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Topic: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB (Read 32038 times) |
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srn437
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http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB
« on: Sep 21st, 2007, 6:28pm » |
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there are 9 coins, one of which is counterfeit. the fake one weighs less. You have a scale that compares their weight. How do you find the counterfeit in one measurement? How about 2?
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TenaliRaman
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #1 on: Sep 21st, 2007, 8:09pm » |
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on Sep 21st, 2007, 6:28pm, srn347 wrote:| How do you find the counterfeit in one measurement? How about 2? |
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ROFL!!!
To answer the question,
since 0/0 is anything, all numbers can be shown to be equal and hence none of the coins is fake.
-- AI
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FiBsTeR
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #2 on: Sep 22nd, 2007, 9:13am » |
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Great title.
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srn437
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #3 on: Sep 22nd, 2007, 3:38pm » |
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thanks(assuming it wasn't sarcasm). And 0/0 isn't involved here. Creative, but irrelevant.
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Sir Col
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #4 on: Sep 22nd, 2007, 4:57pm » |
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on Sep 22nd, 2007, 3:38pm, srn347 wrote:| thanks(assuming it wasn't sarcasm). |
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Surely you're not serious? Have you actually seen the title you used for this thread?
Solution:
Place three coins on one side of the balance and three coins on the other. If it balances the fake is among the three coins not weighed. If it doesn't balance then you know which pile of three it's in, as the fake coin is lighter.
Take the three coins containing the fake and place two of the coins on the balance. If they balance the third is fake, it they don't balance you know which one is fake.
srn347, as an extension... if you were allowed three separate weighings, what is the most coins that you could work with to identify the fake coin?
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srn437
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #5 on: Sep 22nd, 2007, 8:01pm » |
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27. And the title is a link to the page I was on when I was entering the title.
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Sir Col
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #6 on: Sep 23rd, 2007, 1:56am » |
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Have you tried going to that "page"? Every URL here on the forum begins with that, but has a lot more after it.
on Sep 22nd, 2007, 8:01pm, srn347 wrote:
Very good, and I assume, therefore, you've discovered the "pattern".
So what if you don't know whether the fake coin is heavier or lighter? Find the maximum number of coins for W weighings. 
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srn437
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #7 on: Sep 23rd, 2007, 2:38pm » |
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For any specific number I could find an answer, but not the specific formula for w. Sometimes using a formula is easier than knowing it. Do you know what it is? Here's one for you:if you have 0 envelopes and 0 letters to put in them, how many ways can you put no letters in the correct envelopes?
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ThudnBlunder
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #8 on: Sep 23rd, 2007, 3:40pm » |
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on Sep 23rd, 2007, 2:38pm, srn347 wrote:| Here's one for you:if you have 0 envelopes and 0 letters to put in them, how many ways can you put no letters in the correct envelopes? |
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00 by convention.
Here's one for you: if there are 4 letters and 4 envelopes, what is the probability that exactly 3 letters will be randomly matched with the correct envelopes?
on Sep 22nd, 2007, 8:01pm, srn347 wrote:| 27. And the title is a link to the page I was on when I was entering the title. |
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Here's another: when are you going to change the name of this thread, now that you are on the same page as the rest of us?
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| « Last Edit: Sep 23rd, 2007, 5:35pm by ThudnBlunder » |
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Sir Col
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #9 on: Sep 23rd, 2007, 3:45pm » |
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on Sep 23rd, 2007, 2:38pm, srn347 wrote:
Yes, which is why I asked the question.
Quote:| Here's one for you:if you have 0 envelopes and 0 letters to put in them, how many ways can you put no letters in the correct envelopes? |
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If there are no letters and no envelopes then the concept of correct/wrong matching is meaningless. It's like saying, if you don't write a random number on a piece of paper and I don't think of a random number, then what is the chance of me guessing your number correctly? There are no numbers to compare. Although we both thought of "nothing", they do not match, as neither of us thought of a number, which was the substance of the comparison. Similarly, is there are no letters and no envelopes then we have eliminated the essential component which we are being asked to determine correct matchings of.
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srn437
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #10 on: Sep 23rd, 2007, 4:51pm » |
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Actually the answer is 0, because the formula for the subfactorial(which is what I asked) is !n=n!/e rounded to the nearest integer. Now what is the answer to your question?
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ThudnBlunder
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #11 on: Sep 23rd, 2007, 5:14pm » |
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on Sep 23rd, 2007, 4:51pm, srn347 wrote:| Actually the answer is 0, because the formula for the subfactorial(which is what I asked) is !n=n!/e rounded to the nearest integer. |
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1) You didn't ask for a subfactorial. You asked for the answer to your question.
2) The formula you use is rounded down to the nearest integer.
3) This formula applies only for n  1
4) The answer to your question is allowed to be equal to 1, but only in order to satisfy the appropriate difference equation. As Sir Col says, your question is meaningless in the physical context in which you put it.
on Sep 23rd, 2007, 4:51pm, srn347 wrote:| Now what is the answer to your question? |
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5) I don't post questions in order to answer them myself. If you don't know the answer, just say so.
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| « Last Edit: Sep 23rd, 2007, 5:38pm by ThudnBlunder » |
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FiBsTeR
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #12 on: Sep 23rd, 2007, 5:23pm » |
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on Sep 23rd, 2007, 3:40pm, ThudanBlunder wrote:| Here's one for you: if there are 4 letters and 4 envelopes, what is the probability that exactly 3 letters will be randomly matched with the correct envelopes? |
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I believe it is the same probability as srn answering the problem correctly, also equal to the probability of him knowing what he is talking about?
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| « Last Edit: Sep 23rd, 2007, 5:24pm by FiBsTeR » |
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ThudnBlunder
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #13 on: Sep 23rd, 2007, 5:45pm » |
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on Sep 23rd, 2007, 5:23pm, FiBsTeR wrote:
I believe it is the same probability as srn answering the problem correctly, also equal to the probability of him knowing what he is talking about? |
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Good job you hid that - no point in making it too easy. In fact, my question is similar to his, except that he cannot mindlessly read off the answer from whatever page the kid is on.
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| « Last Edit: Sep 25th, 2007, 2:07am by ThudnBlunder » |
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srn437
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #14 on: Sep 23rd, 2007, 8:29pm » |
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I did ask the subfactorial because that's what it is. The factorial was also only meant for integers, but half integers also work. Just because you can't apply certain functions(like 0/0), doesn't mean you can't). If this confuses you, that means you need to read it again. does anyone here know the answer to the w thing?
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ThudnBlunder
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #15 on: Sep 23rd, 2007, 8:46pm » |
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on Sep 23rd, 2007, 8:29pm, srn347 wrote:| ...does anyone here know the answer to the w thing? |
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Yes, I do.
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| « Last Edit: Sep 25th, 2007, 12:37am by ThudnBlunder » |
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srn437
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #16 on: Sep 23rd, 2007, 9:01pm » |
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Does anyone(or someone) have any solutions that are actually in english mathematics. Also, no one actually is just anyone.
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Barukh
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #17 on: Sep 24th, 2007, 12:26am » |
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Again: didn't we agree to Ignore?
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Sir Col
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #18 on: Sep 24th, 2007, 12:31am » |
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As I've not had any direct dealings with him yet, I am willing to give him the benefit of the doubt. I may come to regret it, but it gives him another chance.
srn347, there is far more to be gained by working it out for yourself rather than read someone else's solution. If you want I can give you pointers to work towards a full solution.
First of all, are you wanting to find the general solution to (i) it is known whether the fake coin is heavier or lights, or, (ii) it is not known?
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Grimbal
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #19 on: Sep 24th, 2007, 12:39am » |
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on Sep 23rd, 2007, 8:29pm, srn347 wrote:| does anyone here know the answer to the w thing? |
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If the number of coins is a multiple of 3, you can make 3 equal heaps and find out in a single weighing which heap has the fake coin.
So, each weighing can reduce by 3 the number of coins that could be fake. Or seen the other way round, each additional weighing lets you find the coin among 3 times as many coins.
With 1 weighing you can find the fake among 3 coins.
With 2 weighings you can find it among 9 coins. 9 is 3 times 3.
With 3 weighings you can find it among 27 coins. 27 is 3 times 9.
The pattern that emerges is:
With W weighings you can find it among 3W coins.
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| « Last Edit: Sep 25th, 2007, 5:03am by Grimbal » |
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ThudnBlunder
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #20 on: Sep 24th, 2007, 2:17am » |
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on Sep 24th, 2007, 12:26am, Barukh wrote:| Again: didn't we agree to Ignore? |
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While I believe you can take a horse to water, towr, Sir Col, and Grimbal seem to believe you can actually make it think!
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| « Last Edit: Sep 24th, 2007, 5:53am by ThudnBlunder » |
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mikedagr8
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #21 on: Sep 24th, 2007, 2:43am » |
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on Sep 24th, 2007, 2:17am, ThudanBlunder wrote:
While I believe you can take a horse to water, towr, Sir Col, and Grimbal seem to believe you can actually make it think! |
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Lol, here's one I heard today.
Quote:| Computers are never stupid. It's just the idiots using them, which make it appear so. |
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srn437
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #22 on: Sep 24th, 2007, 9:49pm » |
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Or maybe it was made by idiots. I knew it had something to do with three.
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Sir Col
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #23 on: Sep 25th, 2007, 2:02am » |
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srn347, you've received a number of positive replies to your problem in this thread, so why don't you ignore the rest and focus on them. It's within your power to rise above the past and show everyone that you really want to be part of this community.
Grimbal has taken the time to provide a well furnished solution to your original problem; a courteous response to that might go down well. And I am willing to give you some hints to help you work towards a solution to the case where you do not know if the fake coin is heavier or lighter.
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srn437
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Re: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/
« Reply #24 on: Sep 25th, 2007, 4:55pm » |
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Ok. For any specific number(for weighings or coins), I can find the other one. I believe the answer to the w thing is 3w.
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