today's logic puzzle - exercise yo brain, level 1

there's a $1 drink vending machine in a local candy shop with three buttons. one is for lemonade, one is for iced tea, and one is "random" (for undecided folks, it puts out either a lemonade or an iced tea with 50/50 chances).

last night, some punk kids came by and peeled all the labels off the buttons, and put them all back on the wrong ones. now none of the buttons are labeled correctly, and your job is to put each label back in its right place.

how much money do you have to spend to figure out which label goes where?

i'd say $2 without thinking hard about it but the real answer is probably something like "rtfm"

EDIT: oh yeah that random one is gay and ****s **** up

This post has been edited by Xgoff on Sep 19 2009, 12:39 AM

the answer is a whole number amount of dollars.

edit: I should say the answer is a positive integer. the rationale is the important part.

This post has been edited by Lightning on Sep 19 2009, 12:42 AM

I say between $6 to $9

'0' is a hole number

the owner is busy playing golf and the customers are impatient.

edit: and sgg's post disappeared so this one doesn't make sense

This post has been edited by Lightning on Sep 19 2009, 12:43 AM

Dang it, I deleted mine instead of editing it.

Anyways...

$6.

You buy 2 of each, this will narrow down the 3 so that, at the most, 2 will have the same thing (2 lemonades, 2 teas, 2 lemonades) so that you know one is real, and one is random. It's most likely that the random one is the lower one, but to play is say, you could spend an extra dollar to be sure.

yeah but you can't make assumptions about randomness

that's the thing about random, though: there is a non-zero probability that it could just happen to keep giving you lemonades at random. you could flesh out the appropriate probability distribution functions and figure out how much you'll probably spend on finding out, but there is a solution that doesn't require that

Push the button labeled "random", because we can assert that it is not the random choice. We now know it to be x (let's say it's lemonade).

That leave two buttons, which produce iced tea and random. We know the button labeled iced tea does not produce iced tea by the problem statement, and we know it does not produce lemonade, because we found the real lemonade button. Therefor it must be the random choice, and by elimination the last button is also known (the one labeled lemonade produced iced tea).

So we only had to spend $1.

this is why rii can make a lua extension that doesn't piss off mmf most of the time

You say you want rationale behind the answer? Well I'm gonna screw around with this because I feel like having fun. :P

I say $2. Why? Because nobody, in their right mind, would put the random button anywhere but the very bottom.

Note: That's not a serious answer, I just felt like being silly.

aaand retriever with the victory.

to anyone who's confused: the problem stated that none of the labels were on the right buttons.

6 dollars minimum, 2 for each slot. If one of them gives out different sodas problem solved. If not, 2$ more for every attempt afterwards between the two buttons that dispensed the same drink until one is different.

this is why i fail logic problems i always miss the ****ing "here's the goddamn key to the whole puzzle tard"

that's okay, you and chippermonkey (while not correct) spent considerably less than the undefined amounts of money that some of the other solutions were spending

lol i just said $2 because i forgot about the random option

then i was like "****"

Yeah, and I said that because "spend 1 dollar figuring out which of the two is the other one, random button is on the bottom, then use the other dollar to buy the other of the tea/lemonade and mix the two."

Good problem though. I wonder if I'd have actually figured it out if I had tried..?

harder one tomorrow if I remember.