December 4th, 2006, 10:44 am
QuoteOriginally posted by: mhughesGoogle search for "generating function". Your generating function is (x+x^2+x^3+x^4+x^5+x^6)^m. You want to find the coefficients of this generating coefficient, which can be done by decomposing it in the way I suggested (or some other way), and writing each as a power series (which is only really difficult for the 1/(1-x)^m part). Then you need to calculate the product of these power series, and find an expression for the coefficient of x^n.Alternatively, you can avoid power series and use only polynomials by decomposing it as (x*(1+x+x^2)*(1+x^3))^m, though I think this would yield double sums instead of single sums (unless it can be simplified of course).I think this function (x+x^2+x^3+x^4+x^5+x^6)^m assume you roll the dice for m times, if you want to use this function, you need add the x^0;The solution for this problem I believe is simple:the expection value of one dice is 3.5 (1/6*1+1/6*2+1/6*3.....)so if we want to get m, the total number we roll should be m/3.5