Can you solve the "scrambled box tops" puzzle?

I don’t know. I took “career aptitude” tests that specifically asked me to rank how much I enjoy “packing things into boxes”, which seemed to have a pretty clear correct answer, and deepened my skepticism about much of the field of psychology.

I am a programmer though :). I was lucky to find I enjoyed it, and worried about robots making all the jobs obsolete even at a young age.

If we change it to state “[…] so that it’s unclear whether any box is correctly labelled,” then I see two strategies, both solved in 3 draws if you’re lucky, 4 if you’re not, though the first has a much higher chance of being lucky.

Tactic 1: Draw one ball from Box 1 and one from Box 2.
If they’re the same colour, then the third box is two of the other colour. Draw one ball from either Box 1 or Box 2, and you will know what the one you picked from contains, which will give you the other by elimination.
If the two drawn from Box 1 and Box 2 are different colours, then draw one more from Box 1. If Box 1 is BW, then you know all three boxes. (Box 2 is two of whatever colour is in Box 2, and Box 3 is two of the other colour).
If Box 1 is not BW, you have to draw one more from Box 2. You know know what is in Box 1 and what is in Box 2, and, by process of elimination, what is in Box 3.

With Tactic 2, I calculate that you’ll have a 3/4 chance that you’ll get your answer in 3 balls, and a fourth ball will guarantee that you know the answer.

Tactic 2: Draw two balls from Box 1…
If you draw BW, then draw one from Box 2. Since both of the other two will have two of the same colour, that’s all you’ll need.
If the two balls in Box 1 are the same colour, you’re boned. Draw 2 balls from Box 2, which will tell you what’s in Box 3 by elimination.

With Tactic 2, I calculate that you’ll have a 1/3 chance that you’ll get your answer in 3 balls, and a fourth ball will guarantee that you know the answer.

I know that this is not the puzzle we’ve been given (see my previous post, above), but I wanted to know: can anyone improve upon that, so that the answer is always known within three balls?

I had half a lame joke about bringing Donald Trump in and getting his gut feeling to rank the boxes by laziness. Seems like an expansion on your strategy.

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@rtkwe had the best answer. I am still puzzling over beating it without “cheating” as I have so far, but I don’t think it’s possible.

Edit: Sorry, it seems @nimelennar and @Omni_Dilletante arrived at it first.

I concur.

I don’t know, I haven’t tried.

Can you stop using click bait titles?

It would take me at least 6 marbles… even then, I might mess up.

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You’ll never believe what marble he pulled out of the box!!

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I also skipped over the bit where it said all boxes are incorrectly labeled. Without that info, the puzzle is just irritating since it doesn’t really have an answer. It’s obvious that with luck you could do it in three, but since you can only take out one marble at a time-- and could therefore draw the same marble 100 times without knowing it-- there’s no upper bound on how long it could take.

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I once did a programming interview that had a few questions sort of like this. I had been pulling quite a lot of overtime so i wasn’t at my best. I said what I thought the answer was, and when they asked how I got it, I said I chose the most counter-intuitive option, because this is the kind of puzzle that prides itself on being “clever”.

I have no regrets about not getting that gig.

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Hey, you were truly thinking outside of the box!

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My favorite puzzle of that type goes:

Suppose you are a bus driver. The bus sets out and makes its first stop where six people board. At the second stop three people get on and four people get off. At the next stop two people get off and seven people get on. At the fourth stop two people board and no one disembarks. At the fifth stop eight people disembark and three people board. When the bus returns to the station four more people disembark. What color are the bus driver’s eyes?

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I only know the answer because I watched Fermat’s Room.

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Kinda hazel

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You forgot the metadata :slight_smile:

I’ve always heard the end of the riddle as, “You were paying attention, right? Okay, what is the name of the bus driver?”

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Quite some time ago, I bought Fermat’s Room on DVD from a rental place that was going out of business, despite knowing nothing at all about it. Is it decent?

I enjoyed it. Rather an odd movie, characters locked in a room full of mystery… why are they there, what’s the connection between them, and why are the walls moving?

Depends on your definition of decent. It’s definitely watchable. It’s a bit geeky, a bit funny and a teeny bit tense. I enjoyed it.

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