Pick a bv and simultaneously try both values as true, distinguishing by marking candidates confirmed by the two cell candidates. Bob readily accepts this blatant trial-and-error method: If we have to go to trial, at least the conclusion has logical weight.Įven though it was not programmed into Sudoku Assistant When the report was written, Bob passes on another suggestion from a friend. These investments are observed facts, not arbitrary supposes. In Sysudoku bipolar chain trials, when we cannot identify the solution with simpler logic, we invest more of the puzzle constraints into larger sets of candidates. He compounds the error by suggesting his trial method as a way to solve a regular XYZ-wing. It only tells us a piece of the solution. Instead Bob starts with an arbitrary candidate, assigns it an arbitrary true (Hypothesis) or false (Disproof) value, then marks chain nodes according to their confirmation or disproof of this guess.īob doesn’t seem to understand that neither the right or wrong state of his hypothesis or disproof guess tells us anything about the logic of the puzzle. Other trials include colors, or alternative directions in chains, or alternative patterns, with one polarity being necessarily false when the other is proved true, and vice versa.īob’s SA report section, Hypothesis and (Dis)Proof, is about chains of two possible states, but he misses completely the idea of constructing as large a bipolar chain as possible, for trial of one or both sides. Sysudokie trials are undertaken when direct methods seem to be exhausted, with one major exception being the verification of alternatives in the Sue de Coq. To support trials I introduced a method of breadth first marking and tracing that permitted the trace writer to document graphically the shortest inference path to a contradiction.Ī recent theoretical triumph of this strategy is the discovery of the double nasty loop that confirms the Hanson and Marans four slink loops and duplicates the “opening volley” SK loop’s removals in the HM Easter Monster. A contradiction then has a good likelihood of confirming a corresponding set of candidates as true. These trials involve the assembly of set of candidates that would be true or false together, and marking the assumption that they are all true. Trials have become an important part of the Sysudoku solving repertoire, as the targeted puzzles have reached extreme and monster class. His acceptance of Gail Nelson’s blatant T&E method confirms my position on the T&E issue. My opinion is that Bob’s strategy contributions and his Sudoku Assistant solving records are both compromised by a willingness to resort to trial-and-error. After having narrowed possibilities somewhat with realistic techniques, some puzzles "require" guessing so as to not put the solver at a competitive disadvantage.This post compares Sysudoku trial strategy with the chain or disproof hypothesis strategy described in Bob Hanson’s Sudoku Assistant report. When I can solve a puzzle in ink, without erasures, with all deductions either positive or negative coming from visualization in my head and not making scratch-work on the paper, the puzzle is solvable by logic.Īre there Sudoku puzzles that are faster to solve by guessing?Īgain, the answer is "yes." In a competitive setting, most solvers would not use the more obscure techniques. Thomas Snyder has given an insightful definition of when a puzzle is solvable logically: However, if you define a "logical solution" as excluding brute-force solving, the answer is probably "yes." There is some imprecise agreement on what constitutes a logical solution under this definition in the puzzling community, but based on this, we will again find that yes, there are definitely Sudoku puzzles that have no logical solution. This one depends on what you accept as a "logical solution." In the strictest sense, the answer is again no. However, there are two interesting variant interpretations of the question:Īre there Sudoku puzzles that can't be solved logically? Any valid Sudoku can be solved without guessing, just by exhaustively trying all possibilities.
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