Guest Posted May 15, 2008 Report Share Posted May 15, 2008 How many solutions are possible in a 9x9 sudoku game? A valid solution with all 81 squared filled is considered one possibility. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted May 15, 2008 Report Share Posted May 15, 2008 (edited) 9!^2 then divided by something. Because there are 9! ways to create a row and then 9! ways to order the rows in 9 columns. However, I have yet to figure out how to get one of each number in each box. >_> Hence, divided by something. EDIT: If you think about it, there are 9! ways to order 1-9 in a box, and then 9! ways to order the boxes on a puzzle... >_> Bah, will post again later! After more thinking! But if anyone can build off this, go ahead. Edited May 15, 2008 by PhoenixTears Quote Link to comment Share on other sites More sharing options...
0 Guest Posted May 15, 2008 Report Share Posted May 15, 2008 (edited) usually just one correct combination per game. -or- 6,670,903,752,021,072,936,960 Edited May 15, 2008 by karlhite Quote Link to comment Share on other sites More sharing options...
0 Guest Posted May 15, 2008 Report Share Posted May 15, 2008 karlhite beat me to the one per game solution! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted May 15, 2008 Report Share Posted May 15, 2008 (edited) Let me rephrase the question. How many 9x9 sudoku "problems" are possible. I have to be honest here, I too know the number, but how to arrive at the solution.... I have no clue. Edited May 15, 2008 by mac Quote Link to comment Share on other sites More sharing options...
0 Guest Posted May 15, 2008 Report Share Posted May 15, 2008 6,670,903,752,021,072,936,960. Or, six sextillion, six hundred and seventy quintillion, nine hundred and three quadrillion, seven hundred and fifty two trillion, twenty one billion, seventy two million, nine hundred and thirty six thousand, nine hundred and sixty. *phew!* Quote Link to comment Share on other sites More sharing options...
0 Guest Posted May 15, 2008 Report Share Posted May 15, 2008 Let me rephrase the question. How many 9x9 sudoku "problems" are possible. I have to be honest here, I too know the number, but how to arrive at the solution.... I have no clue. Mac, the solution is arrived at only after a computer used complex algorithms and "brute force" to find out the right equation. The equation isn't very hard to find (search for Sudoku Mathematics on Wikipedia to start out with), but I couldn't tell you why what is what. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted May 15, 2008 Report Share Posted May 15, 2008 You only need one book of say fifty problems then just erase them and start again! There is a way to build these problems probably, like a dark hole, I've been meaning to look into it! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted May 15, 2008 Report Share Posted May 15, 2008 You have 9! * 9! ways to fill up the grid without any rules other than 1-9 in a row (or column). * subtract (exponent) decreasing ways to fill the rows according to column rules (no duplicates in the column) * subtract (power) decreasing ways to arrange numbers in each 3x3 box Quote Link to comment Share on other sites More sharing options...
0 akaslickster Posted May 16, 2008 Report Share Posted May 16, 2008 6,670,903,752,021,072,936,960. Or, six sextillion, six hundred and seventy quintillion, nine hundred and three quadrillion, seven hundred and fifty two trillion, twenty one billion, seventy two million, nine hundred and thirty six thousand, nine hundred and sixty. *phew!* If this is correct. I would never of solved it alone. Quote Link to comment Share on other sites More sharing options...
0 akaslickster Posted May 16, 2008 Report Share Posted May 16, 2008 6561 possible solutions but all puzzles begin different.How many solutions are possible in a 9x9 sudoku game? A valid solution with all 81 squared filled is considered one possibility. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted May 16, 2008 Report Share Posted May 16, 2008 Only one. =D Quote Link to comment Share on other sites More sharing options...
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How many solutions are possible in a 9x9 sudoku game? A valid solution with all 81 squared filled is considered one possibility.
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