Analysis of xx-ph-00000893-H199-base.sdk
Contents
Original Sudoku
level: hard
position: 98.7.....7.6...8...5.......4..9..6......3..5......2..1.6...1..3..78..4......5..2. initial
Autosolve
position: 98.7.....7.6...8...5.......4..9..6......3..5......2..1.6...1..3..78..4......5..2. autosolve
Pair Reduction Variants
Deep Pair Reduction
Time used: 0:00:31.978338
The following important HDP chains were detected:
* DIS # E7: 2,4 # C4: 5,8 => CTR => C4: 1,2,3 * DIS # E7: 2,4 + C4: 1,2,3 # C7: 5,8 => CTR => C7: 9 * DIS # E7: 2,4 + C4: 1,2,3 + C7: 9 # D3: 2,4 => CTR => D3: 1,3,6 * DIS # E7: 2,4 + C4: 1,2,3 + C7: 9 + D3: 1,3,6 # F8: 6,9 => CTR => F8: 3 * DIS # E7: 2,4 + C4: 1,2,3 + C7: 9 + D3: 1,3,6 + F8: 3 => CTR => E7: 7,9 * PRF E7: 7,9 # C7: 5,8,9 # A8: 1,3 => SOL * STA E7: 7,9 # C7: 5,8,9 + A8: 1,3 * CNT 6 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 98.7.....7.6...8...5.......4..9..6......3..5......2..1.6...1..3..78..4......5..2. | initial |
| 98.7.....7.6...8...5.......4..9..6......3..5......2..1.6...1..3..78..4......5..2. | autosolve |
| 982713564736549812154268379421975638698134257573682941265491783317826495849357126 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (1) D7: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E4,D5: 1.. / E4 = 1 => 2 pairs (_) / D5 = 1 => 2 pairs (_) H8,G9: 1.. / H8 = 1 => 2 pairs (_) / G9 = 1 => 3 pairs (_) I5,H6: 4.. / I5 = 4 => 2 pairs (_) / H6 = 4 => 2 pairs (_) B2,B9: 4.. / B2 = 4 => 1 pairs (_) / B9 = 4 => 2 pairs (_) F4,D6: 5.. / F4 = 5 => 2 pairs (_) / D6 = 5 => 2 pairs (_) G7,I8: 5.. / G7 = 5 => 3 pairs (_) / I8 = 5 => 2 pairs (_) C4,F4: 5.. / C4 = 5 => 2 pairs (_) / F4 = 5 => 2 pairs (_) A8,I8: 5.. / A8 = 5 => 3 pairs (_) / I8 = 5 => 2 pairs (_) D2,D6: 5.. / D2 = 5 => 2 pairs (_) / D6 = 5 => 2 pairs (_) G1,G7: 5.. / G1 = 5 => 2 pairs (_) / G7 = 5 => 3 pairs (_) A5,A6: 6.. / A5 = 6 => 2 pairs (_) / A6 = 6 => 2 pairs (_) E7,F9: 7.. / E7 = 7 => 4 pairs (_) / F9 = 7 => 3 pairs (_) E3,F3: 8.. / E3 = 8 => 2 pairs (_) / F3 = 8 => 2 pairs (_) H7,I9: 8.. / H7 = 8 => 3 pairs (_) / I9 = 8 => 6 pairs (_) * DURATION: 0:00:10.260615 START: 01:54:18.991849 END: 01:54:29.252464 2020-11-23 * CP COUNT: (14) * INCONCLUSIVE * DEEP PAIR REDUCTION * DURATION: 0:00:31.707655 START: 01:54:34.660571 END: 01:55:06.368226 2020-11-23 * SOLUTION FOUND * SAVE PR GRAPH xx-ph-00000893-H199-base-pr-002.dot * REASONING * DIS # E7: 2,4 # C4: 5,8 => CTR => C4: 1,2,3 * DIS # E7: 2,4 + C4: 1,2,3 # C7: 5,8 => CTR => C7: 9 * DIS # E7: 2,4 + C4: 1,2,3 + C7: 9 # D3: 2,4 => CTR => D3: 1,3,6 * DIS # E7: 2,4 + C4: 1,2,3 + C7: 9 + D3: 1,3,6 # F8: 6,9 => CTR => F8: 3 * DIS # E7: 2,4 + C4: 1,2,3 + C7: 9 + D3: 1,3,6 + F8: 3 => CTR => E7: 7,9 * PRF E7: 7,9 # C7: 5,8,9 # A8: 1,3 => SOL * STA E7: 7,9 # C7: 5,8,9 + A8: 1,3 * CNT 6 HDP CHAINS / 44 HYP OPENED
Header Info
893;H199;GP;22;11.30;11.30;9.50
Solution
position: 982713564736549812154268379421975638698134257573682941265491783317826495849357126 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 # E7: 2,4 => UNS * INC # E7: 7,9 => UNS * INC # C7: 2,4 => UNS * INC # C7: 5,8,9 => UNS * INC # D2: 2,4 => UNS * INC # D3: 2,4 => UNS * CNT 6 HDP CHAINS / 6 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E7: 2,4 => UNS * INC # E7: 7,9 => UNS * INC # C7: 2,4 => UNS * INC # C7: 5,8,9 => UNS * INC # D2: 2,4 => UNS * INC # D3: 2,4 => UNS * CNT 6 HDP CHAINS / 6 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # E7: 2,4 => UNS * INC # E7: 7,9 => UNS * INC # C7: 2,4 => UNS * INC # C7: 5,8,9 => UNS * INC # D2: 2,4 => UNS * INC # D3: 2,4 => UNS * DIS # E7: 2,4 # C4: 5,8 => CTR => C4: 1,2,3 * DIS # E7: 2,4 + C4: 1,2,3 # C7: 5,8 => CTR => C7: 9 * DIS # E7: 2,4 + C4: 1,2,3 + C7: 9 # D3: 2,4 => CTR => D3: 1,3,6 * DIS # E7: 2,4 + C4: 1,2,3 + C7: 9 + D3: 1,3,6 # F8: 6,9 => CTR => F8: 3 * DIS # E7: 2,4 + C4: 1,2,3 + C7: 9 + D3: 1,3,6 + F8: 3 => CTR => E7: 7,9 * INC E7: 7,9 # C7: 2,4 => UNS * INC E7: 7,9 # C7: 5,8,9 => UNS * INC E7: 7,9 # D2: 2,4 => UNS * INC E7: 7,9 # D3: 2,4 => UNS * INC E7: 7,9 # F9: 7,9 => UNS * INC E7: 7,9 # F9: 3,4,6 => UNS * INC E7: 7,9 # G7: 7,9 => UNS * INC E7: 7,9 # H7: 7,9 => UNS * INC E7: 7,9 # C7: 2,4 => UNS * INC E7: 7,9 # C7: 5,8,9 => UNS * INC E7: 7,9 # D2: 2,4 => UNS * INC E7: 7,9 # D3: 2,4 => UNS * INC E7: 7,9 # F9: 7,9 => UNS * INC E7: 7,9 # F9: 3,4,6 => UNS * INC E7: 7,9 # G7: 7,9 => UNS * INC E7: 7,9 # H7: 7,9 => UNS * INC E7: 7,9 # C7: 2,4 # C1: 2,4 => UNS * INC E7: 7,9 # C7: 2,4 # C3: 2,4 => UNS * INC E7: 7,9 # C7: 2,4 # D2: 2,4 => UNS * INC E7: 7,9 # C7: 2,4 # D3: 2,4 => UNS * INC E7: 7,9 # C7: 2,4 # F9: 7,9 => UNS * INC E7: 7,9 # C7: 2,4 # F9: 3,4,6 => UNS * INC E7: 7,9 # C7: 2,4 # G7: 7,9 => UNS * INC E7: 7,9 # C7: 2,4 # H7: 7,9 => UNS * INC E7: 7,9 # C7: 2,4 => UNS * INC E7: 7,9 # C7: 5,8,9 # C1: 1,3 => UNS * INC E7: 7,9 # C7: 5,8,9 # B2: 1,3 => UNS * INC E7: 7,9 # C7: 5,8,9 # C3: 1,3 => UNS * INC E7: 7,9 # C7: 5,8,9 # D3: 1,3 => UNS * INC E7: 7,9 # C7: 5,8,9 # G3: 1,3 => UNS * INC E7: 7,9 # C7: 5,8,9 # H3: 1,3 => UNS * PRF E7: 7,9 # C7: 5,8,9 # A8: 1,3 => SOL * STA E7: 7,9 # C7: 5,8,9 + A8: 1,3 * CNT 43 HDP CHAINS / 44 HYP OPENED