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Philosophy and Rants
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We follow the standard convention that Sudoku puzzles should have clues that satisfy a 180-degree rotational symmetry. That is, if you rotate the puzzle 180 degrees, the cells with clues in them are in the same locations. (This is also a standard convention for the black cells of most crossword puzzles.) The best puzzle makers include this rotational symmetry -- or at least some form of symmetry or pattern -- in their puzzles, and also pay attention to how the puzzles actually play. Many Sudoku books are filled with puzzles that are generated only by computer, but not ours! Each of our puzzles gets actual human attention. We strive to make each of our puzzles a work of art, by creating designs that not only have symmetry, but are also beautiful, interesting, fun to play, and complementary to any puzzle variation or extra regions. We also sometimes hide little jokes or Easter eggs in our puzzles. |
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There are lots of books and websites that can teach you strategies for solving Sudoku puzzles. These strategies range from the simple to the complex, with names like X-wings, swordfish, and naked pairs, and can act as efficient shortcuts to working out some of the more complicated logic that arises when playing Sudoku puzzles. These techniques are fine for regular Sudoku puzzles, but we especially like making puzzle variations that force you to come up with your own new solving strategies. For us, the most fun part of playing any puzzle is to figure out how to play! |
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Brainfreeze Puzzles are the experts in crazy, twisted Sudoku variations. Some of our variations are based on puzzles that have been around for a while (like "Sudoku X" and "Greater Than"), but many of them are original variations you will only see at Brainfreeze Puzzles (like "Worms", "Stripes", and "Clock Sudoku"). But no matter how twisted the variation, each of our puzzles has its roots in Sudoku; we try to preserve the play and feel of regular Sudoku puzzles in all of our variations. In each puzzle where extra conditions have been added to the usual rules of Sudoku, those conditions are necessary to solve the puzzle. Since Sudoku variants have extra information in their design, they can have fewer clues than standard Sudoku puzzles. (The smallest number of initial clues known for a standard Sudoku puzzle to have a unique solution is 17, or 18 if symmetry is imposed; some of our variations can have as few as 8, or even no initial clues, and still have a unique solution.) |
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Rating Sudoku puzzles is a difficult and somewhat subjective process, and rating variants of Sudoku puzzles is even more so. Some Sudoku makers rate their puzzles by using a computer to track the number and difficulty of standard solving techniques that are necessary to solve the puzzle. But if you don't happen to use these particular techniques, then you may not agree with this type of difficulty rating. At Brainfreeze Puzzles we create our ratings by having a computer play each puzzle thousands of times, in thousands of different ways, and keeping track of the difficulty level each time. We also play each puzzle ourselves to verify that the difficulty ratings are reasonable. Our Sudoku variation puzzles range from Level 1 (relatively easy) to Level 3 (head-scratching!). Our regular Sudoku puzzles are rated on a scale from Level 1 (very easy) to Level 5 (painful!!). |
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We don't provide solutions to the puzzles on this website, because you can always verify your own solution when you are done with the puzzle. Just check that each row, column, and block has all of the numbers 1--9, and that any additional variation conditions are also satisfied. We don't want you to peek at the solution before you figure it out yourself! We also want people to be able to use our website puzzles for various competitions or classroom activities, and don't want to give away the answers. Having said that, of course our book COLOR SUDOKU contains all of the solutions to its puzzles, and all of our custom and syndicated puzzles come with solutions. |
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So you're solving a Sudoku puzzle, and you're stuck. Should you guess? NO! Each Sudoku puzzle has just ONE solution, but there are more Sudoku solution boards than all the grains of sand on all the world's beaches combined. Looking for the correct solution by guessing is like finding a very small needle in a very large haystack. Each number you put in the grid should be there for a reason, and should be the ONLY possible number you could put in that cell. But what if you are playing a very difficult puzzle, and none of your Sudoku strategies are working? Occasionally you might encounter a puzzle for which the strategies that you know are not sufficient to find the solution. In this case you might guess a number to eliminate it; for example, if a given cell could only contain a 4 or a 7, you might temporarily fill in a 4 for that cell, and then show that this choice causes a contradiction or impossibility in the puzzle. Then you would know for certain that the number for that cell must be the other choice, namely the 7. In fact, this type of guessing-to-eliminate probably happens all the time in your head when you're playing Sudoku; you think something like "could a 8 go here? ...no, since there is already an 8 in this row", and thereby eliminate that choice of 8. Some claim that their puzzles are solvable "only by logic", or "with no guessing". While that does mean something in terms of the difficulty of the puzzles and the techniques necessary to solve them, this definition of "guessing" makes sense only in terms of a pre-stated list of techniques that are deemed the "logic" of solving. "Guessing" in this context would mean following a chain of logic outside of this predetermined list of logical strategies -- and that's not necessarily guessing, it's just more complicated logic. So to summarize: Don't guess, guessing-to-eliminate is sometimes a good strategy, you are guessing all the time, and there is no such thing as guessing. |
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It's a small point, but an important one if you're a math geek: When we say "the numbers 1--9" when describing the rules of Sudoku, we really mean the integers 1--9, that is, the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9. The set of all numbers 1--9 is actually the interval [1,9], a set of real numbers whose cardinality is uncountably infinite (and which includes, for example, 8.72, π, and e). |