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Discussion Starter #1 (Edited)
You have four boxes of nails each containing 200 nails. One box of nails is defective, but the defect cannot be seen. The non-defective nails weigh 2.0 grams each. The defective ones weigh 2.1 grams each. You have a scale, but can only use it once. How can you determine which box of nails is defective?

PM the answer to me.


This is the answer I was looking for (obviously, there are other possibilities):

Go Steelers said:
Remove 1 nail from box #1, 2 nails from box #2, 3 nails from box #3 and 4 nails from box #4. Then weight the 10 nails you just gathered.

If the total weight of those 10 nails is 20.1 grams, then box #1 is defective. If the total weight is 20.2 grams, then box #2 is defective. If the total weight is 20.3 grams, then box #3 is defective and if the total weight is 20.4 grams, then box #4 is defective.

This answer is the most complicated one, but it seems right from what I can see. If anyone finds a flaw that I missed, let me know. In the meantime, SilverGoat04 gets a point.

SilverGoat04 said:
Let's call the four boxes A, B, C, and D. The full weight of each individual non-defective box is 400 and the full weight of the defective box is 420.

Take one nail out of box A and put it into B. Now the possibilities for the weight of B are:

402 (if both A and B contain non-defective nails)
402.1 (if A contains the defective nails)
422 (if B contains the defective nails)

Now, I would take one nail out of box C. The possible weights of box C would then be:

398 (if it is a non-defective box)
417.9 (if it is the defective box)

If I put both box B and box C onto the scale, the combined weight possibilities are:

1) 800 (if A, B, and C were non-defective)

2) 800.1 (if B and C were non-defective, but A has the defective nails, one of which is now inside of B)

3) 820 (if B already contained the defective nails, then C could not be defective and C would thus have a weight of 398)

4) 819.9 (if A and B were non-defective, but C is the defective nail box)

For scenario 1, I would conclude that box D is the defective box.

For scenario 2, I would conclude that A is the defective box.

For scenario 3, B contains the defective nails.

For scenario 4, C contains the defective nails.
This question is closed.
 

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Jimmy Rustler
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LOL, reminds me of a story from work... We ordered labels from our paper supply co. Our receiving manager thought he needed to count the labels to make sure we weren't shorted, so he weighed all the boxes and figured out we were about 100 or so labels short on the order. My manager says to him 'How much time did you spend figuring this out?' Guy says 'About 4 hours'.

Labels cost about $.01 or less at the time... :rolleyes:
 

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Omnicidal maniac
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Does anyone else know how easy it is to feel the difference between 400 grams and 420 grams. The scale would be unnecessary. I refuse to even try to figure out if there is any logic to this question.
 

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Discussion Starter #8
Scores:

GoSteelers: 5
brada: 3
2KSE: 2
SilverGoat04: 1
InjunRAIV: 1
Douggo: 0
KissMyGoat: 0
 

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Discussion Starter #10
Silvergoat deserves more than one point for that!
I was kind of thinking that, too, but wanted to be fair to everyone who gave the correct answer. How much extra do you think I should give her? If everyone's alright with it, I will.
 

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I was kind of thinking that, too, but wanted to be fair to everyone who gave the correct answer. How much extra do you think I should give her? If everyone's alright with it, I will.
I have no problem with you giving silvergoat extra points for that answer!!

When I first looked at the problem, I started to go down a similar path, but then I started to worry about the weight of the boxes themselves....then it dawned on me to think about removing nails from the boxes.
 

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Jimmy Rustler
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I was kind of thinking that, too, but wanted to be fair to everyone who gave the correct answer. How much extra do you think I should give her? If everyone's alright with it, I will.
I'm thinking like 5,000! BTW, what is the actual cash value of a LS1GTO QOTD point?
 

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Discussion Starter #14
I'm thinking like 5,000! BTW, what is the actual cash value of a LS1GTO QOTD point?
Maybe you can talk to some of the sponsors, and see if you can get them to donate prizes to the top or top three scorers, each month.
 

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'Nova GIRL
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Haha, thanks for thinking my horrible over thinking of this problem warrants some bonus points. :) I got stuck on taking one nail from one box and putting it in another and there was no turning back until it got as complex as possible. I'll definitely take 5,000 extra points if they have a cash value! :D
 

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I am surprised no one posted the easiest way:

Put all 4 boxes on the scale.
Remove 1 box at a time, while looking at the scale.
When the weight is reduced by 420g, you found the bad box.
The other 3 boxes will reduce the weight by 400g.

:)
 

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I thought of that, but that's technically using the scale more than once...
Its alot better than taking nails out of differnet boxes and then weighing all of them! If you take nails out of A and put them in B, weigh them and they weigh correct, you are screwed. I guess you just guess on C or D?
 
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