Math problem 83 or something, Real mathematicians can't count Options

[Raijinili]

Say that when you take pistachios, you take ten per handful, you eat the unshelled ones, take off the shells of the shelled ones, and drop the newly unshelled ones back into the bowl.
If you had a bowl of 100 shelled pistachios, how many grabs would it take to eat them all?

[jcdietz03]

It is true. I meant to say "less than or equal to"

The worst case scenario (for most pistachios left after 19 grabs) is if you picked up shelled ones whenever they are available. This will reduce the number in the bowl the slowest.

So after 10 grabs you would have 100 unshelled. After 19 grabs, you would have 10 unshelled left. Any other combination will reduce the number in the bowl faster. There are other permutation that will result in 10 unshelled left after 19 grabs, but there are no permutations that result in more than 10 pistachios after 19 grabs. Or if there are, name one.

If you mixed it up a bit more (left shelled ones in the bowl when they are available) you would have even less than 10 left after the 19th grab, but some would be shelled.

This post has been edited by jcdietz03: Feb 3 2008, 09:48 PM