After having narrowed possibilities somewhat with realistic techniques, some puzzles "require" guessing so as to not put the solver at a competitive disadvantage. You can randomly remove one digit and replace it with another but the logic behind the Sudoku puzzle is that you take the time to apply logic and mathematical reasoning. If you start by taking the low-hanging fruit the easiest parts of the puzzle that the grid already gives you you can build from that to complete the more difficult areas. When you are solving a Sudoku puzzle, and you place a digit randomly to the grid, you are one step closer to the solution but perhaps no closer to the right solution. 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. Sudoku puzzles can be complex, but one of the first lessons that Sudoku beginners need to understand is that the game often offers some easy clues. Thomas Snyder has given an insightful definition of when a puzzle is solvable logically: Since the introduction of the numerical puzzle in. 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. The interesting fact about Sudoku is that it is a trivial puzzle to solve. 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? I use 4 terms regularly, a block is the 3x3 area of squares separated by the thicker lines, a row is the horizontal line of numbers, a column is the vertical line of numbers, and a cell is any individual square on the board. In other words, no number may appear morethan once in any row, column, or block. Any valid Sudoku can be solved without guessing, just by exhaustively trying all possibilities. To solve a regular Sudoku puzzle, place a number intoeach cell of the diagram so that each row across, each col-umn down, and each block within the larger diagram(there are 9 of these) will contain every number from 1through 9.
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