Analysis of xx-top95-066-base.sdk
Contents
Original Sudoku
level: hard
position: 34.6.......7.......2..8.57......5....7..1..2....4......36.2..1.......9.......7.82 initial
Autosolve
position: 345671298..725.....2..8.57....7.5....7..1..2....4.2....36.2..1.......9.......7.82 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C4: 1,9 => CTR => C4: 2,3,4,8 * DIS # D5: 3,9 => CTR => D5: 8 * DIS # F5: 8,9 => CTR => F5: 3,6 * CNT 3 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C4: 1,9 => CTR => C4: 2,3,4,8 * DIS C4: 2,3,4,8 # D5: 3,9 => CTR => D5: 8 * STA C4: 2,3,4,8 + D5: 8 * CNT 2 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: 345671298..725.....2..8.57....7.5....7.81..2....4.2....36.2..1.......9.......7.82 pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:49.232088
The following important HDP chains were detected:
* DIS # A2: 1,9 # C6: 1,9 => CTR => C6: 3,8 * DIS # A2: 1,9 + C6: 3,8 # I5: 3,6 => CTR => I5: 4,5,9 * PRF # A2: 1,9 + C6: 3,8 + I5: 4,5,9 # G5: 4 => SOL * STA # A2: 1,9 + C6: 3,8 + I5: 4,5,9 + G5: 4 * CNT 3 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 34.6.......7.......2..8.57......5....7..1..2....4......36.2..1.......9.......7.82 | initial |
| 345671298..725.....2..8.57....7.5....7..1..2....4.2....36.2..1.......9.......7.82 | autosolve |
| 345671298..725.....2..8.57....7.5....7.81..2....4.2....36.2..1.......9.......7.82 | pair_reduction |
| 345671298987253146621984573264795831573816429198432657836529714712348965459167382 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (4) C3: 1,9 D3: 3,9 F7: 8,9 G7: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D8,D9: 1.. / D8 = 1 => 5 pairs (_) / D9 = 1 => 11 pairs (_) A4,C4: 2.. / A4 = 2 => 4 pairs (_) / C4 = 2 => 16 pairs (_) A8,C8: 2.. / A8 = 2 => 16 pairs (_) / C8 = 2 => 4 pairs (_) A4,A8: 2.. / A4 = 2 => 4 pairs (_) / A8 = 2 => 16 pairs (_) C4,C8: 2.. / C4 = 2 => 16 pairs (_) / C8 = 2 => 4 pairs (_) F2,F3: 4.. / F2 = 4 => 9 pairs (_) / F3 = 4 => 5 pairs (_) E8,E9: 4.. / E8 = 4 => 4 pairs (_) / E9 = 4 => 0 pairs (X) F3,I3: 4.. / F3 = 4 => 5 pairs (_) / I3 = 4 => 9 pairs (_) A5,I5: 5.. / A5 = 5 => 4 pairs (_) / I5 = 5 => 11 pairs (_) H6,H8: 5.. / H6 = 5 => 4 pairs (_) / H8 = 5 => 9 pairs (_) A3,I3: 6.. / A3 = 6 => 4 pairs (_) / I3 = 6 => 12 pairs (_) E9,G9: 6.. / E9 = 6 => 11 pairs (_) / G9 = 6 => 7 pairs (_) F5,F8: 6.. / F5 = 6 => 11 pairs (_) / F8 = 6 => 11 pairs (_) G6,I6: 7.. / G6 = 7 => 6 pairs (_) / I6 = 7 => 4 pairs (_) A7,A8: 7.. / A7 = 7 => 17 pairs (_) / A8 = 7 => 4 pairs (_) A8,I8: 7.. / A8 = 7 => 4 pairs (_) / I8 = 7 => 17 pairs (_) G6,G7: 7.. / G6 = 7 => 6 pairs (_) / G7 = 7 => 4 pairs (_) A2,B2: 8.. / A2 = 8 => 5 pairs (_) / B2 = 8 => 11 pairs (_) D5,F5: 8.. / D5 = 8 => 5 pairs (_) / F5 = 8 => 0 pairs (X) G4,G6: 8.. / G4 = 8 => 4 pairs (_) / G6 = 8 => 6 pairs (_) * DURATION: 0:00:24.694442 START: 00:18:53.733721 END: 00:19:18.428163 2017-05-04 * CP COUNT: (20) * CLUE FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:49.006339 START: 00:20:11.977886 END: 00:21:00.984225 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-066-base-pr-002.dot * REASONING * DIS # A2: 1,9 # C6: 1,9 => CTR => C6: 3,8 * DIS # A2: 1,9 + C6: 3,8 # I5: 3,6 => CTR => I5: 4,5,9 * PRF # A2: 1,9 + C6: 3,8 + I5: 4,5,9 # G5: 4 => SOL * STA # A2: 1,9 + C6: 3,8 + I5: 4,5,9 + G5: 4 * CNT 3 HDP CHAINS / 37 HYP OPENED
Header Info
Top 95 Sudokus 066 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 345671298987253146621984573264795831573816429198432657836529714712348965459167382 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 # A2: 1,9 => UNS * INC # B2: 1,9 => UNS * INC # A3: 1,9 => UNS * DIS # C4: 1,9 => CTR => C4: 2,3,4,8 * INC # C4: 2,3,4,8 => UNS * INC # C6: 1,9 => UNS * INC # C9: 1,9 => UNS * INC # F2: 3,9 => UNS * INC # F3: 3,9 => UNS * DIS # D5: 3,9 => CTR => D5: 8 * INC # D5: 8 => UNS * INC # D9: 3,9 => UNS * INC # D7: 8,9 => UNS * INC # D7: 5 => UNS * INC # A7: 8,9 => UNS * INC # A7: 4,5,7 => UNS * DIS # F5: 8,9 => CTR => F5: 3,6 * INC # F5: 3,6 => UNS * INC # I7: 4,7 => UNS * INC # I8: 4,7 => UNS * INC # A7: 4,7 => UNS * INC # A7: 5,8,9 => UNS * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 1,9 => UNS * INC # B2: 1,9 => UNS * INC # A3: 1,9 => UNS * DIS # C4: 1,9 => CTR => C4: 2,3,4,8 * INC C4: 2,3,4,8 # C6: 1,9 => UNS * INC C4: 2,3,4,8 # C9: 1,9 => UNS * INC C4: 2,3,4,8 # A2: 1,9 => UNS * INC C4: 2,3,4,8 # B2: 1,9 => UNS * INC C4: 2,3,4,8 # A3: 1,9 => UNS * INC C4: 2,3,4,8 # C6: 1,9 => UNS * INC C4: 2,3,4,8 # C9: 1,9 => UNS * INC C4: 2,3,4,8 # F2: 3,9 => UNS * INC C4: 2,3,4,8 # F3: 3,9 => UNS * DIS C4: 2,3,4,8 # D5: 3,9 => CTR => D5: 8 * INC C4: 2,3,4,8 + D5: 8 # D9: 3,9 => UNS * INC C4: 2,3,4,8 + D5: 8 # D9: 3,9 => UNS * INC C4: 2,3,4,8 + D5: 8 # D9: 1,5 => UNS * INC C4: 2,3,4,8 + D5: 8 # F2: 3,9 => UNS * INC C4: 2,3,4,8 + D5: 8 # F3: 3,9 => UNS * INC C4: 2,3,4,8 + D5: 8 # D9: 3,9 => UNS * INC C4: 2,3,4,8 + D5: 8 # D9: 1,5 => UNS * INC C4: 2,3,4,8 + D5: 8 # A7: 8,9 => UNS * INC C4: 2,3,4,8 + D5: 8 # A7: 4,5,7 => UNS * INC C4: 2,3,4,8 + D5: 8 # I7: 4,7 => UNS * INC C4: 2,3,4,8 + D5: 8 # I8: 4,7 => UNS * INC C4: 2,3,4,8 + D5: 8 # A7: 4,7 => UNS * INC C4: 2,3,4,8 + D5: 8 # A7: 5,8,9 => UNS * INC C4: 2,3,4,8 + D5: 8 # A2: 1,9 => UNS * INC C4: 2,3,4,8 + D5: 8 # B2: 1,9 => UNS * INC C4: 2,3,4,8 + D5: 8 # A3: 1,9 => UNS * INC C4: 2,3,4,8 + D5: 8 # C6: 1,9 => UNS * INC C4: 2,3,4,8 + D5: 8 # C9: 1,9 => UNS * INC C4: 2,3,4,8 + D5: 8 # F2: 3,9 => UNS * INC C4: 2,3,4,8 + D5: 8 # F3: 3,9 => UNS * INC C4: 2,3,4,8 + D5: 8 # D9: 3,9 => UNS * INC C4: 2,3,4,8 + D5: 8 # D9: 1,5 => UNS * INC C4: 2,3,4,8 + D5: 8 # D9: 5,9 => UNS * INC C4: 2,3,4,8 + D5: 8 # D9: 1,3 => UNS * INC C4: 2,3,4,8 + D5: 8 # A7: 5,9 => UNS * INC C4: 2,3,4,8 + D5: 8 # A7: 4,7,8 => UNS * INC C4: 2,3,4,8 + D5: 8 # A7: 8,9 => UNS * INC C4: 2,3,4,8 + D5: 8 # A7: 4,5,7 => UNS * INC C4: 2,3,4,8 + D5: 8 # I7: 4,7 => UNS * INC C4: 2,3,4,8 + D5: 8 # I8: 4,7 => UNS * INC C4: 2,3,4,8 + D5: 8 # A7: 4,7 => UNS * INC C4: 2,3,4,8 + D5: 8 # A7: 5,8,9 => UNS * STA C4: 2,3,4,8 + D5: 8 * CNT 46 HDP CHAINS / 46 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 1,9 => UNS * INC # B2: 1,9 => UNS * INC # A3: 1,9 => UNS * INC # C6: 1,9 => UNS * INC # C9: 1,9 => UNS * INC # F2: 3,9 => UNS * INC # F3: 3,9 => UNS * INC # D9: 3,9 => UNS * INC # D9: 1,5 => UNS * INC # D9: 5,9 => UNS * INC # D9: 1,3 => UNS * INC # A7: 5,9 => UNS * INC # A7: 4,7,8 => UNS * INC # A7: 8,9 => UNS * INC # A7: 4,5,7 => UNS * INC # I7: 4,7 => UNS * INC # I8: 4,7 => UNS * INC # A7: 4,7 => UNS * INC # A7: 5,8,9 => UNS * INC # A2: 1,9 # A4: 1,9 => UNS * INC # A2: 1,9 # A6: 1,9 => UNS * INC # A2: 1,9 # A9: 1,9 => UNS * DIS # A2: 1,9 # C6: 1,9 => CTR => C6: 3,8 * INC # A2: 1,9 + C6: 3,8 # C9: 1,9 => UNS * INC # A2: 1,9 + C6: 3,8 # C9: 1,9 => UNS * INC # A2: 1,9 + C6: 3,8 # C9: 4 => UNS * INC # A2: 1,9 + C6: 3,8 # C9: 1,9 => UNS * INC # A2: 1,9 + C6: 3,8 # C9: 4 => UNS * INC # A2: 1,9 + C6: 3,8 # F2: 3,9 => UNS * INC # A2: 1,9 + C6: 3,8 # F3: 3,9 => UNS * INC # A2: 1,9 + C6: 3,8 # E4: 3,6 => UNS * INC # A2: 1,9 + C6: 3,8 # E6: 3,6 => UNS * INC # A2: 1,9 + C6: 3,8 # G5: 3,6 => UNS * DIS # A2: 1,9 + C6: 3,8 # I5: 3,6 => CTR => I5: 4,5,9 * INC # A2: 1,9 + C6: 3,8 + I5: 4,5,9 # G5: 3,6 => UNS * PRF # A2: 1,9 + C6: 3,8 + I5: 4,5,9 # G5: 4 => SOL * STA # A2: 1,9 + C6: 3,8 + I5: 4,5,9 + G5: 4 * CNT 36 HDP CHAINS / 37 HYP OPENED