Analysis of zz-www.sudokuwiki.org-0345-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=345
level: hard
position: ........1.....2.3.....3.42...42..56...6..4....1.8.......5..63...8.7....99..1..... initial
Autosolve
position: ........1.....2.3.....3.42...42..56...63.4....1.86......5..63...8.7....99..1..... autosolve
Pair Reduction Variants
Deep Pair Reduction
Time used: 0:00:24.468446
The following important HDP chains were detected:
* DIS # E7: 4,9 # C9: 2,7 => CTR => C9: 3 * DIS # E7: 4,9 + C9: 3 # B1: 2,7 => CTR => B1: 3,4,5,6,9 * DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 # A7: 1 => CTR => A7: 2,7 * DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 # B5: 2,7 => CTR => B5: 5,9 * DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 + B5: 5,9 # A1: 4,6 => CTR => A1: 2,3,5 * DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 + B5: 5,9 + A1: 2,3,5 # A2: 4,6 => CTR => A2: 1 * PRF # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 + B5: 5,9 + A1: 2,3,5 + A2: 1 => SOL * STA E7: 4,9 * CNT 7 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ........1.....2.3.....3.42...42..56...6..4....1.8.......5..63...8.7....99..1..... | initial |
| ........1.....2.3.....3.42...42..56...63.4....1.86......5..63...8.7....99..1..... | autosolve |
| 352647891149582736678931425834219567596374182217865943725496318481723659963158274 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (2) D7: 4,9 F8: 3,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,F3: 1.. / E2 = 1 => 3 pairs (_) / F3 = 1 => 3 pairs (_) E4,F4: 1.. / E4 = 1 => 3 pairs (_) / F4 = 1 => 3 pairs (_) G5,H5: 1.. / G5 = 1 => 3 pairs (_) / H5 = 1 => 5 pairs (_) A7,H7: 1.. / A7 = 1 => 3 pairs (_) / H7 = 1 => 4 pairs (_) E2,E4: 1.. / E2 = 1 => 3 pairs (_) / E4 = 1 => 3 pairs (_) F3,F4: 1.. / F3 = 1 => 3 pairs (_) / F4 = 1 => 3 pairs (_) G5,G8: 1.. / G5 = 1 => 3 pairs (_) / G8 = 1 => 5 pairs (_) I4,I6: 3.. / I4 = 3 => 3 pairs (_) / I6 = 3 => 4 pairs (_) F8,F9: 3.. / F8 = 3 => 3 pairs (_) / F9 = 3 => 5 pairs (_) H6,I6: 4.. / H6 = 4 => 3 pairs (_) / I6 = 4 => 4 pairs (_) E5,F6: 5.. / E5 = 5 => 5 pairs (_) / F6 = 5 => 4 pairs (_) A6,F6: 5.. / A6 = 5 => 5 pairs (_) / F6 = 5 => 4 pairs (_) A8,B9: 6.. / A8 = 6 => 3 pairs (_) / B9 = 6 => 2 pairs (_) A8,G8: 6.. / A8 = 6 => 3 pairs (_) / G8 = 6 => 2 pairs (_) A4,A5: 8.. / A4 = 8 => 3 pairs (_) / A5 = 8 => 5 pairs (_) A4,I4: 8.. / A4 = 8 => 3 pairs (_) / I4 = 8 => 5 pairs (_) D7,E7: 9.. / D7 = 9 => 2 pairs (_) / E7 = 9 => 8 pairs (_) * DURATION: 0:00:12.353350 START: 19:09:23.439806 END: 19:09:35.793156 2019-04-28 * CP COUNT: (17) * INCONCLUSIVE * DEEP PAIR REDUCTION * DURATION: 0:00:24.275807 START: 19:09:41.269823 END: 19:10:05.545630 2019-04-28 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0345-base-pr-002.dot * REASONING * DIS # E7: 4,9 # C9: 2,7 => CTR => C9: 3 * DIS # E7: 4,9 + C9: 3 # B1: 2,7 => CTR => B1: 3,4,5,6,9 * DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 # A7: 1 => CTR => A7: 2,7 * DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 # B5: 2,7 => CTR => B5: 5,9 * DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 + B5: 5,9 # A1: 4,6 => CTR => A1: 2,3,5 * DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 + B5: 5,9 + A1: 2,3,5 # A2: 4,6 => CTR => A2: 1 * PRF # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 + B5: 5,9 + A1: 2,3,5 + A2: 1 => SOL * STA E7: 4,9 * CNT 7 HDP CHAINS / 20 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=345
Solution
position: 352647891149582736678931425834219567596374182217865943725496318481723659963158274 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: 4,9 => UNS * INC # E7: 2,8 => UNS * INC # D1: 4,9 => UNS * INC # D2: 4,9 => UNS * INC # F9: 3,5 => UNS * INC # F9: 8 => UNS * CNT 6 HDP CHAINS / 6 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E7: 4,9 => UNS * INC # E7: 2,8 => UNS * INC # D1: 4,9 => UNS * INC # D2: 4,9 => UNS * INC # F9: 3,5 => UNS * INC # F9: 8 => UNS * CNT 6 HDP CHAINS / 6 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # E7: 4,9 => UNS * INC # E7: 2,8 => UNS * INC # D1: 4,9 => UNS * INC # D2: 4,9 => UNS * INC # F9: 3,5 => UNS * INC # F9: 8 => UNS * INC # E7: 4,9 # A7: 2,7 => UNS * DIS # E7: 4,9 # C9: 2,7 => CTR => C9: 3 * INC # E7: 4,9 + C9: 3 # A7: 2,7 => UNS * INC # E7: 4,9 + C9: 3 # A7: 1 => UNS * DIS # E7: 4,9 + C9: 3 # B1: 2,7 => CTR => B1: 3,4,5,6,9 * INC # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 # B5: 2,7 => UNS * INC # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 # B5: 2,7 => UNS * INC # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 # B5: 5,9 => UNS * INC # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 # A7: 2,7 => UNS * DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 # A7: 1 => CTR => A7: 2,7 * DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 # B5: 2,7 => CTR => B5: 5,9 * DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 + B5: 5,9 # A1: 4,6 => CTR => A1: 2,3,5 * DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 + B5: 5,9 + A1: 2,3,5 # A2: 4,6 => CTR => A2: 1 * PRF # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 + B5: 5,9 + A1: 2,3,5 + A2: 1 => SOL * STA E7: 4,9 * CNT 20 HDP CHAINS / 20 HYP OPENED