## 12 marbles and a scale....kinda like 8

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ptveite
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### 12 marbles and a scale....kinda like 8

you have 12 marbles where 11 weigh the same amount and one has a different weight. Can you determine which one has a different weight in just 3 weighings?

Yakk
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Yes!

GreedyAlgorithm
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Yakk wrote:Yes!

We need some kind of fuzzy recognizer that says "it looks like this thread has been started several times before, perhaps you should check?"
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Cauchy
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Isn't it possible to do 13 marbles in 3 weighings?

AntonT
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D'oh, I missed this thread and posted another for 27, it's actually possible to do 27 with 3 weighings. Oops.

jestingrabbit
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I've gotta point out that you can only do 27 with three weighings once you know whether the 'other' marble is heavier or lighter. Otherwise, I believe that 12 is the maximum.

AntonT
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D'oh, wait, - 27 is with a balancing scale. Different approach.

Ansain
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I can do This Puzzle exactly the same with 13 or 12 marbles.
divide the marbles into three groups of four measure two of them against each other (if you have 13 leave out the group of five) If the scale balances then it is simple to do, measure three that you know are correct against three unsure to tell you whether they are heavier or lighter, then measure two of those three against each other to tell which of the three it is. If the initial groups of four are of balance then take one from the group that was heavier, and four from the group you left out and measure them against the other three from the group that was lighter and two from the group that was lighter. The third measurement here is obvious and different depending on the results from the second.

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hahahah! this was the very first puzzle i got on my first day at uni in maths.

If the first two sets of 4 (W1) are not balanced, not which one is heavier. Call the heavier A and lighter B. The remaining marbles are the same weight and are called C. a sub 1 to 4 E A and b sub 1 to 4 E B. Weigh a sub 1 to 3 and b sub 1 and 2 against 4 from C and a sub 4 (W2). If equal, then either b3 or b4 is fake. the lighter of the 2 is fake (W3i). If the group with C in it is heavier, then a4, b1 or b2 is the fake. weigh b1 against b2(W3ii). the lighter (if any) is the fake, if not, it's a4. If the group with C from the second weighing is lighter, then a1, a2 or a3 is fake. the heaviest from these 3 (a1 vs a2 is W3iii) is the fake.
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gmalivuk
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Ansain wrote:I can do This Puzzle exactly the same with 13 or 12 marbles.

No, you can't. You can only do 13 in three weighings if you already have, before starting, a supply of known good marbles. This is a ready conclusion from the fact that, even if you do have a stock of good coins, you cannot completely solve 5 unknown coins in only two weighings. (For two weighings and a handful of good ones you can only solve up to 4 unknown coins.)

A quick search will give you the other thread where this was all discussed and proven before, for the more general case of n marbles and k weighings.
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Ansain
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No, you can't.

I suppose if the puzzle was asking me to both determine which marble was incorect and whether it weighed more then I would have a problem. However, this thread doesnt say anything about determining whether or not it weighs more or less, just isolating the wrong marble.

gmalivuk
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Ansain wrote:I suppose if the puzzle was asking me to both determine which marble was incorect and whether it weighed more then I would have a problem. However, this thread doesnt say anything about determining whether or not it weighs more or less, just isolating the wrong marble.

However, I suspect that it was a problem in the original post, since usually with 12 you're supposed to also find whether the bad marble is too heavy or too light. (This is because, in addition to 13 marbles, I think you can also do 14 or 15 with three weighings if you don't need to say what kind the bad marble is.)
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oblivimous
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GreedyAlgorithm wrote:
Yakk wrote:Yes!

We need some kind of fuzzy recognizer that says "it looks like this thread has been started several times before, perhaps you should check?"

Couldn't it just scan for "hats" "marbles" "prisoners" "light switch" "one of them always lies"...?

Did I miss any?

gmalivuk
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oblivimous wrote:
GreedyAlgorithm wrote:
Yakk wrote:Yes!

We need some kind of fuzzy recognizer that says "it looks like this thread has been started several times before, perhaps you should check?"

Couldn't it just scan for "hats" "marbles" "prisoners" "light switch" "one of them always lies"...?

Did I miss any?

Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
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bbctol
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gmalivuk wrote:
oblivimous wrote:
GreedyAlgorithm wrote:
Yakk wrote:Yes!

We need some kind of fuzzy recognizer that says "it looks like this thread has been started several times before, perhaps you should check?"

Couldn't it just scan for "hats" "marbles" "prisoners" "light switch" "one of them always lies"...?

Did I miss any?

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oblivimous
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bbctol wrote:
gmalivuk wrote:
oblivimous wrote:
GreedyAlgorithm wrote:
Yakk wrote:Yes!

We need some kind of fuzzy recognizer that says "it looks like this thread has been started several times before, perhaps you should check?"

Couldn't it just scan for "hats" "marbles" "prisoners" "light switch" "one of them always lies"...?

Did I miss any?