what is the sudoku equation?
84916
Main article: Mathematics of Sudoku\n\nThe general problem of solving Sudoku puzzles on n2 x n2 boards of n x n blocks is known to be NP-complete [8]. This gives some indication of why Sudoku is difficult to solve, although on boards of finite size the problem is finite and can be solved by a deterministic finite automaton that knows the entire game tree.\n\nSolving Sudoku puzzles (as well as any other NP-hard problem) can be expressed as a graph colouring problem. The aim of the puzzle in its standard form is to construct a proper 9-colouring of a particular graph, given a partial 9-colouring. The graph in question has 81 vertices, one vertex for each cell of the grid. The vertices can be labelled with the ordered pairs (x,&#92;, y), where x and y are integers between 1 and 9. In this case, two distinct vertices labelled by (x,&#92;, y) and (x',&#92;, y') are joined by an edge if and only if:\n\n    * x = x'&#92;, or,\n    * y = y'&#92;, or,\n    * &#92;lceil x/3 &#92;rceil = &#92;lceil x'/3 &#92;rceil and &#92;lceil y/3 &#92;rceil = &#92;lceil y'/3 &#92;rceil\n\nThe puzzle is then completed by assigning an integer between 1 and 9 to each vertex, in such a way that vertices that are joined by an edge do not have the same integer assigned to them.\n\nA valid Sudoku solution grid is also a Latin square. There are significantly fewer valid Sudoku solution grids than Latin squares because Sudoku imposes the additional regional constraint. Nonetheless, the number of valid Sudoku solution grids for the standard 9×9 grid was calculated by Bertram Felgenhauer in 2005 to be 6,670,903,752,021,072,936,960 [9] (sequence A107739 in OEIS). This number is equal to 9! × 722 × 27 × 27,704,267,971, the last factor of which is prime. The result was derived through logic and brute force computation. The derivation of this result was considerably simplified by analysis provided by Frazer Jarvis and the figure has been confirmed independently by Ed Russell. Russell and Jarvis also showed that when symmetries were taken into account, there were 5,472,730,538 solutions [10] (sequence A109741 in OEIS). The number of valid Sudoku solution grids for the 16×16 derivation is not known.\n\nThe maximum number of givens that can be provided while still not rendering the solution unique is four short of a full grid; if two instances of two numbers each are missing and the cells they are to occupy form the corners of an orthogonal rectangle, and exactly two of these cells are within one region, there are two ways the numbers can be assigned. Since this applies to Latin squares in general, most variants of Sudoku have the same maximum. The inverse problem—the fewest givens that render a solution unique—is unsolved, although the lowest number yet found for the standard variation without a symmetry constraint is 17, a number of which have been found by Japanese puzzle enthusiasts [11] [12], and 18 with the givens in rotationally symmetric cells.
956102
Here is the equation\n\n(246,92)U ---> (4,2)He + (242,90)Th + 2Gamma
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If you are talking about the Sudoku problem that is something about which Mills knows and they do watch anyone who tries to use it.  They do reserve the right to ban people who are attempting to cheat on Millsberry.\n\nAs for other cheats - there are none.  There are lots of tips that I would be happy to share if you can tell me what you wish to do on Millsberry.
974937
please complete the equation
513219
Perfect Squares\n\nEdit: First Four to be precise
262222
the answer is 96012000\n\nuse the equation \ns= n( 2*a+(n-1)d)/2
792339
A quadratic equation is a second-order polynomial equation in a single variable x\nax^2+bx+c==0,\n(1)\n\nwith a!=0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has two solutions. These solutions may be both real, or both complex.\n\nAmong his many other talents, Major General Stanley in Gilbert and Sullivan's operetta the Pirates of Penzance impresses the pirates with his knowledge of quadratic equations in "The Major General's Song" as follows: "I am the very model of a modern Major-General, I've information vegetable, animal, and mineral, I know the kings of England, and I quote the fights historical, From Marathon to Waterloo, in order categorical; I'm very well acquainted too with matters mathematical, I understand equations, both the simple and quadratical, About binomial theorem I'm teeming with a lot o' news-- With many cheerful facts about the square of the hypotenuse."\n\nThe roots x can be found by completing the square,\nx^2+b/ax==-c/a\n(2)\n(x+b/(2a))^2==-c/a+(b^2)/(4a^2)==(b^2-4ac)/(4a^2)\n(3)\nx+b/(2a)==(+/-sqrt(b^2-4ac))/(2a).\n(4)\n\nSolving for x then gives\nx==(-b+/-sqrt(b^2-4ac))/(2a).\n(5)\n\nThis equation is known as the quadratic formula.\n\nThe first known solution of a quadratic equation is the one given in the Berlin papyrus from the Middle Kingdom (ca. 2160-1700 BC) in Egypt. This problem reduces to solving\nx^2+y^2=100\n(6)\ny=3/4x\n(7)\n\n(Smith 1953, p. 443). The Greeks were able to solve the quadratic equation by geometric methods, and Euclid's Eric Weisstein's World of Biography (ca. 325-270 BC) Data contains three problems involving quadratics. In his work Arithmetica, the Greek mathematician Diophantus Eric Weisstein's World of Biography (ca. 210-290) solved the quadratic equation, but giving only one root, even when both roots were positive (Smith 1951, p. 134).\n\nA number of Indian mathematicians gave rules equivalent to the quadratic formula. It is possible that certain altar constructions dating from ca. 500 BC represent solutions of the equation, but even should this be the case, there is no record of the method of solution (Smith 1953, p. 444). The Hindu mathematician Aryabhata (475 or 476-550) gave a rule for the sum of a geometric series that shows knowledge of the quadratic equations with both solutions (Smith 1951, p. 159; Smith 1953, p. 444), while Brahmagupta Eric Weisstein's World of Biography (ca. 628) appears to have considered only one of them (Smith 1951, p. 159; Smith 1953, pp. 444-445). Similarly, Mahavira (ca. 850) had substantially the modern rule for the positive root of a quadratic. Sridhara (ca. 1025) gave the positive root of the quadratic formula, as stated by Bhaskara (ca. 1150; Smith 1953, pp. 445-446). The Persian mathematicians al-Khwarizmi Eric Weisstein's World of Biography (ca. 825) and Omar Khayyám Eric Weisstein's World of Biography (ca. 1100) also gave rules for finding the positive root.\n\nViète Eric Weisstein's World of Biography was among the first to replace geometric methods of solution with analytic ones, although he apparently did not grasp the idea of a general quadratic equation (Smith 1953, pp. 449-450).\n\nAn alternate form of the quadratic equation is given by dividing (◇) through by x^2:\na+b/x+c/(x^2)==0\n(8)\nc(1/(x^2)+b/(cx))+a==0\n(9)\nc(1/x+b/(2c))^2==c(b/(2c))^2-a==(b^2)/(4c)-(4ac)/(4c)==(b^2-4ac)/(4c).\n(10)\n\nTherefore,\n1/x+b/(2c)==+/-(sqrt(b^2-4ac))/(2c)\n(11)\n1/x==(-b+/-sqrt(b^2-4ac))/(2c)\n(12)\nx==(2c)/(-b+/-sqrt(b^2-4ac)).
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Sudoku puzzles are just a type of logic puzzle. They would work just as well if you used letters or symbols instead of numbers, so don't let the fact that they involve numbers fool you into thinking that they rely on some mathematical relationship.\n\nI have been doing these types of puzzles for years, as they were already in American puzzle books when I first started buying them approximately 20 years ago. I think that the very best thing you can do is practice, practice, practice.\n\nI know that a lot of people favor the method of starting small, and working on individual boxes first, then moving on to the vertical and horizontal lines. For me, that isn't the method that works the best. First, I look at the entire puzzle to see if one number is represented more often than the others. If it is, that's usually the number I work on placing first. Once all the boxes have that number in it, I usually move on to the second most commonly placed number. I do look at the boxes and vertical and horizontal lines, obviously, but I try to make it as easy for myself as possible by looking at the puzzle as a whole rather than tackling a small part of it first. Once all the boxes have at least two numbers placed correctly, I find that the puzzle becomes much easier, and I continue from there, usually using the larger lines rather than the small boxes themselves. But that's just me.\n\nIt takes a while to learn how to do any sort of logic puzzle, and I think for most people, it is largely a matter of trial and error to find out what works best for them. The bottom line is that if you want to increase your skills in doing Sudoku puzzles, your best bet is to practice and try different strategies until you find the one that you are most comfortable with. Happy puzzling!
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something is wrong w/ your puzzle, because if you look in the fourth column, there are two 2s.\n\n* thanks for fixing it,  below are the number in the shape of the sudoku puzzle \n8 6 9 5 4 1 2 3 7\n2 3 1 6 7 8 4 5 9\n4 5 7 2 9 3 6 1 8\n6 1 4 8 3 2 9 7 5\n7 9 5 4 1 6 8 2 3\n3 2 8 9 5 7 1 4 6\n1 8 2 7 6 5 3 9 4\n5 4 6 3 2 9 7 8 1\n9 7 3 1 8 4 5 6 2
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what is 2 + 2 = ?????? \n\nThis is an equation.
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It has a solution, indeed. It actually has two solutions, -3 and 7. To find it out, set each pair of nomials, (e.g. (x + 3)) to zero. So it would be (x+3)=0. Then solve for x. Do the same for the other nomial, and there you have it.
840893
hi its an interesting mathematical puzzle\nhere is where u can get more info\nhttp://en.wikipedia.org/wiki/Tower_of_Hanoi
48921
When you begin a new puzzle, it already has some "starting numbers."  Count the number of starting number in each row and write it to the right of the row.  Then count the number per column, and write it at the top of each column.  Pick the column with the highest starting count, and then find the empty square in that column that has the highest starting row count.  Figure out which number to put in that one square (there will usually only be 1 or 2 possibilities).  Continue in that column until you find a square with 3 or more possible choices.  Then go to the column with the next highest starting count, and proceed like that.  This method works pretty fast in general.
238690
Let S=1+2+3+4+5+...+(n-2)+(n-1)+n\nThen it's the same as S=n+(n-1)+(n-2)+...+3+2+1.\nAddding these two formulas you'll get\n2S=(n+1)+(n+1)+(n+1)+...+(n+1).\nSince there are n terms on the right side,\n we conclude that \n2S=n(n+1) or\n\nS=n(n+1)/2.\n\nHence, in your case it will be\nS=1+2+3+...+966=[966*967]/2=467061.
898885
I love Sudoku and have no idea what you want.
346407
I think it is order(N squared), so not very good. It's a variant of bubble sort, which you can google. Plus you never know when you're done!
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History of Sudoku and Killer Sudoku Variations \n\nAll of us, by now should have heard of SuDoku... if you haven't, you must have been living in a box. Or maybe it is the other way around, those of us that are hooked on SuDoku are now living in a box (in the form of a 9x9 grid).\n\nAnyway, if you have always wondered about how this little number puzzle came about, it actually first appeared in the U.S. in the May 1979 issue of Dell Pencil Puzzles & Word Games where it was called Number Place. It is believed to be the creation of a retired architect named Howard Garns, age 74 at the time.\n\nSeveral years later, in 1984 it was adopted by a puzzle group in Japan and named "Suuji Wa Dokushin Ni Kagiru" ("the numbers must be single") As it became popular, this was shortened to SuDoku (Su=number, Doku=single) and was trademarked.\n\nOther magazines in Japan, soon copied the puzzle but went with the more generic name Nanbaapureesu (phonetically "Number Place") and often just used the English spelling. Later when it was rediscoved in the U.S. and the U.K. it was titled "SuDoku" which leads to an interesting scenario. Japanese speakers call it by its English name (Number Place) and English speakers call it by its Japanese name (SuDoku).\n\nIf you are interested in reading more of the historical details or learning about numerous sudoku variations (including Killer SuDoku a.k.a. Samunamupure or Samunanpure, Greater Than SuDoku, Samurai SuDoku, Relay SuDoku, etc.) there are a couple links below.