brainaching puzzle

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brainaching puzzle

Post by dante » Wed Apr 15, 2009 12:49 pm

Hello everyone,

Here's a good puzzle, not so easy I think.

There are TEN pots full of gold. In any of the pots, except for ONE, there are coins which weigh exactly TEN grams, and only in one pot the coins weigh NINE grams.
The task is to identify in which of the ten pots are the coins which weigh NINE grams, by taking out any number of the coins you wish from the pots but measuring only once. So,you can take whatever number of coins from the pots but you are allowed to measure (= put coins on the scale ) only once on a digital scale.

Enjoy :)
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Re: brainaching puzzle

Post by Phil White » Wed Apr 15, 2009 1:10 pm

You missed an important piece of information. Each pot must contain at least ten coins. The usual statement of the puzzle is that the pots all contain 100 coins, but the number is arbitrary as long as it is above 10.
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Signature: Phil White
Non sum felix lepus

Re: brainaching puzzle

Post by dante » Wed Apr 15, 2009 3:21 pm

Hello Phil White,

You know the answer :) . I disagree about your remark though. Here's what I wrote :
There are TEN pots full of gold.
"Full" gives enough information in my opinion ,and leaves no doubt that the number of the coins is bigger than ten.
In my mind "pot full of gold" brings up an image of like hundreds of golden coins in it . Or its only how pots with gold are usualy pictured in the literature for children around here :) I just can't imagine a pot full of gold with, say, seven coins in it. Those should be gigantic coins or the pot should be tiny.
Here's the Google images result for "pot full of gold" http://images.google.com/images?hl=sr&l ... 0&aq=f&oq=
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Re: brainaching puzzle

Post by russcable » Wed Apr 15, 2009 4:14 pm

dante wrote:coins which weigh exactly TEN grams ... the coins weigh NINE grams.
It's not clear as stated whether the coins together weigh 10 grams and 9 grams, or whether each coin weighs 10 or 9 grams.

"full of gold" is not clear. You could fill the pots with solid gold and then put 2 aluminum coins on top and satisfy the problem as stated.
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Re: brainaching puzzle

Post by dante » Wed Apr 15, 2009 5:59 pm

In nine pots the coins weigh TEN grams each and in one pot there are coins which weigh NINE grams each. I hope I'm making myself clear this time :)

I still stick with what I've said before about the clarity of "full of gold" expression in this context. Your interpretation is certainly possible but only theoretically. I've checked again the google images results for "pot full of gold" and I must tell you that I haven't found a single pot with solid gold in it :). Not to mention the combination of coins and solid gold.
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Re: brainaching puzzle

Post by russcable » Wed Apr 15, 2009 6:11 pm

This type of puzzle often hinges on the exact wording of the puzzle (cf the controversy over "words that end in -gry"). Inexact wording causes people to rocket off down blind alleys or creates an unsolvable puzzle. Even if what you really meant to say can be reasoned out from what you actually said, it leaves people frustrated that you didn't state the problem clearly in the first place.
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Re: brainaching puzzle

Post by dante » Wed Apr 15, 2009 7:38 pm

All right russcable, my english is still too weak to enter this kind of discussion, its clear I guess :).
Still in my mind, putting the puzzle with giving the exact number of coins in the pots, as Phil suggested is how that should be put, would only lead the solver down the blind alley as you said russcable. Its better if the number of coins is not stated since the answer has nothing to do with the exact number of the coins in the pots. If you give someone 100 coins as a variable that can only make things harder, simply because it could be 77 or 63 or 15 in the pots,and also different number of coins in different pots, or whatever number in any of them and it wouldn't make any difference.
Still, the question is..do you have the answer to the puzzle? :)
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Re: brainaching puzzle

Post by Ken Greenwald » Wed Apr 15, 2009 7:55 pm

Dante, I’ve never seen this particular one before. Nice problem – I like it! I solved it assuming you meant the coins weighed 10 and 9 grams ‘each’ and that there were at least 10 coins in each pot. And I agree that it is not good for there to be ambiguity in the wording of a math problem. I don’t think that there is much ambiguity in your question, but there is a bit, as pointed out above. However, in this instance saying that there must be at least 10 coins in a pot full of coins does give a hint as to how to solve the problem. Phil’s “the pots all contain 100 coins” (would be better to say “each pot contains 100 coins”) would not be as revealing.

I'll hold off giving my solution till others have had a chance to give it a try or until you say time is up.
_________________

Ken – April 15, 2009
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Re: brainaching puzzle

Post by dante » Wed Apr 15, 2009 8:41 pm

Hello Ken,

I'm glad you liked the puzzle :) .It was a few years ago when I was asked to solve this puzzle and I admit it took me an hour of bumping my head against the wall to figured it out :)
I must say decidedly this time that I'm sure that the required minimal number of the coins shouldn't be given in the puzzle question. The pots surely don't need to contain a hundred coins each and it would be also misleading to say that the pots need to contain ten coins each too. I'll skip further elaboration for now and let people solve the puzzle on their own.
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Re: brainaching puzzle

Post by Erik_Kowal » Thu Apr 16, 2009 8:15 am

Dante,

If we take your clarification of 'measure' as meaning 'put coins on the scale', then the solution is very straightforward if the coins to be weighed are placed on the scale one at a time.

To solve the problem, one need only take one coin from each of the pots and place it singly on the scales while keeping a constant eye on the display. Any coin placed on the scales which does not result in a displayed value that increments to 10 grams or a multiple thereof will have come from the pot that contains the 9-gram coins.

If this is the correct solution, then all discussion about whether the pots are 'full' of gold, or the minimum or maximum number of coins that each pot contains, is irrelevant.

Or is my solution just too easy to be true?
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Re: brainaching puzzle

Post by dante » Thu Apr 16, 2009 8:42 am

Hello Erik,

The point of the puzzle is that you're not allowed to put the coins on the scale more than once. If you were allowed to put them on the scale in succession that wouldn't be interesting. Whatever number of coins you picked you need to put it all at once on the scale. After reading that (total) weight of the coins you picked you'll be able to tell the pot with the lighter coins.
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Re: brainaching puzzle

Post by Erik_Kowal » Thu Apr 16, 2009 9:04 am

In that case, I say there is no possible solution.

However, since you and several others here are claiming to have one, I am even now preparing to eat my words.
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Re: brainaching puzzle

Post by dante » Thu Apr 16, 2009 9:10 am

Hello Erik,

You've made me smile thank you :) There is a solution actually and Ken and me are living witnesses that it can be solved :)
I'm editing to add one thought that came across my mind as to the minimal number of the coins in the pots. In writing puzzles we have a limited communication and that is why puzzles are always much better when asked directly where the solver can ask for additional information. I recalled that the question about the total number of the coins in the pots I might have asked too. I think that a plausible answer may be like : "its some indefinite big number of the coins, and it is irrelevant for the solution of the puzzle"
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Re: brainaching puzzle

Post by Phil White » Thu Apr 16, 2009 11:11 am

We have all become coy.

Take 1 coin from pot 1, 2 from pot 2, 3 from pot 3 and so on and weigh them all together.

If all the coins in all the pots weighed 10 grams, the total weight would be
(1 x 10 g) + (2 x 10 g) + (3 x 10 g) ... (10 x 10 g) = 550 g

If pot 1 contains the 9 g coins, the weight would be 1 g short of 550 g, because we only have 1 coin from pot 1. If pot 2 contains the 9 g coins, we would be 2 g short, and so on.

Generically,
number of the pot with 9 g coins = (total weight if all coins were 10 g) - (measured weight)
or, for this example,
pot = 550 - (measured weight)

As I say, I have only seen (or more to the point heard) the problem stated in such a way as to include the number of coins (diamonds, pebbles) in the pots (bags, chests), and as far as I remember, it has usually been 100 pots or bags. Stating that number is, as you rightly point out, a red herring provided that the number is greater than or equal to the number of receptacles (and, of course, the pots don't have to contain the same number of coins at all). But red herrings are all part of puzzling.
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Signature: Phil White
Non sum felix lepus

Re: brainaching puzzle

Post by dante » Thu Apr 16, 2009 2:00 pm

Your explanation of the puzzle is correct Phil. As to the this disputable question with stating the number of the coins in the pots, I guess that it is not so straightforward a question and I think that it allows people to choose the wording they think will make the puzzle more intriguing. As I said my position is that stating that the pots contain 100 coins each makes that fact a relevant variable of the puzzle in my mind though it certainly is not and so mislead the solver and I wouldn't opt for that wording for that reason.
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