## 8 marbles, one scale, infinite possilbilites!

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Arkohn
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Joined: Sat Jan 06, 2007 7:57 pm UTC

### 8 marbles, one scale, infinite possilbilites!

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?

Vaniver
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Joined: Fri Oct 13, 2006 2:12 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
closed-minded spiritualist
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Location: San Francisco
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.

"With math, all things are possible." —Rebecca Watson

Think0028
Posts: 6
Joined: Tue Apr 10, 2007 10:26 pm UTC
3,3, and 2
is the easiest way to modify it.

Shadowfish
Posts: 309
Joined: Tue Feb 27, 2007 2:27 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
Posts: 74
Joined: Mon Mar 26, 2007 5:12 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.

skeptical scientist
closed-minded spiritualist
Posts: 6142
Joined: Tue Nov 28, 2006 6:09 am UTC
Location: San Francisco
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.

"With math, all things are possible." —Rebecca Watson

Shpadoinkle
Posts: 74
Joined: Mon Mar 26, 2007 5:12 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.

Solt
Posts: 1912
Joined: Tue Mar 27, 2007 5:08 am UTC
Location: California
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.
"Welding was faster, cheaper and, in theory,
produced a more reliable product. But sailors do
not float on theory, and the welded tankers had a
most annoying habit of splitting in two."
-J.W. Morris

Arkohn
Posts: 83
Joined: Sat Jan 06, 2007 7:57 pm 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]

morjax
Posts: 50
Joined: Mon Apr 23, 2007 4:00 pm UTC
Location: Twin Cities, Minnesota
The real riddle is how to protect yourself when the scale explodes

Alexithymia
Posts: 21
Joined: Wed Apr 25, 2007 11:44 pm UTC
Location: Southern/northern California depending on season.
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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