 => CTR => E3: 1,6,9 * DIS # F3: 4,5 => CTR => F3: 1,9 * DIS # E1: 5,9 => CTR => E1: 4,8 * DIS # E2: 5,9 => CTR => E2: 6,8 * DIS # E3: 5,9 => CTR => E3: 1,4,6 * DIS # F3: 5,9 => CTR => F3: 1,4 * DIS # F9: 5,9 => CTR => F9: 4 * PRF # B3: 5,9 => SOL * DIS # E3: 5,9 => CTR => E3: 1,4,6 * DIS # F3: 5,9 => CTR => F3: 1,4 * DIS # A7: 4,5 => CTR => A7: 9 * PRF # E1: 4,5 => SOL * DIS # E3: 4,5 => CTR => E3: 1,6,9 * PRF # D1: 4,9 => SOL * DIS # A7: 4,5 => CTR => A7: 9 * DIS # D7: 9 => CTR => D7: 4,5 * DIS # A9: 6,9 => CTR => A9: 4,5 * DIS # A9: 6,9 => CTR => A9: 4,5 * CNT 18 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E3: 4,5 => CTR => E3: 1,6,9 * DIS E3: 1,6,9 # F3: 4,5 => CTR => F3: 1,9 * PRF E3: 1,6,9 + F3: 1,9 # B3: 6,9 => SOL * STA E3: 1,6,9 + F3: 1,9 + B3: 6,9 * CNT 3 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1......6....2...........7.....8..2.7.7....4..3.............6.31.2..3..5...8...... | initial |
| 1.2..736.7.32..14.8..3..72..168.329727.6..48338..72516..7.26831.21738.54.381...72 | autosolve |
| 152947368763285149894361725416853297275619483389472516947526831621738954538194672 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) C3: 4,5 F2: 5,9 I3: 5,9 A4: 4,5 C5: 5,9 C6: 4,9 E4: 4,5 D6: 4,9 B7: 4,5 A8: 6,9 G8: 6,9 G9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E3,F3: 1.. / E3 = 1 => 16 pairs (_) / F3 = 1 => 15 pairs (_) E5,F5: 1.. / E5 = 1 => 15 pairs (_) / F5 = 1 => 16 pairs (_) E3,E5: 1.. / E3 = 1 => 16 pairs (_) / E5 = 1 => 15 pairs (_) F3,F5: 1.. / F3 = 1 => 15 pairs (_) / F5 = 1 => 16 pairs (_) A4,C6: 4.. / A4 = 4 => 0 pairs (*) / C6 = 4 => 0 pairs (X) E4,D6: 4.. / E4 = 4 => 0 pairs (X) / D6 = 4 => 0 pairs (_) A4,E4: 4.. / A4 = 4 => 0 pairs (*) / E4 = 4 => 0 pairs (X) C6,D6: 4.. / C6 = 4 => 0 pairs (X) / D6 = 4 => 0 pairs (_) C3,C6: 4.. / C3 = 4 => 0 pairs (*) / C6 = 4 => 0 pairs (X) F3,F9: 4.. / F3 = 4 => 0 pairs (X) / F9 = 4 => 14 pairs (_) A4,C5: 5.. / A4 = 5 => 0 pairs (X) / C5 = 5 => 0 pairs (_) A4,E4: 5.. / A4 = 5 => 0 pairs (X) / E4 = 5 => 0 pairs (_) C3,C5: 5.. / C3 = 5 => 0 pairs (X) / C5 = 5 => 0 pairs (_) D1,D7: 5.. / D1 = 5 => 21 pairs (_) / D7 = 5 => 0 pairs (*) B2,B3: 6.. / B2 = 6 => 16 pairs (_) / B3 = 6 => 14 pairs (_) E2,E3: 6.. / E2 = 6 => 14 pairs (_) / E3 = 6 => 16 pairs (_) A8,A9: 6.. / A8 = 6 => 9 pairs (_) / A9 = 6 => 0 pairs (X) G8,G9: 6.. / G8 = 6 => 0 pairs (X) / G9 = 6 => 9 pairs (_) B2,E2: 6.. / B2 = 6 => 16 pairs (_) / E2 = 6 => 14 pairs (_) B3,E3: 6.. / B3 = 6 => 14 pairs (_) / E3 = 6 => 16 pairs (_) A8,G8: 6.. / A8 = 6 => 9 pairs (_) / G8 = 6 => 0 pairs (X) A9,G9: 6.. / A9 = 6 => 0 pairs (X) / G9 = 6 => 9 pairs (_) E1,E2: 8.. / E1 = 8 => 13 pairs (_) / E2 = 8 => 17 pairs (_) I1,I2: 8.. / I1 = 8 => 17 pairs (_) / I2 = 8 => 13 pairs (_) E1,I1: 8.. / E1 = 8 => 13 pairs (_) / I1 = 8 => 17 pairs (_) E2,I2: 8.. / E2 = 8 => 17 pairs (_) / I2 = 8 => 13 pairs (_) C5,C6: 9.. / C5 = 9 => 0 pairs (X) / C6 = 9 => 0 pairs (_) G8,G9: 9.. / G8 = 9 => 9 pairs (_) / G9 = 9 => 0 pairs (X) C6,D6: 9.. / C6 = 9 => 0 pairs (*) / D6 = 9 => 0 pairs (X) A7,D7: 9.. / A7 = 9 => 11 pairs (_) / D7 = 9 => 0 pairs (X) A8,G8: 9.. / A8 = 9 => 0 pairs (X) / G8 = 9 => 9 pairs (_) * DURATION: 0:00:53.688069 START: 03:54:04.710477 END: 03:54:58.398546 2017-05-04 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B7,C3,C5,C6,D6,E4,F2,G8,G9,I3) * 1.2..736.7.32..14.8..3..72..168.329727.6..48338..72516..7.26831.21738.54.381...72 * PAIR C3: 4,5 BLK 1 B1: 4,5,9 # reduction candidate for 4,5 B1: 4,5 # 15 pairs B3: 4,5,6,9 # reduction candidate for 4,5 B3: 4,5 # 18 pairs * PAIR C3: 4,5 ROW 3 E3: 4,5,1,6,9 # reduction candidate for 4,5 E3: 4,5 => CTR * 1.2.873657532691488643.1729.168.329727.61.48338..72516..7526831.21738.54538194672 E3: 1,6,9 # 12 pairs F3: 4,5,1,9 # reduction candidate for 4,5 F3: 4,5 => CTR * 1.2.8736575326914886431572941685329727.6.148338..72516..7526831.21738.545381..672 F3: 1,9 # 15 pairs * PAIR F2: 5,9 BLK 2 D1: 5,9,4 # reduction candidate for 5,9 D1: 5,9 # 16 pairs E1: 5,9,4,8 # reduction candidate for 5,9 E1: 5,9 => CTR * 1.24.736876328.14.8..36172..1684329727.615483384972516..7.26831.21738.54.381.4.72 E1: 4,8 # 13 pairs E2: 5,9,6,8 # reduction candidate for 5,9 E2: 5,9 => CTR * 1.248736.7632..1488..36172..1684329727.615483384972516..7.26831.21738.54.381.4.72 E2: 6,8 # 13 pairs E3: 5,9,1,4,6 # reduction candidate for 5,9 E3: 5,9 => CTR * 1.2.8736.7.326.1488643.172.416853297275619483389472516.47526831.21738.54538194.72 E3: 1,4,6 # 12 pairs F3: 5,9,1,4 # reduction candidate for 5,9 F3: 5,9 => CTR * 1.2..736.7.326.14886431.72.41685329727.6.148338..72516..7.26831.21738.54.381.4.72 F3: 1,4 # 13 pairs * PAIR F2: 5,9 ROW 2 B2: 5,9,6 # reduction candidate for 5,9 B2: 5,9 # 14 pairs I2: 5,9,8 # reduction candidate for 5,9 I2: 5,9 # 17 pairs * PAIR F2: 5,9 COL F F5: 5,9,1 # reduction candidate for 5,9 F5: 5,9 # 15 pairs F9: 5,9,4 # reduction candidate for 5,9 F9: 5,9 => CTR * 1425.736.7.32.914.8953.472..168.329727.6.14833849725169.74268316217389544381..672 F9: 4 # 14 pairs * PAIR I3: 5,9 BLK 3 I1: 5,9,8 # reduction candidate for 5,9 I1: 5,9 # 13 pairs I2: 5,9,8 # reduction candidate for 5,9 I2: 5,9 # 17 pairs * PAIR I3: 5,9 ROW 3 B3: 5,9,4,6 # reduction candidate for 5,9 B3: 5,9 => SOLVED * 152947368763285149894361725416853297275619483389472516947526831621738954538194672 B3: 4,6 # 13 pairs E3: 5,9,1,4,6 # reduction candidate for 5,9 E3: 5,9 => CTR * 1.2.8736.7.326.1488643.172.416853297275619483389472516.47526831.21738.54538194.72 E3: 1,4,6 # 12 pairs F3: 5,9,1,4 # reduction candidate for 5,9 F3: 5,9 => CTR * 1.2..736.7.326.14886431.72.41685329727.6.148338..72516..7.26831.21738.54.381.4.72 F3: 1,4 # 13 pairs * PAIR A4: 4,5 COL A A7: 4,5,9 # reduction candidate for 4,5 A7: 4,5 => CTR * 1.25.736.7.32.914.8.43..72..168.329727.691483389472516..7926831.21738.54.381.5.72 A7: 9 # 11 pairs A9: 4,5,6,9 # reduction candidate for 4,5 A9: 4,5 # 11 pairs * PAIR C5: 5,9 ROW 5 E5: 5,9,1 # reduction candidate for 5,9 E5: 5,9 # 16 pairs F5: 5,9,1 # reduction candidate for 5,9 F5: 5,9 # 15 pairs * PAIR E4: 4,5 COL E E1: 4,5,8,9 # reduction candidate for 4,5 E1: 4,5 => SOLVED * 152947368763285149894361725416853297275619483389472516947526831621738954538194672 E1: 8,9 # 13 pairs E3: 4,5,1,6,9 # reduction candidate for 4,5 E3: 4,5 => CTR * 1.2.873657532691488643.1729.168.329727.61.48338..72516..7526831.21738.54538194672 E3: 1,6,9 # 12 pairs E9: 4,5,9 # reduction candidate for 4,5 E9: 4,5 # 15 pairs * PAIR D6: 4,9 COL D D1: 4,9,5 # reduction candidate for 4,9 D1: 4,9 => SOLVED * 152947368763285149894361725416853297275619483389472516947526831621738954538194672 D1: 5 # 21 pairs D7: 4,9,5 # reduction candidate for 4,9 D7: 4,9 # 21 pairs * PAIR B7: 4,5 BLK 7 A7: 4,5,9 # reduction candidate for 4,5 A7: 4,5 => CTR * 1.25.736.7.32.914.8.43..72..168.329727.691483389472516..7926831.21738.54.381.5.72 A7: 9 # 11 pairs A9: 4,5,6,9 # reduction candidate for 4,5 A9: 4,5 # 11 pairs * PAIR B7: 4,5 ROW 7 D7: 4,5,9 # reduction candidate for 4,5 D7: 9 => CTR * 1.25.736.7.32.914.8.43.172.41685329727.6..48338.472516..7926831.21738.54.381...72 D7: 4,5 # 11 pairs * PAIR B7: 4,5 COL B B1: 4,5,9 # reduction candidate for 4,5 B1: 4,5 # 15 pairs B3: 4,5,6,9 # reduction candidate for 4,5 B3: 4,5 # 18 pairs * PAIR A8: 6,9 BLK 7 A9: 6,9,4,5 # reduction candidate for 6,9 A9: 6,9 => CTR * 1.25.736.7.32.914.8.43.172.41685329727.6..48338.472516..7926831.21738.54.381...72 A9: 4,5 # 11 pairs * PAIR G9: 6,9 ROW 9 A9: 6,9,4,5 # reduction candidate for 6,9 A9: 6,9 => CTR * 1.25.736.7.32.914.8.43.172.41685329727.6..48338.472516..7926831.21738.54.381...72 A9: 4,5 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-036-base-pr-000.dot * REASONING * DIS # E3: 4,5 => CTR => E3: 1,6,9 * DIS # F3: 4,5 => CTR => F3: 1,9 * DIS # E1: 5,9 => CTR => E1: 4,8 * DIS # E2: 5,9 => CTR => E2: 6,8 * DIS # E3: 5,9 => CTR => E3: 1,4,6 * DIS # F3: 5,9 => CTR => F3: 1,4 * DIS # F9: 5,9 => CTR => F9: 4 * PRF # B3: 5,9 => SOL * DIS # E3: 5,9 => CTR => E3: 1,4,6 * DIS # F3: 5,9 => CTR => F3: 1,4 * DIS # A7: 4,5 => CTR => A7: 9 * PRF # E1: 4,5 => SOL * DIS # E3: 4,5 => CTR => E3: 1,6,9 * PRF # D1: 4,9 => SOL * DIS # A7: 4,5 => CTR => A7: 9 * DIS # D7: 9 => CTR => D7: 4,5 * DIS # A9: 6,9 => CTR => A9: 4,5 * DIS # A9: 6,9 => CTR => A9: 4,5 * CNT 18 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A8,B7,C3,C5,C6,D6,E4,F2,G8,G9,I3) * 1.2..736.7.32..14.8..3..72..168.329727.6..48338..72516..7.26831.21738.54.381...72 * PAIR C3: 4,5 BLK 1 B1: 4,5,9 # reduction candidate for 4,5 B1: 4,5 # 15 pairs B3: 4,5,6,9 # reduction candidate for 4,5 B3: 4,5 # 18 pairs * PAIR C3: 4,5 ROW 3 E3: 4,5,1,6,9 # reduction candidate for 4,5 E3: 4,5 => CTR * 1.2.873657532691488643.1729.168.329727.61.48338..72516..7526831.21738.54538194672 F3: 4,5,1,9 # reduction candidate for 4,5 F3: 4,5 => CTR * 1.2.8736575326914886431572941685329727.6.148338..72516..7526831.21738.545381..672 * RESTART * PAIR RESTART * PAIR C3: 4,5 BLK 1 B3: 4,5,6,9 # reduction candidate for 4,5 B3: 6,9 => SOLVED * 152947368763285149894361725416853297275619483389472516947526831621738954538194672 * DURATION: 0:00:06.965479 START: 03:55:45.638416 END: 03:55:52.603895 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-036-base-pr-001.dot * REASONING * DIS # E3: 4,5 => CTR => E3: 1,6,9 * DIS E3: 1,6,9 # F3: 4,5 => CTR => F3: 1,9 * PRF E3: 1,6,9 + F3: 1,9 # B3: 6,9 => SOL * STA E3: 1,6,9 + F3: 1,9 + B3: 6,9 * CNT 3 HDP CHAINS / 6 HYP OPENED
Header Info
Top 500 Minimum 17 036 solution: 152947368763285149894361725416853297275619483389472516947526831621738954538194672 info: 1366 FNBHWXY S8.f 47570 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 152947368763285149894361725416853297275619483389472516947526831621738954538194672 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: 4,5 => UNS * INC # B3: 4,5 => UNS * DIS # E3: 4,5 => CTR => E3: 1,6,9 * INC # E3: 1,6,9 => UNS * DIS # F3: 4,5 => CTR => F3: 1,9 * INC # F3: 1,9 => UNS * INC # D1: 5,9 => UNS * DIS # E1: 5,9 => CTR => E1: 4,8 * INC # E1: 4,8 => UNS * DIS # E2: 5,9 => CTR => E2: 6,8 * INC # E2: 6,8 => UNS * DIS # E3: 5,9 => CTR => E3: 1,4,6 * INC # E3: 1,4,6 => UNS * DIS # F3: 5,9 => CTR => F3: 1,4 * INC # F3: 1,4 => UNS * INC # B2: 5,9 => UNS * INC # I2: 5,9 => UNS * INC # F5: 5,9 => UNS * DIS # F9: 5,9 => CTR => F9: 4 * INC # F9: 4 => UNS * INC # I1: 5,9 => UNS * INC # I2: 5,9 => UNS * PRF # B3: 5,9 => SOL * INC # B3: 4,6 => UNS * DIS # E3: 5,9 => CTR => E3: 1,4,6 * INC # E3: 1,4,6 => UNS * DIS # F3: 5,9 => CTR => F3: 1,4 * INC # F3: 1,4 => UNS * DIS # A7: 4,5 => CTR => A7: 9 * INC # A7: 9 => UNS * INC # A9: 4,5 => UNS * INC # E5: 5,9 => UNS * INC # F5: 5,9 => UNS * PRF # E1: 4,5 => SOL * INC # E1: 8,9 => UNS * DIS # E3: 4,5 => CTR => E3: 1,6,9 * INC # E3: 1,6,9 => UNS * INC # E9: 4,5 => UNS * PRF # D1: 4,9 => SOL * INC # D1: 5 => UNS * INC # D7: 4,9 => UNS * DIS # A7: 4,5 => CTR => A7: 9 * INC # A7: 9 => UNS * INC # A9: 4,5 => UNS * INC # D7: 4,5 => UNS * DIS # D7: 9 => CTR => D7: 4,5 * INC # B1: 4,5 => UNS * INC # B3: 4,5 => UNS * DIS # A9: 6,9 => CTR => A9: 4,5 * INC # A9: 4,5 => UNS * DIS # A9: 6,9 => CTR => A9: 4,5 * INC # A9: 4,5 => UNS * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 4,5 => UNS * INC # B3: 4,5 => UNS * DIS # E3: 4,5 => CTR => E3: 1,6,9 * DIS E3: 1,6,9 # F3: 4,5 => CTR => F3: 1,9 * INC E3: 1,6,9 + F3: 1,9 # B3: 4,5 => UNS * PRF E3: 1,6,9 + F3: 1,9 # B3: 6,9 => SOL * STA E3: 1,6,9 + F3: 1,9 + B3: 6,9 * CNT 6 HDP CHAINS / 6 HYP OPENED