Analysis of xx-ph-00000894-H200-base.sdk
Contents
Original Sudoku
level: hard
position: 98.7.....7.6...8....5......4...3..2...89..7.......1..5.9.4..6......5...3.....2.1. initial
Autosolve
position: 98.7.....7.6...8....5......4...3..2...89..7.......1..5.9.4..6......5...3.....2.1. autosolve
Pair Reduction Variants
Deep Pair Reduction
Time used: 0:00:40.360591
The following important HDP chains were detected:
* DIS # I4: 1,9 # D4: 5,6 => CTR => D4: 8 * DIS # I4: 1,9 + D4: 8 # B9: 5,6 => CTR => B9: 3,4,7 * DIS # I4: 1,9 + D4: 8 + B9: 3,4,7 # E3: 2,4 => CTR => E3: 1,6,8,9 * DIS # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 # A6: 2,6 => CTR => A6: 3 * DIS # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 + A6: 3 # D3: 2,6 => CTR => D3: 1,3 * DIS # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 + A6: 3 + D3: 1,3 # G3: 1,9 => CTR => G3: 2,3 * DIS # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 + A6: 3 + D3: 1,3 + G3: 2,3 # B2: 1,2 => CTR => B2: 3 * PRF # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 + A6: 3 + D3: 1,3 + G3: 2,3 + B2: 3 # E3: 8,9 => SOL * STA # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 + A6: 3 + D3: 1,3 + G3: 2,3 + B2: 3 + E3: 8,9 * CNT 8 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 98.7.....7.6...8....5......4...3..2...89..7.......1..5.9.4..6......5...3.....2.1. | initial |
| 98.7.....7.6...8....5......4...3..2...89..7.......1..5.9.4..6......5...3.....2.1. | autosolve |
| 981763254736524891245189367457836129128945736369271485593418672812657943674392518 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (1) G4: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E7,D8: 1.. / E7 = 1 => 2 pairs (_) / D8 = 1 => 2 pairs (_) I7,G8: 2.. / I7 = 2 => 2 pairs (_) / G8 = 2 => 2 pairs (_) F7,D9: 3.. / F7 = 3 => 2 pairs (_) / D9 = 3 => 3 pairs (_) H7,G9: 5.. / H7 = 5 => 2 pairs (_) / G9 = 5 => 2 pairs (_) A7,H7: 5.. / A7 = 5 => 2 pairs (_) / H7 = 5 => 2 pairs (_) D2,D4: 5.. / D2 = 5 => 2 pairs (_) / D4 = 5 => 2 pairs (_) G1,G9: 5.. / G1 = 5 => 2 pairs (_) / G9 = 5 => 2 pairs (_) H3,I3: 7.. / H3 = 7 => 2 pairs (_) / I3 = 7 => 2 pairs (_) F4,E6: 7.. / F4 = 7 => 5 pairs (_) / E6 = 7 => 4 pairs (_) I4,H6: 8.. / I4 = 8 => 3 pairs (_) / H6 = 8 => 3 pairs (_) C4,C6: 9.. / C4 = 9 => 2 pairs (_) / C6 = 9 => 3 pairs (_) F8,E9: 9.. / F8 = 9 => 2 pairs (_) / E9 = 9 => 2 pairs (_) * DURATION: 0:00:08.667034 START: 02:06:14.440114 END: 02:06:23.107148 2020-11-23 * CP COUNT: (12) * INCONCLUSIVE * DEEP PAIR REDUCTION * DURATION: 0:00:40.163084 START: 02:06:28.957345 END: 02:07:09.120429 2020-11-23 * SOLUTION FOUND * SAVE PR GRAPH xx-ph-00000894-H200-base-pr-002.dot * REASONING * DIS # I4: 1,9 # D4: 5,6 => CTR => D4: 8 * DIS # I4: 1,9 + D4: 8 # B9: 5,6 => CTR => B9: 3,4,7 * DIS # I4: 1,9 + D4: 8 + B9: 3,4,7 # E3: 2,4 => CTR => E3: 1,6,8,9 * DIS # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 # A6: 2,6 => CTR => A6: 3 * DIS # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 + A6: 3 # D3: 2,6 => CTR => D3: 1,3 * DIS # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 + A6: 3 + D3: 1,3 # G3: 1,9 => CTR => G3: 2,3 * DIS # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 + A6: 3 + D3: 1,3 + G3: 2,3 # B2: 1,2 => CTR => B2: 3 * PRF # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 + A6: 3 + D3: 1,3 + G3: 2,3 + B2: 3 # E3: 8,9 => SOL * STA # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 + A6: 3 + D3: 1,3 + G3: 2,3 + B2: 3 + E3: 8,9 * CNT 8 HDP CHAINS / 22 HYP OPENED
Header Info
894;H200;GP;22;11.30;11.30;9.50
Solution
position: 981763254736524891245189367457836129128945736369271485593418672812657943674392518 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 # I4: 1,9 => UNS * INC # I4: 6,8 => UNS * INC # C4: 1,9 => UNS * INC # C4: 7 => UNS * INC # G3: 1,9 => UNS * INC # G3: 2,3,4 => UNS * CNT 6 HDP CHAINS / 6 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # I4: 1,9 => UNS * INC # I4: 6,8 => UNS * INC # C4: 1,9 => UNS * INC # C4: 7 => UNS * INC # G3: 1,9 => UNS * INC # G3: 2,3,4 => UNS * CNT 6 HDP CHAINS / 6 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # I4: 1,9 => UNS * INC # I4: 6,8 => UNS * INC # C4: 1,9 => UNS * INC # C4: 7 => UNS * INC # G3: 1,9 => UNS * INC # G3: 2,3,4 => UNS * DIS # I4: 1,9 # D4: 5,6 => CTR => D4: 8 * DIS # I4: 1,9 + D4: 8 # B9: 5,6 => CTR => B9: 3,4,7 * INC # I4: 1,9 + D4: 8 + B9: 3,4,7 # E1: 2,4 => UNS * INC # I4: 1,9 + D4: 8 + B9: 3,4,7 # E2: 2,4 => UNS * DIS # I4: 1,9 + D4: 8 + B9: 3,4,7 # E3: 2,4 => CTR => E3: 1,6,8,9 * INC # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 # E1: 2,4 => UNS * INC # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 # E2: 2,4 => UNS * DIS # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 # A6: 2,6 => CTR => A6: 3 * DIS # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 + A6: 3 # D3: 2,6 => CTR => D3: 1,3 * DIS # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 + A6: 3 + D3: 1,3 # G3: 1,9 => CTR => G3: 2,3 * INC # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 + A6: 3 + D3: 1,3 + G3: 2,3 # I2: 1,9 => UNS * INC # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 + A6: 3 + D3: 1,3 + G3: 2,3 # I2: 2,4 => UNS * INC # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 + A6: 3 + D3: 1,3 + G3: 2,3 # C1: 1,2 => UNS * DIS # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 + A6: 3 + D3: 1,3 + G3: 2,3 # B2: 1,2 => CTR => B2: 3 * PRF # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 + A6: 3 + D3: 1,3 + G3: 2,3 + B2: 3 # E3: 8,9 => SOL * STA # I4: 1,9 + D4: 8 + B9: 3,4,7 + E3: 1,6,8,9 + A6: 3 + D3: 1,3 + G3: 2,3 + B2: 3 + E3: 8,9 * CNT 21 HDP CHAINS / 22 HYP OPENED