How many possible ways are there to fill a Sudoku-2 puzzle?
464335
I normally hate referring people to wikipedia articles, since it is so often inaccurate, but this one is quite good (link is below).  If you scroll down, there is a table that gives just what you're looking for.\n\n2x2 grid: 288 possible solutions\n3x3 grid: 6.7*10^21 possible solutions!
540500
Here you go (requires VB.NET)\n\nhttp://www.codeproject.com/useritems/sudoku.asp
46941
" Fill in the grid so that every row,\nevery column, and every 3x3 box\ncontains the digits 1 through 9.\nRead this page:\nhttp://www.sudoku.com/
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.
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Moocow is only partly correct - the smallest cases known have 17 numbers, but it has not been proven that this is the minimum.\n\nFrom the American Scientist:\nFor order 3 [standard-sized Sudoku puzzles,] the minimum number of givens is unknown. Gordon Royle of the University of Western Australia has collected more than 24,000 examples of uniquely solvable grids with 17 givens, and he has found none with fewer than 17, but a proof is lacking.
801584
If the number begins with 5, there are still three of the odd digits available to fill the last place.  If a 3 is used for the last place, the others are filled using 1, 2, 3, 4, and so there are 4! arrangements.\nIf 1 is used for the last place, that leaves 2, 3, 3, 4 for the others, and so the number of arrangements is  4!/2! because of the repeated 3.  So that gives \n4! + 4!/2! = 36\n\nIf it begins with a 3, the last place can be filled with 1, 3, or 5, and  the numbers left to fill the remaining four places are all different and so the number of possibilities is\n3*4! =72\n\nIf it begins with a 2 or 4 ( two choices), and the last with 1 or 5 (two choices), there are 4!/2! ways of filling the other places because 3 is repeated.\n2*2*4!/2! = 48\n\nIf it begins with 2 or 4 and ends with 3, then the other four digits are all different, and the number of possibilities is\n2*4! = 48\n\nAdding all these together gives 204.  Yes.
133517
the solutions is 7,8,3,2 or 7,6,5,2. The problem works with both sets of numbers.
13554
http://www.codeproject.com/csharp/sudoku.asp
588212
READ PATIENTLY AND WITH FULL ATTENTION\n\n[In SUDOKU, row means the horizontal line of small boxes and column means the vertical line of small boxes; there are altogether 9 rows and 9 columns in a standard SUDOKU problem]\n\nTry to use the method of elimination. This means that check whether it is possible for a certain number to be in a box; choose first the mostly populated 3x3 box. Also notice which numbers are missing in the same row or column in which the concerned box lie (remember that integers only 1 to 9 can be present in a row or column or a 3x3 box and in each case ecah of the 9 integers can occur only once). In most cases you will find that a certain numbers cannot be inserted in that particular box simply because these are either in the same row or in the same column as the box. Make a list of these numbers which are not possible. Add to this list the numbers which are in the same 3x3 box (but which are not in the list) as the concerned box. Thus you might find that you have eliminated 8 numbers which is the only thing you want (as only numbers from 1 to 9 can be inserted in the boxes).
959412
The answer is 9! / (6!*3!).\n\nYou're dealing with combinations and not permutations, so we don't care which person is which... you really have nine chairs, six of which are occupied and three of which are empty. Forget about ABCDEF being the six people: Let X represent an occupied chair, and O an empty chair.\n\nIf you need to create a list of all possible combinations, just start with the X'es all to the left and the O's to the right, then do a bubble sort thingy.\n\nXXXXXXOOO\nXXXXXOXOO\nXXXXXOOXO\nXXXXXOOOX\nXXXXOXXOO\nXXXXOXOXO\nXXXXOXOOX\nXXXXOOXXO\nXXXXOOXOX\nXXXXOOOXX\netc.\n\nIf you grind your way through the whole list, you'll find there are 84 combinations. There's some neat stuff going on here with triangular numbers: you can see that there's one arrangement where the first O is in the 7th position, three where the first O is in the 6th position, six where the first O is in the 5th position... follow the pattern and you'll see that there are 1+3+6+10+15+21+28 combinations in the list. That adds up to 84.\n\nHopefully that helps!
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The first letter can be any one of the 5 letters\nThe second one can be any of the 4 remaining letters\nand so on\n\nSo the answer is 5 x 4 x 3 x 2 x 1 = 120 different ways\n\nIf two of the letters are the same (eg green) then divide by (2 x 1) to give 60\n\nIf three of the letters are the same (eg eerie) then divide by (3 x 2 x 1) to give 20\n\nIf there are two pairs of letters (eg yuppy) then divide by (2 x 1) x (2 x 1) to give 30
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Wikipedia has lots of good details on Sudoku including manual algorithms for solving, as well as computer algorithms.  I wasn't sure which one you wanted.\n\nFor solving it yourself, the most obvious way to start it by eliminating rows and columns for a region until there is only one choice for where a digit goes.\n\nFor computer solving, there is the brute force depth-first search known as Ariadne's thread.  It essentially tries a solution and keeps going until it finds an inconsistency, then it backtracks.  Other methods follow the human style of solving by putting all possible numbers in each square and then eliminating them until there is only one choice.  This then cascades to affecting other squares, etc.
695512
Answers choices are:\n     1, 4, 3, 2, 2,\n      3, 1, 4, 2, 1,\n      1, 1, 4, 2, 1\n      3, 2, 3, 4, 1\n      3, 4, 1, 2, 4
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FINISHING MOVES....\n1:1\n2:1\n3:2\n4:1\n5:1\n6:2\n7:1\n8:2\n9:2\n10:1\n11:1\n12:1\n13:2\n14:3\n15:3\nSUBMISSIONS....\n1:1\n2:1\n3:3\n4:1\n5:2\n6:1\n7:2\n8:2
122777
I have heard of Sudoku. My father introduced me to the game. I can't say I am addicted to it yet but I do enjoy solving one or two occasionaly. \n\nIf you are addicted to it check the link in the sources. It offers thousands of free puzzles.
661664
you can use a dot to separate two or more algarism blocks, like:\n999.999.999\n\nThis way you will have 1000 * 1000 * 1000 combinations of algarisms. Since 000.000.000 until 999.999.999.\n\n000.000.000, 000.000.001, 000.000.002, ..., 999.999.997, 999.999.998, 999.999.999
203700
293 different ways\n1 dollar coin \n2 half dollars \n1 HD 1Q 2D IN \n1 HD 1Q 2D 5P \n1 HD 1Q 1D 3N \n1 HD 1Q 1D 2N 5P \n1 HD 1Q 1D 1N 10P \n1 HD 1Q 1D 15P\n1 HD 1Q 5N\n1 HD 1Q 4N 5P\n1 HD 1Q 3N 10P\n1 HD 1Q 2N 15P\n1 HD 1Q 1N 20 P\n1 HD 1Q 25P\n1 HD 5D\n1 HD 4D 2N\n1HD 4D 1N 5P\n1 HD 4D 10P\n1 HD 3D 4N\n1 HD 3D 3N 5P\n1 HD 3D 2N 10P\n1 HD 3D 1N 15P\n1 HD 3D 20P\n1 HD 2D 6N\n1 HD 2D 5N 5P\n1 HD 2D 4N 10P\n1 HD 2D 3N 15P\n1 HD 2D 2N 20P\n1 HD 2D 1N 25P\n1 HD 2D 30P\n1 HD 1D 8N\n1 HD 1D 7N 5P\n1 HD 1D 6N 10P\n1 HD 1D 5N 15P\n1 HD 1D 4N 20P\n1 HD 1D 3N 25 P\n1 HD 1D 2N 30 P\n1 HD 1D 1N 35P\n1 HD 1D 40P\n1 HD 10N\n1 HD 9N 5P\n1 HD 8N 10P\n1 HD 7N 15 P\n1 HD 6N 20P\n\n1 HD 5N 25P\n\n1 HD 4N 30P\n\n1HD 3N 35P\n\n1 HD 2N 40P\n\n1 HD 1N 45P\n\n1 HD 50P\n\n4Q\n\n3Q 2D 1N\n\n3Q 2D 5P\n\n3Q 1D 3N\n\n3Q 1D 2N 5P\n\n3Q 1D 1N 10P\n\n3Q 1D 15P\n\n3Q 5N\n\n3Q 4N 5P\n\n3Q 3N 10P\n\n3Q 2N 15P\n\n3Q 1N 20 P\n\n3Q 25P\n\n2Q 5D\n\n2Q 4D 2N\n\n2Q 4D 1N 5P\n\n2Q 4D 10P\n\n2Q 3D 4N\n\n2Q 3D 3N 5 P\n\n2Q 3D 2N 10P\n\n2Q 3D 1N 15P\n\n2Q 3D 20P\n\n2Q 2D 6N\n\n2Q 2D 5N 5P\n\n2Q 2D 4N 10 P\n\n2Q 2D 3N 15P\n\n2Q 2D 2N 20P\n\n2Q 2D 1N 25P\n\n2Q 2D 30P\n\n2Q 1D 8N\n\n2Q 1D 7N 5P\n\n2Q 1D 6N 10P\n\n2Q 1D 5N 15P\n\n2Q 1D 4N 20P\n\n2Q 1D 3N 25P\n\n2Q 1D 2N 30P\n\n2Q 1D 1N 35P\n\n2Q 1D 40P\n\n2Q 50P\n\n2Q 10N\n\n2Q 9N 5P\n\n2Q 8N 10P\n\n2Q 7N 15P\n\n2Q 6N 20P\n\n2Q 5N 25P\n\n2Q 4N 30P\n\n2Q 3N 35P\n\n2Q 2N 40P\n\n2Q 1N 45P\n\n1Q 7D 1N\n\n1Q 7D 5P\n\n1Q 6D 3N\n\n1Q 6D 2N 5P\n\n1Q 6D 1N 10P\n\n1Q 6D 15P\n\n1Q 5D 5N\n\n1Q 5D 4N 5P\n\n1Q 5D 3N 10P\n\n1Q 5D 2N 15P\n\n1Q 5D 1N 20P\n\n1Q 5D 25P\n\n1Q 4D 7N\n\n1Q 4D 6N 5P\n\n1Q 4D 5N 15P\n\n1Q 4D 4N 20P\n\n1Q 4D 3N 25P\n\n1Q 4D 2N 30P\n\n1Q 4D 1N 35P\n\n1Q 4D 40P\n\n1Q 3D 9N\n\n1Q 3D 8N 5P\n\nQ 3D 7N 10P\n\n1Q 3D 6N 15P\n\n1Q 3D 5N 20P\n\n1Q 3D 4N 25P\n\n1Q 3D 3N 30P\n\n1Q 3D 2N 35P\n\n1Q 3D 1N 40P\n\n1Q 3D 45P\n\n1Q 2D 11N\n\n1Q 2D 10N 5P\n\n1Q 2D 9N 10P\n\n1Q 2D 8N 15P\n\n1Q 2D 7N 20 P\n\n1Q 2D 6N 25P\n\n1Q 2D 5N 30P\n\n1Q 2D 4N 35P\n\n1Q 2D 3N 40P\n\n1Q 2D 2N 45P\n\n1Q 2D 1N 50P\n\n1Q 2D 55P\n\n1Q 1D 13N\n\n1Q 1D 12N 5P\n\n1Q 1D 11N 10P\n\n1Q 1D 10N 15P\n\n1Q 1D 9N 20P\n\n1Q 1D 8N 25P\n\n1Q 1D 7N 30P\n\n1Q 1D 6N 35P\n\n1Q 1D 5N 40P\n\n1Q 1D 4N 45P\n\n1Q 1D 3N 50P\n\n1Q 1D 2N 55P\n\n1Q 1D 1N 60P\n\n1Q 1D 65P\n\n1Q 15N\n\n1Q 14N 5P\n\n1Q 13N 10P\n\n1Q 12N 15P\n\n1Q 11N 20P\n\n1Q 10N 25P\n\n1Q 9N 30P\n\n1Q 8N 35P\n\n1Q 7N 40P\n\n1Q 6N 45P\n\n1Q 5N 50P\n\n1Q 4N 55P\n\n1Q 3N 60P\n\n1Q 2N 65P\n\n1Q 1N 70P\n\n1Q 75P\n\n10D\n\n9D 2N\n\n9D 1N 5P\n\n9D 10P\n\n8D 4N\n\n8D 3N 5P\n\n8D 2N 10P\n\n8D 1N 15P\n\n8D 20P\n\n7D 6N\n\n7D 5N 5P\n\n7D 4N 10P\n\n7D 3N 15P\n\n7D 2N 20P\n\n7D 1N 25P\n\n7D 30P\n\n6D 8N\n\n6D 7N 5P\n\n6D 6N 10P\n\n6D 5N 15P\n\n6D 4N 20P\n\n6D 3N 25P\n\n6D 2N 30P\n\n6D 1N 35P\n\n6D 40P\n\n5D 10N\n\n5D 9N 5P\n\n5D 8N 10P\n\n5D 7N 15P\n\n5D 6N 20P\n\n5D 5N 25P\n\n5D 4N 30P\n\n5D 3N 35P\n\n5D 2N 40P\n\n5D 1N 45P\n\n5D 50P\n\n4D 12N\n\n4D 11N 5P\n\n4D 10N 10P\n\n4D 9N 15P\n\n4D 8N 20P\n\n4D 7N 25P\n\n4D 6N 30P\n\n4D 5N 35P\n\n4D 4N 40P\n\n4D 3N 45P\n\n4D 2N 50P\n\n4D 1N 55P\n\n4D 60P\n\n3D 14N\n\n3D 13N 5P\n\n3D 12N 10P\n\n3D 11N 15P\n\n3D 10N 20P\n\n3D 9N 25P\n\n3D 8N 30P\n\n3D 7N 35P\n\n3D 6N 40P\n\n3D 5N 45P\n\n3D 4N 50P\n\n3D 3N 55P\n\n3D 2N 60P\n\n3D 1N 65P\n\n3D 70P\n\n2D 16N\n\n2D 15N 5P\n\n2D 14N 10P\n\n2D 13N 15P\n\n2D 12N 20P\n\n2D 11N 25P\n\n2D 10N 30P\n\n2D 9N 35P\n\n2D 8N 40P\n\n2D 7N 45P\n\n2D 6N 50P\n\n2D 5N 55P\n\n2D 4N 60P\n\n2D 3N 65P\n\n2D 2N 70P\n\n2D 1N 75P\n\n2D 80P\n\n1D 18N\n\n1D 17N 5P\n\n1D 16N 10P\n\n1D 15N 15P\n\n1D 14N 20P\n\n1D 13N 25P\n\n1D 12N 30P\n\n1D 11N 35P\n\n1D 10N 40P\n\n1D 9N 45P\n\n1D 8N 50P\n\n1D 7N 55P\n\n1D 6N 60P\n\n1D 5N 65P\n\n1D 4N 70P\n\n1D 3N 75P\n\n1D 2N 80P\n\n1D 1N 85P\n\n1D 90P\n\n20N\n\n19N 5P\n\n18N 10P\n\n17N 15P\n\n16N 20P\n\n15N 25P\n\n14N 30P\n\n13N 35P\n\n12N 40P\n\n11N 45P\n\n10N 50P\n\n9N 55P\n\n8N 60P\n\n7N 65P\n\n6N 70P\n\n5N 75P\n\n4N 80P\n\n3N 85P\n\n2N 90P\n\n1N 95P\n\n100P\n\n1 HD 2Q