the "how many redhots" game   (geekin, random re me)

we've got a gumball machine thing full of redhots in our office and whoever guesses closest to the number of redhots actually in the thing without going over wins tickets to The Producers (note: depending what kind of tickets they are, that's like $600!). first runner up wins the gumball machine.

the part that holds the candy is a sphere about 5" in diameter, 60% filled with redhots, which are equilateral triangles with 1/3" sides and about 1/8" thick. the volume of the sphere is about 65.5"^2; 60% of that is 39.3"^2.

the volume of a redhot is about 0.004846875"^2, based on the volume of a trapezoid tank. if the redhots could be arranged perfectly with no gaps inside of the sphere, you could fit 9825 of them in there, if i did that right. but since it's impossible to arrange them perfectly, this is where the (rest of the) guesstimate comes in... i'm thinking somewhere in the 6-7k neighborhood. anyone care to check my math?