8 marbles, one scale, infinite possilbilites!

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Arkohn
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8 marbles, one scale, infinite possilbilites!

Postby Arkohn » Wed Apr 11, 2007 2:03 am UTC

Ok, so, you got 8 marbles, and they're all exactly the same in every single way, except for one which is slightly denser, causing it to be .000001 pounds heavier. You have with you the most sensitive balancing scale on earth, but after two uses, it will explode. How do you give yourself an 100% to identify the dense marble?

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Vaniver
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Postby Vaniver » Wed Apr 11, 2007 2:13 am UTC

Divide them into three groups (so you have three in each group). Compare the weights of Group A and Group B. If they are the same, the aberrant marble must be in Group C. If Group A or Group B is heavier, then the aberrant marble must be in that group.
Divide the group that contains the marble into three groups. Repeat, and you will know which marble is the heavy marble.
I mostly post over at LessWrong now.

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skeptical scientist
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Postby skeptical scientist » Wed Apr 11, 2007 2:57 am UTC

That strategy actually works for 9 marbles, but can easily be made to work for 8.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

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Think0028
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Postby Think0028 » Wed Apr 11, 2007 3:17 am UTC

3,3, and 2
is the easiest way to modify it.

Shadowfish
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Postby Shadowfish » Wed Apr 11, 2007 4:29 am UTC

Dude, first I see this puzzle in my CS class, then I see it in a magazine, and now here? It's sure popular.

Edit: The black and white prisoner hats also came up in my CS class. The only possible explanation is that you are my prof.

Shpadoinkle
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Postby Shpadoinkle » Fri Apr 13, 2007 5:15 am UTC

Vaniver wrote:
Divide them into three groups (so you have three in each group). Compare the weights of Group A and Group B. If they are the same, the aberrant marble must be in Group C. If Group A or Group B is heavier, then the aberrant marble must be in that group.
Divide the group that contains the marble into three groups. Repeat, and you will know which marble is the heavy marble.


Uhh... no, you only get two uses of the scale, remember? If you did it that way, you'd have it narrowed down to one group.


skeptical scientist wrote:That strategy actually works for 9 marbles, but can easily be made to work for 8.


To repeat, only two uses of the scale.

Think0028 wrote:
3,3, and 2
is the easiest way to modify it.


I'm not seeing how.
You get TWO uses of the scale. Measuring the two groups of three will tell you in which group it is. If it's in the group of 2, then you can use the second use of the scale in order to tell which of those two it is, but if it's any of the other six marbles, then I can't figure out how you tell which group, much less which individual marble it is with only a single weighing.

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skeptical scientist
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Postby skeptical scientist » Fri Apr 13, 2007 5:22 am UTC

Shpadoinkle wrote:
Vaniver wrote:
Divide them into three groups (so you have three in each group). Compare the weights of Group A and Group B. If they are the same, the aberrant marble must be in Group C. If Group A or Group B is heavier, then the aberrant marble must be in that group.
Divide the group that contains the marble into three groups. Repeat, and you will know which marble is the heavy marble.


Uhh... no, you only get two uses of the scale, remember? If you did it that way, you'd have it narrowed down to one group.


skeptical scientist wrote:That strategy actually works for 9 marbles, but can easily be made to work for 8.


To repeat, only two uses of the scale.

Think0028 wrote:
3,3, and 2
is the easiest way to modify it.


I'm not seeing how.
You get TWO uses of the scale. Measuring the two groups of three will tell you in which group it is. If it's in the group of 2, then you can use the second use of the scale in order to tell which of those two it is, but if it's any of the other six marbles, then I can't figure out how you tell which group, much less which individual marble it is with only a single weighing.

It's in the heavier one...
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

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Shpadoinkle
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Postby Shpadoinkle » Fri Apr 13, 2007 5:37 am UTC

skeptical scientist wrote:It's in the heavier one...


Okay, now that I think about it, it will work. If it's in either of the groups of three, then you can take the heavier group and measure two of the marbles, and if they're the same, then by default it's the one you didn't weigh on your second use.

So, yeah, disregard about what I said in my earlier post, it's late, brain no worky.

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Solt
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Postby Solt » Fri Apr 13, 2007 8:23 am UTC

It's not a scale, it's a balance.

Scale = absolute weight

balance = compare weight of two objects, tells you only which one is heavier.



The puzzle is impossible to solve with a scale, but possible with a balance.
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Arkohn
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Postby Arkohn » Fri Apr 13, 2007 11:04 am UTC

I thought they were called balance scales, or balancing scales.

But yeah, what's-his-name got it right. I never thought about it, but it is possible with 9. You make 3 groups for 3, (or 2 groups of 3 and a group of 2)

[spoiler]You weigh group A against group B, take whichever is heavier, weigh any of the two marbles in the group. If one is heavier, that's it, if they're both the same, it's the one you left out. If A and B are the same weight, then you just do that for C.[/spoiler]

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morjax
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Postby morjax » Mon Apr 23, 2007 4:32 pm UTC

The real riddle is how to protect yourself when the scale explodes

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Alexithymia
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Postby Alexithymia » Thu Apr 26, 2007 1:44 am UTC

Shadowfish wrote:Dude, first I see this puzzle in my CS class, then I see it in a magazine, and now here? It's sure popular.

Edit: The black and white prisoner hats also came up in my CS class. The only possible explanation is that you are my prof.

... UCR?...

Puzzles seem to be quite popular in CS classes. I got the black/white prisoner one on the first day of one of my classes. Can't remember which though.


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