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[ed boy]

That's why I specified an arbitrarily large number of pills in each bottle.

[Sowelu]

You are in charge of distributing pills to sick people are part of a medical trial. You are given lots of bottles of pills (an arbitrarily large amount).

Hmm, I think the number of pills per bottle was kind of vague there (what 'arbitrarily large' attached to), but that works!

[ed boy]

Your friend Jimmy is thinking of a number which is either one, two or three. You do not know which number it is. In order to work it out, you can ask him one question, to which he will either answer "Yes", "No", or "I cannot truthfully answer yes or no".

What do you ask him?

[Ricky]

Ask Jimmy if it's odd, then guess.

[Urist Imiknorris]

EDIT: no, my idea won't work.

I was going to say "is your number prime?"

[Darvi]

"is it bigger than two?"

[Urist Imiknorris]

"is it bigger than two?"

If not, then it's 1 or 2. We need absolute certainty.

[Darvi]

My question is ambiguous enough to mean either "strictly bigger than" or "bigger than or equals to". If he doesn't know what I mean, he can't give a proper answer if it's two.

[Urist Imiknorris]

Is the square root of (your number minus two) greater than 0?

If 3, yes.
If 2, no.
If 1, cannot truthfully answer.

[Nikov]

The needy want, but never need
Oft declared, never acheived
Many tried, never succeeded
Many died, the past unheeded

[Earthquake Damage]

My question is ambiguous enough to mean either "strictly bigger than" or "bigger than or equals to". If he doesn't know what I mean, he can't give a proper answer if it's two.

No, it isn't.  If you mean "at least two" then don't say "greater than two".  You can't reasonably (key word, that) argue "it's ambiguous because I may not have said what I meant" and expect his answer to reflect that.

[Sowelu]

Your friend Jimmy is thinking of a number which is either one, two or three. You do not know which number it is. In order to work it out, you can ask him one question, to which he will either answer "Yes", "No", or "I cannot truthfully answer yes or no".

What do you ask him?

Is (1 / (your number - 2)) both odd and negative?

Yes:  His number is 1.  (It equates to 1 / -1, or -1, so it is odd and negative)
No:  His number is 3.  (It equates to 1 / 1, or 1, so it is odd but not negative)
Cannot truthfully answer:  His number is 2.  (It equates to 1 / 0, which is either undefined or positive-infinity depending on what level of pedantry you've been taught.  Both undefined nor positive-infinity cannot be truthfully answered yes or no as being odd)

[Leafsnail]

If you're going with positive infinity, though, then it definitely isn't negative, and therefore you could say "false".

For undefined I'm not so sure, but I don't think you could say that undefined is actually negative or odd - it's just not a number at all.  If you asked "Is this banana odd and negative" then I would answer "No".

[Sowelu]

Ack, you're right.  And I should have done "odd and positive" I suppose, but yeah, I guess I have no idea what other people would say about 'undefined' there.

[Urist Imiknorris]

If you're going with positive infinity, though, then it definitely isn't negative, and therefore you could say "false".

For undefined I'm not so sure, but I don't think you could say that undefined is actually negative or odd - it's just not a number at all.  If you asked "Is this banana odd and negative" then I would answer "No".

But is the banana even or positive?

Also, you can probably induce an electric charge on a banana (positive or negative), and you must admit bananas are pretty odd.