Analysis of cracking-the-cryptic-beyond-diabolical-base.sdk
Contents
Original Sudoku
level: medium
position: 1..4..7...2..5..8...3..6..9.1..4..7...2..5..89..3..6..7....8..28..2..9...9..7..1. initial
Autosolve
position: 1..4..7...2..5..8...3..6..9.1..4..7...2..5.989..3..6..7....8..28..2..9.729..7.81. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 4,6 => CTR => C2: 7,9 * DIS # A5: 4,6 => CTR => A5: 3 * PRF # B3: 4,5 => SOL * DIS # F1: 3 => CTR => F1: 2,9 * DIS # D5: 7 => CTR => D5: 1,6 * DIS # E7: 1,6 => CTR => E7: 3,9 * DIS # G4: 3,5 => CTR => G4: 2 * DIS # F8: 1 => CTR => F8: 3,4 * CNT 8 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 4,6 => CTR => C2: 7,9 * DIS C2: 7,9 # A5: 4,6 => CTR => A5: 3 * DIS C2: 7,9 + A5: 3 # I2: 1,3 => CTR => I2: 4,6 * PRF C2: 7,9 + A5: 3 + I2: 4,6 # H3: 2 => SOL * STA C2: 7,9 + A5: 3 + I2: 4,6 + H3: 2 * CNT 4 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1..4..7...2..5..8...3..6..9.1..4..7...2..5..89..3..6..7....8..28..2..9...9..7..1. | initial |
| 1..4..7...2..5..8...3..6..9.1..4..7...2..5.989..3..6..7....8..28..2..9.729..7.81. | autosolve |
| 189432765627951384453786129516849273372165498948327651731698542865214937294573816 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) A2: 4,6 A3: 4,5 F4: 2,9 E5: 1,6 I4: 3,5 D9: 5,6 F9: 3,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G5,I6: 1.. / G5 = 1 => 0 pairs (X) / I6 = 1 => 10 pairs (_) C7,C8: 1.. / C7 = 1 => 7 pairs (_) / C8 = 1 => 0 pairs (X) I2,I6: 1.. / I2 = 1 => 0 pairs (X) / I6 = 1 => 10 pairs (_) G4,H6: 2.. / G4 = 2 => 9 pairs (_) / H6 = 2 => 0 pairs (X) F4,G4: 2.. / F4 = 2 => 0 pairs (X) / G4 = 2 => 9 pairs (_) G3,G4: 2.. / G3 = 2 => 0 pairs (X) / G4 = 2 => 9 pairs (_) A4,A5: 3.. / A4 = 3 => 0 pairs (X) / A5 = 3 => 9 pairs (_) B7,B8: 3.. / B7 = 3 => 8 pairs (_) / B8 = 3 => 13 pairs (_) A5,G5: 3.. / A5 = 3 => 9 pairs (_) / G5 = 3 => 0 pairs (X) F9,I9: 3.. / F9 = 3 => 14 pairs (_) / I9 = 3 => 0 pairs (X) F8,F9: 4.. / F8 = 4 => 14 pairs (_) / F9 = 4 => 0 pairs (X) D7,D9: 5.. / D7 = 5 => 18 pairs (_) / D9 = 5 => 7 pairs (_) A3,A4: 5.. / A3 = 5 => 9 pairs (_) / A4 = 5 => 0 pairs (*) C2,B3: 7.. / C2 = 7 => 15 pairs (_) / B3 = 7 => 0 pairs (X) D5,F6: 7.. / D5 = 7 => 0 pairs (X) / F6 = 7 => 15 pairs (_) B3,D3: 7.. / B3 = 7 => 0 pairs (X) / D3 = 7 => 15 pairs (_) B5,D5: 7.. / B5 = 7 => 15 pairs (_) / D5 = 7 => 0 pairs (X) C2,C6: 7.. / C2 = 7 => 15 pairs (_) / C6 = 7 => 0 pairs (X) F2,F6: 7.. / F2 = 7 => 0 pairs (X) / F6 = 7 => 15 pairs (_) D4,E6: 8.. / D4 = 8 => 16 pairs (_) / E6 = 8 => 0 pairs (X) C4,D4: 8.. / C4 = 8 => 0 pairs (X) / D4 = 8 => 16 pairs (_) D3,D4: 8.. / D3 = 8 => 0 pairs (X) / D4 = 8 => 16 pairs (_) C1,C2: 9.. / C1 = 9 => 8 pairs (_) / C2 = 9 => 0 pairs (X) D4,F4: 9.. / D4 = 9 => 0 pairs (X) / F4 = 9 => 9 pairs (_) D7,E7: 9.. / D7 = 9 => 0 pairs (X) / E7 = 9 => 7 pairs (_) E1,E7: 9.. / E1 = 9 => 0 pairs (X) / E7 = 9 => 7 pairs (_) * DURATION: 0:00:28.167039 START: 23:38:52.448787 END: 23:39:20.615826 2020-09-20 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,D9,E5,F4,F9,I4) * 1..4..7...2..5..8...3..6..9.1..4..7...2..5.989..3..6..7....8..28..2..9.729..7.81. * PAIR A2: 4,6 BLK 1 C2: 4,6,7,9 # reduction candidate for 4,6 C2: 4,6 => CTR * 1894..7...2..57.8.573..6..9.18.49275..27.53989573826417...985.28.52.19.729.574813 C2: 7,9 # 8 pairs * PAIR A2: 4,6 ROW 2 I2: 4,6,1,3 # reduction candidate for 4,6 I2: 4,6 # 13 pairs I2: 1,3 # 9 pairs * PAIR A2: 4,6 COL A A5: 4,6,3 # reduction candidate for 4,6 A5: 4,6 => CTR * 1..43275662.951483543786129318.49275..2..53989..3..6417....85.28..2.49.7296573814 A5: 3 # 9 pairs * PAIR A3: 4,5 BLK 1 B3: 4,5,7,8 # reduction candidate for 4,5 B3: 4,5 => SOLVED * 189432765627951384453786129516849273372165498948327651731698542865214937294573816 B3: 7,8 # 8 pairs * PAIR A3: 4,5 ROW 3 G3: 4,5,1,2 # reduction candidate for 4,5 G3: 4,5 # 14 pairs H3: 4,5,2 # reduction candidate for 4,5 H3: 4,5 # 10 pairs * PAIR F4: 2,9 COL F F1: 2,9,3 # reduction candidate for 2,9 F1: 3 => CTR * 1..4.37...2..5..8...3..6..9.1..4..7...2..5.989..3..6..7....8..28..2..9.729..74813 F1: 2,9 # 13 pairs * PAIR E5: 1,6 BLK 5 D5: 1,6,7 # reduction candidate for 1,6 D5: 7 => CTR * 1..43.7...2.957381.73186..9.1.8492733427651989873216..7.1.98..28..2149.729..7381. D5: 1,6 # 15 pairs * PAIR E5: 1,6 COL E E7: 1,6,3,9 # reduction candidate for 1,6 E7: 1,6 => CTR * 1..49.73..2915..8..73..6..9.1..4927...27.5.989.73..6..7..9.8..28..23.9.729.574813 E7: 3,9 # 8 pairs E8: 1,6,3 # reduction candidate for 1,6 E8: 1,6 # 12 pairs * PAIR I4: 3,5 BLK 6 G4: 3,5,2 # reduction candidate for 3,5 G4: 3,5 => CTR * 1..42.73..2..53.8...38162.9.18942.75..2.65.989..38762173..985.28..2319.729.574813 G4: 2 # 9 pairs * PAIR I4: 3,5 ROW 4 A4: 3,5,6 # reduction candidate for 3,5 A4: 6 # 13 pairs A4: 3,5 # 11 pairs * PAIR I4: 3,5 COL I I1: 3,5,6 # reduction candidate for 3,5 I1: 3,5 # 22 pairs I9: 3,5,4,6 # reduction candidate for 3,5 I9: 3,5 # 11 pairs * PAIR D9: 5,6 BLK 8 D7: 5,6,1,9 # reduction candidate for 5,6 D7: 1,9 # 14 pairs D7: 5,6 # 12 pairs * PAIR D9: 5,6 ROW 9 C9: 5,6,4 # reduction candidate for 5,6 C9: 5,6 # 9 pairs I9: 5,6,3,4 # reduction candidate for 5,6 I9: 5,6 # 22 pairs * PAIR F9: 3,4 BLK 8 F8: 3,4,1 # reduction candidate for 3,4 F8: 1 => CTR * 1..4..736.27953.8.5.3716..9.1.849275.721653989..3276417.1.98..28..2.19.729..74813 F8: 3,4 # 14 pairs * PAIR F9: 3,4 ROW 9 I9: 3,4,5,6 # reduction candidate for 3,4 I9: 5,6 # 22 pairs I9: 3,4 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH cracking-the-cryptic-beyond-diabolical-base-pr-000.dot * REASONING * DIS # C2: 4,6 => CTR => C2: 7,9 * DIS # A5: 4,6 => CTR => A5: 3 * PRF # B3: 4,5 => SOL * DIS # F1: 3 => CTR => F1: 2,9 * DIS # D5: 7 => CTR => D5: 1,6 * DIS # E7: 1,6 => CTR => E7: 3,9 * DIS # G4: 3,5 => CTR => G4: 2 * DIS # F8: 1 => CTR => F8: 3,4 * CNT 8 HDP CHAINS / 31 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,D9,E5,F4,F9,I4) * 1..4..7...2..5..8...3..6..9.1..4..7...2..5.989..3..6..7....8..28..2..9.729..7.81. * PAIR A2: 4,6 BLK 1 C2: 4,6,7,9 # reduction candidate for 4,6 C2: 4,6 => CTR * 1894..7...2..57.8.573..6..9.18.49275..27.53989573826417...985.28.52.19.729.574813 * PAIR A2: 4,6 ROW 2 I2: 4,6,1,3 # reduction candidate for 4,6 I2: 1,3 # 18 pairs I2: 4,6 # 13 pairs * PAIR A2: 4,6 COL A A5: 4,6,3 # reduction candidate for 4,6 A5: 4,6 => CTR * 1..43275662.951483543786129318.49275..2..53989..3..6417....85.28..2.49.7296573814 * PAIR RESTART * PAIR A2: 4,6 ROW 2 I2: 4,6,1,3 # reduction candidate for 4,6 I2: 1,3 => CTR * 1..4..7..62..5.48.4.3..6..951..4..733427651989..3..6..7....83.283.2149.729..7.81. * PAIR RESTART * PAIR A3: 4,5 ROW 3 H3: 4,5,2 # reduction candidate for 4,5 H3: 2 => SOLVED * 189432765627951384453786129516849273372165498948327651731698542865214937294573816 * DURATION: 0:00:06.594310 START: 23:39:37.380321 END: 23:39:43.974631 2020-09-20 * SOLUTION FOUND * SAVE PR GRAPH cracking-the-cryptic-beyond-diabolical-base-pr-001.dot * REASONING * DIS # C2: 4,6 => CTR => C2: 7,9 * DIS C2: 7,9 # A5: 4,6 => CTR => A5: 3 * DIS C2: 7,9 + A5: 3 # I2: 1,3 => CTR => I2: 4,6 * PRF C2: 7,9 + A5: 3 + I2: 4,6 # H3: 2 => SOL * STA C2: 7,9 + A5: 3 + I2: 4,6 + H3: 2 * CNT 4 HDP CHAINS / 8 HYP OPENED
Header Info
https://www.youtube.com/watch?v=8C-A7xmBLRU
Solution
position: 189432765627951384453786129516849273372165498948327651731698542865214937294573816 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:
* DIS # C2: 4,6 => CTR => C2: 7,9 * INC # C2: 7,9 => UNS * INC # I2: 4,6 => UNS * INC # I2: 1,3 => UNS * DIS # A5: 4,6 => CTR => A5: 3 * INC # A5: 3 => UNS * PRF # B3: 4,5 => SOL * INC # B3: 7,8 => UNS * INC # G3: 4,5 => UNS * INC # H3: 4,5 => UNS * INC # F1: 2,9 => UNS * DIS # F1: 3 => CTR => F1: 2,9 * INC # D5: 1,6 => UNS * DIS # D5: 7 => CTR => D5: 1,6 * DIS # E7: 1,6 => CTR => E7: 3,9 * INC # E7: 3,9 => UNS * INC # E8: 1,6 => UNS * DIS # G4: 3,5 => CTR => G4: 2 * INC # G4: 2 => UNS * INC # A4: 3,5 => UNS * INC # A4: 6 => UNS * INC # I1: 3,5 => UNS * INC # I9: 3,5 => UNS * INC # D7: 5,6 => UNS * INC # D7: 1,9 => UNS * INC # C9: 5,6 => UNS * INC # I9: 5,6 => UNS * INC # F8: 3,4 => UNS * DIS # F8: 1 => CTR => F8: 3,4 * INC # I9: 3,4 => UNS * INC # I9: 5,6 => UNS * CNT 31 HDP CHAINS / 31 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C2: 4,6 => CTR => C2: 7,9 * INC C2: 7,9 # I2: 4,6 => UNS * INC C2: 7,9 # I2: 1,3 => UNS * DIS C2: 7,9 # A5: 4,6 => CTR => A5: 3 * INC C2: 7,9 + A5: 3 # I2: 4,6 => UNS * DIS C2: 7,9 + A5: 3 # I2: 1,3 => CTR => I2: 4,6 * INC C2: 7,9 + A5: 3 + I2: 4,6 # H3: 4,5 => UNS * PRF C2: 7,9 + A5: 3 + I2: 4,6 # H3: 2 => SOL * STA C2: 7,9 + A5: 3 + I2: 4,6 + H3: 2 * CNT 8 HDP CHAINS / 8 HYP OPENED