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?

[Elnendil]

Isn't there an equation for this? I'll see if I can figure it out.

First scoop, there is a 100% chance of getting 10 unshelled. Second scoop there's a 1900/99% chance of getting a pistachio for each pistachio out of ten. Hmm.

Also:

There's no end

Yes, there is. There is a finite amount of pistachios in the bowl. That means there is a finite amount of scoops to get them all out if eat at least one. With each scoop afterwards up to a finite point, you are eating either 0 or 10, and you are either unshelling 0 or 10, which add up to the unshelled number.

I would say 20 just by looking at it, but maybe thats the "trick". If one were to luckily get all shelled first, then unshelled, with 10 in hand, it would take 10 turns both times. And if one were to always repick the same unshelled pistachios (as in failure to acquire new shelled pistachios every other pick), it would also end up to be 20 as you would take one scoop to unshell, and one scoop to eat. Which would be the opposite results of each other. This should hold up to multiple bowls, by the way. As in, if you were to split the bowls into ten bowls, it would still take 20, since each bowl you would take all of them and unshell all of them, since pulling them apart and putting them together equals the same thing (For example, 296x90 = (200+90+6)(90) (26640 = 18000+8100+540) (or (100)=(10)(10)).

If that isn't the answer, why don't you post it later so I learn something. I've always been the person who was rusty on the basics but knowedgeable on complex shit. Thats generally how math majors should take the field anyways. Thats why most public school books have the answers in the back. Its so if you get the wrong answer, you can recheck your work to see where you slipped up. Use it all the time.

This post has been edited by Elnendil: May 1 2010, 03:55 AM