Analysis of xx-ph-00299047-12_12_03-base.sdk
Contents
Original Sudoku
level: hard
position: ........1.....2.34..4...52...5..3.6..1..7....8..9.......6..42...7..1....9..8....5 initial
Autosolve
position: ........1.....2.34..4...52...5..3.6..1..7....8..9.......6..42...7..1....9..8....5 autosolve
Pair Reduction Variants
Deep Pair Reduction
Time used: 0:00:42.942457
The following important HDP chains were detected:
* DIS # F3: 6,7 # E4: 2,4 => CTR => E4: 8 * DIS # F3: 6,7 + E4: 8 # B4: 2,4 => CTR => B4: 9 * DIS # F3: 6,7 + E4: 8 + B4: 9 # A4: 7 => CTR => A4: 2,4 * DIS # F3: 6,7 + E4: 8 + B4: 9 + A4: 2,4 # G9: 3,4 => CTR => G9: 6,7 * DIS # F3: 6,7 + E4: 8 + B4: 9 + A4: 2,4 + G9: 6,7 # D1: 6,7 => CTR => D1: 3,4,5 * PRF # F3: 6,7 + E4: 8 + B4: 9 + A4: 2,4 + G9: 6,7 + D1: 3,4,5 # D2: 6,7 => SOL * STA # F3: 6,7 + E4: 8 + B4: 9 + A4: 2,4 + G9: 6,7 + D1: 3,4,5 + D2: 6,7 * CNT 6 HDP CHAINS / 53 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ........1.....2.34..4...52...5..3.6..1..7....8..9.......6..42...7..1....9..8....5 | initial |
| ........1.....2.34..4...52...5..3.6..1..7....8..9.......6..42...7..1....9..8....5 | autosolve |
| 529348671781652934364197528495283167612475893837961452156734289278519346943826715 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (1) F9: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D4,F6: 1.. / D4 = 1 => 2 pairs (_) / F6 = 1 => 2 pairs (_) A7,C9: 1.. / A7 = 1 => 2 pairs (_) / C9 = 1 => 3 pairs (_) D4,G4: 1.. / D4 = 1 => 2 pairs (_) / G4 = 1 => 2 pairs (_) A7,H7: 1.. / A7 = 1 => 2 pairs (_) / H7 = 1 => 3 pairs (_) C2,C9: 1.. / C2 = 1 => 2 pairs (_) / C9 = 1 => 3 pairs (_) F3,F6: 1.. / F3 = 1 => 2 pairs (_) / F6 = 1 => 2 pairs (_) D8,E9: 2.. / D8 = 2 => 4 pairs (_) / E9 = 2 => 4 pairs (_) D1,E1: 4.. / D1 = 4 => 2 pairs (_) / E1 = 4 => 2 pairs (_) A8,B9: 4.. / A8 = 4 => 6 pairs (_) / B9 = 4 => 3 pairs (_) H5,H6: 5.. / H5 = 5 => 2 pairs (_) / H6 = 5 => 2 pairs (_) A5,B6: 6.. / A5 = 6 => 2 pairs (_) / B6 = 6 => 2 pairs (_) I3,I8: 6.. / I3 = 6 => 1 pairs (_) / I8 = 6 => 2 pairs (_) A4,C6: 7.. / A4 = 7 => 2 pairs (_) / C6 = 7 => 3 pairs (_) D7,F9: 7.. / D7 = 7 => 4 pairs (_) / F9 = 7 => 2 pairs (_) E4,F5: 8.. / E4 = 8 => 2 pairs (_) / F5 = 8 => 2 pairs (_) B7,C8: 8.. / B7 = 8 => 2 pairs (_) / C8 = 8 => 3 pairs (_) B4,C5: 9.. / B4 = 9 => 2 pairs (_) / C5 = 9 => 2 pairs (_) E7,F8: 9.. / E7 = 9 => 2 pairs (_) / F8 = 9 => 3 pairs (_) * DURATION: 0:00:12.731538 START: 00:13:23.752457 END: 00:13:36.483995 2020-12-25 * CP COUNT: (18) * INCONCLUSIVE * DEEP PAIR REDUCTION * DURATION: 0:00:42.662129 START: 00:13:40.535715 END: 00:14:23.197844 2020-12-25 * SOLUTION FOUND * SAVE PR GRAPH xx-ph-00299047-12_12_03-base-pr-002.dot * REASONING * DIS # F3: 6,7 # E4: 2,4 => CTR => E4: 8 * DIS # F3: 6,7 + E4: 8 # B4: 2,4 => CTR => B4: 9 * DIS # F3: 6,7 + E4: 8 + B4: 9 # A4: 7 => CTR => A4: 2,4 * DIS # F3: 6,7 + E4: 8 + B4: 9 + A4: 2,4 # G9: 3,4 => CTR => G9: 6,7 * DIS # F3: 6,7 + E4: 8 + B4: 9 + A4: 2,4 + G9: 6,7 # D1: 6,7 => CTR => D1: 3,4,5 * PRF # F3: 6,7 + E4: 8 + B4: 9 + A4: 2,4 + G9: 6,7 + D1: 3,4,5 # D2: 6,7 => SOL * STA # F3: 6,7 + E4: 8 + B4: 9 + A4: 2,4 + G9: 6,7 + D1: 3,4,5 + D2: 6,7 * CNT 6 HDP CHAINS / 53 HYP OPENED
Header Info
299047;12_12_03;dob;22;11.30;11.30;9.40
Solution
position: 529348671781652934364197528495283167612475893837961452156734289278519346943826715 solved
See section Deep 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 # G9: 6,7 => UNS * INC # G9: 1,3,4 => UNS * INC # F1: 6,7 => UNS * INC # F3: 6,7 => UNS * CNT 4 HDP CHAINS / 4 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G9: 6,7 => UNS * INC # G9: 1,3,4 => UNS * INC # F1: 6,7 => UNS * INC # F3: 6,7 => UNS * CNT 4 HDP CHAINS / 4 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # G9: 6,7 => UNS * INC # G9: 1,3,4 => UNS * INC # F1: 6,7 => UNS * INC # F3: 6,7 => UNS * INC # G9: 6,7 # D8: 2,3 => UNS * INC # G9: 6,7 # D8: 5,6 => UNS * INC # G9: 6,7 # B9: 2,3 => UNS * INC # G9: 6,7 # C9: 2,3 => UNS * INC # G9: 6,7 # F1: 6,7 => UNS * INC # G9: 6,7 # F3: 6,7 => UNS * INC # G9: 6,7 # G1: 6,7 => UNS * INC # G9: 6,7 # G2: 6,7 => UNS * INC # G9: 6,7 => UNS * INC # G9: 1,3,4 # E7: 5,9 => UNS * INC # G9: 1,3,4 # E7: 3 => UNS * INC # G9: 1,3,4 # F1: 5,9 => UNS * INC # G9: 1,3,4 # F1: 6,7,8 => UNS * INC # G9: 1,3,4 # F1: 6,7 => UNS * INC # G9: 1,3,4 # F3: 6,7 => UNS * INC # G9: 1,3,4 => UNS * INC # F1: 6,7 # D1: 6,7 => UNS * INC # F1: 6,7 # D2: 6,7 => UNS * INC # F1: 6,7 # D3: 6,7 => UNS * INC # F1: 6,7 # A1: 6,7 => UNS * INC # F1: 6,7 # G1: 6,7 => UNS * INC # F1: 6,7 # H5: 5,8 => UNS * INC # F1: 6,7 # H5: 4,9 => UNS * INC # F1: 6,7 # H6: 1,5 => UNS * INC # F1: 6,7 # H6: 4,7 => UNS * INC # F1: 6,7 # E7: 5,9 => UNS * INC # F1: 6,7 # E7: 3 => UNS * INC # F1: 6,7 # G9: 6,7 => UNS * INC # F1: 6,7 # G9: 1,3,4 => UNS * INC # F1: 6,7 => UNS * INC # F3: 6,7 # D1: 6,7 => UNS * INC # F3: 6,7 # D2: 6,7 => UNS * INC # F3: 6,7 # D3: 6,7 => UNS * INC # F3: 6,7 # A3: 6,7 => UNS * INC # F3: 6,7 # I3: 6,7 => UNS * DIS # F3: 6,7 # E4: 2,4 => CTR => E4: 8 * INC # F3: 6,7 + E4: 8 # D5: 2,4 => UNS * INC # F3: 6,7 + E4: 8 # E6: 2,4 => UNS * INC # F3: 6,7 + E4: 8 # A4: 2,4 => UNS * DIS # F3: 6,7 + E4: 8 # B4: 2,4 => CTR => B4: 9 * INC # F3: 6,7 + E4: 8 + B4: 9 # A4: 2,4 => UNS * DIS # F3: 6,7 + E4: 8 + B4: 9 # A4: 7 => CTR => A4: 2,4 * INC # F3: 6,7 + E4: 8 + B4: 9 + A4: 2,4 # D5: 2,4 => UNS * INC # F3: 6,7 + E4: 8 + B4: 9 + A4: 2,4 # E6: 2,4 => UNS * INC # F3: 6,7 + E4: 8 + B4: 9 + A4: 2,4 # G9: 6,7 => UNS * DIS # F3: 6,7 + E4: 8 + B4: 9 + A4: 2,4 # G9: 3,4 => CTR => G9: 6,7 * DIS # F3: 6,7 + E4: 8 + B4: 9 + A4: 2,4 + G9: 6,7 # D1: 6,7 => CTR => D1: 3,4,5 * PRF # F3: 6,7 + E4: 8 + B4: 9 + A4: 2,4 + G9: 6,7 + D1: 3,4,5 # D2: 6,7 => SOL * STA # F3: 6,7 + E4: 8 + B4: 9 + A4: 2,4 + G9: 6,7 + D1: 3,4,5 + D2: 6,7 * CNT 52 HDP CHAINS / 53 HYP OPENED