To the mathematicians: Can you tell me (with a proof) how many possible sudoku puzzles could be created?
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6670903752021072936960\n\nThey wrote  an article that can be found here:\nhttp://www.afjarvis.staff.shef.ac.uk/sudoku/sudoku.pdf\n\nThere is also a whole dicussion on wheather symetrical Soduko puzzles are actually the same puzzle.
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I'm writing up a proof right now that this is not possible.\n\nCheck out the pdf at:\nhttp://www.geocities.com/euleratuo/
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Sudoku puzzles are good at exercising your reasoning and pattern recognition skills.\n\nYou can even play onliine here:\nhttp://www.websudoku.com/
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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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There are exactly 343 combinations.  I can list them all, but others have already cluttered this thread quite well on their own.  ^.^\n\nYou can think of the solution set as a series of tiered combinations.  These would start with those sets beginning with a $50 bill, which can contain up to 2 x $50,  2 x $20, 5 x $10, etc. which I believe someone has started already in this thread.  Or group them as pairs, triplets, etc. with the equation 50j+20k+10l+5m+1n=100, which may be a bit easier for calculations.  Or a convergent series, where A=(ways to form $5), B=(ways to form $10, including A-sets), etc.  With any method, find the different combinations for each set, then add them all up.\n\nDoing this is still tedious and prone to mistakes, and thus probably not much of an improvement over manually listing all of the combinations one by one.  It can also quickly become an insane exercise for larger values (for example, add the $2 bill, or find change for $200, or even worse).  So instead of trying to think this problem through mathematically, I found it much easier to think it through as a programming problem.  It lends itself very readily to a simple recursive subroutine using the following pseudocode:\n\nmake an empty stack\nset total combinations to 0\ncall CheckCurrency\nprint total combinations found\n\nrecursive subroutine CheckCurrency\n- if total currency in stack = 100\n- - add 1 to the total combinations\n- - (optional: display stack contents)\n- - end recursion\n- if total currency in stack > 100\n- - end recursion\n- if total currency in stack < 100, then\n- - for each valid denomination (50,20,10,5,1)\n- - - if the denomination < = smallest denomination in the stack\n- - - - push it to the stack\n- - - - call CheckCurrency\n- - - - pop it from the stack\nend of subroutine\n\nThis required only a few minutes to design, another few minutes to code, another few minutes to debug, less than 2 seconds to run, and has the wonderful bonus of being able to display every single combination if desired.  It would also be trivial to modify it so that, for example, you can find all combinations if you also include the $2 bill.  (The answer is:  4562 combinations.)  Or to find all combinations totalling $200.  (The answer is: 2930 combinations.)\n\nThe line that checks if the denomination is less than or equal to the smallest denomination currently in the stack is present to avoid a common mistake:  We want the total combinations, not total permutations.  Otherwise, the stack "50 20 20 10" would be counted differently than the stacks "50 20 10 20" and "50 10 20 20", and even "10 20 20 50".  The total permutations is much, much greater, especially if you consider each bill as unique.  Five $20 dollar bills alone have 5!=120 permutations because, after all, they are all completely different $20 bills.  Imagine the number of permutations of 100 x $1 bills, and everything in between.  o.O
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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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I have an older uncle who recently picked up Sudoku.  He says he thinks it has helped sharpen his mind.  He's about 60 years  old.
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There is an infinite number of solutions, \nthe set of solutions is :\n{(k,-k+12):k belongs to the set of real numbers}
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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.
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100 pieces in the puzzle?
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hi its an interesting mathematical puzzle\nhere is where u can get more info\nhttp://en.wikipedia.org/wiki/Tower_of_Hanoi
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the solutions is 7,8,3,2 or 7,6,5,2. The problem works with both sets of numbers.
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Oh Dear! lots of dodgy maths out there!\nWelcome to Mr Cantor's infinity paradise hotel!\nWe got infinite rooms, but they're all full just now.\nDon't worry!.. we'll squeeze you in!..I'll just get every guest to move one room along\nNow you can get in room1\nHey there's an infinite stretch limo arrived with an infinite number of guests..no probs just get all our guests to move from room n to 2n!\nYes infinity is an uncountable number, but you can still do mathematical ops with it\nHope that helps, you can work out the rest foor yourselves. PS always agree with your wife- she's right even when she's wrong-now that's a true paradox
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Here you go (requires VB.NET)\n\nhttp://www.codeproject.com/useritems/sudoku.asp
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The web site I give below has some tips to get you started.  If you google (or yahoo!) for "sudoku" you'll find plenty of material.
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11\n\nany perfect square will have an odd number of factors
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Have you tried these?  Surely you've been told that division by 0 isn't possible, so there's your answer for 7.  I'm not doing any others on Yahoo answers (too many at once), but if you really need help and are willing to do as much as possible for yourself I'll help you if you email h_chalker@yahoo.com.au, but nasty Maths teachers like me won't just hand you 7 answers on a plate!