==> pickover/pickover.15.s <== In article <1992Oct30.173903.108937@watson.ibm.com> you write: : Consider a 9x9 grid of beautiful crystal wineglasses. Throw 32 cherries : at the grid. A glass is considered occupied if it contains at least one : cherry. (With each throw a cherry goes into one of the glasses.) How : many different patterns of occupied glasses can you make? (A glass with : more than one cherry is considered the same as a glass with one cherry : in the pattern). Assuming that rotated patterns are allowed, then it is (simply) sum( 81!/(81-n)! , n=1->32) . Since, if a total of n different classes are filled, then the number of combinations is 81!/(81-n)!. Since there can be from 1 to 32 glasses filled, the total # is just the sum of these... : : 2. Same as above except that you place 8 cherries in glasses (x,y) and : then determine the other positions by placing cherries at (x,-y), : (-x,y), (-x,-y) leading to 32 cherries in the grid. Consider the array : of glasses centered at the origin. How many different patterns of : occupied glasses can you make? (A glass with more than one cherry is : considered the same as a glass with one cherry in the pattern). This limitation basically reduces the number of available spots, from 9x9 to 5x5. Also, I only have to worry about 8 occupied spaces. Soo... #of comb. = sum( (25!/(25-n)!, n=1->8) : : 3. Can your results be extrapolated to an NxN grid with M cherries : thrown at it for both problems? With a odd N, and M = 4k (evenly divs by 4), then for 1.... #of comb = sum( (N^2)!/(N^2-n)! , n=1->M) for 2.... #of comb = sum( (((N+1)/2)^2)!/(((N+1)/2)^2-n)! , n=1->M/4) -- Michael Neylon aka Masem the Great and Almighty Thermodynamics GOD! // | Senior, Chemical Engineering, Univ. of Toledo \\ // Only the | Summer Intern, NASA Lewis Research Center \ \X/ AMIGA! | mneylon@jupiter.cse.utoledo.edu / --------+ How do YOU spell 'potato'? How 'bout 'lousy'? +---------- "Me and Spike are big Malcolm 10 supporters." - J.S.,P.L.C.L