Charles Darwin (c1880)Īlthough I am fully convinced of the truth of the views given in this volume, I by no means expect to convince experienced naturalists whose minds are stocked with a multitude of facts all viewed, during a long course of years, from a point of view directly opposite to mine. There seems to be no more design in the variability of organic beings and in the action of natural selection, than in the course which the wind blows. We can no longer argue that, for instance, the beautiful hinge of a bivalve shell must have been made by an intelligent being, like the hinge of a door by man. The old argument of design in nature, as given by Paley, which formerly seemed to me to be so conclusive, fails, now that the law of natural selection has been discovered. This is the first time I have noticed that happening, but I suppose this means that there can be more than one right way to solve at least some Sudoku puzzles. Everything added up just as well as it did in the solution on the answer page. Yet I could find no place in the puzzle as I had solved it, that would produce an error anywhere in the puzzle. But the interesting thing was, when I checked my solution with the answer sheet in the back, I found that even before I filled in those last four squares I had put different numbers in many of the squares than the official solution showed. So I just filled them in with one of the two possible numbers and solved it from there. I came across a puzzle a few minutes ago that had the last four squares open and I could find no reason that either of the two options for number placement would not work equally well.that is, I could fill in the squares either of two ways without messing up the puzzle. As Exterminator says, formal logic is considered math, so are many logical problems at the core, while logic at large as for example as fallacies in reasoning is in the philosophical domain. Btw, the coloring is just a map to a large class of "coloring problems" in mathematics. :-) What you are probably trying to say, correctly I believe, is that this game as so many other doesn't yet have a known best strategy. More precisely, we reinterpret the Sudoku puzzle as a vertex coloring problem in graph theory", the authors as mathematicians, and the publication in "Notices of the AMS" is a tip off. I think the key words of "chromatic polynomials" in the title, the key sentences "We will reformulate many of these questions in a mathematical context and attempt to answer them. The puzzles can be solved using colors instead of numbers." Eh, no. "I've always thought that the Sudoku puzzles were more like logic puzzles than mathematical puzzles and the article confirms that impression. One could argue that the Sudoku puzzle develops logical skills necessary for mathematical thought.How many of you are hooked? Some of the puzzles classified under the “fiendish” category involve a slightly more refined version of this elimination process, but the general strategy is the same. A simple process of elimination often leads one to complete the puzzle. However, the puzzle can be systematically solved by keeping track of the unused colors in each row, in each column, and in each sub-grid. The novice is usually stumped after some time. Secondly, simply by scanning rows and columns, it is easy to enter the “missing colors”, and this gives the solver some encouragement to persist. First,it is sufficiently difficult to pose a serious mental challenge for anyone attempting to do the puzzle. It is interesting to note that the Sudoku puzzle is extremely popular for a variety of reasons. Here's what the authors say about the popularity of these puzzles. The puzzles can be solved using colors instead of numbers. I've always thought that the Sudoku puzzles were more like logic puzzles than mathematical puzzles and the article confirms that impression. There are two different ways to fill in the blank cells. The puzzle shown on the right is an example. However-and here's the encouraging part-there are sometimes more than one right answer. Unfortunately, most of them are still wrong. Ram Murty in the Notices of the American Mathematical Society confirms what many of us have known for years: there's more than one way to solve a Sudoku puzzle.
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