Analysis of xx-top500-190-base.sdk
Contents
Original Sudoku
level: medium
position: 93..........41........5.8........1.476.............5.....2.6.3....3...7...1...... initial
Autosolve
position: 935...41..8.41.75...7.5.8...5....1.47641.538......45.7578246931...3812753215..648 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F3: 3,9 => SOL * DIS # F3: 2 => CTR => F3: 3,9 * DIS # I3: 6,9 => CTR => I3: 2,3 * PRF # I3: 2,3 => SOL * PRF # I3: 2,6 => SOL * DIS # I3: 3,9 => CTR => I3: 2,6 * PRF # E1: 7 => SOL * DIS # I3: 3,9 => CTR => I3: 2,6 * PRF # I3: 2,6 => SOL * PRF # I3: 2,9 => SOL * DIS # F3: 2,9 => CTR => F3: 3 * PRF # F3: 3 => SOL * DIS # F4: 7,9 => CTR => F4: 2,8 * DIS # E4: 2,9 => CTR => E4: 3,6,7 * DIS # F4: 2,9 => CTR => F4: 7,8 * DIS # E6: 2,9 => CTR => E6: 3,6 * PRF # I3: 2,9 => SOL * DIS # E4: 7,9 => CTR => E4: 2,3,6 * DIS # F4: 7,9 => CTR => F4: 2,8 * CNT 19 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # F3: 3,9 => SOL * STA F3: 3,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 93..........41........5.8........1.476.............5.....2.6.3....3...7...1...... | initial |
| 935...41..8.41.75...7.5.8...5....1.47641.538......45.7578246931...3812753215..648 | autosolve |
| 935872416682419753147653892259738164764125389813964527578246931496381275321597648 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A2: 2,6 C2: 2,6 A3: 1,4 B3: 1,4 F2: 3,9 D3: 6,9 I1: 2,6 I2: 3,9 H3: 2,9 A4: 2,8 B6: 1,9 E5: 2,9 I5: 2,9 A8: 4,6 B8: 4,9 C8: 6,9 E9: 7,9 F9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,B3: 1.. / A3 = 1 => 13 pairs (_) / B3 = 1 => 13 pairs (_) A6,B6: 1.. / A6 = 1 => 13 pairs (_) / B6 = 1 => 13 pairs (_) A3,A6: 1.. / A3 = 1 => 13 pairs (_) / A6 = 1 => 13 pairs (_) B3,B6: 1.. / B3 = 1 => 13 pairs (_) / B6 = 1 => 13 pairs (_) A2,C2: 2.. / A2 = 2 => 13 pairs (_) / C2 = 2 => 13 pairs (_) E5,I5: 2.. / E5 = 2 => 0 pairs (*) / I5 = 2 => 0 pairs (X) F2,F3: 3.. / F2 = 3 => 0 pairs (X) / F3 = 3 => 0 pairs (_) I2,I3: 3.. / I2 = 3 => 0 pairs (*) / I3 = 3 => 0 pairs (X) C4,C6: 3.. / C4 = 3 => 21 pairs (_) / C6 = 3 => 19 pairs (_) E4,E6: 3.. / E4 = 3 => 19 pairs (_) / E6 = 3 => 21 pairs (_) F2,I2: 3.. / F2 = 3 => 0 pairs (X) / I2 = 3 => 0 pairs (_) F3,I3: 3.. / F3 = 3 => 0 pairs (*) / I3 = 3 => 0 pairs (X) C4,E4: 3.. / C4 = 3 => 21 pairs (_) / E4 = 3 => 19 pairs (_) C6,E6: 3.. / C6 = 3 => 19 pairs (_) / E6 = 3 => 21 pairs (_) A3,B3: 4.. / A3 = 4 => 13 pairs (_) / B3 = 4 => 13 pairs (_) A8,B8: 4.. / A8 = 4 => 13 pairs (_) / B8 = 4 => 13 pairs (_) A3,A8: 4.. / A3 = 4 => 13 pairs (_) / A8 = 4 => 13 pairs (_) B3,B8: 4.. / B3 = 4 => 13 pairs (_) / B8 = 4 => 13 pairs (_) A2,C2: 6.. / A2 = 6 => 13 pairs (_) / C2 = 6 => 13 pairs (_) I1,I3: 6.. / I1 = 6 => 0 pairs (*) / I3 = 6 => 0 pairs (X) H4,H6: 6.. / H4 = 6 => 19 pairs (_) / H6 = 6 => 20 pairs (_) A8,C8: 6.. / A8 = 6 => 13 pairs (_) / C8 = 6 => 13 pairs (_) D3,I3: 6.. / D3 = 6 => 0 pairs (*) / I3 = 6 => 0 pairs (X) A2,A8: 6.. / A2 = 6 => 13 pairs (_) / A8 = 6 => 13 pairs (_) C2,C8: 6.. / C2 = 6 => 13 pairs (_) / C8 = 6 => 13 pairs (_) E9,F9: 7.. / E9 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) D1,D4: 7.. / D1 = 7 => 19 pairs (_) / D4 = 7 => 19 pairs (_) D1,F1: 8.. / D1 = 8 => 15 pairs (_) / F1 = 8 => 19 pairs (_) A4,A6: 8.. / A4 = 8 => 19 pairs (_) / A6 = 8 => 16 pairs (_) A6,D6: 8.. / A6 = 8 => 16 pairs (_) / D6 = 8 => 19 pairs (_) F1,F4: 8.. / F1 = 8 => 19 pairs (_) / F4 = 8 => 15 pairs (_) B8,C8: 9.. / B8 = 9 => 13 pairs (_) / C8 = 9 => 13 pairs (_) E9,F9: 9.. / E9 = 9 => 0 pairs (*) / F9 = 9 => 0 pairs (X) F2,I2: 9.. / F2 = 9 => 0 pairs (*) / I2 = 9 => 0 pairs (X) E5,I5: 9.. / E5 = 9 => 0 pairs (X) / I5 = 9 => 0 pairs (_) B6,B8: 9.. / B6 = 9 => 13 pairs (_) / B8 = 9 => 13 pairs (_) * DURATION: 0:01:16.123821 START: 09:12:12.176540 END: 09:13:28.300361 2017-05-04 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A4,A8,B3,B6,B8,C2,C8,D3,E5,E9,F2,F9,H3,I1,I2,I5) * 935...41..8.41.75...7.5.8...5....1.47641.538......45.7578246931...3812753215..648 * PAIR F2: 3,9 BLK 2 F3: 3,9,2 # reduction candidate for 3,9 F3: 3,9 => SOLVED * 935872416682419753147653892259738164764125389813964527578246931496381275321597648 F3: 2 => CTR * 935...41..8.413759..79528...5....1.47641.538......45.7578246931...3812753215..648 * PAIR D3: 6,9 ROW 3 I3: 6,9,2,3 # reduction candidate for 6,9 I3: 6,9 => CTR * 935...41..8.41.753..7.53829.5....1.4764195382.....45.7578246931...381275321579648 I3: 2,3 => SOLVED * 935872416682419753147653892259738164764125389813964527578246931496381275321597648 * PAIR D3: 6,9 COL D D4: 6,9,7,8 # reduction candidate for 6,9 D4: 6,9 # 20 pairs D6: 6,9,8 # reduction candidate for 6,9 D6: 6,9 # 16 pairs * PAIR I1: 2,6 BLK 3 I3: 2,6,3,9 # reduction candidate for 2,6 I3: 2,6 => SOLVED * 935872416682419753147653892259738164764125389813964527578246931496381275321597648 I3: 3,9 => CTR * 935...416.8.41.75...765.82..5....1.4764195382...8.45.7578246931...381275321579648 * PAIR I1: 2,6 ROW 1 E1: 2,6,7 # reduction candidate for 2,6 E1: 7 => SOLVED * 935872416682419753147653892259738164764125389813964527578246931496381275321597648 E1: 2,6 # 21 pairs * PAIR I2: 3,9 BLK 3 I3: 3,9,2,6 # reduction candidate for 3,9 I3: 3,9 => CTR * 935...416.8.41.75...765.82..5....1.4764195382...8.45.7578246931...381275321579648 I3: 2,6 => SOLVED * 935872416682419753147653892259738164764125389813964527578246931496381275321597648 * PAIR H3: 2,9 BLK 3 I3: 2,9,3,6 # reduction candidate for 2,9 I3: 2,9 => SOLVED * 935872416682419753147653892259738164764125389813964527578246931496381275321597648 I3: 3,6 # 19 pairs * PAIR H3: 2,9 ROW 3 F3: 2,9,3 # reduction candidate for 2,9 F3: 2,9 => CTR * 935...41..8.413759..7.5.823.5....1.4764195382.....45.7578246931...381275321579648 F3: 3 => SOLVED * 935872416682419753147653892259738164764125389813964527578246931496381275321597648 * PAIR H3: 2,9 COL H H4: 2,9,6 # reduction candidate for 2,9 H4: 2,9 # 20 pairs H6: 2,9,6 # reduction candidate for 2,9 H6: 2,9 # 19 pairs * PAIR A4: 2,8 BLK 4 A6: 2,8,1 # reduction candidate for 2,8 A6: 2,8 # 13 pairs A6: 1 # 13 pairs * PAIR A4: 2,8 ROW 4 F4: 2,8,7,9 # reduction candidate for 2,8 F4: 7,9 => CTR * 935..841..8.41.75...7.52893.5....1.47641.538......45.7578246931...3812753215..648 F4: 2,8 # 21 pairs * PAIR E5: 2,9 BLK 5 E4: 2,9,3,6,7 # reduction candidate for 2,9 E4: 2,9 => CTR * 935.6.412.8.41.75...795.8...53...1.47641.538.....345.7578246931...3812753215..648 E4: 3,6,7 # 18 pairs F4: 2,9,7,8 # reduction candidate for 2,9 F4: 2,9 => CTR * 935..8412.8.41975...7.5.8...5....1.4764125389.....45.7578246931...381275321597648 F4: 7,8 # 20 pairs E6: 2,9,3,6 # reduction candidate for 2,9 E6: 2,9 => CTR * 935.6.412.8.41.75...795.8...5..3.1.47641.538...3..45.7578246931...3812753215..648 E6: 3,6 # 19 pairs * PAIR I5: 2,9 BLK 6 H4: 2,9,6 # reduction candidate for 2,9 H4: 2,9 # 20 pairs H6: 2,9,6 # reduction candidate for 2,9 H6: 2,9 # 19 pairs * PAIR I5: 2,9 COL I I3: 2,9,3,6 # reduction candidate for 2,9 I3: 2,9 => SOLVED * 935872416682419753147653892259738164764125389813964527578246931496381275321597648 I3: 3,6 # 19 pairs * PAIR E9: 7,9 COL E E4: 7,9,2,3,6 # reduction candidate for 7,9 E4: 7,9 => CTR * 935.6.412.8.41.75...795.8...53...1.47641.538.....345.7578246931...3812753215..648 E4: 2,3,6 # 18 pairs * PAIR F9: 7,9 COL F F4: 7,9,2,8 # reduction candidate for 7,9 F4: 7,9 => CTR * 935..841..8.41.75...7.52893.5....1.47641.538......45.7578246931...3812753215..648 F4: 2,8 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-190-base-pr-000.dot * REASONING * PRF # F3: 3,9 => SOL * DIS # F3: 2 => CTR => F3: 3,9 * DIS # I3: 6,9 => CTR => I3: 2,3 * PRF # I3: 2,3 => SOL * PRF # I3: 2,6 => SOL * DIS # I3: 3,9 => CTR => I3: 2,6 * PRF # E1: 7 => SOL * DIS # I3: 3,9 => CTR => I3: 2,6 * PRF # I3: 2,6 => SOL * PRF # I3: 2,9 => SOL * DIS # F3: 2,9 => CTR => F3: 3 * PRF # F3: 3 => SOL * DIS # F4: 7,9 => CTR => F4: 2,8 * DIS # E4: 2,9 => CTR => E4: 3,6,7 * DIS # F4: 2,9 => CTR => F4: 7,8 * DIS # E6: 2,9 => CTR => E6: 3,6 * PRF # I3: 2,9 => SOL * DIS # E4: 7,9 => CTR => E4: 2,3,6 * DIS # F4: 7,9 => CTR => F4: 2,8 * CNT 19 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A4,A8,B3,B6,B8,C2,C8,D3,E5,E9,F2,F9,H3,I1,I2,I5) * 935...41..8.41.75...7.5.8...5....1.47641.538......45.7578246931...3812753215..648 * PAIR F2: 3,9 BLK 2 F3: 3,9,2 # reduction candidate for 3,9 F3: 3,9 => SOLVED * 935872416682419753147653892259738164764125389813964527578246931496381275321597648 * DURATION: 0:00:02.723830 START: 09:14:12.397866 END: 09:14:15.121696 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-190-base-pr-001.dot * REASONING * PRF # F3: 3,9 => SOL * STA F3: 3,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 190 solution: 935872416682419753147653892259738164764125389813964527578246931496381275321597648 info: 1840 FNBTWY S8.f 39174 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 935872416682419753147653892259738164764125389813964527578246931496381275321597648 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 # F3: 3,9 => SOL * DIS # F3: 2 => CTR => F3: 3,9 * DIS # I3: 6,9 => CTR => I3: 2,3 * PRF # I3: 2,3 => SOL * INC # D4: 6,9 => UNS * INC # D6: 6,9 => UNS * PRF # I3: 2,6 => SOL * DIS # I3: 3,9 => CTR => I3: 2,6 * INC # E1: 2,6 => UNS * PRF # E1: 7 => SOL * DIS # I3: 3,9 => CTR => I3: 2,6 * PRF # I3: 2,6 => SOL * PRF # I3: 2,9 => SOL * INC # I3: 3,6 => UNS * DIS # F3: 2,9 => CTR => F3: 3 * PRF # F3: 3 => SOL * INC # H4: 2,9 => UNS * INC # H6: 2,9 => UNS * INC # A6: 2,8 => UNS * INC # A6: 1 => UNS * INC # F4: 2,8 => UNS * DIS # F4: 7,9 => CTR => F4: 2,8 * DIS # E4: 2,9 => CTR => E4: 3,6,7 * INC # E4: 3,6,7 => UNS * DIS # F4: 2,9 => CTR => F4: 7,8 * INC # F4: 7,8 => UNS * DIS # E6: 2,9 => CTR => E6: 3,6 * INC # E6: 3,6 => UNS * INC # H4: 2,9 => UNS * INC # H6: 2,9 => UNS * PRF # I3: 2,9 => SOL * INC # I3: 3,6 => UNS * DIS # E4: 7,9 => CTR => E4: 2,3,6 * INC # E4: 2,3,6 => UNS * DIS # F4: 7,9 => CTR => F4: 2,8 * INC # F4: 2,8 => UNS * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # F3: 3,9 => SOL * STA F3: 3,9 * CNT 1 HDP CHAINS / 1 HYP OPENED