Marbles, Just for fun...

Actually this is not really a maths question, more a logic one. Hope that's okay, I thought it might degenerate too much in chit chat.
This is one of a few questions posed in job interview. It's supposed to be answered quite quickly, it's simplicity reflects this. I'm just posting it here because, well, I like it and you lot might too.


You are given a bag of 24 marbles all identical is size and weight except for one which is ever so slightly heavier.

At you disposal is a set of scales.

How many times do you need to use the scales in order to determine which is the heavier marble?

4?

12 --/\-- 12 take the heavy side

6 --/\-- 6 take the heavy side

3 --/\-- 3 take the heavy side

1 --/\-- 1 if one side is heavy; thats the one: if they balance your extra one is heavy

there's a better solution, give it a minute and the penny will drop.

I am going to assume that you need to be able to determine it with 100% certainty? Otherwise, you could take two marbles at random, place them on the scale, and if you're very lucky you will have taken the heavier marble --> only one weigh required. The question doesn't really address this, but I don't think a solution like that is acceptable... Right? ;)

Spoiler Warning (highlight the text with your mouse to read it)

Weigh 8v8 [8 left out]; if they balance throw them out, if they don't take heavier side.
3v3 [2 left out]; if they balance throw them out; if they don't take heavier side.
1v1, possibly with one left out; take heavier side; if one is left out and they balance, take that one.

3 :)

jemidiah, you got it. (again)
If you think the puzzle worth it maybe edit your post.

:)

Hint

(if anybody's particularly interested without getting the answer) 24 is divisible by both 2 and 3. The 3 is important.

Quote:

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Originally Posted by jemidiah

Spoiler Warning

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I hope you don't mind, I changed the text colour of your solution so that it can't be read accidentally. :)

What I like about this problem is that the number of measurements required to determine the culprit for N marbles goes by the power of 3. So, if it takes M measurements to figure it out for N marbles in one instance it takes M + 1 measurements to figure out for 3 * N marbles.

Quote:

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Originally Posted by si_the_geek

I hope you don't mind, I changed the text colour of your solution so that it can't be read accidentally. :)

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Good idea :thumb:

I say zero.

If you gently shake the bag of marbles for a while, then the heavier marble will slowly settle to the bottom.