By extension, it can also be used to describe something that’s characteristic to a person or thing in a more metaphorical way, such as “the singer’s trademark rhythm.” The word trademark, first recorded in the mid-1500s, literally is the mark (as a name or logo) that is proprietary to a business ( trade). What does the trademark symbol (™) mean?Ī trademark is a name, symbol, or mark that distinguishes a product or brand from other products or brands. So what’s the deal with each, and what makes them different from each other? Let’s decode the symbol soup. No matter how small, however, they are powerful and convey a lot of meaning. They can be large or close to microscopic. After having narrowed possibilities somewhat with realistic techniques, some puzzles "require" guessing so as to not put the solver at a competitive disadvantage.If you’ve ever purchased a product, read a book, or watched a movie (read: everyone currently on this page), then you’ve likely seen four symbols time and time again: ™, ®, ©, and ℠. 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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