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?

[Raijinili]

An example isn't a proof.

[jcdietz03]

An example isn't a proof.

It's been too long since I did proofs.
That's the answer, amirite?

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You need to pick up each one twice in order to eat it. There are 100, so you need 200 grabs.
As long as there are >10 pistachios in the bowl, you'll be able to grab 10, and by doing so, you reduce the "number of operations to go" by 10.

After 19 grabs, there will be <10 pistachios in the bowl. I don't know how I know this. It might be b/c it isn't true.

Here's a try at the proof for that though:
On average, every 2 operations, 1 pistachio disappears. This means that, on average, after 190 operations (19 grabs), there will be 5 pistachios left in the bowl.
100 to start with (minus) (190 operations * 1 pistachio / 2 operations) = 5 pistachios left after 190 ops.

On the 20th grab, you cannot grab 10 pistachios, b/c there are less than 10 for you to grab. Because you pick up less than 10, you can only complete the number of operations equal to the number of pistachios you picked up. Also, all the pistachios in the bowl at this point will be unshelled. On the 21st grab, all the remaining pistachios will be unshelled (because any unshelled ones you got on the 20th grab will now be unshelled), thus completing the task.