gavinksong

Why? The least number of apples Alice can place in a room is 0, not 1. 0 is a non-negative integer, and thus a valid option for Alice. Uhh... I didn't say that. It was k-man. :| That said, that's a pretty trivial correction. It seems that when you quoted me quoting k-man, you accidentally removed the spoiler brackets (apparently along with the innermost quotation brackets). Could you be more careful about that in the future?

This is incorrect because the minimum requirement only advances three months at a time. It does not suddenly jump forward by a year.

Oh wait.

That's what I thought, too. Or at least if I understood you correctly... There's only one colored dot in the center of each view, but they are not all the same color. I can't figure out how to reconcile that...

To be honest, I don't know the actual solution to this problem. It was a bonus problem on an exam, but I never got the exam back. Do you care to try and solve for the standard deviation, or is that too much?

Hahaha. I can't believe it! You even showed us the image that you made for the explanation of the problem. ... Did you think of this problem yourself, bonanova? I apologize for reposting an old puzzle. Come on, guys. All the ideas that have been proposed so far (By karthick and plasmid) are valuable. Just put them together.

Your analysis isn't wrong; doing it like that won't work. Try another approach. Go on. Very interesting. I'm also now wondering about the puzzle itself.. What should Bob do: have a strategy that ensures he rejects the room with least number of apples, Oh... Haha. No, it's nothing like that. Bob only wins if he rejects the smallest room, regardless of how many apples he gets total.

Your analysis isn't wrong; doing it like that won't work. Try another approach. Go on.

Hmm. It seems I read over the part where you estimated the probability to be 1/3. I can tell you that is not the case, possibly because it is an estimate. The actual probability is 1/2, as it was shown by k-man and wolfgang. I'm sorry.

Your analysis isn't wrong; doing it like that won't work. Try another approach.

That was clever trying to reduce the problem into one with a known solution, bonanova. Unfortunately, the strategy you came up with is exactly the same as k-man's first strategy. k-man, Don't give up yet. Think about it a little bit more after mulling over my final hint.

Karthick, I hope you haven't given up. Although your proof made the mistake that plasmid's proof successfully avoided, it may be easier for you to correct your reasoning than it is for plasmid. In that respect, you may actually be closer to finding a solution with your "residue" argument. Don't give up!

Nope. The answer is much simpler.

Perhaps the solution isn't very intuitive, but a regular person would still do something similar.

Huh. I suppose this could be an alternative solution to the problem? But if course, this wasn't the solution I had in mind. For the sake of clarity, from now on assume that Alice knows Bob's strategy. Thus, the distribution of apples is not completely random, but chosen in such a way to try and minimize Bob's chances of winning (if possible).

Oh... Haha. :S That makes a lot more sense.

I believe you, antel0pe, simply because you say so. Multiple choice is a fav of teachers. Thanks for contributing. Nice meta argument, bonanova.

That is correct. Although to be clear, it isn't just that your proof isn't convincing or rigorous enough, the result is also incorrect.

That was the reply??? O.o That's a small paper!

Your answer is incorrect...

This problem is more interesting than it looks at first glance. Unfortunately, although you did get the same answer as plasmid, in some respects, his reasoning for rational numbers is slightly "more correct" - partially because it's more general and less prone to error. Your remainder argument pretty much sums to a confirmation of the existence of a least common multiple between 360 and any rational number, which would normally be sufficient but I'm afraid the OP is slightly trickier than that.